Rare-Earth-Doped Fiber Lasers and Amplifiers, Revised and Expanded

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Rare-Earth-Doped Fiber Lasers and Amplifiers Second Edition, Revised and Expanded

edited by

Michel J. F. Digonnet Stanford University Stanford, California

Marcel Dekker, Inc.

New York • Basel

TM

Copyright © 2001 by Marcel Dekker, Inc. All Rights Reserved.

The first edition was published as Rare Earth Doped Fiber Lasers and Amplifiers, Michel J. F. Digonnet, ed. (Marcel Dekker, Inc., 1993). ISBN: 0-8247-0458-4 This book is printed on acid-free paper. Headquarters Marcel Dekker, Inc. 270 Madison Avenue, New York, NY 10016 tel: 212-696-9000; fax: 212-685-4540 Eastern Hemisphere Distribution Marcel Dekker AG Hutgasse 4, Postfach 812, CH-4001 Basel, Switzerland tel: 41-61-261-8482; fax: 41-61-261-8896 World Wide Web http:/ /www.dekker.com The publisher offers discounts on this book when ordered in bulk quantities. For more information, write to Special Sales/Professional Marketing at the headquarters address above. Copyright  2001 by Marcel Dekker, Inc. All Rights Reserved. Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage and retrieval system, without permission in writing from the publisher. Current printing (last digit): 10 9 8 7 6 5 4 3 2 1 PRINTED IN THE UNITED STATES OF AMERICA

OPTICAL ENGINEERING Founding Editor Brian J. Thompson University of Rochester Rochester, New York

Editorial Board Toshimitsu Asakura Hokkai-Gakuen University Sapporo, Hokkaido, Japan

Nicholas F. Borrelli Corning, Inc. Corning, New York

Chris Dainty Imperial College of Science, Technology, and Medicine London, England

Bahram Javidi University of Connecticut Storrs, Connecticut

Mark Kuzyk Washington State University Pullman, Washington

Hiroshi Murata The Furukawa Electric Co., Ltd. Yokohama, Japan

Edmond J. Murphy JDS/Uniphase Bloomfield, Connecticut

Dennis R. Pape Photonic Systems Inc. Melbourne, Florida

Joseph Shamir Technion–Israel Institute of Technology Hafai, Israel

David S. Weiss Heidelberg Digital L.L.C. Rochester, New York

1. Electron and Ion Microscopy and Microanalysis: Principles and Applications, Lawrence E. Murr 2. Acousto-Optic Signal Processing: Theory and Implementation, edited by Nor man J. Berg and John N. Lee 3. Electro-Optic and Acousto-Optic Scanning and Deflection, Milton Gottlieb, Clive L. M. Ireland, and John Martin Ley 4. Single-Mode Fiber Optics: Principles and Applications, Luc B. Jeunhomme 5. Pulse Code Formats for Fiber Optical Data Communication: Basic Principles and Applications, David J. Morris 6. Optical Materials: An Introduction to Selection and Application, Solomon Musikant 7. Infrared Methods for Gaseous Measurements: Theory and Practice, edited by Joda Wormhoudt 8. Laser Beam Scanning: Opto-Mechanical Devices, Systems, and Data Storage Optics, edited by Gerald F. Marshall 9. Opto-Mechanical Systems Design, Paul R. Yoder, Jr. 10. Optical Fiber Splices and Connectors: Theory and Methods, Calvin M. Miller with Stephen C. Mettler and Ian A. White 11. Laser Spectroscopy and Its Applications, edited by Leon J. Radziemski, Richard W. Solarz, and Jeffrey A. Paisner 12. Infrared Optoelectronics: Devices and Applications, William Nunley and J. Scott Bechtel 13. Integrated Optical Circuits and Components: Design and Applications, edited by Lynn D. Hutcheson 14. Handbook of Molecular Lasers, edited by Peter K. Cheo 15. Handbook of Optical Fibers and Cables, Hiroshi Murata 16. Acousto-Optics, Adrian Korpel 17. Procedures in Applied Optics, John Strong 18. Handbook of Solid-State Lasers, edited by Peter K. Cheo 19. Optical Computing: Digital and Symbolic, edited by Raymond Arrathoon 20. Laser Applications in Physical Chemistry, edited by D. K. Evans 21. Laser-Induced Plasmas and Applications, edited by Leon J. Radziemski and David A. Cremers 22. Infrared Technology Fundamentals, Irving J. Spiro and Monroe Schlessinger 23. Single-Mode Fiber Optics: Principles and Applications, Second Edition, Re vised and Expanded, Luc B. Jeunhomme 24. Image Analysis Applications, edited by Rangachar Kasturi and Mohan M. Trivedi 25. Photoconductivity: Art, Science, and Technology, N. V. Joshi 26. Principles of Optical Circuit Engineering, Mark A. Mentzer 27. Lens Design, Milton Laikin 28. Optical Components, Systems, and Measurement Techniques, Rajpal S. Sirohi and M. P. Kothiyal 29. Electron and Ion Microscopy and Microanalysis: Principles and Applications, Second Edition, Revised and Expanded, Lawrence E. Murr 30. Handbook of Infrared Optical Materials, edited by Paul Klocek 31. Optical Scanning, edited by Gerald F. Marshall 32. Polymers for Lightwave and Integrated Optics: Technology and Applications, edited by Lawrence A. Hornak 33. Electro-Optical Displays, edited by Mohammad A. Karim 34. Mathematical Morphology in Image Processing, edited by Edward R. Dougherty 35. Opto-Mechanical Systems Design: Second Edition, Revised and Expanded, Paul R. Yoder, Jr. 36. Polarized Light: Fundamentals and Applications, Edward Collett 37. Rare Earth Doped Fiber Lasers and Amplifiers, edited by Michel J. F. Digonnet 38. Speckle Metrology, edited by Rajpal S. Sirohi

39. Organic Photoreceptors for Imaging Systems, Paul M. Borsenberger and David S. Weiss 40. Photonic Switching and Interconnects, edited by Abdellatif Marrakchi 41. Design and Fabrication of Acousto-Optic Devices, edited by Akis P. Goutzoulis and Dennis R. Pape 42. Digital Image Processing Methods, edited by Edward R. Dougherty 43. Visual Science and Engineering: Models and Applications, edited by D. H. Kelly 44. Handbook of Lens Design, Daniel Malacara and Zacarias Malacara 45. Photonic Devices and Systems, edited by Robert G. Hunsberger 46. Infrared Technology Fundamentals: Second Edition, Revised and Expanded, edited by Monroe Schlessinger 47. Spatial Light Modulator Technology: Materials, Devices, and Applications, edited by Uzi Efron 48. Lens Design: Second Edition, Revised and Expanded, Milton Laikin 49. Thin Films for Optical Systems, edited by Francoise R. Flory 50. Tunable Laser Applications, edited by F. J. Duarte 51. Acousto-Optic Signal Processing: Theory and Implementation, Second Edition, edited by Norman J. Berg and John M. Pellegrino 52. Handbook of Nonlinear Optics, Richard L. Sutherland 53. Handbook of Optical Fibers and Cables: Second Edition, Hiroshi Murata 54. Optical Storage and Retrieval: Memory, Neural Networks, and Fractals, edited by Francis T. S. Yu and Suganda Jutamulia 55. Devices for Optoelectronics, Wallace B. Leigh 56. Practical Design and Production of Optical Thin Films, Ronald R. Willey 57. Acousto-Optics: Second Edition, Adrian Korpel 58. Diffraction Gratings and Applications, Erwin G. Loewen and Evgeny Popov 59. Organic Photoreceptors for Xerography, Paul M. Borsenberger and David S. Weiss 60. Characterization Techniques and Tabulations for Organic Nonlinear Optical Materials, edited by Mark G. Kuzyk and Carl W. Dirk 61. Interferogram Analysis for Optical Testing, Daniel Malacara, Manuel Servin, and Zacarias Malacara 62. Computational Modeling of Vision: The Role of Combination, William R. Uttal, Ramakrishna Kakarala, Spiram Dayanand, Thomas Shepherd, Jagadeesh Kalki, Charles F. Lunskis, Jr., and Ning Liu 63. Microoptics Technology: Fabrication and Applications of Lens Arrays and Devices, Nicholas Borrelli 64. Visual Information Representation, Communication, and Image Processing, edited by Chang Wen Chen and Ya-Qin Zhang 65. Optical Methods of Measurement, Rajpal S. Sirohi and F. S. Chau 66. Integrated Optical Circuits and Components: Design and Applications, edited by Edmond J. Murphy 67. Adaptive Optics Engineering Handbook, edited by Robert K. Tyson 68. Entropy and Information Optics, Francis T. S. Yu 69. Computational Methods for Electromagnetic and Optical Systems, John M. Jarem and Partha P. Banerjee 70. Laser Beam Shaping, Fred M. Dickey and Scott C. Holswade 71. Rare-Earth-Doped Fiber Lasers and Amplifiers: Second Edition, Revised and Expanded, edited by Michel J. F. Digonnet 72. Lens Design: Third Edition, Revised and Expanded, Milton Laikin 73. Handbook of Optical Engineering, edited by Daniel Malacara and Brian J. Thompson 74. Handbook of Imaging Materials: Second Edition, Revised and Expanded, edited by Arthur S. Diamond and David S. Weiss 75. Handbook of Image Quality: Characterization and Prediction, Brian W. Keelan

76. Fiber Optic Sensors, edited by Francis T. S. Yu and Shizhuo Yin 77. Optical Switching/Networking and Computing for Multimedia Systems, edited by Mohsen Guizani and Abdella Battou 78. Image Recognition and Classification: Algorithms, Systems, and Applications, edited by Bahram Javidi 79. Practical Design and Production of Optical Thin Films: Second Edition, Revised and Expanded, Ronald R. Willey 80. Ultrafast Lasers: Technology and Applications, edited by Martin E. Fermann, Almantas Galvanauskas, and Gregg Sucha 81. Light Propagation in Periodic Media: Differential Theory and Design, Michel Nevière and Evgeny Popov 82. Handbook of Nonlinear Optics, Second Edition, Revised and Expanded, Richard L. Sutherland

Additional Volumes in Preparation

Optical Remote Sensing: Science and Technology, Walter Egan

From the Series Editor

It has now been a significant number of years since the first edition of Rare Earth Doped Fiber Lasers and Amplifiers was published in 1993 under the editorship of Michel J. F. Digonnet. It was Volume 37 of this series of books on optical engineering. In the modern vernacular this subject matter of rare earth doped fibers and amplifiers ‘‘has legs’’—that is, it has vibrant currency and an outstanding future potential. A great deal of progress has been made in the field since 1993, with new technological developments in both lasers and amplifiers leading in turn to a wider wavelength range and higher bandwidths. The impact of these developments has provided a major impetus to the rapidly expanding communications business; hence the new edition has been significantly revised and expanded. The original edition had 13 contributing authors for the 12 chapters. Six of these same experts have contributed to the new edition, together with another 12 colleagues equally expert and involved with this field. There are still a dozen chapters, but their organization and often their titles have changed to reflect the state of the art. The revised and expanded text will be the new definitive work in this field for some time to come. Brian J. Thompson

iii

Preface to the Second Edition

It has been more than eight years since the first comprehensive book on rare earth doped fibers, Rare Earth Doped Fiber Lasers and Amplifiers, appeared in print. Since that time, considerable work on the general subject of rare earth doped fibers has been carried out around the world, in both academic and industrial environments, and in both research and R&D. Although this effort has covered a large number of devices, none has experienced a more resounding success than the erbium-doped fiber amplifier (EDFA). This amplifier exhibited such unique, near-ideal characteristics, and the need of the communication industry for such a device was so strong, that the EDFA has evolved from a laboratory prototype to a mature field device in just a few years. EDFAs now constitute the keystone of a new breed of long-haul optical communication systems based entirely on optical fibers. Since the mid-1980s, fiber links up to thousands of kilometers in length, each utilizing dozens of EDFAs to periodically replenish the optical signals, have been deployed across oceans and between major cities in several countries. These novel systems, with their enormous bandwidth that can ultimately reach thousands of gigabits of information per second, are now competing directly with long-established communication technologies. EDFAs have also become important research tools, and they are being used in a variety of other optical systems, as reflected by the fact that they are commercially available from dozens of manufacturers worldwide. Several other areas of research have also produced astounding new results. Work on the praseodymium-doped fluoride fiber amplifier has resulted in the development of the first fiber amplifier at 1.3 µm for second-window communication applications. New laser cavity designs have led to fiber lasers with record narrow linewidths in the few kilohertz range. Novel fiber gratings have also been developed that, when combined with a standard EDFA, produce an improved amplifier exhibiting a gain spectrum that is independent of signal wavelength, an essential feature in communication networks. Broadband fiber sources have also been greatly improved. There have also been impressive new findings in blue-green fiber lasers, far infrared lasers, mode-locked and Q-switched fiber lasers, and the study of the impact of rare earth concentration and clustering on device efficiency, to name a few.

v

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Preface to the Second Edition

This second edition is the result of a collective effort, involving some of the best experts in the field, to incorporate these new developments and produce an updated, comprehensive volume. Almost all chapters underwent some degree of revision. In several cases these revisions are fairly substantial, especially concerning the topics of fiber lasers, broadband fiber sources, and EDFAs. In addition, two new chapters were added to address new topics of research in the areas of short wavelength fiber lasers, and 1.3-µm fiber amplifiers. The main objective of this new volume is again to provide the scientific community with a detailed review of the state of the art in the many branches of this maturing field. As an exhaustive reference source, it targets an audience of scientists in academia, as well as scientists, engineers, and technicians in industry. To make it also suitable for beginners—in particular, graduate students—we preserved the self-contained character of the original version by retaining the introductory sections covering the basic principles of this technology. Michel J. F. Digonnet

Preface to the First Edition

Rare earth doped fibers are at the core of a new and rapidly expanding branch of optics. By combining the optical gain of rare earth ions with the large optical confinement available in a single mode optical fiber, these fibers offer a fascinating medium with which to produce devices that are both very small and extremely efficient. The anticipated outcome is an array of novel, compact, and practical laser devices with drive power requirements so much lower than their traditional bulk-optic counterparts that they can be driven by a simple, inexpensive diode laser. During the past seven years this concept has been investigated with most of the rare earths, in both silica and fluoride fibers. This sustained effort has led to the demonstration of an impressive variety of miniature, highly efficient laser sources and amplifiers. The spectrum of possibilities offered by this new technology is staggering, ranging from blue and far infrared continuous-wave lasers to 1.3-µm and 1.55µm amplifiers, optical switches, and femtosecond lasers. Because of their efficiency, compactness, mechanical and thermal stability, and excellent coupling to single mode communication fibers, these devices are now expected to play a fundamental role in several important commercial applications. The potential of fiber amplifiers and narrow-band lasers in optical communication systems, which stimulated the initial development of this technology, was confirmed by the spectacular emergence of erbium-doped fiber amplifiers. These amplifiers, which operate in the important 1.55-µm telecommunication window, turned out to exhibit nearly ideal properties for their intended applications, including high gain, low noise, low interchannel cross-talk, and low drive power. They were met with such enthusiasm that they evolved from laboratory devices to commercial products in just a few years. Practical field components are now being deployed by several countries in novel optical transmission systems. Although not as far advanced, narrow-band, frequency-stable fiber lasers are being developed as sources for communication systems and metrology applications. Rare earth doped fibers are also finding applications as sensors and as broadband sources for fiber gyroscopes. Many other future applications are envisioned. Doped fibers possess enhanced nonlinear properties that are very attractive for future phase and amplitude modulators and fast all-optical switches for communication and sensor networks. Short wavelength fiber lasers utilizing

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Preface to the First Edition

ions with higher energy laser transitions or up-conversion mechanisms could also find applications in high-density optical data storage. In the last few years an increasing number of laboratories worldwide have become involved in research and development of optical devices and systems based on rare earth doped fibers. The major objective of this volume is to provide this growing scientific community with a detailed review of the state of the art in the most important areas of this field. To this end, it was intended to be as self-consistent as possible given the multidisciplinary nature of this field. The subjects covered include fiber fabrication methods, spectroscopy, principles, and performance characteristics of continuous-wave and pulsed fiber lasers and fiber amplifiers, and applications of erbium-doped fiber amplifiers to communication systems. This book is suitable for beginners, in particular graduate students, scientists, engineers, and technicians, seeking an understanding of the fundamental principles and performance of rare earth doped fiber devices. It is also sufficiently exhaustive to serve as a source of reference for experienced practitioners. Michel J. F. Digonnet

Contents

From the Series Editor Brian J. Thompson Preface to the Second Edition Preface to the First Edition Chapter 1

Rare Earth Doped Fiber Fabrication: Techniques and Physical Properties Jay R. Simpson

iii v vii

1

Chapter 2

Optical and Electronic Properties of Rare Earth Ions in Glasses William J. Miniscalco

17

Chapter 3

Continuous-Wave Silica Fiber Lasers Michel J. F. Digonnet

113

Chapter 4

Visible Fluoride Fiber Lasers D. S. Funk and J. G. Eden

171

Chapter 5

Narrow-Linewidth Fiber Lasers Nigel Langford

243

Chapter 6

Broadband Fiber Sources Michel J. F. Digonnet

313

Chapter 7

Q-Switched Fiber Lasers Michel Morin, Robert Larose, and François Brunet

341

Chapter 8

Mode-Locked Fiber Lasers Martin E. Fermann and Martin Hofer

395

ix

x

Contents

Chapter 9

Rare Earth Doped Infrared-Transmitting Glass Fibers J. S. Sanghera, L. B. Shaw, and I. D. Aggarwal

Chapter 10

Erbium-Doped Fiber Amplifiers: Basic Physics and Characteristics E. Desurvire

449

531

Chapter 11

Erbium-Doped Fiber Amplifiers: Advanced Topics Paul F. Wysocki

583

Chapter 12

1.3-µm Fiber Amplifiers Kazuo Fujiura and Shoichi Sudo

681

Index

755

Contributors

I. D. Aggarwal Naval Research Laboratory, Washington, D.C. François Brunet Institut National d’Optique, Sainte-Foy, Que´bec, Canada E. Desurvire

Columbia University, New York, New York

Michel J. F. Digonnet

Stanford University, Stanford, California

J. G. Eden University of Illinois, Urbana, Illinois Martin E. Fermann Kazuo Fujiura D. S. Funk

IMRA America, Ann Arbor, Michigan

NTT Photonics Laboratories, Tokai-mura, Ibaraki, Japan

National Institute of Standards and Technology, Boulder, Colorado

Martin Hofer IMRA America, Ann Arbor, Michigan Nigel Langford University of Strathclyde, Glasgow, Scotland Robert Larose Institut National d’Optique, Sainte-Foy, Que´bec, Canada William J. Miniscalco GTE Laboratories Incorporated, Waltham, Massachusetts Michel Morin

Institut National d’Optique, Sainte-Foy, Que´bec, Canada

J. S. Sanghera

Naval Research Laboratory, Washington, D.C.

L. B. Shaw

Naval Research Laboratory, Washington, D.C. xi

xii

Contributors

Jay R. Simpson CIENA Corporation, Linthieum, Maryland Shoichi Sudo NTT Science & Core Technology Laboratory Group, Atsugi-shi, Kanagawa, Japan Paul F. Wysocki Leco Corporation, St. Joseph, Missouri

1 Rare Earth Doped Fiber Fabrication: Techniques and Physical Properties JAY R. SIMPSON CIENA Corporation, Linthieum, Maryland

1.1 INTRODUCTION The recent interest in optical amplifiers and lasers based on rare earth doped fibers has stimulated a new look at fiber fabrication methods. The use of optical fiber to reduce the required pump power for gain in glass lasers and amplifiers was first demonstrated in the early 1960s by Snitzer and co-workers [1,2]; revisited in the 1970s by Stone and Burrus [3], it has been pursued with vigor since 1985. The rebirth of this field has been stimulated primarily by the application of optical amplifiers and fiber lasers to optical communications. This commercial interest, combined with the availability of high-power semiconductor pump lasers and low-insertion–loss wavelength division multiplexers and isolators, has resulted in rapid development of active fiber devices. The bias toward fiber communications has provided a strong incentive to consider active fiber designs and compositions compatible with standard low-attenuation, silica-based fiber. Specifically, the ability to connect active fiber components to doped silica telecommunications fiber by fusion splicing, with low insertion loss and low reflectivity, allows the interconnection of reliable, low-noise, high-gain amplifiers. This same telecommunication bias has likewise directed rare earth doped fiber fabrication toward variations on traditional doped silica processing. There exists however, in addition to this mainstay, a growing body of work on the less compatible compound and fluoride glass active devices that may overcome the current emphasis on doped silica by offering other operating wavelengths, higher gain, higheroutput power, or broaderband operation. It is the function of this chapter to describe the methods developed for fabricating rare earth doped, silica-based fibers, emphasizing how processing affects the physical properties and performance of the resulting fibers. This topic has also been reviewed in earlier papers [4–7]. 1

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Simpson

1.2 WAVEGUIDE DESIGNS Before addressing specific fabrication methods, let us consider the waveguide configurations used to bring the pump, signal, and active media together. Although the configuration most widely used consists of a rare earth doped fiber core, which allows the pump and signal to propagate together in a single-mode fiber, as described in Section 1.2.3, there are a number of alternative fiber device geometries worthy of consideration. 1.2.1 Evanescent Field The wings or evanescent field of the optical signal guided by a single-mode fiber may be used to interact with an active material outside the core region. One approach to enhancing this effect is to locally taper the guide, thereby causing the optical power to increase outside the glass material bounds of the fiber over a length of several millimeters. This tapering method has been used to demonstrate a 20-dB–gain amplifier, for a pump power below 1 W, with a dye solution circulating around the tapered fiber region [8]. Both the signal at 750 nm and the pump at 650 nm were copropagating in the core. Similarly, the active media can be incorporated in the cladding glass, as has been demonstrated for erbium (Er) or neodymium (Nd) [9,10]. Reported gain for an erbium-doped cladding structure was 0.6 dB for a 1.55-µm signal, with a 1.48-µm pump power of 50 mW. The evanescent field may also be accessed by polishing away a portion of the fiber cladding, thus creating a structure similar to a D-shaped fiber. Pulsed amplification of 22 dB for one such dye evanescent amplifier has been achieved [11]. The pump power required for these devices to obtain a sizable gain far exceeds that needed for schemes in which active media are contained in the core. However, by using this evanescent interaction, active media, such as dyes, which cannot be incorporated into a glass, can be explored. 1.2.2 Double Clad Another approach to achieving interaction of guided pump light with an active medium uses a single-mode guide or the signal surrounded by a multimode pump guide. Pump light is launched from the fiber end into the undoped cladding, propagating in a zig-zag pattern through the doped core as it travels along the fiber [12,13]. Configurations with the core offset in a circular cladding and a core centered in an elliptical cladding have been demonstrated [12]. A high brightness neodymium fiber laser based on the latter design provided an output greater than 100 mW for an 807-nm–diode array laser pump power of 500 mW [12]. The guiding geometry of this configuration was designed to maximize the use of power available from laser diode arrays, thereby producing higher-output powers. We refer the reader to Chapter 3 for details on the operation of these fibers. 1.2.3 Core Confined The most efficient conversion of pump to signal photons uses the design in which both pump and signal are confined in the fiber core. This configuration has been made especially attractive by the availability of commercial, low-insertion loss, low-reflectivity fiber couplers, which can be chosen to combine a variety of pump and signal wavelengths onto a common output fiber.

Rare Earth Doped Fiber Fabrication

3

For this design, the launched pump threshold power P th provides a reasonable figure of merit for the efficiency of a fiber laser or amplifier, a lower value being preferred. This quantity is proportional to [14] P th ⬀ A eff εp σe τf

A eff σe τf εp

⫽ ⫽ ⫽ ⫽

(1)

effective core area fractional absorbed pump power stimulated emission cross-section pump fluorescence lifetime

The efficiency of this device, therefore, can be increased by diminishing the effective core area, increasing the pump absorption cross section, increasing the pump fluorescence lifetime, and increasing the stimulated emission cross section. Furthermore, of these parameters, decreasing the mode field diameter (decreasing A eff ) has the greatest effect on increasing the gain/pump power slope. Further improvement can be achieved by confining the rare earth to the central portion of the core, where the pump and signal intensities are generally highest [14–16]. The optimized waveguide design then requires consideration of both the device configuration and a number of material and waveguide properties determined by the fabrication methods used. 1.3 HOST COMPOSITIONS The glass host composition affects the solubility of the rare earth dopant which, in turn, may affect the fluorescence lifetime, absorption, emission, and excited state absorption cross sections of the dopant transitions. As seen in the expression for the pump threshold [see Eq. (1)], these quantities affect the ultimate ability of the active material to provide gain. Devices of general interest span rare earth concentrations of tens to several thousand parts per million (ppm), resulting in devices of one to tens of meters long. For some applications dopant levels of 1 ppm and less are advantageous, resulting in devices several kilometers long. For all designs, the rare earth should ideally be confined as a delta function in the center of the core for maximum gain per unit pump power. Practically, there is a necessary tradeoff between the confinement and the rare earth concentration. The more confined structures require a higher rare earth concentration for an equivalent length, eventually running into the clustering limit for the particular host glass composition [16]. Clustering is to be avoided in that it induces fluorescence quenching and reduces the performance of the device (see Chap. 2). Commercially available bulk laser glasses are typically based on phosphate or multicomponent silicate host compositions, which have been developed to accommodate several weight percent concentrations of rare earth oxides without clustering. Host glasses compatible with this relatively high concentration of rare earth oxide without clustering require the open, chain-like structure of phosphate glasses or the addition of modifier ions (Ca, Na, K, Li, or other) to open the silicate structure and increase solubility [17, 18]. The limitation owing to clustering in a predominantly silica host without modifier ions has been well documented [19]. The maximum erbium concentration in silica for optimum amplifier performance has been suggested to be under 100 ppm [20]. However a 14.4-dB gain, 900-ppm erbium-doped silica fiber amplifier has been reported, indicating that higher concentrations can produce useful devices [21]. When only index-

4

Simpson

raising dopants of germanium (Ge) and phosphorus are used to modify the silica structure, as in standard telecommunications fiber (typically 5.0 mol% GeO 2, 0.5 mol% P 2 O 5), the limit to rare earth incorporation before the onset of fluorescence quenching is thought to be near 1000 ppm for Nd [22]. The addition of aluminum oxide, considered to be in part a network modifier, has also been used to improve the solubility of rare earth ions [3, 22–26]. Rare earth concentrations of 2% have been claimed without clustering using fiber host compositions of 8.5 mol% Al 2 O 3 [25]. A detailed study of the fluorescence quenching in Nd-doped SiO 2 /Al 2 O 3 /P 2 O 5 for Nd levels up to 15 wt% indicated that a phase separation of the rare earth oxide occurs at these high concentrations [26]. In addition to the solubility and fluorescence line shape, excited-state absorption can be substantially affected by the host composition [25]. This competing absorption phenomenon (see Chap. 2) can seriously diminish the efficiency of an active fiber device. A decrease in the excited-state absorption for erbium-doped fibers going from a germanosilicate host to an aluminosilicate host has been verified [24], demonstrating the importance of host selection for a given rare earth ion or laser transition. In addition to interactions between host and rare earth ions, it is necessary to consider background losses from impurity absorption and scattering mechanisms that decrease the efficiency of the fiber device. The effect of internal loss is most dramatic in distributed amplifiers, where pump light must travel long distances in the process of distributing gain. The magnitude of this effect has been calculated for the distributed erbium amplifier by adding a pump and signal loss term to the rate equations [27]. These calculations indicate that for a 50-km distributed amplifier with near-optimum Er dopant level for transparency, an increase in the background loss from 0.2 to 0.3 dB/km (10–15 dB/span) results in a fivefold increase in the required pump power. This emphasizes the need for state-of-theart low-background attenuation in fibers for distributed amplifiers. For devices a few meters long, the background loss may be kept near the fusion splice losses, namely between a hundreth and a few tenths of a decibel, with little reduction in performance.

1.4 FABRICATION METHODS 1.4.1 Low-Loss Communication Fiber The standard methods of fabricating doped silica fiber fall into two basic categories, both based on the reaction of halides, such as SiCl 4, GeCl 4, POCl 3, SiF 4, and BCl 3, to form the desired mix of oxides. Category 1 reacts the chlorides in a hydrogen flame and collects the resulting soot on a mandrel for subsequent sintering to a transparent glass. Processes based on this method are commonly referred to as vapor axial deposition (VAD) [28] and outside vapor deposition (OVD) [29]. Category 2 reacts the chlorides inside a substrate tube that becomes part of the cladding, simultaneously reacting, depositing, or sintering as a torch plasma fireball or microwave cavity traverses the tube. Processes based on this method are commonly referred to as modified chemical vapor deposition (MCVD) [30], plasma chemical vapor deposition (PCVD) [31], and intrinsic microwave chemical vapor deposition (IMCVD) [32]. All these methods create a preform, or large-geometry equivalent, which is desired in the fiber. The preform is then drawn into an optical fiber by heating one end to the softening temperature and pulling it into a fiber at rates of 1–10 m/s. Several reviews of general fiber fabrication methods have already been published [33,34].


5

Index-raising dopant ions, such as germanium, phosphorus, aluminum, and titanium, and index-lowering dopants such as boron and fluorine, are introduced into the reaction stream as halide vapors carried by oxygen at a temperature near 30°C. The halide compounds of rare earth ions are, however, generally less volatile than the commonly used chlorides and fluorides of the index-modifying dopants, thereby requiring volatilizing and delivering temperatures of a few hundred degrees (Fig. 1) [35,37]. This requirement has stimulated the vapor and liquid phase handling methods to be discussed. 1.4.2 Rare Earth Vapor Phase Methods to deliver rare earth vapor species to the reaction/deposition zone of a preform process have been devised for both MCVD and VAD or OVD techniques. The configurations employed for MCVD are shown in Figure 2, for which rare earth dopants are delivered to an oxidation reaction region along with other index-controlling dopants. The low vapor pressure rare earth reactant is accommodated either by taking the vapor source close to the reaction zone and immediately diluting it with other reactants (see Fig. 2a–c) or by delivering the material as an aerosol or higher vapor pressure organic compound (see Fig. 2d,e). The heated frit source (see Fig. 2a) was made by soaking a region of porous soot previously deposited on the upstream inner wall of an MCVD tube with a rare earth chloride–ethanol solution [38]. On heating to 900°C and being allowed to dry, the sponge became a vapor source. Two other source methods (see Fig. 2b,c) use the heated chloride directly as a source after dehydrating [39–42]. The dehydration is necessary in that most rare earth chlorides are, in fact, hydrated. Dehydration may be accomplished by heating the material to nearly 900°C with a flow of Cl 2, SOCl 2, or SF 6. The attraction of the heated source injector method is that the rare earth reactant source is isolated from potentially unwanted reactions with the SiCl 4, GeCl 4, or POCl 3 index-raising reactants.

Figure 1 Vapor pressures of reactant halides, including index-raising ions and a representative rare earth ion, Er.

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Simpson

Figure 2 Low vapor pressure dopant delivery methods for MCVD.

A variation of the heated chloride source method requires a two-step process referred to as transport-and-oxidation [43]. Here, the rare earth chloride was first transported to the downstream inner wall by evaporation and condensation, followed by a separate oxidation step at higher temperatures. The resulting single-mode fiber structure consisted of a P 2 O 5 /SiO 2 cladding and a Yb 2 O 3 /SiO 2 core, one of the few reported uses of a rare earth dopant as an index-raising constituent. A 1-mol% Yb 2 O 3 /SiO 2 core provided the 0.29% increase in refractive index over the near silica index cladding. The aerosol delivery method, shown in Figure 2d, overcomes the need for heated source compounds by generating a vapor at the reaction site [44–47]. A feature of this method is the ability to create an aerosol at a remote location and pipe the resulting suspension of liquid droplets of rare earth dopant into the reaction region of the MCVD substrate tube with a carrier gas. The aerosols delivered this way were generated by a 1.5-MHz– ultrasonic nebulizer commonly used in room humidifiers. Both aqueous and organic liquids have been delivered by this technique, allowing the incorporation of lead, sodium, and gallium, as well as several rare earths. Given that most of the aerosol fluid materials contain hydrogen, dehydration after deposition is required for low OH content. Vapor transport of rare earth dopants may also be achieved by using organic compounds that have higher vapor pressures than the chlorides, bromides, or iodides (see Fig. 1) [37]. These materials can be delivered in lines heated to 200°C, rather than the severalhundred degree requirements for chlorides. The application of this source to MCVD has been reported using three concentric input delivery lines (see Fig. 2e) [48]. Multiple rare


7

Figure 3 Low vapor pressure dopant delivery methods for VAD or OVD: (a) vapor and aerosol; (b) all vapor.

earth doping and high dopant levels are reported with this method, along with background losses of 10 dB/km and moderate OH levels of near 20 ppm. Rare earth vapor, aerosol, and solution transport may also be used to dope preforms fabricated by the OVD or VAD hydrolysis processes. Such doping may be achieved either during the soot deposition (Fig. 3) or after the soot boule has been created (Figs. 4 and 5). The introduction of low vapor pressure dopants to VAD was initially reported using a combination of aerosol and vapor delivery (see Fig. 3a) [49]. The incorporation of cerium, neodymium, and erbium has been accomplished in the OVD method by introducing rare earth organic vapors into the reaction flame, as shown in Figure 3b [13,50,51]. Cerium, for example, was introduced as an organic source, cerium β-diketonate [Ce(fod)4]. The high vapor pressure of this compound allowed delivery to the reaction flame by a more traditional bubbler carrier system with heated delivery lines [50]. Another high vapor pressure organic compound used was the rare earth chelate RE(thd)3 (2,2,6,6-tetramethyl3,5-heptanedione) [48]. Here a 1.0-wt% Nd 2 O 3 double-clad fiber was fabricated for highoutput powers, with background losses of 10 dB/km. Concentrations of Yb 2 O 3 as high as 11 wt%, as required for the double-clad laser, were also achieved by this method.

Figure 4

Postdeposition low vapor pressure dopant incorporation for VAD or OVD by vapor impregnation of a soot boule.

8

Simpson

Figure 5

Postdeposition low vapor pressure dopant incorporation for VAD or OVD by solution impregnation followed by drying and sintering.

Although no rare earth solution aerosol flame demonstrations have been reported, delivery of a nebulized aqueous solution of lead nitrate has been reported, showing the feasibility of this technique [49]. Likewise, there appears to be no report mentioning the delivery of rare earth chloride vapor to OVD or VAD flame reactions, although it is a likely method. The soot boules generated by OVD and VAD undergo a secondary drying and sintering process, which provides another opportunity for dopant incorporation. Rare earth dopant vapors have been incorporated in the glass by this postdeposition diffusion process during sintering (Fig. 5) [52]. Control of the incorporated dopant is achieved by a combination of dopant concentration in the sintering atmosphere and the pore size or density of the soot preform. Other dopants such as AlCl 3 and fluorine have been introduced this way as well [53,54]. 1.4.3 Rare Earth Solutions One of the first reported means for incorporating low-volatility halide ions into high-purity fiber preforms used a liquid phase ‘‘soot impregnation method’’ [55]. A pure silica soot boule was first fabricated by flame hydrolysis, with a porosity of 60–90% (pore diameter of 0.001–10 µm). The boule was immersed in a methanol solution of the dopant salt for 1 h and then allowed to dry for 24 h, after which the boule was sintered in a He/O 2 /Cl 2 atmosphere to a bubble-free glass rod (see Fig. 5). The dopant concentration was controlled by varying the ion concentration in the solution. This general technique, later referred to as molecular stuffing, has been used to incorporate Nd and Ca in silica [56,57]. A variation of this solution-doping technique combining MCVD and the solution doping has more recently been reported (Fig. 6) [58]. Here, an unsintered (porous) layer of silica is first deposited inside a silica tube by the MCVD process. This layer is doped by filling the tube with an aqueous rare earth chloride solution; this solution is allowed to soak for nearly 1 h, and then the solution is drained. The impregnated layer is dried at high temperatures in the presence of flowing chlorine/oxygen mixture. Index-raising dopants such as aluminum have also been incorporated by this method [25]. Although this process would seem to be inherently less pure, it has produced doped fibers with background losses of 0.3 dB/ km [59]. This general method has also been extended by replacing aqueous solutions with


9

Figure 6 MCVD/solution-doping.

ethyl alcohol, ethyl ether, or acetone solvents for Al 3⫹ and rare earth halides. Solubilities vary widely among the rare earth nitrates, bromides, and chlorides, and all are useful. Fibers made with these nonaqueous solvents contained a relatively low OH impurity level as evidenced by the less than 10-dB/m absorption at 1.38 µm [60]. Aqueous solution methods may also produce low OH fibers with proper dehydration techniques. As erbium-doped silica amplifiers were developed, it became clear that confinement of the dopant to the central region of the core was very important, as were uniformity and homogeneity of the deposit. To this end, another MCVD dopant method was developed, referred to as sol–gel dipcoating [61]. The process coats the inside of an MCVD substrate tube with a rare earth-containing sol, which subsequently gels, leaving a thin dopant layer (Fig. 7). Both rare earth and index-raising dopants may be combined. The coating sol is formed by hydrolyzing a mixture of a soluble rare earth compound with Si(OC 2H 5) 4 (TEOS). The viscosity of the gel slowly increases with time as hydrolysis polymerizes the reactants. Deposition of the film then proceeds by filling the inside of the MCVD support tube with the gel, followed by draining. The gel layer thickness is controlled by the viscosity of the gel which, in turn, is determined by its age and the rate at which the gel liquid is drained. Film thickness of a fraction of a micrometer is typical, thereby allowing a well-confined dopant region. The coated tube is returned to the glassworking lathe for subsequent collapse. 1.4.4 Rod and Tube The first optical fibers were made by drawing a preform assembly made of a core rod and cladding tube of the proper dimensions and indices [1]. Recent adaptations of this

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Figure 7 Sol-gel dipcoating process for MCVD. method have been demonstrated for making compound glass core compositions [62]. To retain the overall compatibility with communication-grade doped silica fiber, a small compound glass rod is inserted into a thick-walled silica tube. The combination is then drawn at the high temperatures required by the silica tube. As a result, a few of the less stable constituents of the compound glass are volatilized. In spite of this, lengths of fiber can be drawn that are long enough for practical use. With interest in distributed Er-doped amplifiers, a need arose for a method to produce uniform and very low dopant levels. Although the solution doping and outside process methods were successful in controlling these low levels of dopant, a new, rod-and-

Figure 8 Seed fiber doping of MCVD.


11

tube–like technique was also devised to meet this challenge. Here the rare earth was introduced into an MCVD preform as the core of a fiber with a 150-µ outside diameter and a 10-µm core diameter (Fig. 8). The ‘‘seed’’ fiber was inserted in the bore of an MCVD preform before the last collapse pass [27]. During the final collapse pass, the fiber becomes a diffusion source for the dopant ions in the center of the preform core. Fibers fabricated by this method have shown losses as low as 0.35 dB/km and well-controlled erbium levels of 0.01 ppm Er 3⫹, corresponding to a ground-state absorption level of only 1 dB/km at 1.53 µm [27]. In a sense this resembles a miniature rod-and-tube process except that the rod is effectively dissolved in the host core, as evidenced by the change in fluorescence spectrum from the seed composition to the core composition.

1.5 PHYSICAL PROPERTIES 1.5.1 Fiber Refractive Index and Composition Profile Both mode field diameter and confinement of the rare earth affect the performance of the fiber device. Both are controlled by the composition profile determined during fabrication. The typical index-raising dopants used in communication-compatible fiber are germanium, aluminum, and phosphorus. The incorporation of these dopants during deposition depends on several factors, including partial pressure of dopant reactant, partial pressure of oxygen, and deposition temperature [63–65]. Both GeO 2 and P 2 O 5 are unstable at high temperatures, causing a depletion and corresponding refractive-index depression during the collapse stage of MCVD. A similar behavior has been reported for the incorporation of erbium in a GeO 2 /SiO 2 host. When Al 2 O 3 or Al 2 O 3 and P 2 O 5 were added, however, no depletion of the erbium in the center was observed [38]. Methods to eliminate the depression in refractive index from germanium depletion have been demonstrated by a flow compensation GeCl 4 or by etching away the depressed index region [66,67]. The smooth refractive index profile that is typical when Al 2 O 3 is used due to its high temperature stability [68–70]. Concentrations of Al 2 O 3 are limited to a few mole percent in binary compositions before crystalization occurs. For this reason GeO 2 is typically added, providing an additional rise in the refractive index. 1.5.2 Strength and Reliability The strength of high-quality optical fiber, a principal concern for reliability, is determined primarily by submicrometer flaws on the glass surface. Intrinsic strengths of silica fiber are near 800 kpsi. However, moisture and surface damage may easily bring this value down to tens of kpsi by static fatigue over a time scale of seconds to years. Commercial fibers are commonly proof tested at 50 kpsi for terrestrial applications and 200 kpsi for undersea cables. Excluding the distributed amplifier, most of the laser or amplifier devices will likely be packaged in coils, a few centimeters in diameter with negligible strength reduction over decades. In the interest of creating small, packaged amplifiers, however, hermetic-coated erbium-doped fibers have been fabricated for spools as small as 15 mm in inside diameter [71]. Other factors that are important determinants of reliability include mechanisms that may reduce the transparency of the fiber with time, notably high-energy radiation and hydrogen in-diffusion. Radiation measurements of erbium amplifiers have been reported that indicate a predicted gain reduction of less than 0.1 dB for a typical terrestrial exposure

12

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dose rate of 0.5 rad/yr over 25 years. A wavelength dependence of the reduced gain was observed, with 1.536-µm signals suffering nearly twice the loss as 1.555-µm signals [72].

1.6 SUMMARY Rare earth-doped fibers can now be fabricated by a wide variety of methods, each suited for different needs, from high concentrations in multicomponent glasses to less than 1 ppm, with background losses comparable with state-of-the-art communications-grade fiber. All the standard methods for making low-loss fiber have found adaptations to include rare earths. The widespread success of these fabrication methods has stimulated the rapid development of fiber lasers and amplifiers for system use. Continued development will likely focus on control of the dopants’ structural environment and position within the refractive index profile of the fiber. Commercialization will require greater attention to reproducibility and control of the factors that determine reliability.

REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12.

13. 14. 15. 16. 17. 18.

Snitzer, E. Proposed fiber cavities for optical lasers. J. Appl. Phys. 32:36–39, 1961. Koester, C. J., E. Snitzer. Amplification in a fiber laser. Appl. Opt. 3:1182–1186, 1964. Stone, J., C. A. Burrus. Nd-doped SiO 2 lasers in end pumped fibre geometry. Appl. Phys. Lett. 23:388–389, 1973. Urquhart, P. Review of rare earth doped fibre lasers and amplifiers. IEE Proc. J. Optoelectron 135:385–407, 1988. Simpson, J. Fabrication of rare earth doped glass fibers. Proc. SPIE 1171:2–7, 1989. DiGiovanni, D. J. Fabrication of rare earth doped optical fiber. Proc. SPIE 1373:2–8, 1990. Ainslie, B. J. A review of the fabrication and properties of erbium-doped fibers for optical amplifiers. 9:220–227, 1991. Mackenzie, H. S., F. P. Payne. Evanescent field amplification in a tapered single-mode optical fibre. Electron. Lett. 26:130–132, 1990. Sankawa, I., H. Izumita, T. Higashi, K. Ishihara, Er 3⫹-doped cladding fibers and their taper component applications. IEEE Photon. Tech Lett. 2:41–42, 1990. Astakhov, A. V., M. M. Butusov, S. L. Galkin. Characteristics of laser effects in active fiber lightguides. Opt. Spektrosk. 59:913–916, 1985. Sorin, W. V., K. P. Jackson, H. J. Shaw. Evanescent amplification in a single-mode optical fibre. Electron. Lett. 19:820–821, 1983. Po, H., E. Snitzer, R. Tumminelli, L. Zenteno, F. Hakimi, N. M. Cho, T. Haw. Double clad high brightness Nd fiber laser pumped by GaAlAs phased array. Proc. OFC’89, postdeadline session, paper PD07, 1989. Bocko, P. L. Rare earth doped optical fibers by the outside vapor deposition process. Proc OFC’89, paper TUG2, 1989. Digonnet, M. J. F., C. J. Gaeta. Theoretical analysis of optical fiber laser amplifiers and oscillators. Appl. Opt. 24:333-342, 1985. Armitage, J. R. Three-level fiber laser amplifier: a theoretical model. Appl. Opt. 27:4831– 4836, 1988. Desurvire E., J. L. Zyskind, C. R. Giles. Design optimization for efficient erbium doped fiber amplifiers. IEEE/OSA J. Lightwave Technol. LT8:1730–1741, 1990. Izumitani, T. S. Optical Glass. American Institute of Physics, New York, 1986, pp 162–172. Originally published as Kogaku Garasu, Kyoritsu Shuppan, Ltd., 1984. Yamashita, T., S. Amano, I. Masuda, T. Izumitani, A. Ikushima. Nd and Er doped phosphate glass fiber lasers. CLEO’88 Proc., paper THH2, 1988.


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19. Snitzer, E. Glass lasers. Appl. Opt. 5:1487–1499, 1966. 20. Shimizu, M., M. Yamada, M. Horigucho, E. Sugita. Concentration effect on optical amplification characteristics of Er-doped silica single-mode fibers. IEEE Photon. Technol Lett. 2:43– 45, 1990. 21. Suyama, M., K. Nakamura, S. Kashiwa, H. Kuwahara. 14.4-dB Gain of erbium-doped fiber amplifier pumped by 1.49 µm laser diode. Proc. OFC’89, postdeadline session paper PD6, 1989. 22. Ainslie, B. J., S. P. Craig, S. T. Davey, D. J. Barber, J. R. Taylor, A. S. L. Gomes. Optical and structural investigation of Nd 3⫹ in silica-based fibers. J. Matr. Sci. Lett. 6:1361–1363, 1987. 23. MacChesney, J. B., J. R. Simpson. Optical waveguides with novel compositions. Proc. OGC’85, paper WH5, p 100, 1985. 24. Arai, K., H. Namikawa, K. Kumata, T. Honda, Y. Ishii, T. Handa. Aluminum or phosphorus co-doping effects on the fluorescence and structural properties of neodymium-doped silica glass. J. Appl. Phys. 59:3430–3436, 1986. 25. Poole, S. B. Fabrication of Al 2 O 3 co-doped optical fibres by a solution-doping technique. Proc. ECOC’88, pp 433–436, 1988. 26. Ainslie, B. J., S. P. Craig, S. T. Davey. The fabrication and optical properties of Nd 3⫹ in silicabased optical fibers. Mater. Lett. 5:143–146, 1987. 27. Simpson, J. R., H.-T., Shang, L. F. Mollenauer, N. A. Olsson, P. C. Becker, K. S. Kranz, P. J. Lemaire, M. J. Neubelt. Performance of a distributed erbrium-doped dispersion-shifted amplifier. IEE/OSA J. Lightwave Technol. LT-9:228–233, 1991. 28. Izawa, T., S. Kobayashi, S. Sudo, F. Hanawa. Continuous fabrication of high silica fiber preform. Integrat. Opt. Fiber Commun. Technol. Dig. Pl-1:375–378, 1977. 29. Keck, D. B., P. C. Schultz. U.S. patent 3,737,292 (1973). 30. MacChesney, J. B., P. B. O’Connor, F. V. DiMarcello, J. R. Simpson, P. D. Lazay. Preparation of low loss optical fibers using simultaneous vapor phase deposition and fusion. Int. Congr. Glass (Kyoto, Jpn) 10th Tech. Diag. 6:40–44, 1974. 31. Koenings, J., D. Kuppers, H. Lydtin, H. Wilson. Deposition of SiO 2 with low impurity content by oxidation of SiCl 4 in nonisothermal plasma. Proceedings of the Fifth International Conference on Chemical Vapor Deposition, 1975, pp 270–281. 32. Stensland, L., P. Gustafson. Fibre manufacture using microwave technique. Ericsson Rev. 4: 152–157, 1989. 33. Miller, S. E., I. P. Kaminow, eds. Optical Fiber Telecommunications, vol. 2. Academic Press, New York, 1988. 34. Li, T. ed. Optical Fiber Communications, vol. 1. Fiber Fabrication. Academic Press, New York, 1985. 35. Shimazaki, E., N. Kichizo. Dampfdruckmessungen an Halogeniden der seltenen Erden. Z. Anorg. Allg. Chem. 314:21–34, 1962. 36. Spedding, F. H., A. H. Daane. The Rare Earths. Wiley, New York, 1961, p 98. 37. Sicre, J. E., J. T. Dubois, K. J. Eisentraut, R. E. Sievers. Volatile lanthanide chelates: II. Vapor pressures, heats of vaporization, and heats of sublimation. J. Am. Chem. Soc. 91:3476–3481, 1969. 38. Ainslie, B. J., J. R. Armitage, S. P. Craig, B. Wakefield. Fabrication and optimisation of the erbium distribution in silica based doped fibres. Proc. ECOC, 1988, pp 62–65. 39. Wall, A., H. Posen, R. Jaeger. Radiation hardening of optical fibers using multidopants Sb/ P/Ce. In: Advances in Ceramics, vol. 2. Physics of Fiber Optics. Bendow and Mitra, 1980, pp 393–397. 40. Poole, S. B., D. N. Payne, M. E. Fermann, Fabrication of low-loss optical fibers containing rare earth ions. Electr. Lett. 21:737–738, 1985. 41. Poole, S. B., D. N. Payne, R. J. Mears, M. E. Fermann, R. I. Laming. Fabrication and characterization of low-loss optical fibers containing rare earth ions. IEEE/OSA J. Lightwave Technol. LT-4(7), 1986.

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42. Simpson, J. R., J. B. MacChesney. Alternate dopants for silicate waveguides. Proc. OFC’82, paper TUCC5, 1982. 43. Watanabe, M., H. Yokota, M. Hoshikawa. Fabrication of Yb 2 O 3 –SiO 2 core fiber by a new process. Proc. ECOC, 1985. 44. Laoulacine, R., T. F. Morse, P. Charilaou, J. W. Cipolla. Aerosol delivery of non-volatile dopants in the MCVD system. paper 62B, Extended Abstracts of the AIChE Annual Meeting, Washington, DC, 1988. 45. Morse, T. F., L. Reinhart, A. Kilian, W. Risen, J. W. Cipolla. Aerosol doping technique for MCVD and OVD. Proc. SPIE 117:72–79, 1989. 46. Morse, T. F., A. Kilian, L. Reinhart, W. Risen, Jr., J. W. Cipolla, Jr. Aerosol techniques for fiber core doping. Proc. OFC 91, paper WA3, 1991, p 63. 47. Morse, T. F., A. Kilian, L. Reinhart, W. Risen, J. W. Cipolla. Aerosol techniques for glass formation. J. Non-Cryst. Solids 129:93–100, 1991. 48. Tumminelli, R. P., B. C. McCollum, E. Snitze. Fabrication of high-concentration rare earth doped optical fibers using chelates. IEEE/OSA J. Lightwave. Technol. LT-8:1680–1683, 1990. 49. Sanada, K., T. Shioda, T. Moriyama, K. Inada, S. Takahashiand, M. Kawachi. PbO doped high silica fiber fabricated by modified VAD. Proceedings of the Sixth European Conference on Optical Communications (IEE), 1980, pp 14–17. 50. Thompson, D. A., P. L. Bocko, J. R. Gannon. New source compounds for fabrication of doped optical waveguide fibers. SPIE 506:170–173, 1984. 51. Abramov, A. A., M. M. Bubnov, E. M. Dianov, A. E. Voronkov, A. N. Guryanov, G. G. Devjatykh, S. V. Ignatjev, Y. B. Zverev, N. S. Karpychev, S. M. Mazavin. New method of production of fibers doped by rare earths. Proc. CLEO’90, paper CTHI36, p 404, 1990. 52. Shimizu, M., F. Hanawa, H. Suda, M. Horiguchi. Transmission loss characteristics of Nddoped silica single-mode fibers fabricated by the VAD method. Jpn. J. Appl. Phys. 28:L476– L478, 1989. 53. Dumbaugh, W. H., P. C. Schultz. Method of producing glass by flame hydrolysis. U.S. patent 3,864,113, 1975. 54. Kyoto, M., H. Kanamori, N. Yoshioka, G. Tanaka, M. Watanabe. Fluorine doping in the VAD sintering process. Proc. OFC’84, paper MGS, pp. 22–23, 1984. 55. Schultz, P. C. Optical absorption of the transition elements in vitreous silica. J. Am. Ceram. Soc. 309–313, 1974. 56. Gozen, T., Y. Kikukawa, M. Yoshida, H. Tanaka, T. Shintani. Development of high Nd 3⫹ content VAD single-mode fiber by molecular stuffing technique. Proc. OFC’88, paper WQ1, 1988. 57. Saifi, M. A., M. J. Andrejco, W. I. Way, A. Von Lehman, A. Y. Yan, C. Lin, F. Bilodeau, K. O. Hill. Er 3⫹-doped GeO 2 –CaO–Al 2 O 3 silica core fiber amplifier pumped at 813 nm. Proc. OFC’91, paper FA6, p 198, 1991. 58. Townsend, J. E., S. B. Poole, D. N. Payne. Solution doping technique for fabrication of rare earth doped optical fibers. Electron Lett. 23: 329–331, 1987. 59. Larsen C. LYCOM. private communications. 60. Cognolato, L., B. Sordo, E. Modone, A. Gnazzo, G. Cocito. Aluminum/erbium active fibre manufactured by a non-aqueous solution doping method. Proc. SPIE 1171:202–208, 1989. 61. DiGiovanni, D. J., J. B. MacChesney. New optical fiber fabrication technique using sol–gel dipcoating. Proc. OFC’91, paper WA2, p 62, 1991. 62. Snitzer, E., R. Tumminelli. SiO 2-clad fibers with selectively volatilized soft glass cores. Opt. Lett. 14: 757–759, 1989. 63. Kleinert, P., D. Schmidt, J. Kirchhof, A. Funke. About the oxidation of SiCl 4 and GeCl 4 in homogeneous gaseous phase. Kristall Technol. 15(9):85–90, 1980. 64. Wood, D. L., K. L. Walker, J. B. MacChesney, J. R. Simpson, R. Csencsits. Germanium chemistry in the MCVD process for optical fiber fabrication. IEE/OSA J. Lightwave Technol. LT-5:277–285, 1987.


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65. Digiovanni, D. J., T. F., J. W. Cipolla. The effect of sintering on dopant incorporation in modified chemical vapor deposition. IEEE/OSA J. Lightwave Technol. LT-7:1967–1972, 1989. 66. Akamatsu, T., K. Okamura, Y. Ueda. Fabrication of graded-index fibers without an index dip by chemical vapor deposition method. Appl. Phys. Lett. 31:515–517, 1977. 67. Hopland, S. Removal of the refractive index dip by an etching method. Electron. Lett. 14: 7574–759, 1978. 68. Ohmori, Y., F. Honawa, M. Nakahara. Fabrication of low-loss optical glass fibre with Al 2 O 3SiO 2 core. Electron. Lett., 10: 410–411, 1974. 69. Simpson, J. R., J. B. MacChesney. Optical fibres with an Al 2 O 3-doped silicate core composition. Electron, Lett. 19: 261–262, 1983. 70. Scott, C. J. Optimization of composition for Al 2 O 3 /P 2 O 5-doped optical fiber. Proc. OFC’84, paper TUM4, pp 70–71, 1984. 71. Oyobe, A., K. Hirabayashi, N. Kagi, K. Nakamura. Hermetic erbium doped fiber coils for compact optical amplifier modules. Proc. OFC’91, paper WL8, 1991. 72. Wada, A., T. Sakai, D. Tanaka, R. Yamauchi. Radiation sensitivity of erbium-doped fiber amplifiers. Proceedings of the Optical Amplifiers and Their Applications Conference, Monterey, CA, paper WD4, 1990.

2 Optical and Electronic Properties of Rare Earth Ions in Glasses WILLIAM J. MINISCALCO GTE Laboratories Incorporated, Waltham, Massachusetts

2.1 GENERAL PROPERTIES 2.1.1 Introduction Rare earth ions have a long history in optical and magnetic applications. Among these, luminescent devices using single crystals, powders, and glasses have been particularly important. Rare earths have important characteristics that distinguish them from other optically active ions: they emit and absorb over narrow wavelength ranges, the wavelengths of the emission and absorption transitions are relatively insensitive to host material, the intensities of these transitions are weak, the lifetimes of metastable states are long, and the quantum efficiencies tend to be high, except in aqueous solutions. These properties all result from the nature of the states involved in these processes and lead to excellent performance of rare earth ions in many optical applications. Devices that provide gain, such as lasers and amplifiers, must have low scattering losses, and one is restricted to using single-crystal or glass hosts. Whereas in many applications crystalline materials are preferred for reasons that include higher peak cross sections or better thermal conductivities, the versatility of glasses and the broader emission and absorption spectra they provide have led to the use of rare earth doped glasses in many applications. Nowhere is this more true than in the area of optical fiber devices. Table 1 lists the wavelengths, transitions, and features of fiber lasers and amplifiers that had been reported as of 1991. Oxide and fluoride hosts are distinguished in the table, because the latter provide more metastable states and greater transparency at wavelengths beyond 2000 nm. The high intensities and long interaction lengths made possible by fiber waveguides make these devices vastly superior to their bulk glass counterparts in most applications. Glass fiber lasers are compa17

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Table 1 Glass Fiber Lasers and Amplifiers Type of host

Operating range (nm)

Dopant ion

Transition

⬇455 ⬇480 ⬇490 ⬇520 ⬇550 ⬇550 601–618 631–641 ⬇651 707–725 ⬇753 803–825 ⬇850 880–886 902–916 900–950 970–1040 980–1000 1000–1150 1060–1110 1260–1350 1320–1400 ⬇1380 1460–1510 ⬇1510 1500–1600 ⬇1660 ⬇1720 1700–2015 2040–2080 2250–2400 ⬇2700 ⬇2900

Tm 3⫹ Tm 3⫹ Pr3⫹ Pr3⫹ Ho 3⫹ Er 3⫹ Pr 3⫹ Pr 3⫹ Sm 3⫹ Pr 3⫹ Ho 3⫹ Tm 3⫹ Er 3⫹ Pr 3⫹ Pr 3⫹ Nd 3⫹ Yb 3⫹ Er 3⫹ Nd 3⫹ Pr 3⫹ Pr 3⫹ Nd 3⫹ Ho3⫹ Tm 3⫹ Tm 3⫹ Er 3⫹ Er 3⫹ Er 3⫹ Tm 3⫹ Ho 3⫹ Tm 3⫹ Er 3⫹ Ho 3⫹

D2 → 3F4 G4 → 3H6 3 P0 → 3H4 3 P1 → 3H5 5 S 2, 5 F 4 → 5 I 8 4 S 3/2 → 4 I 15/2 3 P0 → 3H6 3 P0 → 3F2 4 G 5/2 → 6 H 9/2 3 P0 → 3F4 5 S 2, 5 F 4 → 5 I 7 3 H 4 → 3 H6 4 S 3/2 → 4 I 13/2 3 P1 → 1G4 3 P1 → 1G4 4 F 3/2 → 4 I 9/2 5 F 5/2 → 5 F 7/2 4 I 11/12 → 4 I 15/2 4 F 3/2 → 4 I 11/2 1 D2 → 3F4 1 G4 → 3H5 4 F 3/2 → 4 I 13/2 5 S 2, 5 F 4 → 5 I 5 3 H4 → 3F4 1 D2 → 1G4 4 I 13/2 → 4 I 15/2 2 H 11/2 → 4 I 9/2 4 S 3/2 → 4 I 9/2 3 F4 → 3H6 5 I7 → 5I8 3 H4 → 3H5 4 I 11/2 → 4 I 13/2 5 I6 → 5I7

a

Oxide

Fluoride

1 1

Yes

No No

Yes Yes Yes Yes Yes Yes Yes Yes

Yes No No No

Yes Yes No Yes Yes No Yes ? No Yes No No Yes Yes No No No

Yes Yes Yes Yes Yes Yes

Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes Yes

Type of transition a UC, UC, UC, UC, UC, UC, UC, UC, 4L UC, UC, 3L 4L 4L 4L 3L 3L 3L 4L 4L 4L 4L 4L ST UC, 3L 4L 4L 3L 3L 4L ST ST

ST 3L 3L 4L 3L 3L 4L 4L 4L ST?

4L

3L, three-level; 4L, four-level; UC, up-conversion; ST, apparent self-terminating.

rable in performance with laser-pumped, bulk, crystalline lasers, and as continuous-wave (cw) amplifiers they are even better. The major exception is in applications requiring highenergy pulses, for which the small volume of the optical fiber cannot provide as much energy storage as bulk media. The characteristics of luminescent devices follow from the optical properties of the ion–host combinations used: if one has the relevant information, it is possible to accurately predict the performance of the laser, amplifier, or superluminescent source. One of the most powerful tools for obtaining the necessary information is optical spectroscopy, which employs absorption and emission processes, although not necessarily confined to the transitions on which the device operates. Sections 2.1.2–2.1.8 examine the origins of the

Rare Earth Doped Glasses: Optical Properties

19

electronic structure of rare earth ions, as well as the processes that induce transitions between the energy levels. Even though theory provides a useful conceptual basis on which to understand the distinguishing characteristics of rare earth ions, the systems are much too complex to permit accurate calculations of the observed properties. Experimental measurements are required to obtain quantitative information and the key parameters in the theoretical analysis. The related issues of the interaction between rare earth ions and the way in which they are incorporated into the glass host are also discussed, as these can have a significant effect on device performance. Sections 2.2–2.4 discuss the spectroscopy of three extensively used ions, Nd 3⫹, Er 3⫹, and Tm 3⫹, together with its implications for device performance. 2.1.2 Electronic and Optical Properties of Rare Earth Ions The rare earths are divided into two groups of 14 elements each. The lanthanides are characterized by the filling of the 4f shell and begin with cerium (Ce), which has an atomic number Z of 58, and end with lutetium (Lu, Z ⫽ 71). The actinides lie below them in the periodic table, filling the 5f shell from thorium (Z ⫽ 90) to lawrencium (Z ⫽ 103). Although these elements share many electronic properties, only the lanthanides are considered here, because they are of greater importance in lasers and amplifiers: many actinides have no isotopes stable enough to be useful for such devices, whereas among the lanthanides only promethium (Pm) has a short half-life (⬍20 yr). The name rare earth is, in fact, a misnomer, for lanthanides other than Pm are not actually rare, and the elements with even atomic numbers are particularly abundant. From the perspective of optical and electronic properties, the most important feature of rare earths is the lanthanide contraction [1]. This is a consequence of imperfect screening by the 4f electrons, which leads to an increase in effective nuclear charge as the atomic number increases in the lanthanide series. As a result, the 4f electrons become increasingly more tightly bound with increasing Z [2]. While neutral lanthanum (La) has the xenon structure plus 5d6s 2, the electrons that are added for the neutral elements that follow are found in the 4f shell and only Ce, gadolinium (Gd), and Lu have a 5d electron. In terms of their spatial extent, the 4f wave functions for La (Z ⫽ 57) lie outside the xenon shell, but by neodymium (Nd, Z ⫽ 60) they have contracted so much that the maximum lies within the 5s 25p 6 closed shells of the xenon structure [2]. A similar, although less pronounced phenomenon, also occurs for the actinides. In condensed matter the trivalent (3⫹) level of ionization is the most stable for lanthanide ions, and most optical devices use trivalent ions. Accordingly, further discussion is confined to these. Ionization preferentially removes the 6s and 5d electrons, and the electronic configuration for these ions (henceforth, referred to as rare earth ions) is that of the xenon structure plus a certain number (1–14) of 4f electrons. The observed infrared (IR) and visible optical spectra of trivalent rare earth ions is a consequence of transitions between 4f states. For most ions this is also true in the ultraviolet (UV) for wavelengths less than 300 nm, although for a few, notably Ce 3⫹ and trivalent praseodymium (Pr 3⫹), 5d levels lie low enough to produce strong, broad absorption bands in the ultraviolet. Figure 1 depicts the radial parts of the 5s, 5p, and 4f wave functions for Ce 3⫹ and illustrates the extent to which the 4f wave functions lie within the closed 5s 25p 6 xenon shell as a result of the lanthanide contraction. This effect is even stronger for the other rare earth ions and has important implications in molecular complexes and condensed matter, because the 5s and 5p electrons shield the 4f electrons from the effects of the

20

Miniscalco

Figure 1 Radial wave functions for Ce 3⫹ in units of the Bohr radius, a 0 . (Courtesy of D. S. Hamilton.)

environment. The consequences for the static interactions are energy levels that are relatively insensitive to host, have small host-induced splittings, and are only weakly mixed with higher energy states. The dynamic consequences are little or no vibronic structure (phonon-assisted transitions) and weak nonradiative relaxation of excited states, which occurs through phonon emission. The net results are optical transitions between 4f states that manifest themselves as narrow, weak bands or sharp lines, and emission that can be highly efficient. These properties are quite different from those of the major category of optical ions, the transition metals. The latter have a much stronger interaction with the host and are characterized by broad, strong emission and absorption bands that are due to vibronically assisted transitions, and also by a much higher nonradiative relaxation rate (lower radiative efficiency). Because the 4f electrons interact only weakly with electrons on other ions, the Hamiltonian can be written for an individual rare earth ion and decomposed as H ⫽ H free ion ⫹ V ion–static lattice ⫹ V ion–dynamic lattice ⫹ V EM ⫹ V ion–ion

(1)

Here H free ion is the Hamiltonian of the ion in complete isolation, V ion–static lattice and V ion–dynamic lattice contain the static and dynamic interactions of ion with the host, V EM treats the interaction of the ion with the electromagnetic field, and V ion–ion describes the interaction between rare earth ions. The physical basis for the optical properties of rare earth ions is discussed in Sections 2.1.3 through 2.1.7. Because the interaction terms in Eq. (1) are weak compared with H free ion , they are discussed separately as perturbations. We shall group them into the general categories of static, which produce the observed electronic structure,


21

and dynamic, which induce transitions between the electronic states. Issues of solubility and how rare earth ions are incorporated into solids are addressed in Section 2.1.8. 2.1.3 Electronic Structure The first two terms in Eq. (1) give rise to the observed electronic structure. Techniques for solving them are discussed in detail by several authors [2–10]. The standard approach for treating H free ion is to employ the central field approximation, in which each electron is assumed to move independently in a spherically symmetric potential formed by the nucleus and the average potential of all other electrons. The solutions to this problem can then be factored into a product of a radial and angular function. Whereas the radial function depends on the details of the potential the spherical symmetry ensures that the angular component is identical with that of a hydrogen atom and can be expressed as spherical harmonics. Except for Ce 3⫹ and Yb 3⫹, which have only one electron (or hole), the solutions of the central-field problem are products of one-electron states that are antisymmetric under the interchange of a pair of electrons, as required by the Pauli exclusion principle. Because these solutions are constructed from hydrogenic states, total orbital angular momentum L and total spin S are ‘‘good’’ quantum numbers (i.e., exact eigenvalues of the Hamiltonian). L and S are the vector sums of the orbital and spin quantum numbers for all the 4f electrons on the ion. Each f electron contributes an orbital quantum number of 3 and spin of 1/2. Total orbital angular momentum is specified by the letters S, P, D, F, G, H, I, K, . . . to represent L ⫽ 0, 1, 2, 3, 4, 5, 6, 7, . . . , respectively. Russell–Saunders coupling (LS coupling) is most often used for the states of lanthanides and actinides. In this scheme L and S are vectorially added to form the total angular momentum J, and the states are labeled 2S⫹1 L J . The quantum numbers (L, S, J, and another arbitrary one) define the terms of the configuration, all of which are degenerate in the central-field approximation, as illustrated in Figure 2. Linear combinations of these states (with the appropriate symmetry for simplifying the calculations) serve as the basis states for evaluating the electron–electron interactions that have been ignored up to this point. Electrons in closed shells impart a constant energy shift to all terms, and thus only the interaction between the 4f electrons need be considered. The angular dependence of the electrostatic interaction is usually treated using the tensor operator methods of Racah [11], whereas the radial part is handled using Slater integrals of the one-electron wave functions. Figure 2 shows how the electrostatic interaction lifts the angular degeneracy and produces a spectrum of states the energies of which now depend on L and S, but not J. Next in the hierarchy is spin–orbit, the strongest of the magnetic interactions. Spin– orbit lifts the degeneracy in total angular momentum and splits the LS terms into J levels (see Fig. 2). If only the diagonal matrix elements of the interaction are considered, different LS terms are not mixed and the states retain their original values of L and S. This is the situation to which Russell–Saunders coupling applies and leads to the Lande interval rule in which the spacing between adjacent levels derived from the same term is proportional to the higher J of the pair. In practice, the separation between LS terms is too small compared with the strength of the spin–orbit interaction, and one must perform an intermediate coupling calculation to diagonalize it and the electrostatic interaction simultaneously. This leads to states that are linear combinations of different LS terms and, therefore, are eigenstates of J, but not of L or S. This is illustrated in Figure 3, which plots the position of the energy levels as a function of the strength of the spin–orbit interaction for Tm 3⫹ [12]. Although both the electrostatic and spin–orbit interactions increase with increasing

22

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Figure 2

Energy diagram illustrating hierarchy of splittings resulting from electron–electron and electron–host interactions.

atomic number, spin–orbit increases more rapidly, and LS mixing is more significant for the high-Z rare earths (Ho, Er, Tm). The multiplets are still identified using Russell– Saunders labels, although confusion sometimes arises because some authors label states using the dominant LS contribution, whereas others use the LS term it would have if the spin–orbit interaction were negligible. In Figure 3 this choice corresponds to either using the composition of the state at the abscissa representing experimentally observed interaction strengths, or labeling a state by its designation at the zero of abscissa. The curvature in Figure 3 illustrates the usual quantum mechanical ‘‘avoided crossings’’ of states and indicates strong LS mixing. This confusion has been a particular problem for certain states of Tm 3⫹ and will be revisited in Section 2.4. In this work we have adopted the more physical convention of labeling the states using their dominant LS contribution for the experimentally observed interaction strengths.


23

Figure 3

Energies of the J multiplets of Tm 3⫹ as a function of the strength of the spin–orbit interaction divided by the characteristic electrostatic interaction. The curvature indicates strong LS mixing. (From Ref. 12.)

The host has the least influence on the electronic structure and changes the positions of these levels only slightly. The static effects of the host on the rare earth dopant customarily are treated by replacing the host with an effective crystal-field potential at the ion site. The potential is usually expanded in a power series of tensor operator components C (k) ⫺q that transform as spherical harmonics, V ion–static lattice ⫽

冱 B [C k q

(k) ⫺q i

]

(2)

ikq

where B kq are the crystal-field components (k ⱕ 6 for f electrons) and the summation i is carried out over all the 4f electrons of the ions. In practice, these ions are often replaced by their point-charge equivalents and only near neighbors are considered. The even-k terms in the expansion split the free ion J multiplets into Stark components generally separated by 10–100 cm ⫺1 (see Fig. 2). The rare earth site symmetry in glasses is usually low enough to lift all but the Kramers degeneracy, which persists for ions, such as Nd 3⫹ and Er 3⫹, with an odd number of electrons. The ion–lattice interaction can mix multiplets with different J values (J mixing), although it usually remains a good quantum number. The odd-k terms admix higher lying states of opposite parity [e.g., (4f ) n⫺1 5d 1] into the (4f ) n configuration. This admixture does not affect the positions of the energy levels, but

24

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it has a very important effect on the strengths of the optical transitions between levels, as will be discussed later. Equation (1) is only approximate, and in reality the host also effects H free ion . The principal mechanism is covalent bonding, the sharing of electrons between the rare earth ion and its ligands, which partially screens the 4f electrons and reduces the effective nuclear charge. This manifests itself as a rescaling of the entire energy level diagram (see Fig. 2), a phenomenon that has been referred to as the nephelauxetic effect [13]. For glasses this translates into host-to-host shifts of up to a few percent in the separations between energy levels. More covalent glasses, such as silicates, emit and absorb at longer wavelengths, whereas more ionic ones, such as fluorides, emit and absorb at shorter wavelengths. Attempts to calculate the positions of the Stark levels from first principles are seldom undertaken because of their complexity and the lack of information on the environment of the rare earth. More often, low-temperature optical measurements of the Stark splittings are used to deduce the nature of the ion site. This approach was applied to Er 3⫹-doped glasses by Robinson using absorption spectra [14,15]. In one of the most extensive investigations to date, Brecher and Riseberg used site selection emission spectroscopy to determine not only the site symmetry but also the distribution of sites for Eu 3⫹-doped silicate [16] and fluoroberyllate [17] glasses. Weber has pointed out, however, that although optical spectroscopy can indicate possible rare earth sites, it cannot be used to prove which of the possibilities are actually present [18]. He sought to overcome these shortcomings using molecular dynamics simulations of the glass structure to provide the rare earth environment to be used as inputs to Eq. (2). For rare earth doped fluoroberyllate glasses, Weber successfully reproduced the Stark splitting and their dependence on composition [18]. Nevertheless, the simple interaction potentials normally used in molecular dynamics simulations are only appropriate for ionic species and can lead to significant errors when applied to covalent glasses such as silicates and phosphates. 2.1.4 Radiative Transitions Interaction of Light with Localized Centers The dynamic interaction terms in Eq. (1) are time-dependent; therefore, they do not lead to stationary states of the system. They are usually treated using time-dependent perturbation theory and result in transitions between the states established by the static interactions. For luminescent devices the most important term is V EM, the interaction with the electromagnetic field, which give rise to the emission and absorption of photons. This involves both the interaction between the electron charge and the electric field and the interaction between the electron spin and the magnetic field. Because the wavelength of even ultraviolet light is much larger than the size of an ion, the phase factor in the interaction terms can be expanded as follows: exp[i(2πνt ⫺ k ⋅ r)] ⫽ exp(i2πνt) [1 ⫺ ik ⋅ r ⫹ ⋅ ⋅ ⋅]

(3)

In this expression ν is the frequency of the light and the wave vector k is much smaller than the reciprocal of the ion size. For either the electric or magnetic interaction, retaining only the first term in the expansion (i.e., exp(⫺ik ⋅ r) ⬇ 1) when calculating transition rates correspond to the dipole approximation. The line strength S a,b of a transition connecting two J multiplets, a and b, is given by S a,b ⫽

冱 | 〈b | D| a 〉| j

i,j

i

2

(4)

25


where the summation is over all components of i and j the a and b multiplets, and D is the interaction operator. Equation (4) assumes an equal population of all components of the initial state, a. An alternative definition assuming a Boltzmann population distribution can also be used [19]. The electric and magnetic dipole interaction operators take the following forms: Electric dipole: D ⫽ µ ed ⫽

冱 er

(5a)

i

i

Magnetic dipole: D ⫽ µ md ⫽

冱 2m (l ⫹ 2s ) e

i

i

(5b)

i

where m and e are the electron mass and charge, r i , l i , and s i are the position, orbital, and spin operators, respectively, for each electron, and the sum is over all f electrons on the ion. An extremely useful quantity is the probability for a spontaneous transition between two levels A a,b , which is also known as the Einstein A coefficient: A a,b ⫽

冢冣

1 64π 4 nν 3 E loc 4πε 0 3hc 3 E

2

1 S a,b ga

(6)

In this expression ε 0 is the permittivity of vacuum, h is Planck’s constant, c is the speed of light in vacuum, n is the index of refraction of the host, ν is the mean photon frequency, g a is the degeneracy of the initial state, g a ⫽ 2J a ⫹ 1. The ratio χ ⫽ (E loc /E ) 2 is referred to as the local field correction and represents the enhancement of the electric field in the vicinity of the ion owing to the polarizability of the medium. Although there is no generally applicable expression for χ, one generally uses the relations that are strictly true only for cases of high local symmetry: Electric dipole: χ ed ⫽

冢冣 n⫹2 3

Magnetic dipole: χ md ⫽ n 2

2

(7a) (7b)

The foregoing equations and those that follow are in SI units; the corresponding expressions in cgs units are the same, with the factor of 4πε 0 replaced by 1. Transition strengths are also commonly expressed in terms of a dimensionless quantity called the oscillator strength f, which is defined in terms of the Einstein A coefficient as follows: f a,b ⫽ 4πε 0

mc 3 1 A a,b 2 2 2 8π n e ν χ

(8)

Oscillator strengths are approximately 1 for fully allowed electric–dipole transitions and roughly seven orders of magnitude weaker for magnetic–dipole transitions. Electric–quadrupole transitions are at least an order of magnitude weaker still and correspond to the second term in the expansion shown in Eq. (3). If a is an excited state that decays only by the emission of photons, its observed relaxation rate is the sum of the probabilities for transitions to all possible final states, f. The total rate is the reciprocal of the excited-state lifetime τ a . 1 ⫽ τa

冱A f

a,f

(9)

26

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Radiative lifetimes for fully allowed electric–dipole transitions are roughly 10 ⫺8 s. The branching ratio, β a,b , for the transition a → b is the fraction of all spontaneous decay processes that occur through that channel and is defined as follows: β a,b ⫽

A a,b ⫽ A a,b τ a ∑ A a,c

(10)

c

The branching ratio, which has an important influence on the performance of a device based on a particular transition, appears often in the discussion of specific ions. It has a significant effect on the threshold of a laser and the efficiency of an amplifier. Other important properties that must be known to describe the characteristics of a luminescent device are the cross sections. In essence, these describe the interaction of light and the ion as a function of the frequency or wavelength of the light. The oscillator strength f a,b for the transition a → b is proportional to the spectral integral of the corresponding cross section σ a,b through f a,b ⫽ 4πε 0

mcn 1 πe 2 χ

冮σ

a,b

(ν)dν ≅ 4πε 0

mcn 1 ∆ν eff σ peak πe 2 χ

(11)

If one requires information only at the photon frequency where the cross section has its maximum value, Eq. (10) indicates how the integral over cross section can be replaced by the peak value of the cross section σ peak times the effective bandwidth of the transition, ∆ν eff . For the latter, the full width at half-maximum (FWHM) generally suffices, although the exact value is seen from Eq. (11) to be the integral of the cross section divided by σ peak . Useful relations for determining stimulated emission cross sections from measurements of the excited-state lifetime and emission spectrum are as follows: 8πn 2 β a,b ⫽ A a,b ⫽ 2 τa c

冮ν σ

β a,b ⫽ A a,b ⫽ 8πn 2 c τa

2

a,b

(ν)dν ⫽

冮I

冮 σ λ(λ) dλ ⫽ 冮 I

a,b

(ν)dν

(12a)

a,b

(λ)dλ

(12b)

a,b

4

In these expressions, I a,b (ν) is the spontaneous emission rate per unit bandwidth (see Eq. 12a), and I a,b (λ) is the spontaneous emission rate per unit wavelength interval (see Eq. 12b) for the a → b transition. The quantity I a,b is proportional to the emission spectrum measured in the appropriate way. [For example, a grating monochromator with a quantum counter detector measures I a,b (λ).] The procedure requires that β a,b be measured or calculated and that one correct for the effects of any other decay mechanism, such as nonradiative relaxation. For cases such as the 1500-nm emission band of Er 3⫹, the method is simple to apply, because nonradiative relaxation is negligible at room temperature for most hosts and the emission is from the first excited state for which β must equal 1. Intensities of Optical Transitions For rare earth ions, the optical transitions from the infrared to the ultraviolet are between states composed of 4f wave functions. Because the initial and final states have the same parity, electric–dipole processes are forbidden and transitions for free ions can occur only by the much weaker magnetic–dipole and electric–quadrupole processes. In solids, however, the odd-k terms in the ion–static lattice interaction [see Eq. (2)] admix higher-lying

27


states of opposite parity into the (4f ) n configuration, thereby introducing a degree of electric–dipole strength into the intra-f-shell transitions. The odd-k terms are nonzero only if the ion site lacks inversion symmetry, as it usually does in glasses. This is an extremely important effect because most visible and infrared rare earth transitions are dominated by this second-order electric–dipole contribution. There are some important exceptions to this rule, including the 4 I 13/2 ↔ 4 I 15/2 transitions of Er 3⫹ at 1500 nm, for which the magnetic– and electric–dipole strengths are comparable, particularly for a silica host. The crystal field interaction [see Eq. (2)] is responsible for the observed shape of the emission and absorption spectra as well. Considering a transition between two J multiplets, the even-k terms determine the positions of the Stark components for each multiplet; therefore, the wavelengths at which emission or absorption occurs. The odd-k terms determine the intensity of the process for each pair of components involved. The crystal field terms vary from material to material, and this is the most important factor affecting the host dependence of the spectra. Moreover, measurements on Er 3⫹-doped glasses have revealed that the host-to-host variation in crystal field splittings is not very large [20,21], leading to the conclusion that it is the variation in intensities of the transition between individual Stark components (i.e., the odd-k crystal field effects) that dominates the shape of the emission and absorption bands. One can, in principle, calculate the intensities and shapes of the bands if the V ion–static lattice is known. In practice, crystal field theory is only qualitative, and even for it the process is too complex to be attractive. However, a useful semiempirical technique for calculating the strength of rare earth transitions was developed independently by Judd [22] and Ofelt [23]. It relies on the assumption, usually satisfied, that the energy range occupied by the (4f ) n multiplets as well as that spanned by the opposite parity states admixed by the odd-k terms of Eq. (2) are small compared with the separation between these two sets of states. The spectrally integrated, electric–dipole strength of the transition from level a and b then reduces to a simple expression involving three empirical parameters (Ω 2 , Ω 4 , and Ω 6) and the appropriate reduced matrix elements: S a,b ⫽ e 2

冱 Ω | 〈b储U t

t⫽2,4,6

(t)

储 a〉| 2 ⫽ 4πε 0

3hcn(2J a ⫹ 1) 1 8π 3 ν χ

冮σ

a,b

(ν)dν

(13)

The reduced matrix elements include the spin–orbit mixing of the LS terms and are found by simultaneously diagonalizing the electrostatic and spin–orbit interactions, as discussed in Section 2.1.3. They are almost independent of material and have been tabulated by a number of authors [24,25]. The host dependence is contained in the three intensity parameters Ω t , which are empirically determined for a given combination of dopant and host. The general procedure is to perform a least-squares fit of Eq. (13) to the integrated absorption bands obtained from a measured spectrum. Once the parameters have been determined, the strength of any radiative transition can be calculated for that dopant–host combination. There is no clear physical meaning to the intensity parameters other than that Ω 2 is correlated with the degree of covalence: ionic materials such as fluorides have very small values of Ω 2 , whereas covalent materials such as silicates have large values. It will be seen that this gives rise to a significant composition dependence for some important transitions. Judd–Ofelt analysis is accurate to about 10–15% and is particularly valuable for obtaining strengths of transitions for which direct measurements are difficult or impossible. Because it provides only integrated transition strengths, determining cross sections also requires the measurement of spectra.

28

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Relations Between Cross Sections Ideally, all cross sections relevant to the operation of a device should be directly measured. Often in the investigation of rare earth transitions, however, it is possible to measure only absolute values for one of the cross-section spectra in an emission/absorption process. If a relative spectrum for the reciprocal process can be measured, there are procedures for scaling it. For bulk samples, it is usually the absorption cross sections that are measured because these are straightforward to obtain using commercial spectrophotometers if the ion concentration is known. Judd–Ofelt intensity parameters can then be extracted from the absorption data, enabling one to calculate the strength of the emission transition and, thereby, scale a measured emission spectrum using Eq. (13). For optical fibers, however, the procedures for obtaining absorption cross sections can be quite complex and inaccurate [26], and it is more convenient to measure stimulated emission cross sections [27–29]. The difficulty of obtaining absorption data for a sufficient number of bands also makes a Judd–Ofelt analysis problematic for fiber samples. An alternative approach is to use the relation between the Einstein A and B coefficients. When generalized to account for the finite line width, this leads to the following connection between the emission and absorption cross sections: ga

冮ν σ 2

a,b

(ν)dν ⫽ g b

冮ν σ 2

b,a

(ν)dν

(14)

where g ⫽ 2J ⫹ 1 are the degeneracies of the J multiplets involved. This expression is often seen in a more approximate form, sometimes referred to as the Ladenburg–Fuchtbauer relation [30], with ν 2 replaced by the square of the average photon frequency and taken outside the integral. Considerable effort has been devoted to determining the cross sections for the 4 I 15/2 ↔ 4I13/2 (1500-nm) transitions of Er 3⫹-doped glasses because of their importance in fiber laser and amplifier applications. Table 2 compares measured emission oscillator strengths with those calculated from measured absorption oscillator strengths using Eq. (14). Also listed are the discrepancies evaluated relative to the calculated value. In all cases the measured oscillator strengths are smaller, usually by 20% or more. This is consistent with reports of significant differences between measured cross sections and those obtained using the Einstein relation for this transition of Er 3⫹ [31–33]. The problem stems from the dependence of the validity of Eq. (14) on at least one of two conditions being met. Either all Stark components of the two multiplets must be equally populated, or all

Table 2

Comparison of Measured Emission Oscillator Strengths and Oscillator Strengths Calculated Using the Einstein Relations Oscillator strength, f Glass

Al/P silica Silicate L22 Fluorophosphate L11 Fluorophosphate L14 Fluorozirconate ZBLAN

Calculated (⫻10 ⫺6)

Measured (⫻10 ⫺6)

Discrepancy (%)

1.75 0.873 1.81 1.75 1.52

1.16 0.821 1.38 1.33 1.26

⫺34 ⫺6 ⫺24 ⫺24 ⫺17


29

the transitions must have the same strength, regardless of the components involved. Either of these conditions ensures that the observed oscillator strength is identical with that of the degenerate (unsplit) two-level case to which the Einstein relation applies. Since the manifold widths for the 4 I 15/2 and 4 I 13/2 states of Er 3⫹-doped glasses are typically 300–400 cm ⫺1 [20,21,34], the first condition is not satisfied at room temperature (kT ⬇ 200 cm ⫺1, where k is Boltzmann’s constant and T is the absolute temperature). Moreover, low-temperature absorption and emission measurements indicate that for all glasses the transition strength is quite sensitive to the Stark levels involved [20,21,34]. Because neither of the foregoing requirements is satisfied, it is not surprising to find that Eq. (14) leads to significant errors. Recently, an alternative analysis technique has been proposed [35] that employs the more general theory of McCumber [36], which was developed for the study of phononterminated lasers based on transition metal ions. The only assumption required by McCumber’s theory is that the time required to establish a thermal distribution within each manifold be short compared with the lifetime of that manifold. From consideration of detailed balance, the absorption and emission cross sections are then related by [36] σ b,a (ν) ⫽ σ a,b (ν)exp

冢

冣

ε ⫺hν kT

(15)

The cross-section spectra are scaled relative to each other by the temperature-dependent parameter ε, which is the net free energy required to excite one Er 3⫹ ion from the 4 I 15/2 to the 4 I 13/2 state at temperature T. In addition to requiring less restrictive assumptions than the Einstein relation, Eq. (15) has the advantage of providing spectral information, and it may be used to generate a relative cross-section spectrum if the spectrum of the inverse process is known. The offset between emission and absorption is readily seen by noting that at only one frequency, ν ⫽ ε/h, are the two spectra equal. At higher frequencies (shorter wavelengths) the absorption cross section is larger, whereas at lower frequencies (longer wavelengths) the emission cross section is larger. The principal disadvantage of a McCumber analysis is that ε is related to the partition function and can be calculated only if the positions of all the Stark levels are known for both manifolds. This has been done for Er 3⫹-doped Al/P silica fiber using the electronic structure reported for similar glasses [20,34]. The calculated and measured emission cross sections are compared in Figure 4. The peak emission cross section, calculated using Eq. (15), and the electronic structure were within 3% of the measured value [35], whereas those determined using Eq. (14) are seen to be too large (see Table 2). To eliminate the need for detailed measurements of the electronic structure, an approximate procedure has been developed for determining ε and usually produces more accurate cross sections than an Einstein analysis [35]. If only the shape of the cross-section spectrum is required, the analysis is much simpler, since an arbitrary scale factor may be used rather than evaluating ε. The McCumber transform [see Eq. (15)] accurately generates the shape of a cross-section spectrum from a measurement of the inverse process for transitions of Er 3⫹ [35], Tm 3⫹ [37], and Nd 3⫹ [38]. 2.1.5 Nonradiative Transitions In addition to changing their electronic state through interaction with the electromagnetic field (emission and absorption of photons), rare earth ions in solids can undergo transitions

30

Miniscalco

Comparison of measured stimulated emission cross section spectrum for Er 3⫹-doped Al/P silica and that generated and scaled using McCumber’s theory.

Figure 4

as a result of their interaction with vibrations of the host material. In crystals this corresponds to the emission and absorption of phonons. Although the absence of translational invariance in glasses means that vibrational modes will not, in general, have a well-defined wave vector, for consistency we shall still refer to these excitations as phonons. If the electronic states are spaced closely enough that they can be bridged by one or two phonons (e.g., the Stark components of a multiplet), the transitions will occur rapidly. This leads to thermal occupation of levels above the ground state or metastable excited state if the separations are on the order of the thermal energy (a few kT or less). These intramultiplet processes are discussed in Section 2.1.6. The energy gaps between J multiplets are generally much larger than kT, and the process proceeds predominantly in the downward direction: the ion makes a nonradiative transition to a lower electronic state through the emission of multiple phonons to conserve energy. If the nonradiative relaxation rate of a level is comparable with its radiative transition rate, the efficiency of luminescent processes originating on that level is degraded. The theory of multiphonon relaxation for rare earth ions was first formulated for crystals by Kiel [39] and extended by Riseberg and Moos [40]. Because transitions occur across gaps many times the energy of the largest phonon, the analysis requires high-order perturbation theory. Although high-order electromagnetic processes (i.e., multiphoton) are extremely weak, multiphonon processes can be significant because the electron–phonon interaction is stronger and phonons have a density of states that typically are 11 orders of magnitude larger than that of photons [39]. As the transition rate falls off rapidly with increasing order of the process (i.e., the number of phonons required to bridge the gap),

31


the dominant contribution to the nonradiative process comes from the highest-energy phonon(s) of the host. The large variation in vibrational spectra among materials makes the nonradiative relaxation rate extremely host-dependent. In contrast, all levels with the same energy gap below them will have roughly the same nonradiative rate for a given host. This rate is relatively independent of the nature of the electronic states involved, or even the identity of the rare earth ion, unless a strong selection rule is involved. These general trends were experimentally established using crystalline hosts [24], and they apply as well to glasses [41]. The theory of nonradiative decay was extended to glass hosts by Layne and co-workers [42], who also performed extensive measurements on oxide [42] and fluoride [43] glasses. For gaps much larger than the energy of the phonons involved, the nonradiative decay rate w nr is inversely proportional to the exponential of the energy gap separating the two levels [42,44]: w nr ⫽ C[n(T) ⫹ 1] p e (⫺α∆E)

(16)

In this expression C and α are host-dependent parameters, ∆E is the energy gap, p is the number of phonons required to bridge that gap, and n(T ) is the Bose–Einstein occupation number for the effective phonon mode, n(T) ⫽

1 exp(បω/kT) ⫺ 1

(17)

where ω is the phonon angular frequency. The parameter α is related to the coupling constant for the interaction γ, by α ⫽ ⫺ln(γ)/បω. The nonradiative rate decreases with decreasing temperature because of the temperature dependence contained in n(T). In practice, C, α, and p (or បω) are considered as empirical parameters that are host-dependent but insensitive to the rare earth ion and energy levels involved. They are obtained by fitting Eq. (16) to the nonradiative rates observed for as many energy gaps as possible using different levels and ions in the same host. Reisfeld and Jørgensen have assembled these parameters from measurements by a large number of authors [44], and the values are listed in Table 3. A crystalline material, LaF 3, has also been included for comparison. Figure 5 depicts the nonradiative rate as a function of energy gap using the parameters in Table 3 together with Eq. (16). Oxides have larger nonradiative rates because their strong covalent bonds result in higher phonon frequencies. The weaker ionic bonds of

Table 3 Parameters Describing the Nonradiative Relaxation of Rare Earth Ions in Glass Host Borate Phosphate Silicate Germanate Tellurite Fluorozirconate Sulfide LaF 3 (crystal) Source: Ref. 44.

C (s ⫺1)

α (10 ⫺3 cm)

បω (cm ⫺1)

⫻ 10 12 ⫻ 10 12 ⫻ 10 12 ⫻ 10 10 ⫻ 10 10 ⫻ 10 10 10 6 6.6 ⫻ 10 8

3.8 4.7 4.7 4.9 4.7 5.19 2.9 5.6

1400 1200 1100 900 700 500 350 350

2.9 5.4 1.4 3.4 6.3 1.59

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Figure 5 Nonradiative relaxation rate as a function of energy gap for the indicated glasses. halide glasses lead to a much lower w nr as well as higher transparency at midinfrared wavelengths (2–8 µm). In general, glasses have much larger nonradiative rates than crystals of similar composition because of the larger effective phonon frequencies (larger C ) and stronger electron–phonon coupling (smaller α). For glasses the vibrations causing nonradiative relaxation are the high-energy, relatively localized, stretching modes of the polyhedra forming the network. Figure 5 includes markers indicating the energy gaps for several states important for lasers and amplifiers. The 6500-cm ⫺1 gap below the 4 I 13/2 level responsible for 1500nm emission of Er 3⫹ is large enough that nonradiative relaxation is significant only at room temperature for borates [45,46]. Phosphate glasses also have large effective phonon frequencies, and there have been reports of slightly reduced quantum efficiencies for this level in some compositions [20]. The 4 F 3/2 level of Nd 3⫹, the metastable state for most of its important transitions, also has a high quantum efficiency in all glasses but borates. In contrast, the first excited state of Tm 3⫹, the 3 F 4 , has a low radiative yield even in silica (see Sec. 2.4). Tellurites [47,48], germanates [48,49], and fluorides [50] have low effective phonon frequencies and, therefore, additional metastable states. Table 1 includes not only the category of host for which gain has been observed, but also indicates whether a fluoride glass is required for reasons of quantum efficiency or infrared transmission. Because fiber synthesis procedures for fluorozirconates are well developed, they are particularly useful and have made possible fiber lasers and amplifiers using metastable states with energy gaps as small as that of the 1 G 4 of Pr 3⫹. Although the latter has been used to achieve high gains at 1300 nm, the small gap leads to low efficiency and high pump power requirements, even for fluorozirconates. Figure 5 illustrates that a significant improvement could be realized using chalcogenide glasses or even fluoride crystals, although these approaches


33

present serious technical difficulties. Equation (16) shows that little improvement can be expected from lowering the temperature, for the exponent p is small for levels with a small energy gap. 2.1.6 Line-Broadening Mechanisms For rare earth doped crystals, the absorption and emission transitions between Stark components of different J multiplets usually can be observed at room temperature as discrete lines. In contrast, individual Stark transitions for glass hosts seldom can be resolved except at temperatures close to absolute zero. This difference is illustrated in Figure 6, which compares the 1060-nm emission of Nd 3⫹ :YAG with that of an Nd 3⫹-doped silicate glass at room temperature. The spectra have been adjusted to fit the same scale to facilitate comparison. In terms of absolute cross sections, the spectra would be scaled such that the areas underneath each are approximately the same. Consequently, crystalline hosts provide high cross sections at nearly discrete wavelengths while glass hosts have lower cross sections over a broad, continuous range of wavelengths. The lower stimulated emission cross sections for glasses reduce the amount of amplified spontaneous emission generated. While this raises the threshold for lasers, it also permits better energy storage for pulsed lasers as well as higher efficiency and lower noise for amplifiers. Both homogeneous and inhomogeneous processes are responsible for broadening the sharp line structure of the crystal into that seen for the glass. The relative contribution of each mechanism has important device implications, and there has been considerable interest in understanding these mechanisms. For a homogeneously broadened transition,

Figure 6 Comparison of the emission spectra for Nd 3⫹-doped YAG and Nd 3⫹-doped ED ⫺2 silicate glass.

34

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a given wavelength will interact with all ions with equal probability. Thus, any pump wavelength will produce the same gain spectrum and any signal wavelength can saturate the entire band. If inhomogeneous broadening dominates, individual sections of the gain spectrum act independently and can be individually addressed by photons of different wavelengths. In a homogeneously broadened system, all the power can be extracted by a signal at any wavelength within the gain spectrum, and signals at different wavelengths can interact with each other by perturbing the gain spectrum. This leads to high efficiency for lasers and power amplifiers, but presents the possibility of cross talk or cross saturation for amplifiers in wavelength division multiplexed (WDM) systems. For an inhomogeneously broadened transition, laser and power amplifier efficiencies will be lower, but there is little interaction between signals in a WDM system. The line width of a laser is also affected, since saturation at only specific wavelengths will distort the gain spectrum in an inhomogeneous system. Consequently, it is more difficult to stabilize a laser in single-longitudinal-mode operation if inhomogeneous broadening dominates. For both crystals and glasses, the homogeneous broadening of transitions between Stark components of different J multiplets is caused by lifetime broadening. This is dominated by rapid phonon-induced transitions between the Stark components within a given multiplet. Optical dephasing measurements indicate that these transitions take place on a picosecond or subpicosecond time scale at low temperatures [51], and they are significantly faster at room temperature. This rapid absorption and emission of phonons is also responsible for the thermal occupation of higher Stark components. Several mechanisms contribute to these effects, and they are usually distinguished on the basis of their temperature dependence. A transition between Stark levels involving the emission or absorption of a single phonon is called a one-phonon direct process and derives its temperature dependence from the phonon occupation number [see Eq. (17)]. At high temperatures (kT ⬎⬎ បω, where ω is the phonon angular frequency); however, the relation simplifies, and one finds a line width that increases linearly with temperature. The Raman process takes place with the emission of one and the absorption of another phonon (in either order). The difference in phonon energies corresponds to the energy of the final electronic transition, but the intermediate state is virtual. At temperatures well below the Debye temperature T D , the Raman process has a T 9 dependence for Kramers ions (odd number of f electrons) and T 7 dependence for other rare earth ions. At temperatures above 0.5T D , it takes on a T 2 dependence. The Orbach process is a resonant Raman process in which the phonon energies match energy gaps between Stark levels, and a real transition is made to an intermediate state. The line width varies exponentially with temperature for the Orbach process. The temperature dependence of rare earth doped crystals is quantitatively explained by a combination of these three processes over a temperature range extending from below 10 K to above room temperature. Above roughly 70 K the line width is controlled by the Raman process and shows the characteristic T 2 dependence. Glasses usually show a similar T m, m ⫽ 2 ⫾ 0.2, behavior at high temperatures, but unlike crystals, it persists down to about 4 K. Moreover, the homogeneous line widths are more than an order of magnitude larger in glasses than in crystals. Even though the investigation of these differences has become an active area of research, a universal explanation is not yet available. Room-temperature homogeneous line widths are difficult to measure, and usually one must rely on extrapolations of low-temperature values and a known dephasing process. Table 4 lists room-temperature homogeneous line widths for a number of Er 3⫹- and Nd 3⫹-

35


Table 4

Room-Temperature Homogeneous (∆ν H ) and Inhomogeneous (∆ν IH ) Line Widths for Er 3⫹- and Nd 3⫹-Doped Glasses

Material 3⫹

Er Ge silica Er 3⫹ Ge silica Er 3⫹ Ge silica Er 3⫹ Al/Ge silica Er 3⫹ Al/P silica Er 3⫹ fluorophosphate (low fluorine) Er 3⫹ fluorophosphate (high fluorine) Er 3⫹ fluorozirconate Nd 3⫹ silicate Nd 3⫹ germanate Nd 3⫹ borosilicate Nd 3⫹ aluminophosphate Nd 3⫹ fluorozirconate

∆ν H (cm ⫺1)

∆ν IH (cm ⫺1)

Ref.

17 17 14 49 8 7–10 20–35 20–35 110 53 116 18 58

30 34 27 49 60 60 60 60 50 92 50 75 66

52 54 56 53 57 57 57 57 55 55 55 55 55

doped glasses. The measurement techniques were cross-modulation [52], hole-burning [53,54], and fluorescence line-narrowing [55–57]. These are the only two ions that have been investigated in detail at room temperature. Composition-to-composition variations of greater than a factor of 5 are found for both Er 3⫹ and Nd 3⫹, and no general trends are apparent. An interesting by-product of these investigations has been the observations for some Er 3⫹-doped glasses of significant departures from the expected T 2 dependence of the homogeneous line width. For Ge silica, Zyskind et al. found m ⫽ 1.61 at the peak (1535 nm) and m ⫽ 0.54 at 1550 nm [54]. The data of Zemon et al. for both the Al/P silica and low fluorine content fluorophosphate were best fit by m ⫽ 1.2 [57]. There is still no explanation for this behavior, or for the difference in ∆ν H between the Al/Ge and Al/P silicas in Table 4. The other broadening mechanism is called inhomogeneous because it results from spectroscopic differences between individual ions. This situation arises because each dopant ion occupies a unique site in a glass and experiences different crystal field parameters B qk [see Eq. (2)]. The disorder in the even-k terms leads to a distribution of energies for a given Stark component and, in a measurement that samples all ions, inhomogeneously broadens the emission and absorption spectra. Although seldom discussed, the corresponding disorder in the odd-k terms will produce variations in transition strengths between a given pair of Stark components. This is an additional inhomogeneous effect in that each ion has a different optical spectrum. Measured inhomogeneous line widths, ∆ν IH are also included in Table 4. Note that they show a much smaller variation relative to host and dopant ion. Inhomogeneous line widths are essentially independent of temperature. For crystals at room temperature and glasses at low temperature, transitions between individual Stark components in different multiplets can be observed. Under these circumstances it is straightforward to determine whether a transition behaves homogeneously or inhomogeneously by comparing the two line widths. For Er 3⫹-doped glasses at room temperature, even the highest components of the 4 I 15/2 and 4 I 13/2 multiplets have some thermal occupation, and the emission and absorption at 1500 nm is a composite of 56 largely unresolved Stark transition. Similarly for Nd 3⫹, the bands at 880, 1060, and 1300

36

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nm comprise 10, 12, and 14 unresolved transitions. This complicates assessments of the degree of homogeneity of these bands. However, low-temperature measurements have found that splittings for the lower Stark components of Er 3⫹-doped glasses, including Aland Al/Ge silica, are typically in the 20- to 50-cm ⫺1 range [20,21,34], roughly the same magnitude as the ion-to-ion variation in the position of a given Stark level. A photon at a wavelength anywhere within the central region of the band will then have a high probability of interacting with one Stark transition or another of every ion in the material. The room-temperature homogeneous line width is of a comparable size and further increases the probability of a photon interacting with all ions with equal probability. Accordingly, one expects quasi-homogeneous behavior for the Er 3⫹ 1500-nm bands: mixed homogeneous and inhomogeneous effects, but with predominantly homogeneous saturation characteristics. This is consistent with the more rigorous analysis by Desurvire et al. [58] and the observation of high efficiencies for power amplifiers [59–61]. Reports of larger inhomogeneous effects for Ge silica [52] than for Al silica have been explained in terms of the smaller homogeneous width for this glass [54]. A similar situation occurs for many Nd 3⫹-doped glasses. Hall and co-workers, who modeled energy extraction from bulk power amplifiers, found a relatively minor departure from homogeneous behavior for the compositions examined [62,63]. This analysis of quasi-homogeneous behavior has assumed signal and pump wavelengths that are not too far from the center of the respective emission and absorption bands. The pump restriction is equivalent to assuming that all ions have equal probability of being excited, a condition that also can be satisfied using broadband excitation, rather than a laser. In the extreme wings of the bands, however, the spectral overlap between ions in different sites is greatly diminished, because the multiplets for different sites are offset. For signal and pump wavelengths in these regions, one expects to see an enhancement of inhomogeneous effects. An investigation of Nd 3⫹-doped Ge/P-silica fiber lasers by Liu et al. is a particularly good example of such behavior [64]. These investigators found that pumping in the long-wavelength tail of the 800-nm–absorption band increased the line width of the laser by nearly a factor of 3 over what was observed pumping near the peak [64]. This is an expected consequence of a gain system dominated by inhomogeneous broadening. 2.1.7 Ion–Ion Interactions Energy Transfer All the preceding discussion has concerned isolated ions only. The interaction between the rare earth ions is treated by V ion–ion , the last term in Eq. (1). From the perspective of luminescent devices, the most important manifestation of this interaction is the transfer or sharing of energy between ions. This exchange may occur among rare earth ions of the same or different species, and it may be either beneficial or deleterious. For example, techniques such as Yb 3⫹ → Er 3⫹ energy transfer have been used since the earliest days of solid-state lasers to improve the pumping efficiency of devices [65]. In contrast, Er 3⫹ → Er 3⫹ energy transfer is an important dissipative mechanism for fiber amplifiers at 1500 nm [66]. Radiative energy transfer involves one ion emitting a photon, which is then reabsorbed by another ion. This process can distort the emission spectrum and cause radiative trapping. That latter leads to apparent excited-state lifetimes that are artificially long, par-


37

ticularly in highly concentrated or large-volume samples. In most situations, it does not result in a significant amount of energy actually being transferred, however, and the more important processes involve excitation transfer between closely spaced ions without the exchange of real photons. These interactions are described using either the short-range exchange or longer-range electric multipolar mechanisms, and many of the considerations in treating the latter are similar to those encountered in the absorption and emission of real photons. Energy transfer is temperature-dependent, because the ion–dynamic lattice interaction is involved. The absorption or emission of phonons is necessary to conserve energy when the transition energies for the ions involved are not equal. Even when the transfer is resonant (i.e., the change in electronic energy on the donating ion exactly equals that on the accepting ion), the phonon-assisted process dominates for crystals [67]. Although the interaction mechanisms are known, it is generally not possible to perform ab initio calculations, and energy transfer usually is analyzed semiempirically. Detailed discussions of the underlying physics of energy transfer can be found [68,69]. When energy transfer takes place between two different species of ions or centers, the type of ion that is optically excited is referred to as the donor, and the one that receives the excitation is called the acceptor. The process can occur in a single step in which the particular donor ion that absorbs the photon transfers its energy to a nearby acceptor. If the donor concentration is high enough, another mechanism that can occur is the migration of the excitation among the strongly coupled donor ions (donor–donor transfer). This proceeds until the excitation reaches a donor close enough to an acceptor to complete the final step of the transfer process. This mechanism is commonly used for sensitizing materials using large donor concentrations (e.g., Yb 3⫹) to absorb the optical excitation and transfer it to the activator or emitting ion (e.g., Er 3⫹) when the latter has weak or poorly placed absorption bands. If the acceptor is a trap or if the donors have a cooperative relaxation mechanism other than transfer to the desired acceptor, energy transfer is a dissipative process that results in the loss of excitation. With a few notable exceptions [70–72], energy transfer is not widely used in fiber devices because of the difficulty of controlling these deleterious side effects. The next three subsections examine the most important dissipative processes. Cross-Relaxation Cross-relaxation, a process in which an ion in an excited state transfers part of its excitation to a neighboring ion, is generally accepted as the primary quenching mechanism for Nd 3⫹ [73]. The cross-relaxation process is illustrated in Figure 7 using as an example Nd 3⫹, for which considerable information is available. If an ion excited into the metastable 4 F 3/2 level interacts with a nearby ion in the ground state (see Fig. 7a), the first ion can transfer part of its energy to the second, leaving both in the intermediate 4 I 15/2 state (see Fig. 7b). Because the energy gaps to the lower-lying states are small, both ions quickly decay nonradiatively to the ground state. The net result is the conversion of the original excitation into heat in a time that is short compared with the radiative lifetime if the energy transfer rate is high. Luminescence decay measurements sample a large number of ions, each with different distances to nearby Nd 3⫹ ions and, therefore, having different cross-relaxation rates. Accordingly, this quenching process will manifest itself as a nonexponential decay that is independent of pump power, for only one excited ion is required for cross-relaxation. This behavior has been observed for Nd 3⫹-doped bulk glasses [74] and fibers [66]. The process depicted in Figure 7 can be generalized to other ions and electronic structures.

38

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Figure 7 The cross-relaxation process illustrated using Nd 3⫹. (a) One of a pair of interacting ions is excited to the 4 F 3/2 metastable state. (b) First ion transfers part of its energy to the second ion, exciting it to the 4 I 15/2 state while decaying to the same level. Both ions then undergo nonradiative relaxation to the ground state.

The ions need not be the same, and both may be in excited (but different) states. Crossrelaxation can be beneficial if one desires the ions to be in the excited states that result from the interaction. Cooperative Up-Conversion The energy transfer or cooperative up-conversion process, illustrated in Figure 8 for the Er 3⫹ ion, is believed to be the major cause of inefficiency for Er 3⫹ devices at 1500 nm [66]. Auzel [75] and Wright [76] have comprehensively reviewed cooperative up-conversion, although only recently has this phenomenon been extensively investigated in glass hosts. Unlike Nd 3⫹, Er 3⫹ has no levels between the important 4 I 13/2 metastable state and the


39

Figure 8 The up-conversion process illustrated for Er 3⫹. (a) Both interacting ions are excited to the metastable 4 I 13/2 level. (b) The donor ion transfers all its energy to the acceptor, leaving itself in the ground state and the acceptor in the 4 I 9/2 state. For oxide glasses, the acceptor ion quickly decays nonradiatively back to the 4 I 13/2 level.

ground state, thus cross-relaxation between an excited ion and one in the ground state cannot occur. However, if two excited ions interact (see Fig. 8a), one can transfer its energy to the other, leaving itself in the ground state and the other in the higher 4 I 9/2 state (see Fig. 8b). This is effectively an Auger process. In oxide glasses, the 4 I 9/2 level quickly relaxes through multiphonon emission back to the 4 I 13/2 state, the net result of the process being to convert one unit of excitation into heat. For fluoride glasses, radiative relaxation of the 4 I 9/2 or 4 I 9/2 levels to the ground state may dominate, in which case both excitations can be lost. By comparing Figures 7 and 8 one sees that up-conversion is the inverse of cross-relaxation. Usually only one of these processes is important for a given ion or set of states, because of the location of the metastable states and the energy mismatches. The

40

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energy mismatch is important in driving the process in a particular direction, because energy seldom can be conserved by the electronic transitions alone, and processes involving the emission of phonons are much faster than those requiring the absorption of phonons. As cooperative up-conversion requires two interacting ions in the excited state, it is not evident at low pumping levels. At high pump powers it appears as accelerated and nonexponential decay, the latter owing to variations in the distance or interaction strength between excited ions. This behavior has been observed [66,77], and further evidence has been the report of up-converted 4 I 11/2 emission at 980 nm when pumping at 1480 nm [78]. Even more convincingly, when pumped at 1500 nm, the decay kinetics of the up-converted luminescence at 800 nm from the 4 I 9/2 state was proportional to the square of the 1500-nm emission, as is expected for a process involving two ions in the 4 I 13/2 state [66,77]. The pump power dependence of the up-conversion mechanism has important device consequences, because the quenching process is most deleterious at the high excited–state populations required for three-level amplifiers to achieve high single-pass gain and good signalto-noise ratio. This is reflected in the amplifier experiments of Kagi et al., which show a large difference between the gains of high- and low-concentration fibers at high pump powers, although the gain thresholds for the two fibers are close [78]. Cooperative upconversion can be beneficial if a single, highly excited ion is the desired product of the pumping process. An example is infrared-to-visible up-conversion in which two or more infrared photons are absorbed and combined on a single ion to provide visible emission. Concentration Quenching Concentration quenching is the reduction in the quantum efficiency of an ion with increasing concentration of that ion. It can occur through any of the foregoing energy transfer processes and has important implications for the performance of luminescent devices because it results in the loss of excitation. Whereas concentration quenching usually manifests itself as a shortening of the excited-state lifetime, this may not be observable under all conditions, as with cooperative up-conversion discussed in the preceding section. To examine concentration effects, we shall use the extensive body of information that exists for Nd 3⫹-doped glasses. Table 5 is drawn from the data of Stokowski et al. [74] and illustrates for the major glass types the range of ion concentrations that reduces the lifetime of the 4 F 3/2 state by a factor of 2. The empirical formula relating the observed lifetime τ obs to the ion concentration ρ is [74]:

Table 5 Nd 3⫹ Concentrations Resulting in a Factor of 2 Reduction in 4 F 3/2 Lifetime Glass type Silicate Phosphate Fluorophosphate Fluorozirconate Fluoroberyllate Source: Ref. 74.

Quenching concentration (10 20 cm ⫺3) 3.9–6.0 3.9–8.6 3.0–4.0 4.2 3.8–5.3


τ obs ⫽

τ0 1 ⫹ (ρ/Q) p

41

(18)

where τ 0 is the lifetime in the limit of zero concentration and Q is the quenching concentration given in Table 5. For the two-ion cross-relaxation mechanism described in the foregoing, which is believed to dominate concentration quenching for Nd 3⫹, p ⬇ 2. This analysis assumes that the rare earth ions are uniformly dispersed throughout the glass and do not cluster. If the concentration is kept to no more than a few percent, this is usually true for multicomponent glasses. Clustering does occur at low concentrations in silica, and this phenomenon is considered in Section 2.1.8. From Eq. (18) one expects less than a 1% reduction in efficiency if ρ is kept to less than 10% of the values in the table. Of the glasses for which data are available, phosphates are the most resistant to quenching and fluorophosphates are the least. The survey of the latter includes mostly high fluorine content compositions. Concentrations in fiber devices normally are kept below 10 19 cm ⫺3, and at these Nd 3⫹ levels no multicomponent glasses should exhibit efficiency problems. Qualitatively similar behavior is expected for Er 3⫹, and this has been confirmed by power amplifier experiments in which differential conversion efficiencies approaching the quantum limit have been achieved using Al- and Al/Ge silica fibers with concentrations in the 10 18- to 10 19-cm ⫺3 range [60,61, 79]. As is discussed in Section 2.1.8, silica co-doped with Al behaves, in many respects, the same as multicomponent silicate glasses. Another deleterious process involves energy transfer to the OH ⫺ complex, which serves as a trap and is extremely effective at quenching excited rare earth ions [45]. At high OH ⫺ concentrations, this can occur through direct transfer from the excited ion; at the low OH ⫺ levels present in optical fibers, however, a more likely process is fast energy transfer between interacting donor ions until the excitation reaches one near an OH ⫺ impurity [45]. The latter mechanism is a type of concentration quenching, because the energy transfer process, hence, the rare earth concentration, will control the quenching rate. Although donor–donor transfer to OH ⫺, has been observed for rare earth doped bulk glass samples [228], it is not consistent with pump-power-dependent behavior reported for Er 3⫹doped silica fibers [66]. 2.1.8 Solubility of Rare Earths in Glasses The foregoing concentration limits for maintaining the efficiency of an amplifier or laser apply only to materials in which the rare earth dopant is uniformly dispersed, as in multicomponent glasses. Pure silica is an exception to these guidelines because it can incorporate only very small amounts of rare earths before microscopic clustering occurs and ion– ion interactions appear. At still higher concentrations, crystalline phases may form [80]. Rare earth ions require large coordination numbers, and Arai et al. have explained this phenomenon with a structural model in which the absence of a sufficient number of nonbridging oxygens to coordinate isolated rare earths in the rigid silica network causes them to cluster in order to share nonbridging oxygens [73]. The Nd 3⫹ concentration for the onset of clustering in pure silica was estimated to be approximately 10 19 cm ⫺3 (⬇1000 ppm-wt) from luminescence decay data [81], whereas fiber amplifier experiments have revealed significant Er 3⫹ ion–ion interactions at levels about 10 18 cm ⫺3 [82]. Power amplifier [60,79] and small-signal amplifier [78] investigations have indicated that quenching also appears at about 10 18 cm ⫺3 for Ge-doped silica. It is expected that four-coordinated

42

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Ge does not alter the tetrahedral silica network sufficiently to significantly increase the solubility of rare earth ions. This suggestion is supported by reports that the emission spectrum of Nd 3⫹-doped pure silica and Ge-doped silica are identical [83]. Since Nd 3⫹ and Er 3⫹ should be equally insoluble in silica, the order-of-magnitude difference in the reported onset of quenching is likely due to either a stronger interaction between Er 3⫹ ions or a greater sensitivity to dissipative processes in amplifier experiments. The addition of Al greatly alleviates the clustering problem, and Nd 3⫹-doped Al silica has been reported to follow the same concentration quenching curve as the multicomponent ED-2 silicate glass [73]. For ED-2, Q ⫽ 3.9 ⫻ 10 20 cm ⫺3 and no significant quenching is expected for Nd 3⫹ concentrations of about 1000 ppm-wt in Al silica. Extensive measurements are not available for Er 3⫹-doped silica co-doped with Al, but power amplifier studies found a level of about 800 ppm-wt provided approximately the same efficiency as very low concentration Ge-doped silica [84]. By comparison, a similar level in Ge silica reduced the efficiency by nearly one order of magnitude from the low concentration limit [60,79]. Arai et al. have explained the role of Al in terms of solution chemistry: Nd 2 O 3 dissolves in Al 2 O 3 but not in SiO 2, whereas Al 2 O 3 dissolves in SiO 2 [73]. Thus Al 2 O 3 forms a solvation shell around the rare earth ion, and the resultant complex is readily incorporated into the silica network [73]. The correlation between the positions of the rare earth and Al ions implied by this model is consistent with the small Al/Nd ratio (⬇10) required to prevent clustering and produce an emission spectrum similar to that of multicomponent silicate glass [73]. In studies of Er 3⫹ amplifiers where silica was co-doped with Ge and Al, a Ge/Al ratio of 10 was sufficient to eliminate quenching effects [79,85] and provide an emission spectrum similar to that of Al-doped silica [85]. With typical fiber parameters, this translates into an Al/Er ratio of about 50. Thus, the properties of the rare earth dopant and the waveguide can be independently controlled using Al doping for the former and Ge doping for the latter. This strategy avoids the crystallization and high background loss problems often encountered when using Al doping alone to produce fibers of high (⬎0.2) numerical aperture (NA). Although Al silica behaves similar to a multicomponent glass when doped with Nd 3⫹, this is not always true for Er 3⫹. As is discussed in Section 2.3, the emission spectrum of Er 3⫹ /Al-co-doped silica is not typical of a silicate glass. Aluminum codoping has an additional benefit in controlling the radial doping profile of rare earths. Confining the Er 3⫹ to the center of the core improves the pump efficiency of amplifiers [86], but the modified chemical vapor deposition (MCVD) perform fabrication process depletes rare earth dopants at the center of the core for Ge- and Ge/P-doped silica [87]. This effect appears to be related to the ‘‘burnout’’ of Ge and P in MCVD preforms, as the rare earth concentration profiles show the same central dip as those of the Ge and P dopants [87]. The mechanism by which the dip occurs is not yet known. The addition of Al, even when co-doped with Ge or P, prevents the depletion of the rare earth [87] and is a straightforward way to improve the efficiency of amplifiers made from MCVD fibers. The effects of P doping are not so clear. For a P/Nd ratio of roughly 15, Arai et al. reported spectroscopic changes and solubility improvements similar to those found for Al doping [73]. In contrast, investigations of Nd 3⫹-doped Ge/P silica fibers found that the P/Nd ratio needed to be an order of magnitude larger to prevent clustering [83,87]. Doping P at less than 1 mol%, a level sufficient to derive full benefit from Al doping, offers no improvement over Ge silica: rare earth concentrations below 10 18 cm ⫺3 are still required to prevent quenching of both Nd 3⫹ [80] and Er 3⫹ [85]. At higher rare earth concentrations, P doping is reported to improve amplifier efficiency somewhat [85]. For very high rare


43

earth levels (ⱖ10 19 cm ⫺3) a crystalline precipitate appears that is rich in phosphorus and rare earths [80]. Adding P increases the amount of Al that can be incorporated before phase separation occurs [88], permitting higher NA fibers to be made without using Ge. The only other co-dopant characterized to any extent has been fluorine. Imai et al. found that F has no effect on the optical spectra of Ce-doped silica [89]. This is because F bonds preferentially to Si and does not affect the ligands in the vicinity of the rare earth ion [89]. Imai and co-workers did not determine whether F can play a role in improving solubility [89], but their structural model for the incorporation of F into the silica network implies that it will not have a beneficial effect. Although only Ce was investigated, these conclusions should apply equally well to other rare earth dopants. Based on the available evidence, it is apparent that Al is the most beneficial co-dopant for rare earth ions in silica fiber.

2.2 NEODYMIUM 2.2.1 General Characteristics Neodymium was used for the first glass laser, a device that was demonstrated by Snitzer [90] not long after the first Nd 3⫹-doped crystalline laser was reported [91]. Although Nd 3⫹ was not the first ion lased in a solid, or even the first rare earth, it has become the most important activator for crystalline and bulk glass lasers because of the power and efficiency available from the transition at approximately 1060 nm. Soon after the first bulk glass laser, a Nd 3⫹-doped fiber laser [92] and an optical amplifier [93] were demonstrated. These early devices operated in only the pulsed mode and were pumped from the side with flashlamps. Notwithstanding these limitations, they achieved high sensitivity as a preamplifier [94] and 47-dB gain [95], both notable accomplishments for the time. Stone and Burrus used the Nd 3⫹ ion to demonstrate the first end-pumped fiber laser and also were the first to employ silica as a host [96]. Much of the impetus for the current activity on active fiber devices arose from the reports of simple procedures for doping single-mode silica fiber with rare earth ions while retaining low loss [97,98] and the operation of a low-threshold, high-slope efficiency, Nd 3⫹-doped fiber laser [99]. Figure 9 depicts the absorption spectrum of a Nd 3⫹-doped ZBLAN [Zr, Ba, La, Al, Na] fluorozirconate glass. Although glass composition has some influence on the positions of the bands (see Sec. 2.1.3), the most obvious effect is a large variation in strength for the 580- and 800-nm bands. The 580-nm band dominates in covalent glasses, such as silica, whereas in ionic glasses, such as fluorides, the 800-nm band has equal or greater strength. Figure 10 presents the energy levels of Nd 3⫹-doped ZBLAN based on the absorption spectrum in Figure 9. Emission has been reported from some of the higher-lying levels for glass hosts [100], and lasing has been achieved in crystals [101]. Nevertheless, the three transitions originating on the 4 F 3/2 at 11,500 cm ⫺1, shown in Figure 10, are of greater technological significance. Figure 11 illustrates the ranges of 4 F 3/2 radiative lifetimes for the most extensively investigated glass types. It is based on the data of Stokowski et al., who calculated it from a Judd–Ofelt analysis [74]. Silicates exhibit the greatest range, nearly an order of magnitude, followed by borosilicates and fluoroberyllates. Silicates and borosilicates differ from the other glasses primarily in having some compositions with extremely low radiative relaxation rates, whereas fluoroberyllates are shifted as a group toward longer lifetimes. The lower index of refraction for fluoride glasses leads to a longer lifetime for a given stimu-

44

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Figure 9 Absorption cross-section spectrum of Nd 3⫹-doped ZBLAN fluorozirconate glass. lated emission cross section (i.e., a larger στ product), a favorable situation for devices operating under cw conditions [see Eq. (12)]. Relaxation of the 4 F 3/2 is primarily radiative for all the more common glasses except borates. The large phonon energy for the latter leads to a high nonradiative relaxation rate (see Sec. 2.1.5), and the excited-state lifetime is quite short. Values as short as 45 µs have been reported [102], and comparing this to the radiative lifetimes in Figure 11, one deduces a quantum efficiency of 10–15%. Accordingly, borate glasses are expected to perform well only as pulsed lasers. The strong 4 I 9/2 → 2 H 9/2 ⫹ 4 F 5/2 absorption transition at about 800 nm (see Fig. 9) is extremely effective for exciting the 4 F 3/2 metastable state, leading to very efficient Nd 3⫹doped crystalline and fiber lasers pumped by AlGaAs diode lasers. Figure 10 lists the ground-state absorption (GSA) wavelength for each level as well as the wavelength of the excited-state absorption (ESA) transition originating from the 4 F 3/2 and terminating on it. Because of the large number of closely spaced excited states, it is remarkable that Nd 3⫹ does not suffer more from ESA. Although the 4 F 3/2 → 2 D 5/2 ESA transition occurs at close to 800 nm, it is extremely weak and does not significantly degrade 800-nm pumping. For all glasses, Judd–Ofelt analysis reveals that its oscillator strength is less than 1% of the GSA transition. Thus pumping is not an issue for Nd 3⫹, and excellent results can be achieved exciting with 800-nm diode lasers for all compositions. The principal consideration for Nd 3⫹ devices is the performance of the three gain transitions indicated in Figure 10 and how these depend on glass composition. The 4 F 3/2 → 4 I 9/2 (⬇900 nm) is a three-level system first lased by Mauer in pulsed mode at 80 K using a silicate glass [103]. Emission cross-section spectra for representative glass compositions are illustrated in Figure 12. The first fiber laser for this transition used silica fiber and operated in the cw mode at room temperature with a tuning range of 900–945 nm [104]. Subsequently, Q-switched and mode-locked operation was also


45

Energy levels of Nd 3⫹ in ZBLAN fluorozirconate labeled using Russell–Saunders coupling. Downward arrows indicate laser transitions demonstrated for glass hosts. The first number to the right of each excited state (GSA column) is the wavelength of the ground-state absorption transition terminating on it. The second number (ESA column) is the wavelength of the ESA transition originating on the 4 F 3/2 and terminating on the labeled level.

Figure 10

achieved [105]. However, this transition is not of great technological interest for fiber or bulk glass devices, and it has not been extensively investigated. The transitions at 1060 and 1300 nm are of more importance and are discussed in the following in greater detail. 2.2.2 The 4F3/2 → 4I 11/2 Transition at 1060 nm Figure 13 illustrates 4 F 3/2 → 4 I 11/2 emission for the Nd 3⫹-doped glasses from Figure 12. Because of its importance in high-power and high-energy laser applications, this is probably the most thoroughly characterized transition for both glass and crystalline hosts. This band provides four-level operation at room temperature. The terminal state lies roughly 10 kT above the ground state, leading to a thermal population of the 4 I 11/2 of only 1 ion in 10 4. In addition, this 2000-cm ⫺1 gap is small enough to provide a high nonradiative relaxation rate and prevent a buildup of population in the terminal level. Figure 10 indicates that the 1060-nm emission band fortuitously lies in a window between ESA transitions. Measurements have found that these ESA bands are quite strong for silica, reducing the spectral region for which gain can be obtained [106,107].

46

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Figure 11

Ranges of radiative lifetimes for the 4 F 3/2 metastable state for the glass hosts indicated. (Data from Ref. 74.)

4 F 3/2 → 4 I 9/2 emission cross section spectra for representative glass compositions illustrating the variation in magnitude and shape. Excited at 800 nm.

Figure 12


Figure 13

4

47

F 3/2 → 4 I 11/2 emission cross section spectra for different glass types. Excited at 800

nm.

Because of its importance in high-energy lasers, the 1060-nm transition is one of the few that has been investigated for inhomogeneous broadening at room temperature. This leads to inefficiencies in power amplifiers, because it prevents all the energy from being extracted by a monochromatic signal. Using resonant fluorescence line-narrowing of the 4 F 3/2 → 4 I 11/2 , Hall et al. succeeded in measuring spectral and polarization inhomogeneities in the 1060-nm–emission band for several silicate and phosphate glasses [62,108]. The effects were relatively weak even for high-fluence, bulk power amplifiers; and extraction efficiencies within 20% of the maximum possible for homogeneous systems are expected for the cases they modeled [62,63]. Stokowski et al. provide a valuable compendium of data on this transition for more than 200 Nd 3⫹-doped glasses [74]. Based on their data, Figure 14 indicates the variation in branching ratio for the major glass types. Although this is the principal decay channel for the 4 F 3/2 state, note that for oxide glasses, and silicates in particular, branching ratios are generally less than 0.5. This is related to the degree of covalent bonding. In general, more ionic glasses favor the 4 F 3/2 → 4 I 11/2 (1060-nm) and 4 F 3/2 → 4 I 13/2 (1300-nm) at the expense of the 4 F 3/2 → 4 I 9/2 (900-nm) transition, and fluorophosphates and fluorides provide better performance under cw conditions for the transitions of greatest interest. Figure 15 illustrates the range of peak emission wavelengths by glass type. Here there is an even clearer trend toward covalency, with the most ionic glasses emitting at the shortest wavelength because of the nephelauxetic effect (see Sec. 2.1.3). Figure 16 shows the range in peak stimulated emission cross sections for this band. The values vary quite widely even within a given glass type. Equation (11) shows that

48

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Ranges of branching ratios for the 4 F 3/2 → 4 I 11/2 transition in the glass hosts indicated. Note the systematic increase for more ionic glasses. (Data from Ref. 74.)

Figure 14

Ranges of peak emission wavelengths for the 4 F 3/2 → 4 I 11/2 transition in the glass hosts indicated. Note the systematic shift to longer wavelengths with increasing covalency. (Data from Ref. 74.)

Figure 15


49

Ranges of peak stimulated emission cross sections for the 4 F 3/2 → 4 I 11/2 transition in the glass hosts indicated. (Data from Ref. 74.)

Figure 16

the peak cross section is directly proportional to the oscillator strength and inversely proportional to the bandwidth. For Er 3⫹ the variation in bandwidth plays the more important role in determining the peak cross section, but its influence is somewhat less for Nd 3⫹. The emission bandwidth ranges depicted in Figure 17 show a variation for the peak cross sections significantly larger than that observed in Figure 16. The trend in bandwidth is

Ranges of emission bandwidths for the 4 F 3/2 → 4 I 11/2 transition in the glass hosts indicated. (Data from Ref. 74.)

Figure 17

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offset by an opposite trend in oscillator strength, leaving the peak cross section as sensitive to the particular composition within a glass type as it is to the glass type. It is also interesting to note that the pattern of increasing bandwidth with increasing covalency illustrated in Figure 17 is the exact opposite of what is observed for Er 3⫹, for which fluoride glasses have the largest bandwidths and silicates the smallest (see Table 2). This provides further evidence that the band shape is not dictated by inhomogeneous broadening or Stark splitting as much as by the distribution of strengths for the constituent Stark transitions. Models are useful for illustrating how the host composition affects the characteristics of Nd 3⫹-doped fiber amplifiers. Even a large-signal model has an analytical solution for a four-level system if amplified spontaneous emission (ASE) and background absorption are neglected. Such a model was developed to analyze the 1300-nm transition, including the effects of ESA [109,110]. It can also be applied to the 1060-nm transition, and because the latter does not suffer from ESA the solution simplifies to A S(L) νs [P(0) ⫺ P(L)] ⫽ [S(L) ⫺ S(0)] ⫹ eff hν s ln νp σ 21 τ S(0)

(19)

where L is the length of the fiber, S and P are the signal and pump powers, respectively, ν s and ν p are the corresponding photon frequencies, and τ is the observed lifetime of the metastable state. For the example being considered, the stimulated emission cross section, σ 21 , is for the transition between the 4 F 3/2 (level 2) and 4 I 11/2 (level 1). The effective area is the core area divided by the overlap integral between the signal mode, the pump modes, and the Nd 3⫹ ion distribution. Assuming a step function distribution for the index, Nd 3⫹ ions, and pump intensity, the effective area is given by A eff ⫽

πr 2c 1 ⫺ exp(⫺2 r 2c /a 2)

(20)

in which r c is the radius of the fiber core and a is the radius of the gaussian signal mode. This approximate solution is adequate to illustrate compositional trends. Digonnet et al. have presented more precise treatments of the pump and signal modes in the context of a small-signal model [111]. The second term on the right-hand side of Eq. (19) dominates in the small-signal regimen. A useful indicator of the performance to be expected from a given transition is the product of the stimulated emission cross section at the wavelength of interest and the excited-state lifetime. Gain efficiency m is an important figure of merit for small-signal amplifiers, and using Eq. (19) it is readily found to be [109,110] m⫽

4.34 σ 21 τ A eff hν p

(21)

in units of decibels per milliwatt. The threshold for a laser also depends on the smallsignal gain and will be inversely proportional to σ 21 τ. For power amplifiers, efficient pump-to-signal conversion calls for the first term on the right-hand side of Eq. (19) to dominate, and the minimum signal power required for this is inversely proportional to the σ 21 τ product. Table 6 lists σ 21 τ products together with the peak stimulated emission cross sections and radiative lifetimes for some representative glass compositions. The calculated radiative lifetime is used because the 4 F 3/2 level decays radiatively for these glasses and is derived from the same calculation as the emission cross section. For comparison, the same quantities are included for Er 3⫹-doped Al silica. Although the analysis of three-level systems is more complicated, it can be shown that the dominant term in the

51


Table 6

Performance-Related Parameters for Nd3⫹ at 1060 nm

Glass Silica ED-2 silicate LG750 phosphate EV-2 phosphate Fluorophosphate LLNL8158 a Fluorophosphate LHG-10 Fluorozirconate ZBLAN Er 3⫹-doped Al silica at 1532 nm

Emission cross section (10 ⫺20 cm 2)

Radiative lifetime (µs)

σ 21 τ product (10 ⫺24 cm 2 s)

1.4 2.5 4.0 4.4 4.3 2.6 3.4 0.5

500 368 352 334 310 475 394 11,000

7.0 9.2 14.1 14.7 13.3 12.4 13.6 55

a

A common or commercial name does not exist for this glass; hence, it is labeled by its number in Ref. 74 prefaced by LLNL. Sources: Ref. 74.

small-signal limit is also proportional to σ 21 τ. Table 6 indicates that Er 3⫹-doped silica is roughly four times better than the best Nd 3⫹-doped glasses, and one should not expect the small-signal gain efficiency for the latter to approach those achieved for Er 3⫹ fiber amplifiers. Indeed, an analysis of the optimum waveguide for 1060 nm fiber amplifiers has predicted a gain efficiency of 1 dB/mW for silica [111]. 2.2.3 The 4 F 3/2 → 4 I 13/2 Transition at 1300 nm Devices The first 4 F 3/2 → 4 I 13/2 glass laser used a La–Ba–Th–borate glass and operated at 1370 nm [112]. Shortly thereafter laser emission was reported from 1350 to beyond 1400 nm using a Ca–Li–borate glass [102]. These were bulk lasers and operated at room temperature in pulsed mode. The transition provides true four-level operation because the terminal level is roughly 20 kT above the ground state (see Fig. 10), sufficiently far to have negligible thermal population at room temperature. In addition, the gap between the terminal state and the next lower one is small enough (2000 cm ⫺1) to provide a fast nonradiative relaxation rate and no population buildup in the 4 I 13/2 is expected. For many glasses exhibiting emission band peaks within the 1300-nm optical communications window, it had initially been hoped that Nd 3⫹-doped fiber amplifiers would be as useful for this window as Er 3⫹-doped fiber amplifiers are for the 1550-nm one. In the first reported attempt to obtain gain on this transition for a glass fiber, Alcock et al. observed, instead, ESA that produced pump-induced loss for silica within the emission band [113]. They found a larger loss at 1320 than at 1340 nm and attributed the ESA to the 4 F 3/2 → 4 G 7/2 transition (see Fig. 10) [113]. The ESA mechanism is illustrated in Figure 18; because both transitions originate on the same level, gain or loss at a particular wavelength is determined solely by which transition is the strongest. At about the same time Po et al. reported lasing at about 1400 nm for a silica fiber [114], verifying the trend suggested by the data of Alcock et al. that the strength of the ESA relative to that of the stimulated emission decreases with increasing wavelength. Recognizing that the relative magnitudes of the ESA and stimulated emission cross sections are also a property of the host, Miniscalco et al. used a Judd–Ofelt analysis to determine that fluorozirconate glass

52

Figure 18

Miniscalco

Illustration of ESA process at 1300 nm for Nd 3⫹.

should be significantly better than silica and demonstrated a ZBLAN fiber laser that exhibited gain at wavelengths less than 1330 nm [115]. Since then, most of the effort to develop Nd 3⫹-doped fiber amplifiers at 1300 nm has concentrated on fluorozirconate glasses. The low branching ratio for this transition has the consequence that 1300-nm amplifiers saturate at low gains as a result of ASE at the much stronger 1060- and 880-nm transitions. This is not a fundamental limitation, for the ASE is at a different wavelength from the signal and pump, and can be removed by a filter. Although theoretical analysis has indicated that high gains can be obtained if the ASE is completely suppressed [107,109,110,116], experimental values have yet to exceed 10 dB [117,118]. Emission Properties Although Jacobs and Weber reported spectroscopic measurements on the 4 F 3/2 → 4 I 13/2 transition for several silicate and phosphate glasses more than 15 years ago [119], very little additional work has been performed in the intervening years. Figure 19 illustrates the range of 4 F 3/2 → 4 I 13/2 branching ratios for the major glass types based on the data of Stokowski et al. [74]. Fluorides, fluorophosphates, and borates have the highest values, whereas those for some silicate compositions are extremely low. Because of their high nonradiative relaxation rate, however, borates are not suitable for amplifiers. Even the best compositions have a branching ratio only slightly higher than 0.1. As discussed in Section 2.3.4, this leads to poor performance compared with both the 1060-nm transition or that of Er 3⫹-doped silica at 1530 nm. Figure 20 illustrates emission spectra for representative glasses. As with the 1060-nm emission, the peak of the 4 F 3/2 → 4 I 13/2 transition varies significantly with compo-


53

Ranges of branching ratios for the 4 F 3/2 → 4 I 13/2 transition in the glass hosts indicated. (Data from Ref. 74.)

Figure 19

4 F 3/2 → 4 I 13/2 emission cross section spectra for different glass types. Note that the more covalent silicate is broader and shifted to longer wavelengths compared with the more ionic glasses such as the fluoroberyllate. Excited at 800 nm.

Figure 20

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sition, following the usual trend of the more covalent glasses emitting at longer wavelengths. Fluoroberyllate glasses emit at the shortest wavelength and silica at the longest, but a composition that peaks at 1310 nm or less has not been reported. Other compositions fall between those illustrated, and some peak values are provided in Table 7. For optical communications applications, significant gain must be provided within a window that extends from 1285 to 1330 nm, and thus silica would be of little use even if its full spectrum could be used. The situation is exacerbated by ESA, which precludes the use of not only the short-wavelength side of the band, but also even the peak for most glasses. Table 7 also lists effective bandwidths, defined as the integral of the spectrum divided by the peak value. For this transition it differs only slightly from the FWHM and is used to allow the inclusion of the data of Jacobs and Weber [119]. As with the 1060-nm transition, the silicates exhibit the broadest emission bands, whereas phosphates and fluorides have the narrowest. Peak cross sections are also given in Table 7; these were determined from the effective bandwidth and a Judd–Ofelt analysis that provided the 4 F 3/2 → 4 I 13/2 radiative transition rate. Table 7 includes the σ 21 τ product, which indicates the influence of the host on lasing threshold and gain efficiency of a small-signal amplifier. The values are three to four times smaller than those in Table 6 for 1060-nm emission, consistent with the lower branching ratio for this transition. It is interesting to note that although the peak cross sections are comparable with those of Er 3⫹ at 1530 nm, the σ 21 τ products are 10–20 times smaller because of the low branching ratios (short lifetimes). Accordingly, one does not expect this transition to provide performance approaching that of Er 3⫹, even if ESA were not an issue. Excited-State Absorption Because measurements are not currently available for many glasses, it is useful to have a technique for estimating the relative strength of the ESA to identify candidates for detailed experimental investigation. The small-signal figure of merit for an amplifier with ESA at the signal wavelength (see next subsection) is proportional to (σ 21 ⫺ σ 24)τ, where τ is the 4 F 3/2 lifetime and σ 21 and σ 24 are the cross sections for stimulated emission and ESA, respectively. Equation (11) shows that the peak cross section is proportional to the oscillaTable 7 Properties of the 4 F 3/2 → 4 I 13/2 Transition at 1300 nm

Glass Silica c Silicate ED-2 a Silicate ED-8 d Silicate LG650 d Phosphate LHG-5 d Phosphate LHG-8 d Phosphate P-107 d Fluorophosphate FK51 a Fluorophosphate LG812 Fluorozirconate ZBLAN a

Peak cross section (10 ⫺21 cm 2)

Emission peak (nm)

Effective bandwidth (nm)

Radiative lifetime b (µs)

σ 21 τ product (10 ⫺24 cm 2 s)

5.2 6.73 8.2 3.1 9.4 11.3 8.9 6.82 7.03 8.33

1366 1334 1334 1325 1323 1323 1324 1324 1320 1316

84 65.6 63 52 49 45.1 55 60.2 58.6 50.8

500 368 327 926 322 338 356 461 464 394

2.6 2.5 2.7 2.9 3.0 3.8 3.2 3.1 3.3 3.3

Sources: aThis work; b Ref. 74; cRef. 100; dRef. 119.


55

tor strength divided by the effective line width. Thus we can form an approximate figure of merit in terms of oscillator strengths, FoM f ⫽ ( f 21 ⫺ f 24)τ, where f 21 and f 24 are the emission and ESA oscillator strengths. The derivation of FoM f is not quantitative, for it assumes that the shapes and positions of the emission and ESA bands are identical and does not consider variations in index of refraction between glasses. It is extremely convenient, however, because a Judd–Ofelt analysis can be used to calculate both the oscillator strengths and the radiative lifetime, making it straightforward to characterize a large number of compositions. Figure 21 illustrates the range of FoM f for several important glass types based on the Judd–Ofelt data of Stokowski et al. [74]. Note that silicates are the worst: this is the only type of glass with compositions for which the ESA oscillator strength exceeds that for emission. Fluoroberyllates are far and away the best glasses, but because of toxicity issues there is currently little activity on these materials. Fluorophosphate glasses are next best and, similar to the fluorozirconates, should be viable candidates for Nd 3⫹-doped devices at 1300 nm. A Judd–Ofelt analysis is only approximate and provides no spectral information; ultimately, each composition of interest must be examined experimentally, either through measurements of the ESA spectrum or by the operation of actual devices. The first systematic investigation of ESA for Nd 3⫹-doped glasses was performed by Morkel et al. for Ge- and Al-doped silica fiber [106]. Figure 22 reproduces their results for Al silica and confirms that ESA is so strong that only for wavelengths beyond 1380 nm can gain be achieved. The situation is even worse for Ge silica, and no gain is realized short of 1400 nm [106]. These measurements revealed that the ESA transition is offset to shorter wavelengths than the emission, thereby leaving the long-wavelength tail of the emission band free from ESA. Following the initial successes with fluorozirconate fiber lasers at 1330– 1350 nm [115,120] Brierley and co-workers obtained the first ESA measurements on a

Figure 21 Calculated figure of merit for small-signal Nd 3⫹ amplifiers at 1300 nm. Note the significant improvement for the more ionic glasses. (Data from Ref. 74.)

56

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Measured gain/loss spectrum for Nd 3⫹-doped Ge silica fiber illustrating the strong ESA transition near 1300 nm. (From S. Zemon, private communication.)

Figure 22

fluorozirconate fiber [121]. Figure 23, based on the data of Zemon et al. [107], compares σ 21 and σ 24 for a ZBLAN glass. The results are very close to those of Brierley et al. [120] and clearly illustrate that the integrated strength of the 4 F 3/2 → 4 I 13/2 gain transition exceeds that of the 4 F 3/2 → 4 G 7/2 ESA transition, as predicted by the Judd–Ofelt analysis [115,122]. The offset between the two bands is present for this composition as well as for silica, and gain can be achieved only for wavelengths longer than approximately 1310 nm [121]. The offset of the ESA to shorter wavelengths has important implications. Whereas it provides a region of gain in the long-wavelength part of the emission band, it virtually ensures a region of loss on the short-wavelength side, where amplifiers for optical communications are desired. To a first approximation, all the energy levels shift together with changes in glass composition, and no significant change in offset between emission and ESA is expected. Zemon et al. have observed some significant deviations from this rule, but no glass has been found for which the ESA band does not overlap a major portion of the emission band [107]. Although the best results on Nd 3⫹-doped fiber amplifiers and lasers have been obtained using fluorozirconate glasses, other compositions have been examined for operation near 1300 nm. Hakimi et al. obtained lasing at 1363 nm for a single-mode silica fiber with an extremely high (14 mol%) P 2 O 5 content [123]. The investigators estimated that at this wavelength the ESA cross section was 78% the size of the stimulated emission cross section [123], indicating that ESA is too strong for this composition to be useful at wavelengths below 1350 nm. A lower threshold and higher slope efficiency were obtained by Grubb et al. for a single-mode fiber laser made from phosphate glass similar to Hoya LHG-8 [124]. It also operated at 1363 nm and a measurement of the gain spectrum revealed ESA-induced loss for wavelengths shorter than about 1350 nm [124]. A planar


57

Figure 23

Stimulated emission and ESA cross section spectra at 1300 nm for a ZBLAN fluorozirconate glass. (Measurements from Ref. 107.)

waveguide laser of Nd 3⫹-doped phosphate glass (Hoya LHG-5) has been reported with emission at both 1355 and 1325 nm [125]. The authors suggest that the Ag doping used to raise the index of refraction to form the waveguide may have contributed to their success at achieving 1325-nm operation by altering the spectroscopic properties of the Nd 3⫹ ion [125]. More recently, however, ESA measurements on the similar LHG-8 glass found that σ 21 exceeds σ 24 over a short-wavelength interval at the peak of σ 21 near 1325 nm [107]. For providing gain at shorter wavelengths, the best composition yet reported has been a high fluorine content fluorophosphate, which shows gain at wavelengths as short as 1295 nm [107]. Figure 24 compares the spectral dependence of the figure of merit for this fluorophosphate and a ZBLAN fluorozirconate composition based on the measurements of Zemon et al. [107]. Although ZBLAN is better for wavelengths longer than 1320 nm, only the fluorophosphate provides gain in the important 1300- to 1310-nm region. Analysis of Amplifier Performance Until recently, it was not generally recognized that even in the absence of ESA, Nd 3⫹doped glasses would exhibit relatively poor performance as 1300-nm fiber amplifiers compared with Er 3⫹ amplifiers. As this transition is considerably weaker than the 4 F 3/2 → 4 I 11/2 and also suffers from ESA, one expects significantly worse results than are obtained at 1060 nm. With the same large-signal model leading to Eq. (19) but now including ESA, one obtains a solution given by [109,110] (1 ⫺ ε)

νs A S(L) [P(0) ⫺ P(L)] ⫽ [S(L) ⫺ S(0)] ⫹ eff hν s ln νp σ 21 τ S(0)

(22)

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Figure 24

Small-signal figure of merit [(σ21 —σ24)τ] for ZBLAN fluorozirconate and LG810 fluorophosphate glass. (Measurements from Ref. 107.)

where ε is the ESA cross section divided by the stimulated emission cross section and the other variables are defined as in Eq. (19). Note that in Eq. (22), ESA appears only as a coefficient of the absorbed pump power. This leads to the interesting consequence that, despite being a process that occurs at the signal wavelength, its effect is equivalent to a reduction in the absorbed pump power. A simple physical explanation is that each absorbed pump photon produces an excited ion that can provide either gain or loss at the signal wavelength. The quantity 1 ⫺ ε is the net effect: it is proportional to the number of pump photons leading to gain minus those leading to loss. A useful approach for comparing hosts relative to all properties but ESA is to define an effective absorbed power P eff ⫽ (1 ⫺ ε) [P(0) ⫺ P(L)]. Figure 25 plots gain as a function of P eff for three glass compositions that have been used in fiber devices: silica, Hoya LHG-8 phosphate, and fluorozirconate. The values and origins of the host-dependent input parameters have been discussed [110]. If ESA is absent, P eff equals the absorbed pump power, and for this case the phosphate glass is appreciably better. Compared with what is obtained for Er 3⫹, the pump powers in Figure 25 required to produce a particular gain are quite high, even for ε ⫽ 0. In addition, the model neglects ASE at 900 and 1060 nm, which quickly saturates the amplifier and prevents the achievement of such high gains. The gain efficiency in the presence of ESA is given by [109,110] m⫽

4.34 (1 ⫺ ε) σ 21 τ(dB/mW ) A eff hν p

(23)

59


Figure 25

Calculated gain as a function of effective pump power for fibers of three representative glass compositions. The signal input is 100 nW and the curvature at high gains indicates the onset of gain saturation.

Table 8 lists gain efficiency for two waveguide designs and values of ε using the same three glass compositions. Ignoring ESA, the phosphate, which is one of the best compositions, is about 50% more efficient than silica, which is one of the worst. Larger improvements can be obtained by using fiber designs with high NAs and short cutoff wavelengths. The most important effect of composition is on ε, which is also wavelength-dependent. Nevertheless, even for the more favorable conditions in Table 8, the efficiencies are significantly less than the 1.3 dB/mW obtained for the inefficient 800-nm pump band of Er 3⫹ [126].

Table 8 Gain Efficiency for Nd3⫹ Fiber Amplifiers at 1300 nm Gain efficiency (dB/mW) ε⫽0 Glass Silica Phosphate LHG-8 Fluorozirconate ZBLAN a

ε ⫽ 0.5

Standard fiber a

Special fiber b

Standard fiber a

Special fiber b

0.072 0.105 0.098

0.426 0.625 0.582

0.036 0.053 0.049

0.213 0.312 0.291

NA, 0.12; cutoff wavelength, 1250 nm. b NA, 0.25; cutoff wavelength, 900 nm.

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The first term on the right-hand side of Eq. (22) is the large-signal term and becomes increasingly important as the magnitude of the input signal increases. In the limit of highly saturated power amplifiers, one can add one photon to the signal for every effective pump photon absorbed (i.e., 1 ⫺ ε times the total number absorbed). As stimulated emission then dominates spontaneous emission, there is no reduction in slope efficiency as a result of the unfavorable branching ratio. As with a laser, the penalty appears as a high threshold for crossing over into the regimen of efficient photon-to-photon conversion. This is illustrated in Figure 26, which plots quantum conversion efficiency (QCE) for the ZBLAN fluorozirconate as a function of pump power for three signal input levels. QCE is the number of photons added to the signal divided by the number of absorbed pump photons. The curves are for ε ⫽ 0.5, a realistic number for the signal wavelength of 1325 nm based on the data of Zemon [107] (see Fig. 23). Changing the input signal from 1 to 10 mW significantly increases the QCE as a consequence of the high signal level required for the large-signal term to dominate in Eq. (22). In contrast, Er 3⫹ power amplifiers exhibit high conversion efficiencies even for signal inputs below 1 mW. For lasers, the low σ 21 τ product leads to a high threshold for obtaining oscillation. ESA further increases the threshold and also reduces the slope efficiency because a large fraction of the pump photons produce loss, not gain. Amplifiers operating on four-level transitions are generally assumed to provide quantum-limited noise performance because the negligible population of the terminal level prevents reabsorption of the signal. It has been pointed out, however, that ESA at the signal wavelength introduces excess noise for the 4 F 3/2 → 4 I 13/2 transition at 1300 nm

Figure 26

Quantum conversion efficiency for a fluorozirconate fiber power amplifier as a function of pump power. Note the sensitivity to signal input power, which is a consequence of the low branching ratio for this transition. Realistic experimental parameters have been used.


61

[110,127]. By analogy with three-level gain systems, a noise penalty can be expected whenever the local gain coefficient is not proportional to the spontaneous emission rate, for this leads to a spontaneous emission rate per unit gain that is higher than the quantum limit [110]. The spontaneous emission rate r sp, at a given wavelength, is a function of the excited-state population and the stimulated emission cross section at that wavelength: r sp ⬀ n 2 σ 21

(24)

For a three-level system, the local gain coefficient, α 3L is proportional to r sp minus the product of the terminal state population and the absorption cross section: α 3L ⬀ n 2 σ 21 ⫺ n 1 σ 12

(25)

In the absence of complete inversion, the noise figure will exceed the quantum limit. For the 4 F 3/2 → 4 I 13/2 transition, the gain coefficient α ESA is proportional to the excited-state population times the difference between the stimulated emission and ESA cross sections: α ESA ⬀ n 2 (σ 21 ⫺ σ 24)

(26)

This also leads to a spontaneous emission rate per unit gain that exceeds the quantum limit. Here inversion is not the issue, and the only way to decrease the noise figure is to reduce the value of σ 24 relative to σ 21. This can be accomplished only by changing the signal wavelength or employing another host glass for which ESA is less significant. This behavior has been confirmed through measurements of the wavelength dependence of the ESA noise penalty for a fluorozirconate fiber amplifier [127]. It vanishes at long wavelengths for which σ 24 ⫽ 0 and approaches a value of 2 dB as the wavelength is decreased to 1330 nm, where ESA is important [127]. 2.3 ERBIUM 2.3.1 General Characteristics After Nd 3⫹, the most extensively studied rare earth laser ion has been Er 3⫹. Figure 27 illustrates an absorption spectrum for Er 3⫹-doped ED-2 silicate glass and Figure 28 shows the corresponding energy level diagram. On the scale of Figure 28, the host exercises a relatively minor influence on the positions of the states (see Sec. 2.1.3). The first Er 3⫹doped glass laser was demonstrated by Snitzer and Woodcock using the 4 I 13/2 → 4 I 15/2 transition at 1500 nm [65]. Even though this is a three-level system, room-temperature operation was possible because the silicate glass was co-doped with Yb 3⫹ as a sensitizer. These results were subsequently improved on by changing to a phosphate glass [128]. For crystalline hosts at room temperature, lasing has been reported only for transitions to the higher Stark components of the ground state [129]. It is interesting that in this respect the laser performs even better as a bulk laser, because the phosphate operates on a transition directly to the lowest component of the ground state and the silicate on the next to lowest. The eight lasing transitions reported for crystalline hosts [129] are indicated in Figure 28. Of these, the most important is the 4 I 11/2 → 4 I 13/2 transition at 2700–2900 nm, which finds applications in laser surgery because it coincides with the fundamental absorption band of the OH stretch vibration. Until the advent of fluorides, only the 1500-nm transition could be operated for glass hosts because the higher-lying states decayed nonradiatively through multiphonon emission (see Sec. 2.1.5). Following the initial demonstra-

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Absorption cross section spectrum of Er 3⫹-doped ED-2 silicate glass. The peaks of the strong bands at 380 and 520 nm are 28 and 19 ⫻ 10 ⫺21 cm 2, respectively.

Figure 27

tions, progress was slow and the principal interest in Er 3⫹-doped glass lasers was as an eye-safe source. More recently, however, it was recognized that this luminescence also spans the third optical communications window, as illustrated in Figure 29. Following the demonstration of a high-gain, low-noise optical amplifier at this wavelength using singlemode silica fiber [130,131], there was a reawakening of interest in Er 3⫹-doped glass, and a surge of activity on silica fiber amplifiers has followed. This has been accompanied by progress in the synthesis of fluoride glass fibers that has led to the demonstration of the five laser transitions indicated in Figure 28 that do not originate on the 4 I 13/2 level. These transitions use upper states that are metastable only in fluoride glasses because of their lower multiphonon relaxation rates. The availability of these additional gain transitions has greatly expanded the utility of Er 3⫹-doped fibers, particularly in applications outside optical communications. From Figure 27 it is apparent that the absorption bands of Er 3⫹ are not only relatively sparse throughout the visible and near infrared, but also relatively weak for wavelengths exceeding 550 nm. Historically, this presented a problem for bulk lasers that were pumped using flashlamps. The original solution was to increase the absorption by co-doping with high concentrations of Yb 3⫹, which would transfer the absorbed energy to the Er 3⫹ [65]. More recently, better performance has been obtained exploiting the weak overlap between Nd 3⫹ emission at about 1050 nm and the Yb 3⫹ absorption band to pump Yb 3⫹, Er 3⫹-codoped glasses with Nd 3⫹ glass [20] and diode-pumped crystalline [132] lasers. The problem of optical pumping that overshadows all other considerations for bulk devices is reduced to a question of cost and convenience for single-mode fiber devices, which are invariably laser pumped. Six of the seven absorption bands between 480 and 1500 nm in Figure 27 have been used to pump fiber lasers and amplifiers, although the bands that match the output of diode lasers are to be preferred. In addition, energy transfer has been


63

Energy levels of Er 3⫹ in ED-2 silicate labeled using Russell–Saunders coupling. The number to the right of each excited state is the wavelength in nanometers of the ground state absorption transition terminating on it. The solid arrows at left indicate the laser transitions demonstrated for crystalline hosts and the hatched arrows at right are those reported for glasses.

Figure 28

investigated as an alternative means to pump fiber lasers and amplifiers. Demonstrations of Yb 3⫹ –Er 3⫹-co-doped fiber lasers pumped by Nd:YAG lasers at 1060 nm [133] and by laser diodes near 820 nm [70] have been reported. More recently, Yb 3⫹ –Er 3⫹-co-doped silica power amplifiers have exhibited output powers in excess of 100 mW when driven by diode-pumped Nd :YAG lasers [72]. Section 2.3.2 considers the important properties at the operating wavelengths, principally cross sections, lifetimes, and bandwidths. Most of the discussion pertains to the 4 I 13/2 → 4 I 15/2 transition at 1500 nm, for this is the most important and most extensively studied one. In contrast to Nd 3⫹, there is no preferred wavelength for diode pumping Er 3⫹, and the choice of excitation band plays an important role in the performance and practicality of these devices. Section 2.3.3 is devoted to issues surrounding the available pump bands. 2.3.2 Properties at the Operating Wavelengths Cross Sections for the 4 I 13/2 → 4 I 15/2 Transition at 1500 nm Because the 4 I 13/2 is the only metastable state for common oxide glasses at room temperature, gain is available only for these materials at the 1500-nm 4 I 13/2 → 4 I 15/2 emission band.

64

Figure 29

Miniscalco

Emission spectrum of Er 3⫹-doped silica fibers.

The strength and the spectrum of this transition are host-dependent and must be examined experimentally to determine the best glass for a given application. Most of the published data for this transition include only oscillator strengths; little has been reported on crosssection and emission spectra. Alekseev et al. [20] present a comprehensive discussion of bulk Er 3⫹-doped glass lasers but include detailed information for only a few glass compositions. Sandoe et al. provide data on compositional trends [30], and cross sections for silica fiber have been measured by several authors [27–29,31,134–136]. Although fiber lasers and amplifiers made from multicomponent silicate glasses were among the first Nd 3⫹doped devices demonstrated [92], only quite recently has an Er 3⫹ amplifier made from such a glass been reported [137]. Phosphate glasses were recognized very early as better hosts for Er 3⫹ bulk lasers [65], and a phosphate glass single-mode fiber laser has been demonstrated [138]. In recent years fluorophosphate glasses have been identified as excellent bulk hosts for rare earth ions, but to date no Er 3⫹-doped fiber devices have been reported. Because of its wider bandwidth at 1500 nm, Er 3⫹-doped fluorozirconate glass has been investigated for fiber amplifier applications [139–141]. Spectra and cross sections have been determined for Er 3⫹-doped fluorophosphate and ZBLAN fluorozirconate glasses [29,134,135]. For a three-level gain system, such as Er 3⫹ at 1500 nm, not only the stimulated emission but also the absorption cross section play important roles in determining the performance of a device. Figures 30 and 31 illustrate the pronounced effect of glass composition on the magnitude and shape of the absorption and stimulated emission cross sections. As discussed earlier, the variations in spectra among glasses are caused primarily by differences in the intensities of the constituent Stark transitions. Table 9 lists integrated


Figure 30

65

Some 1500-nm–absorption cross-section spectra for different glass types, illustrating the variation in magnitude and shape.

Figure 31

Some 1500-nm–emission cross-section spectra for different glass types.

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Table 9 Integrated 4 I 15/2 → 4 I 13/2 Absorption for Er3⫹-Doped Glasses Glass

Ka (10 ⫺8 cm 2 /s)

Silicate L22 c Silicate S8 a Silicate S7 a Silicate S6 a Silicate ED2 c Al/P silica b Borate S23 a Borate S18 a Phosphate S1 a Phosphate S4 a Phosphate L28 c Fluorophosphate L14 a Fluorophosphate L11 c Fluorozirconate ZBLAN c Ba-Zn-La-Th fluoride c

2.6 3.0 3.7 4.0 3.5 5.1 4.7 5.9 3.2 4.4 5.5 5.1 5.5 4.6 4.6

Sources: a Ref. 30; b, Ref 26; c, Ref. 142.

absorption cross sections K a ⫽ ∫σ 12 (ν)dν, for compositions representing several important glass types [26,30,142]. The use of K a instead of the more conventional oscillator strength [see Eq. (11)] permits the extensive survey by Sandoe et al. [30] to be included in the table. It is seen that the host affects the integrated absorption strength by slightly more than a factor of 2. Silicates generally have the smallest values, whereas phosphates, fluorophosphates, and borates can achieve significantly larger values. Because there is a significant magnetic–dipole contribution to this transition, the low K a seen for many silicates indicates that a relatively small amount of electric–dipole strength has been added by the crystal field. The Al/P silica is a notable exception from this pattern and is seen to have a transition strength similar to those of phosphate and fluorophosphate glasses. Germanate glasses also have weak transition strengths [48,49], as might be expected from their structural similarity to silicates. Within the silicates, transition strength decreases with increasing atomic number of the alkaline earth, S6–S8 containing Mg, Ca, and Sr, respectively [30]. For simple phosphates the opposite holds true, with K a increasing from Mg (S1) through Ba (S4) [30]. A high silica content tends to reduce K a: L22 differs from S7 primarily in having 71 versus 57 mol% silica. In contrast, increasing the B 2 O 3 content from 74 to 88 mol% causes the increase in absorption strength from borate S23 to S18 [30]. Values for the fluoride glasses fall midway in the large range spanned by the phosphates. Among fluorophosphates, K a is sensitive to the relative amounts of oxygen and fluorine. It varies from that of a strong phosphate to a value nearer the fluoride glasses as the oxygen/fluorine ratio goes from 1.5 for L11 to 0.15 for L14. The peak cross section is determined by the shape of the absorption or emission band as well as the integrated area K. Table 10 gives peak values of the stimulated emission cross section σ 21 and absorption cross section σ 12 for representative glasses, as well as the wavelengths at which they occur [136,142]. The absorption and emission oscillator strengths, f 12 and f 21, respectively, are also included. Measured lifetimes are also found in

4

f 12 (10 ⫺6)

1531.4

1535.8 1532.6 1532.0 1530.6 1530.6

0.821 1.38 1.33 1.26

5.5 5.6 5.8 7.9 7.3 7.2 5.8 5.0 0.737 1.53 1.48 1.29 1.27

1.25

1536.4 1532.6 1531.4 1530.4 1529.4

1530.1

Peak λ (nm)

Peak σ 21 (10 ⫺21 cm 2)

Peak λ (nm)

1.17

f 21 (10 ⫺6)

5.5 5.1 4.7 7.9 5.8 7.0 5.8 5.0 4.8

Peak σ 12 (10 ⫺21 cm 2)

a b b b c c c c c

Source

Sources: (a) Private communication from Singh; all other data from Ref. 142. (b) Ref. 136 emission from Table 3, absorption from Table 6. (c) Private communication R.S. Quimby; all other data from Ref. 142.

10.8 10.2 10.2 12.1 14.5 8.25 9.5 9.4

Lifetime (ms)

Absorption

Emission

I 13/2 ↔ 4 I 15/2 Transition Strengths for Er 3⫹-Doped Glasses

Al/P silica Al silica Ge/Al silica Ge silica Silicate L22 Fluorophosphate (low fluorine) Fluorophosphate (high fluorine) Fluorozirconate ZBLAN Ba-Zn-Lu-Th fluoride

Glass

Table 10

Rare Earth Doped Glasses: Optical Properties 67

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Table 10. The peaks of absorption and emission generally lie within 1 nm of each other for a given glass, indicating that the same pair of Stark components dominates both emission and absorption. Low temperature measurements have revealed these to be the lowest level of each manifold [20,34,143]. With the exception of the silicate and Ge and Ge/P silica (not included), the wavelengths of peak emission for all compositions fall in a narrow range close to 1531.5 nm. The finding of longer emission wavelengths observed for silicates, including pure, Ge, and Ge-co-doped silica, usually is attributed to the nephelauxetic effect and is consistent with the longer wavelength emission observed for the more covalent Nd 3⫹-doped glasses as well. Again, Al/P silica is unusual and has characteristics more in keeping with a fluorophosphate or fluoride glass. The oscillator strengths of the L22 silicate in Table 10 are unusually low, but the very narrow bandwidths lead to peak cross sections comparable with those of the other glasses. For comparison, a lifetime of 8.8 ms and peak σ21 of 7.3 ⫻ 10 ⫺21 cm 2 have been reported for an Er 3⫹-doped phosphate glass [138]. Alekseev et al. provide peak cross sections for several phosphate glasses, all of which fall into the range 6 ⫻ 10 ⫺21 to 8 ⫻ 10 ⫺21 cm 2 [20]. This confirms the expectation that phosphate and high phosphorus content fluorophosphate (e.g., L11) glasses provide the highest cross sections. Ignoring L22, the emission and absorption oscillator strengths vary by only ⫾10%, whereas the peak cross sections fluctuate by ⫾20%. This additional factor of 2 arises from differences in bandwidth, an issue that is discussed later. The oscillator strengths in Table 10 include a magnetic–dipole contribution of 0.49 ⫻ 10 ⫺6; thus, the relative variations of the material-dependent electric–dipole contribution actually are much larger than the changes in the total oscillator strength. The success of the Er 3⫹-doped silica fiber amplifier at 1500 nm is largely due to the long lifetime for the metastable state. This permits the large population inversions needed for high gain and low noise to be achieved using low power cw pumping. It also leads to the absence of distortion and cross talk for modulation frequencies above about 100 kHz in saturated amplifiers [52,144–146]. Table 10 shows that silicates have the longest lifetimes, consistent with their lower oscillator strengths [see Eq. (8)], but even the shortest lifetimes are only about 20% less than that of Al/P silica. Bandwidths for the 4 I 13/2 → 4 I 15/2 Transition at 1500 nm It is desirable for tunable lasers to have a wide wavelength range over which they deliver relatively constant power. Similarly, optical amplifiers are more useful if they provide gain that is relatively independent of signal wavelength. This relaxes the wavelength tolerances on transmitters in a single-channel system, increases the number of optical channels that can be multiplexed without gain compensation techniques, and reduces distortion caused by chirp in the transmitter in AM systems. For a three-level system, however, there is no procedure for quantitatively predicting the tunability of a laser or bandwidth of an amplifier short of a numerical fiber laser or amplifier model. This is because the spectrum of the gain coefficient is a superposition of the spectra of the 4I15/2 → 4 I 13/2 absorption and 4 I 13/2 → 4 I 15/2 emission cross sections. The superposition is determined by the local inversion which, in turn, is a function of position within the fiber. For an amplifier, the problem is greatly simplified if the population inversion is complete over the entire length of the fiber. The logarithm of the gain spectrum will then be proportional to the linear spectrum of the stimulated emission cross section. This condition is automatically satisfied in four-level systems but requires very high pump levels for three-level devices. For the 1500-nm transition of Er 3⫹, incomplete inversion leads to reabsorption of the signal by ions in the ground state. Because the absorption spectrum is offset from the emission


69

spectrum, the reabsorption process will alter not only the value of the gain, but also change the shape of the gain spectrum. This effect has been discussed by Armitage, who points out that relatively constant gain can be obtained over a range of 40 nm through the proper choice of fiber length [147]. Highly saturated power amplifiers also have a relatively flat gain spectrum because of their lower inversion. Increasing the fiber length also can be exploited to shift the operating wavelength of an untuned laser to a longer wavelength. Although the gain spectrum of an amplifier can be flattened by lowering the inversion or using fiber lengths that are longer than optimum, it exacts a penalty in noise figure. Similarly, this leads to less than optimum performance for a laser. Identifying glasses with a wider, fully inverted bandwidth accomplishes this objective, with the possible drawback of reduced efficiency. To illustrate the wide range of bandwidths and shapes available from glasses, Figure 32 compares normalized emission spectra for several compositions, including those representing the extremes of the range. More extensive data are provided in Table 11, which lists measured full widths at half-maximum for compositions representing most of the glass types suitable for optical applications. Because of differences in the shape of the emission spectrum, particularly the strength of the 1530-nm peak relative to the 1550-nm shoulder, FWHM is not necessarily a good indication of bandwidth in high-gain amplifiers. Table 11 includes gain bandwidths that have been calculated for the fully inverted amplifier, which represents the worst case. The columns are labeled by the gain at the peak of the spectrum because the bandwidth narrows with increasing gain for a homogeneously broadened transition or an unsaturated inhomogeneously broadened transition. Experimental values for highly inverted Ge silica [131] and Al/Ge silica [148] amplifiers are in good

Figure 32

Some 1500-nm–emission spectra normalized to emphasize variations in bandwidth.

70

Table 11

Miniscalco 1500-nm Bandwidths for Er 3⫹ Glasses Gain bandwidth (nm)

Glass Pure silica fiber Ge silica fiber P silica fiber Ge/P silica fiber Al/P silica fiber Silicate ED2 Phosphate L27 Fluorophosphate L74 Fluorophosphate L56 Fluorozirconate ZBLAN Fluorohafnate F114 Ba–Zn–Lu–Th fluoride Borate L87

FWHM (nm)

20-dB peak

30-dB peak

40-dB peak

7.94 24.9 25.1 24.7 43.3 20.4 27.1 32.0 43.3 63.3 63.8 59.2 41.2

3.0 5.4 5.4 5.2 7.9 4.0 4.5 5.3 7.8 16.4 17.3 15.5 7.4

2.2 4.2 4.3 3.8 6.4 3.3 3.6 3.7 5.8 11.7 13.2 10.1 5.6

2.2 3.5 3.5 3.2 5.3 2.8 3.1 3.3 5.0 9.0 10.4 8.3 5.1

agreement with those of the similar Ge/P and Al/P silica compositions, respectively, in Table 11. The assumption of complete population inversion cannot be used to estimate the bandwidth of a saturated amplifier or the tuning curve of a laser, both of which require numerical models. Table 11 represents the worst case, for the lower inversion of these saturated devices produces significantly wider bandwidths or tuning ranges than indicated. A definite correlation between glass type and bandwidth that emerges from Table 11 will also be indicative of the relative trend in laser-tuning curves. Ignoring Al/P silica, the silicate and phosphate glasses are seen to have the narrowest emission spectra. The heavy-metal fluoride glasses display the largest FWHMs; this appears to be related to the coordination of Er 3⫹ by fluoride ions. In these glasses rare earth ions are believed to substitute only for network formers, resulting in less inhomogeneous broadening as well as a more symmetric and lower crystal field strength than for oxide glasses [149]. This is consistent with the observed Stark splittings [21], and on this basis alone narrower emission bands would be expected. The large measured bandwidths lead one to the conclusion that the distribution of strengths among the Stark transitions determines the spectral shape, rather than the Stark splittings. Fluorophosphates have intermediate values of bandwidth and show a significant dependence on composition, which is discussed later. Although the borate glass has an FWHM comparable with that of the widest fluorophosphate, only one composition was examined, and the range of bandwidths is not known for this type of glass. Once again the Al/P silica is unusual for a silicate glass, having an FWHM more typical of a borate or high fluorine content fluorophosphate glass. With the exception of silica, fluorophosphates show the greatest sensitivity to composition. The clearest correlation is with anion content, and Table 12 illustrates how the bandwidth depends on the oxygen/fluorine ratio. Compositions containing mostly oxygen have an FWHM of about 34 nm compared with roughly 43 nm for those with mostly fluorine. The transition between these two types of behavior, which occurs between oxygen/fluorine ratios of 0.4 and 0.9, could not be examined in detail because glass compositions in this range were not available. Inhomogeneous broadening is a commonly

71


Table 12

1500-nm Bandwidths for Fluorophosphate Glasses Gain bandwidth (nm)

O/F a

FWHM (nm)

20 dB peak

30 dB peak

40 dB peak

2.3 1.5 1.2 1.1 1.0 0.94 0.44 0.19 0.17 0.15

32.0 33.6 36.8 34.8 34.6 33.7 41.3 43.8 43.7 43.3

5.3 5.1 5.9 5.5 5.6 5.4 7.2 7.4 7.9 7.8

3.7 3.9 4.6 4.2 4.1 4.1 5.6 5.5 6.2 5.8

3.3 3.4 4.0 3.7 3.7 3.6 4.8 4.7 5.0 5.0

a

Oxygen/fluoride ratio.

used, but unsubstantiated, explanation for large bandwidths in mixed anion glasses. The relatively discontinuous nature of the change in width argues against it. Another possibility is that the Er 3⫹ site is similar in symmetry and crystal field strength to a phosphate glass or a fluoride glass, depending on the anion ratio. Although a complete understanding of bandwidths and tuning ranges for the 1500-nm transition requires further investigation, the available data clearly indicate the preferred compositions. Only borates, fluorides, and high fluorine content fluorophosphates offer similar or better bandwidths than Al/P silica. Borate glasses, however, must be dismissed because the metastable state is quenched by nonradiative relaxation at room temperature. Table 11 indicates that under fully inverted conditions, only fluoride glasses provide wider gain bandwidths than Al/P silica. Recent experiments with fluorozirconate fiber amplifiers bear this out [139–141]. Other Er 3ⴙ Transitions Lasers and amplifiers have been demonstrated for other transitions of Er 3⫹ using crystalline and fluoride glass hosts (see Table 1). These materials have lower effective phonon frequencies, and the resultant reduction in the multiphonon emission rate leads to additional metastable states. Brierley and co-workers have reported more than 20 separate emission transitions for Er 3⫹-doped fluorozirconate glass [150], and several of these have produced gain. The Er 3⫹ states up to about 20,000 cm ⫺1 are discussed in the following, in addition to any involved in laser transitions reported for crystalline hosts. One of the most important of these additional metastable states is the 4 I 11/2, which is the upper level for the 4 I 11/2 → 4 I 15/2 transition at about 980 nm, and the 4 I 11/2 → 4 I 13/2 near 2700 nm. The former is a three-level laser, first demonstrated by Allain et al. using ZBLAN fluorozirconate fibers [151]. Next to the 1500-nm transition, the one at 2700 nm has been the most extensively characterized. Although it has been lased in a variety of oxide and fluoride crystals [129], laser action for glasses has been reported for fluorides only. This was first done pulsed using a flashlamp-pumped bulk sample [152] followed by cw lasing with a fiber [153]. More recently an 800-nm diode-pumped fiber laser [154] and an amplifier producing more than 18 dB gain [155] have been reported. Operation at

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2700 nm is called self-terminating because the 4 I 13/2 level has a longer lifetime than the 4 I 11/2. It has been pointed out that this does not automatically preclude cw operation [156], but for this particular transition, cw performance is greatly enhanced if an additional process, such as pump ESA [153] or cooperative up-conversion, is used to deplete the terminal state. Table 13 summarizes the published characteristics of both transitions for several fluoride glasses [50,153,157–159]. With the exception of the measured lifetimes, the values in the table are derived from Judd–Ofelt analysis. The most critical property is the radiative yield of the 4 I 11/2 level, which is seen to be high by comparing the observed lifetime τ obs and calculated radiative lifetime τ rad. The branching ratios β are all roughly the same for all glasses, with about 80% going directly to the ground state and the remainder to the 4 I 13/2 intermediate level. The latter, however, will receive a higher fraction of the excitation than the branching ratio, for it collects all nonradiative relaxation from the 4 I 11/2 manifold. Table 13 also includes calculated peak cross sections, which are nearly an order of magnitude larger at 2700 nm, despite the lower branching ratio because a factor of λ 4 appears in the relation between transition rate and cross section [see Eq. (12b)]. The relatively long lifetime of the 4 I 11/2 state is particularly advantageous in amplifier applications, and the 4 I 11/2 → 4 I 13/2 is one of the three Er3⫹ transition for which optical amplifiers have been demonstrated [155]. The other important state in fluoride glasses is the 4 S 3/2, which is metastable by virtue of the gap (⬃3000 cm ⫺1) between it and the next lower level, 4 F 9/2. It is responsible for the other gain transitions reported for glasses, all in fluorozirconate fibers: the 4 S 3/2 → 4 I 15/2 at 550 nm [160,161], the 4 S 3/2 → 4 I 13/2 at 850 nm [162,163], and the 4 S 3/2 → 4 I 9/2 at 1720 nm [164]. Lasing has also been reported at 1660 nm and attributed to the 2 H 11/2 → 4 I 9/2 transition [164]. The latter is possible only because the 2 H 11/2 multiplet is thermally populated from the 4 S 3/2 , at room temperature, an effect that has been analyzed for Er 3⫹doped tellurite [48] and ZBLA [50] glasses. Known properties for transitions originating on the 4 S 3/2 and 2 H 11/2 levels are listed in Tables 14 and 15, respectively [50,164,165]. Based on a comparison of the calculated radiative and measured lifetimes, the quantum yield of the 4 S 3/2 should be adequate for efficient fiber lasers, even at room temperature, and this has been substantiated by the 38% slope efficiency reported for an 800-nm upconversion pumped 4 S 3/2 → 4 I 13/2 laser at 850 nm [162]. The additional radiative decay channel through the thermally populated 2 H 11/2 state acts to shorten the observed lifetimes Table 13

Transitions Originating on the 4 I 11/2 State →4 I 15/2 980 nm

Lifetime Glass ZBLA ZBLA ZBLAN ZBLANP BZYTZ BZYTL PZGL

τ obs (ms)

τ rad (ms)

β

6.7 6.0 6.7 7.8 7.4 6.0 6.0

9.2 9.2 5.9

0.83 0.83 0.82

7.8 7.5 6.4

0.77 0.83 0.82

σp (10 ⫺21 cm 2)

→4 I 13/2 2700 nm β

σp (10 ⫺21 cm 2)

1.5

0.17 0.17 0.18

11.1 44

2.0 2.2 1.8

0.23 0.17 0.18

19.6 15.4 12.0

Ref. 50 157 158 153 157 159 157

73


Table 14

Transitions Originating on the 4 S 3/2 State Branching ratio β

Lifetime Glass

τ obs (µs)

τ rad (µs)

→4 I 15/2 550 nm

→4 I 13/2 850 nm

→4 I 11/2 1250 nm

→4 I 9/2 1700 nm

Ref.

ZBLANP ZBLA ZBLA PZGL

500 450 290 450

860 630 860

0.67 0.66 0.67

0.27 0.28 0.27

0.02 0.02 0.02

0.04 0.04 0.04

164 50 165 165

in Table 14. From the data of Shinn et al. [50], the net result is a reduction of roughly 20% in the lifetime of the 4 S 3/2. The branching ratios strongly favor the 4 S 3/2 → 4 I 15/2 (550-nm) transition to the ground state, although for crystals lasing has been reported only at low temperature [166]. For a fluorozirconate fiber, however, up-conversion lasing has been achieved at room temperature by pumping at 800 nm [160]. This is the same pumping scheme used for the 850-nm up-conversion laser, and the latter transition was reported to compete strongly with the desired 550-nm one [160]. This seems to indicate that the depletion of the 4 I 13/2 terminal state for 850-nm operation by pump ESA is much more effective than the depletion of the ground state, which is required for three-level operation at 550 nm. One would expect that it would be preferable to pump at a wavelength for which there is no ESA from the 4 I 13/2 state, and this has been confirmed by Allain et al., who demonstrated a 550-nm up-conversion laser pumped at 980 nm [161]. It can be seen from Table 14 that the transitions at 850 and 1720 nm correspond, respectively, to the second and third highest transition probabilities from the 4 S 3/2 level. Indeed, in addition to the laser [162], an upconversion fluorozirconate fiber amplifier has produced 23-dB gain at 850 nm [163]. Operation on the 4 S 3/2 → 4 I 11/2 transition at about 1250 nm has been reported for crystalline fluoride hosts [167,168], but the low branching ratios in Table 14 raise some question about whether such operation is possible in glass. The low branching ratios from the 2 H 11/2 to any but the ground state (see Table 15) cast doubt on the foregoing assignment of the 1660-nm lasing transition. Using the model of Shinn et al., which neglects the Stark splittings, the effective gap for ZBLA between the 4 S 3/2 and 2 H 11/2 is about 830 cm ⫺1 [50], about 4 kT at room temperature. The separation for ED-2 silicate seen in Figure 28 (⬇850 cm ⫺1) suggests that this gap is not very sensitive to glass composition. By applying the Boltzmann factor and degeneracy ratio, one finds that the already low gain coefficient for the 2 H 11/2 → 4 I 9/2 transition must be further reduced Table 15

Transitions Originating on the 2 H 11/2 State Branching ratio β

Glass

→4 I 15/2 520 nm

→4 I 13/2 800 nm

→4 I 11/2 1100 nm

→4 I 9/2 1500 nm

Ref.

ZBLA PZGL

0.93 0.91

0.04 0.05

0.01 0.02

0.01 0.02

165 165

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by a factor of about 20 at room temperature and 2 ⫻ 10 6 at 77 K. Because operation at 1660 nm has been reported at both these temperatures, it is unlikely that the 2 H 11/2 state participates. An alternative explanation is that all transitions originate from the lower Stark level of the 4 S 3/2: the 1720 nm going to the highest and the 1660 nm to the lowest component of the 4 I 9/2 terminal state. This is consistent with the observed temperature dependence as well as the width (⬃200 cm ⫺1) found for the 4 I 9/2 manifold of ZBLAN from lowtemperature excitation spectra [21]. The 4 F 9/2 state is another potential upper laser level in fluoride glasses, the 4 F 9/2 → 4 I 15/2 transition at 660–670 nm having been lased in fluoride crystals at 77 K [166,169]. Table 16 lists the available information for this state [50,157,165,170] and indicates that because the branching ratio to the ground state exceeds 0.9 for all glasses, this is the only potential gain transition from this level. The measured lifetimes at room temperature are all quite low compared with the radiative lifetimes, revealing that the 4 F 9/2 is too highly quenched by multiphonon emission to provide gain even in a fluoride glass. As with crystalline hosts, operation of this three-level laser may be possible at low temperature because the radiative yield doubles if the temperature is reduced to 100 K or lower [50], and the higher components of the 4 I 15/2 terminal state will be unoccupied. From the data of Shinn et al. [50], however, we estimate that the quantum efficiency of this level never exceeds 25% even at absolute zero, guaranteeing low efficiency as a small-signal amplifier. Although lasing has been reported on the 2 H 9/2 → 4 I 13/2 transition at 560 nm for a BaY 2 F 8 crystal at 77 K [166], the 2 H 9/2 level is highly quenched in fluoride glasses because the energy gap to the next lower level is too small for the effective phonon frequencies of these materials. The room-temperature lifetime in a BZYTZ [Ba, Zr, Yt, Zn] glass is about 8 µs [157] compared with a radiative lifetime of about 400 µs [50,165]. From the analysis of Shinn et al. [50], we estimate that the quantum efficiency of this level is 1% or less, even for temperatures lower than 80° K, suggesting that there is little possibility of obtaining gain for a glass host. As expected from Figure 28, the 4 I 9/2 is also quenched by nonradiative relaxation with a room-temperature lifetime of 12 µs for a BZYTZ glass [157], compared with a radiative lifetime that ranges from 5 [165] to 8 ms [50]. There has been a report of a 1-ms lifetime for the 4 I 9/2 state in ZBLANP [164]. However, the measurements were performed pumping the 2 H 11/2 at 514 nm; thus they are more indicative of the lifetime of the 4 S 3/2 level, which will act as a reservoir for the excitation that cascades down to the 4 I 9/2 by nonradiative relaxation. A similar effect has been observed by Eyal et al. for the 4 F 9/2 and for the 5 F 5 of Ho 3⫹ [157], in which pumping a higher-lying metastable state produces a long apparent lifetime for the state whereas direct excitation reveals the true decay rate. The process can be modeled using a simple set of rate equations, and one finds that, despite the persistence of emission from the short-lived state, there is no Table 16 Transitions Originating on the 4 F 9/2 State 4

Lifetime Glass

τ obs (µs)

τ rad (µs)

β

σ p (10 ⫺21 cm 2)

145 169 180 358

920 730 970 790

0.92 0.91

11.2

ZBLA ZBLA BZYTZ PZGL a

F 9/2 → 4 I 15/2 660 nm

Source: Ref. 170.

0.90

5.2 a

Ref. 50 165 157 165


75

accumulation of population. Thus significant gain is not possible on a transition from this level, nor will one to this level be self-terminating. 2.3.3 Pump Wavelengths General Considerations Fiber lasers and amplifiers have been pumped using nearly every Er 3⫹ absorption band in Figure 27 that lies at wavelengths greater than 450 nm. The first consideration in the choice of pump wavelength is the gain transition desired, followed by efficiency and the availability of pump sources. ESA at the pump wavelength is an important process, which can be either detrimental or beneficial. Figure 33 illustrates the pump ESA process through an example in which the absorption of a photon in the 800-nm ground-state absorption band excites an Er 3⫹ ion into the 4 I 9/2 state. For silica it quickly relaxes from this state to the 4 I 13/2 level through multiphonon emission. An ion in the metastable state can then be promoted to the 2 H 11/2 level through the absorption of a second 800-nm photon. From Figure 33 it can be seen that a GSA transition followed by an ESA transition removes two pump photons and produces one highly excited ion. In common oxide glasses the 2 H 11/2 terminal state for this 800-nm ESA process quickly decays through the intervening levels back to the 4 I 13/2 state through multiphonon emission, the net result being the conversion of the second pump photon into heat. Because only the 4 I 13/2 → 4 I 15/2 (1500-nm) transition can be operated for oxide glasses, pump ESA is a serious dissipative process for these materials and avoiding it is a primary concern in optimizing device performance.

Figure 33

Illustration of ESA at 800-nm–pump band. Ion excited to 4 I 9/2 level by a pump photon relaxes nonradiatively to the 4 I 13/2 metastable state, from which it absorbs additional pump photons.

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Figure 34 superimposes the GSA spectrum and the pump-induced change in absorption for a silica glass. Where the latter is positive, the absorption has increased due to ESA from the 4 I 13/2. Only where the pump-induced change in absorption is negative and a mirror image of the GSA spectrum exists is there a pump band without significant ESA. Among the GSA bands illustrated in Figure 34, as well as those at shorter wavelengths only the one at 980 nm is completely free of ESA from the 4 I 13/2 level. Figure 35 contains an Er 3⫹ energy level diagram in which the higher excited states are labeled with the wavelength of the ESA transition terminating on it that originates on the 4 I 13/2. Fluoride glasses have additional metastable states, each having its own ESA spectrum. The second column on the right in Figure 35 indicates the wavelengths of ESA transitions originating on the 4 I 11/2 level. Fluoride glasses are particularly useful for transitions originating on levels above the 4 I 13/2, and ESA can be exploited for up-conversion pumping in which two or more long-wavelength photons are used to generate one highly excited ion. Moreover, some of these transitions terminate on a metastable state, and for these it is advantageous to pump at a wavelength for which there is strong ESA from the terminal level to depopulate it. The latter process was originally used with direct pumping—that is, using photons that have sufficient energy to reach the upper level from the ground state [153]. For a 4 S 3/2 → 4 I 13/2 (850-nm) laser, the two processes were recently combined in a procedure in which pumping at a single wavelength and ESA up-conversion occurred in a three-step process [162,163]. The 800-nm pump photon first excites the 4 I 9/2, which relaxes nonradiatively

Figure 34

Comparison of the ground state absorption coefficient and the pump-induced change in absorption coefficient for Ge/P silica. Negative changes in the absorption coefficient correspond to bleaching of absorption bands (increased transmission), whereas positive changes indicate regions of strong ESA. The spectra have been scaled using the 980-nm band, which is free from ESA.


77

Figure 35

Energy levels of Er 3⫹ in ED-2 silicate glass, labeled on the right by the wavelengths of the ESA transition to that level originating on the 4 I 13/2 and 4 I 11/2 states.

to the 4 I 11/2 , which is metastable in fluoride glasses (see Fig. 35). An ESA transition at 800 nm promotes the 4 I 11/2 to the 4 F 3/2 , which relaxes to the 4 S 3/2 upper level of the gain transition. The additional ESA process at 800 nm recycles the excitation from the 4 I 13/2 terminal level back up to the 4 S 3/2 to maintain inversion. Up-conversion processes other than ESA can also be used to depopulate metastable terminal levels. The procedure was originally demonstrated using the 4 I 11/2 → 4 I 13/2 (2700-nm) transition by pumping the 4 I 13/2 state of Er 3⫹-doped CaF 2 at 1540 nm and relying on cooperative up-conversion to promote the excitation to the 4 I 11/2 level [171]. Cooperative and ESA up-conversion pumping not only increase the number of pump bands available for a given transition, but also allow long-wavelength excitation sources to be used for short-wavelength devices. Because of the high inversion required, traveling-wave amplifiers are more sensitive to pump wavelength than lasers and superluminescent sources. The dependence of device performance on pump wavelength has been extensively investigated only for the important 1500-nm transition. Gains close to 40 dB have been achieved pumping at 654 [172] and 820 nm [173], 46.5 dB has been reported for an amplifier driven near 1480 nm [174], and 54 dB has been realized by pumping the 980-nm band [175]. The absorption band used, as well as the particular pump wavelength within it, will also have a significant effect on the efficiency of the device and, in the case of an amplifier, the signal-to-noise

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ratio. Practical considerations such as reliability, package size, cost, and power consumption dictate that fiber devices be pumped by diode lasers in most applications. For devices operating at 1500 nm one must consider the tradeoffs between developing a new diode laser at a good pump band such as 980 nm, or using a mature technology such as highpower AlGaAs lasers to excite the relatively poor pump band at 800 nm. Resonantly pumping the 1480-nm band is an intermediate case. When using fluoride glasses and gain transitions terminating on the 4 I 11/2 or 4 I 13/2 levels, the strong ESA at the 800-nm pump band is an advantage. High-power diode lasers are not currently available for the 650-nm absorption band, and it does not offer high efficiency for 1500-nm devices. Unless one wishes to exploit ESA up-conversion for exciting levels above the 4 S 3/2, there appears to be no advantage to pumping fluoride glasses at 650 nm. It is equivalent to pumping at 800 nm because the 4 F 9/2 level is nonradiative even at low temperatures. In general, the available evidence indicates that the 980- and 1480-nm pump bands are the best for pumping 1500-nm devices in oxide glasses, with the 800-nm band a distant third. Pedersen and co-workers have systematically compared the performance of silica fiber amplifiers for these three pump bands [176]. Figure 36 plots the minimum pump power required to achieve a specified small-signal gain, and Figure 37 shows the minimum pump power needed for a particular signal output for a power amplifier. The 980-nm band provides higher efficiency (in dB/mW) and signal-to-noise ratio for small-signal amplifiers [176]. It also leads to better noise figures and quantum conversion efficiencies for power

Figure 36

Calculated minimum pump power required to achieve a specified small-signal gain for 800-, 980-, and 1480-nm pumping. The curve for 800-nm pumping assumes codirectional pumping and the optimum pump wavelength within the 800-nm band for the specified gain. Fiber lengths have been optimized for gain at every point on the curves. (From Ref. 176.)


79

Figure 37

Calculated minimum pump power required to achieve a specified signal output power for 800-, 980-, and 1480-nm pumping of power amplifiers. The curve for 800-nm pumping assumes codirectional pumping and the optimum pump wavelength within the 800-nm band for the specified gain. Fiber lengths have been optimized for gain at every point on the curves. (From Ref. 176.)

amplifiers [176]. Quantum conversion efficiency is defined as the number of photons added to the signal for every pump photon coupled into the fiber. The power conversion efficiencies for power amplifiers are higher for 1480-nm pumping because the energy per photon is lower. For wall-plug efficiency, however, it should be noted that 980-nm InGaAs strainlayer lasers have roughly twice the slope efficiency of 1480-nm quaternary lasers. Efficiency considerations for fiber lasers are similar to those of power amplifiers. For fluoride glasses, only the 1480-nm band is practical for 1500-nm operation because of the higherlying metastable states. The situation is completely reversed for exciting the higher metastable states in fluoride glasses: because the 800-nm ground-state absorption band overlaps strong ESA bands from both the 4 I 13/2 and 4 I 11/2 levels, this should be the best band for pumping all transitions for these glasses except that at 1500 nm. Details of the 800-, 1480-, and 980-nm pump bands are discussed in the following, with particular emphasis on 1500-nm operation. 800-nm Pump Band The 4 I 15/2 → 4 I 9/2 transition gives rise to an absorption band peaking near 800 nm, which suggests the possibility of pumping by high-power, relatively inexpensive AlGaAs diode lasers. Even in crystals and fluoride glasses, the 4 I 9/2 state is short-lived, decaying by multiphonon emission. In the absence of ESA or cooperative up-conversion, 800-nm pumping can be used for emission transitions originating on the 4 I 13/2 level for oxides and

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the 4 I 11/2 for fluorides. This is not a suitable band for populating the 4 I 13/2 state in fluorides because the 4 I 11/2 is metastable, and only a small fraction of the excitation will reach the desired level. In most instances, the performance of 1500-nm amplifiers pumped in this band has been rather poor because the GSA transition is weak and overlaps a much stronger 4 I 13/2 ESA band. The 4 I 11/2 level also has an ESA band near 800 nm that can impair operation at 980 and 2700 nm. Figure 38 compares 4 I 15/2 → 4 I 9/2 absorption cross-section spectra for several glass compositions and reveals quite significant host-to-host variations for this band. Relevant properties for the 800-nm band are listed in Table 17. The spectra peak at nearly the same wavelength for all the compositions, and the widths fall into a relatively narrow distribution. The sole exception to these patterns is the Al/P silica, which is unusual in many other respects. The variation in oscillator strengths is ⫾20% neglecting the L22 silicate, somewhat larger than for the 1500- and 980-nm absorption bands. The range of peak cross sections is still greater, with some compositions having appreciably higher values than the Al/P silica. On the basis of cross sections alone, Table 17 indicates that other glasses should provide better performance at 1500 nm than silica. The more important consideration, however, is ESA, and the best results have been obtained pumping in the long-wavelength wing of the absorption band, well away from the peak where the ESA process dominates [173]. Figure 38 reveals that this approach works only because of the fortuitous long-wavelength wing to this absorption band. ESA is most severe under the conditions of a highly excited state population necessary for a high-gain, low-noise, traveling-wave amplifier in this three-level system. It is a less serious problem for lasers and power amplifiers because the inversion can be kept low by limiting

Figure 38

Absorption cross-section spectra for the 800-nm band.

81


Table 17

4

I 15/2 → 4 I 9/2 Absorption Transition at 800 nm

Glass a

Al/P silica Silicate L22 Silicate ED-2 Phosphate L12 Phosphate L28 Fluorophosphate L11 Fluorophosphate L14 Fluorozirconate ZBLAN Ba–Zn–Lu–Th

Oscillator strength (10 ⫺8)


Peak wavelength (nm)

FWHM (nm)

22.2 11.5 17.8 22.5 25.1 26.8 25.4 18.6 18.9

6.48 4.17 6.23 8.07 10.7 9.68 7.79 6.44 5.90

793.4 796.6 798.0 799.8 798.6 800.8 800.6 800.6 799.8

22.3 19.4 19.5 16.5 15.2 16.5 18.9 17.7 19.9

Sources: M. P. Singh, private communication; all else Ref. 142.

the cavity losses or saturating the amplifier. This is consistent with the demonstration of low-threshold fiber lasers pumped in the 800-nm band [177,178]. The ESA problem for 1500-nm devices pumped at the 800-nm band was first pointed out by Armitage et al. [179]. The process can be characterized by a parameter R ESA , defined as the ratio of the ESA cross section to the GSA cross section at the pump wavelength. Subsequent investigations have revealed that, for silica, R ESA is sensitive to the co-dopants [180,181]. At 810 nm, R ESA ⬇ 2 for Ge silica [180], while the addition of large amounts of P reduces it to 1 or less [180,181]. A value of approximately 1 was also found for Al silica [180] and Al/P silica [181]. Codoping Ge silica with B [180] or F [181] had no beneficial effect. Fluorozirconate fibers were reported to have R ESA ⬍ 1 for all wavelengths greater than 800 nm [181]. These results are consistent with a Judd–Ofelt analysis by Andrews et al., who predicted that glass composition could make as much as a factor of 2 difference in the integrated strength of the ESA transition, with fluoride and fluorophosphate glasses expected to be the best [122]. The suitability of a particular glass, however, depends on the spectral details of the GSA and ESA bands. This information cannot be provided by a Judd–Ofelt analysis; it must be determined experimentally. Recently Zemon and co-workers have reported ESA measurements on Er 3⫹-doped bulk glasses [182] and fibers [183,184]. Figure 39 shows that the ESA cross section σ 24 for an Al/P-silica fiber exceeds the GSA cross section σ 13 over the complete pump band except near 820 nm [183,184], and explains the higher gains realized for Al silica amplifiers pumped at about 820 nm [185]. In contrast, Figure 40 reveals that for the L11 fluorophosphate GSA is larger than ESA over most of the pump band, including the peak [183,184]. The difference is a consequence of both the predicted reduction in ESA oscillator strength [122] and the narrower spectra for the L11 glass. The latter leads to a greater offset between the GSA and ESA bands. Other glasses examined are intermediate in properties between these two [183,184]. The cross-section ratio R ESA can be used as a figure of merit for gain efficiency and is plotted as a function of wavelength for these two glasses in Figure 41. To the advantage of the fluorophosphate glass apparent from this figure should be added the larger peak stimulated emission cross section found in Table 10. These spectroscopic differences have been translated into predicted performance differences using quantitative, large-signal fiber amplifier models [183,184,186]. Figure 42 compares the quantum conversion efficiency of power amplifiers made from Al/P silica and

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Figure 39

Comparison of ESA and GSA cross-section spectra for Al/P silica.

Figure 40

Comparison of ESA and GSA cross-section spectra for L11 fluorophosphate.


83

Figure 41 ESA-to-GSA cross-section ratio R ESA as a function of wavelength for Al/P silica and L11 fluorophosphate.

L11 fluorophosphate glass as a function of pump wavelength. As expected, the fluorophosphate provides significantly better performance through the pump band, and a similar advantage is found for small-signal amplifiers [186]. Among glasses for which data are available, the L11 composition is among the most favorable relative to reduced ESA at 800 nm [183,184]. Zemon and co-workers also observed ESA bands in the 880- to 900-nm range from two additional metastable states of Er 3⫹-doped ZBLAN [182,183]. Figure 43 shows not only the two ESA bands originating on the 4 I 13/2 level that are seen for oxide glasses, but also one from the 4 F 9/2 level being pumped at 647 nm and two from the 4 I 11/2. This rich ESA spectrum, the bottlenecking of excitation at the higher levels [187], and the relaxation of these upper levels directly to the ground state (cf., branching ratios in Tables 13–15) indicate that Er 3⫹-doped fluoride glasses are suitable as 1500-nm lasers and amplifiers only if resonantly pumped directly into the 4 I 13/2 state. However, the 800-nm band is useful for pumping the 4 I 11/2 → 4 I 15/2 (980-nm) and 4 I 11/2 → 4 I 13/2 (2700-nm) transitions, as well as any relying on ESA or cooperative up-conversion from the 4 I 11/2 or 4 I 13/2 level. Although the very strong 4 I 11/2 → 4 F 3/2 ESA transition at 810 nm is helpful for up-conversion and directly pumped devices terminating on the 4 I 11/2, it can seriously degrade the performance of 980- and 2700-nm devices. The latter disadvantage was confirmed through the observation that the excitation spectrum of a 2700-nm ZBLAN fiber laser had a dead zone centered at about 810 nm [188], in agreement with the ESA band seen in Figure 43. Operation at 980 nm should not be significantly affected by the 4 I 13/2 → 2 H 11/2 ESA transition at 790 nm, because the 4 I 13/2 is largely unpopulated. Gain at 2700 nm can be improved, however,

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Figure 42 Calculated quantum conversion efficiency as a function of pump wavelength for A1/ P silica and L11 fluorosphosphate fibers. Fiber NA is 0.3, cutoff wavelength is 800 nm, and pumping is bidirectional with 100 mW. (Data from Ref. 186.)

because ESA will help depopulate the metastable terminal state. The value of this process, which has been verified through pumping 2700-nm fluorozirconate fiber lasers at other wavelengths at which the 4 I 13/2 level has ESA bands [153,189], is consistent with the observation by Allen et al. of a slight shift in the optimum pump wavelength away from the GSA peak toward the 790-nm ESA peak [188]. An even more interesting illustration was the demonstration of an up-conversion laser for the 4 S 3/2 → 4 I 13/2 (850-nm) transition, which used an 800-nm pump to populate the 4 S 3/2 level by ESA from the 4 I 13/2 terminal and 4 I 11/2 states [162]. Although ESA can be beneficial through populating initial states or depopulating terminal states of desired transitions, these processes have not been well studied. 1480-nm Pump Band Snitzer et al. first demonstrated that 1500-nm Er 3⫹ amplifiers and lasers can be excited directly into the 4 I 13/2 metastable state by pumping near 1480 nm [190]. The other gain transitions of fluoride materials cannot be directly excited at this wavelength, however, because their upper levels are higher-lying states. Armitage et al. have determined that the ESA band for the 4 I 13/2 → 4I9/2 transition (see Fig. 35) lies near 1670 nm [191], too long a wavelength to effectively pump the 4 I 13/2 level. Accordingly, ESA is not a concern for 1500-nm devices, but neither can it be used to up-conversion pump higher states. Cooperative up-conversion from the resonantly pumped 4 I 13/2 level can accomplish this. Pulsed lasing on the 4 I 11/2 → 4 I 13/2 (2800 nm) has been achieved for Er 3⫹-doped CaF 2


85

Figure 43

Pump-induced change in transmission for Er 3⫹-doped ZBLAN fluorozirconate glass excited at 647 nm. ESA transitions originating on three metastable states are indicated.

pumped in the terminal state at 1540 nm, using an Er 3⫹-doped glass laser [171]. Nevertheless, fiber devices are not usually doped to Er 3⫹ concentrations high enough for cooperative processes to be adequate for this purpose. Excellent results have been obtained by pumping silica and fluorozirconate 1500-nm lasers and amplifiers in the 1470- to 1490-nm range. This procedure, combined with the commercial availability of high-power diode lasers for this band, has led to extensive use of resonantly pumped amplifiers in systems demonstrations and field trials for optical communications applications. Although superficially a two-level system, resonant pumping produces gain because of the shift between the absorption and emission cross-section spectra depicted in Figure 44 for an Al/P silica fiber. This offset is observed for all glasses and is a consequence of nonuniformly populated Stark levels, as kT at room temperature (⬃200 cm ⫺1) is less than the width of both the 4 I 13/2 and 4 I 15/2 manifolds (300–400 cm ⫺1). The relation between emission and absorption is governed by Eq. (15), which describes how the spectral offset increases with decreasing temperature. Reasons for the excellent performance achieved by resonant pumping can also be found in Figure 44. Despite being in the wing of the absorption band, the cross sections are comparable with those at 980 nm. Because the 4 I 15/2 → 4 I 13/2 absorption band is quite broad and does not vary significantly over this interval, great care need not be exercised in selecting the wavelength of the pump laser, and highly multimode pumps will suffice. An additional benefit is the absence of ESA in this region. The principal drawback to resonant pumping results from the incomplete offset between emission and absorption. Figure 44 shows that the stimulated emission cross section

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Figure 44

Cross-section spectra for Al/P silica showing offset between emission and absorption.

is appreciable at all wavelengths for which the absorption cross section is large enough to be useful. This reduces pump absorption and prevents full inversion from being obtained at any pump power. Although high gain can still be achieved for small-signal amplifiers by increasing the fiber length, the restriction on inversion ensures that some penalty in signal-to-noise ratio is unavoidable. A simple analysis can be used to draw some general conclusions about this fundamental noise penalty. The fraction of ions in the 4 I 13/2 metastable state has been calculated as a function of wavelength for several compositions using measured absorption and emission cross sections. In the high-power limit, parameters such as the spontaneous and stimulated emission rates, signal power, and waveguide parameters, drop out of the expression for the maximum achievable excited state fraction, η max . The result simplifies to η max ⫽

σ 12 (ν p) n2 ⫽ n σ 12 (ν p) ⫹ σ 12 (ν p)

(27)

where n is the total Er 3⫹ concentration, n 2 is population of the 4 I 13/2 level, and σ 12 (ν p) and σ 21 (ν p) are the absorption and stimulated emission cross sections, respectively, at the pump frequency. Excited-state fractions are plotted as a function of wavelength in Figure 45. Only three compositions are shown because of the similarity between the curves of all glasses examined. In the high-power, high-gain (gains ⬎10) limit, the amplifier noise factor is given by F⫽

2n 2 σ 21 (ν s) n 2 σ 21 (ν s) ⫺ n 1 σ 21 (ν s)

(28)


Figure 45

87

Excited-state fraction η as a function of pump wavelength in the high-power limit.

where the cross sections are those at the signal frequency. By solving Eq. (27) for n 2 , substituting into Eq. (28), and using n ⫽ n 1 ⫹ n 2 , one obtains the minimum noise factor in terms of the cross sections: F min ⫽

2 σ 21 (ν p)σ 12 (ν s) 1⫺ σ12 (ν p)σ 21 (ν s)

(29)

Since the pump and signal frequencies are just different points in the same absorption and emission spectra, one may substitute the McCumber relation (Eq. 15) for both cross section ratios, and Eq. (29) becomes F min ⫽

2 1 ⫺ exp[⫺(hν p ⫺ hν s)/kT]

(30)

Thus, the minimum noise factor does not depend on the glass composition used, but is a function of temperature and the difference in energy between the pump and signal photons only. For pumping at 1480 nm, Eq. (30) predicts a minimum noise figure (⫽10 log 10 F min) of 4.1 dB for a signal at 1550 nm and 4.7 dB for one at 1532 nm, the gain peak for silica co-doped with Al. These values are consistent with measurements [192,193], and Table 18 compares minimum noise figures calculated from Eq. (30) with those calculated using measured cross sections and Eq. (29). The agreement is remarkably good for such a simple analysis. The significance of Eq. (30), however, goes beyond the particular Er 3⫹ transition under consideration, for ε, the only parameter in Eq. (15) that refers to the levels, ion, or

88

Table 18

Miniscalco Minimum Noise Figures for Er3⫹ Amplifiers Pumped at 1480 nm Minimum noise figure (dB)

Glass Al/P Silica Silicate L22 Fluorophosphate (low F) Fluorophosphate (high F) Fluorozirconate ZBLAN

From McCumber

From cross sections

Signal wavelength (nm)

4.7 4.6 4.7 4.7 4.8

4.8 4.4 4.6 4.6 4.9

1531.4 1535.8 1532.6 1532.0 1530.6

even host involved, has dropped out of the expression. Accordingly, Eq. (30) can be applied to any resonantly pumped transition of any optically pumped gain system, including those as diverse as semiconductors and organic dye molecules. 980-nm Pump Band The 4 I 15/2 → 4 I 11/2 transition of Er 3⫹ corresponds to an absorption band peaking between 970 and 980 nm, which has been quite valuable for exciting fiber devices at 1500 nm. Amplifiers pumped in this band have shown not only the best performance relative to gain and gain efficiency, but also have achieved quantum-limited noise figures of about 3 dB [193,194], signal output powers greater than 500 mW [59], and quantum conversion efficiencies of 90% [61]. Laser outputs of 250 mW or more for an output wavelength range of 50 nm have been reported for 540 mW launched at 980 nm [79]. This success is due to the large absorption cross section for this band, coupled with the absence of ESA from the 4 I 13/2 at this wavelength. For oxide glasses, there is also negligible stimulated emission at the pump wavelength because of the short lifetime for the 4 I 11/2 state. For fluoride glasses this band is not suitable for pumping the 1500-nm transition because the decay of the 4 I 11/2 state is dominated by radiative relaxation directly to the ground state. Devices relying on ESA up-conversion from the 4 I 13/2 cannot be pumped at 980 nm because there is no ESA. For fluoride glasses this band is most useful for pumping the 4 I 11/2 → 4 I 15/2 (980-nm) and 4 I 11/2 → 4 I 15/2 (2700-nm) transitions, as well as up-conversion processes originating on the 4 I 11/2 level. ESA corresponding to the 4 I 11/2 → 4 F 7/2 transition (see Fig. 35) was first reported at 970–980 nm for Er 3⫹- doped LiYF 4 [195], and subsequently for silica [196], as well as fluorozirconate and fluorophosphate glasses [197]. As with the ESA at 800 nm, it is observed to be stronger than the GSA transition [195,197]. The 980-nm ESA band may be useful for fluoride glass devices that rely on ESA up-conversion from the 4 I 11/2 level. The only apparent candidate is the 4 S 3/2 → 4 I 11/2 (⬇1250-nm) transition, which has been lased for Er 3⫹-doped CaF 2 [167] and LiYF 4 [168]. The low branching ratio for this transition in Table 14, however, does not suggest the likelihood of good performance. Despite the short lifetime of the 4 I 11/2 in silica, it has been suggested that this ESA process may nevertheless reduce efficiency, particularly for power amplifiers [196]. Pumping the 980-nm band is a resonant excitation process if emission at 980 or 2700 nm is desired. Although this has yet to be investigated, the same considerations discussed in the preceding section on 1480-nm pumping of the 1500-nm transition will apply. Here, the absorption and stimulated emission cross sections at the pump wavelength will be those connecting the 4 I 11/2 upper level and the 4 I 15/2 ground state. The signal cross

89


Figure 46

Absorption cross-section spectra for the 980-nm band.

sections will be between the 4 I 11/2 and 4 I 15/2 manifolds for 980-nm emission, and between the 4 I 11/2 and 4 I 13/2 levels for 2700-nm emission. In either case, one expects a temperaturedependent limitation on the maximum inversion that can be obtained. Figure 46 illustrates the variations with glass composition of the absorption crosssection spectrum for the 4 I 15/2 → 4 I 11/2 transition. The peak cross sections at 980 nm are seen to be three to four times greater than those at 800 nm and are comparable with those at 1480 nm. The wavelengths of the cross-section peak in Table 19 show the usual trend with degree of covalency, the silicates and phosphates lying at longer wavelength and the Table 19

4

I 15/2 → 4 I 11/2 Absorption Transition at 980 nm

Glass

Oscillator strength (10 ⫺8)


Peak wavelength (nm)

FWHM (nm)

63.8 20.4 29.1 39.5 48.7 47.9 45.4 37.3

31.2 9.50 13.1 20.1 24.7 24.6 21.5 21.5

978.6 980.8 980.2 975.2 978.8 973.8 973.4 973.8

16.6 22.1 22.2 17.7 18.1 17.1 17.8 15.1

Al/P a Silicate L22 Silicate ED2 Phosphate L12 Phosphate L28 Fluorophosphate L11 Fluorophosphate L14 Fluorozirconate ZBLAN Sources: aRef. 26; all else Ref. 142.

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fluorides and fluorophosphates at shorter wavelength. With the exception of the ZBLAN fluorozirconate and the unusual L22 and ED2 silicates, the bandwidths are all clustered between approximately 17 and 18 nm. Most of the oscillator strengths fall within a ⫾15% range and, as a result of the relatively narrow distribution of bandwidths, the peak cross sections show a similarly small range with a few exceptions. Initially there had been concern that the narrowness of the 980-nm pump band would require tight tolerances on the wavelengths of the pump lasers. A series of investigations have revealed that high gains can still be obtained for pump wavelengths well away from the peak of the absorption band [148,198,199]. Pumping away from the peak of a band with a high cross section is equivalent to pumping at the absorption peak of a band with a low cross section. Pedersen et al. have pointed out that the noise figure of an amplifier will increase as the pump wavelength is moved away from the peak of the absorption band, particularly if the fiber length is increased to maintain gain [200,201]. For an efficient fiber design and practical pumping levels, these investigators find that both the gain and noise figure penalties are less than 1 dB for pump wavelengths ranging from 965 to 995 nm [200,201].

2.4 THULIUM 2.4.1 General Characteristics The first Tm 3⫹-doped glass laser was reported by Gandy et al. at approximately 1900 nm using an Li–Mg–Al silicate glass [202]. Although a moderate level of activity has been maintained on the infrared transitions of Tm 3⫹-doped crystals, only since the recent upsurge of interest in fiber lasers has a significant level of effort on Tm 3⫹-doped glasses emerged. Similar to Er 3⫹, Tm 3⫹ has useful emission in a silica host as well as several additional transitions when fluoride glasses are used. Much of the interest in Tm 3⫹ stems from its emission that occurs in the gaps between the bands of Nd 3⫹ and Er 3⫹ in the range 1400–2700 nm. Figure 47 illustrates the absorption spectrum of Tm 3⫹ in a high fluorine content fluorophosphate glass. From this, the energy level diagram presented in Figure 48 has been deduced. The absorption spectrum in Figure 47 is nearly indistinguishable from that of a fluorozirconate glass (cf., Sanz et al. [203]) except that the ultraviolet edge of the latter is shifted to a shorter wavelength, as is expected for fluoride materials that have larger fundamental gaps. There is a lack of uniformity among authors in labeling the states at 6000 and 13,000 cm ⫺1. As discussed in Section 2.1.3, these differences arise from the strong mixing of the LS terms induced by the spin–orbit interaction. In this work these states are designated by their dominant LS contribution. The transitions for which laser action has been reported are indicated in Figure 48 for both crystalline and glass hosts. In examining Tm 3⫹ for luminescent transitions that may provide gain, one of the primary considerations is the availability of metastable states. Unlike Er 3⫹ and Nd 3⫹, for which states that are metastable in most glasses can be excited by infrared absorption bands, for Tm 3⫹ only the high-lying 1 G 4 and 1 D 2 are metastable in most glasses. Table 20 lists the first seven excited states for Tm 3⫹ together with an effective energy gap separating each level from the one just below it. This and the effective phonon frequency are the parameters that control the nonradiative relaxation rate (see Sec. 2.1.5). The gaps are derived from Figure 48, assuming that the excitation occupies an energy range of kT (⬇200 cm ⫺1) and decays to the middle of the next lower state. The effective gap for the 4 I 13/2 state of Er 3⫹ calculated in this way is 6400 cm ⫺1, a value large enough to ensure that radiative decay dominates for all glasses except those with extremely large


Figure 47

91

Absorption cross-section spectrum of Tm 3⫹-doped high fluorine content fluorophos-

phate glass.

phonon energies. The important 3 F 4 and 3 H 4 states of Tm 3⫹, however, are seen to have energy gaps small enough to render their quantum efficiency very sensitive to host glass composition (cf. Fig. 5). The energy gaps below the 3 H 5, 3 F 3, and 3 F 2 levels are so small that multiphonon emission causes them to have extremely short lifetimes, and it is unlikely that a population inversion can be achieved for any of these states regardless of host or temperature. Only for the 1 D 2 is the effective gap equal to that of the 4 I 13/2 of Er 3⫹. The small effective gaps for most of the levels in Figure 48 illustrates why the choice of host has a greater influence on device efficiency for Tm 3⫹ than for the principal transitions of Er 3⫹ or Nd 3⫹. In addition, it has been suggested that the electron–phonon coupling might be stronger for Tm 3⫹ than for most rare earths, thereby producing a higher multiphonon emission rate [204]. Several additional factors must be considered when using high-lying states, such as the 1 G 4 and 1 D 2, for the upper level of a gain transition. Both pump and signal ESA are potentially more serious because in addition to transitions to higher f shell states, it is now possible to excite 4f → 5d, charge transfer, and photoionization transitions. These not only have wider bandwidths than intra-f-shell transitions, but they are many orders of magnitude stronger, as they are electric–dipole allowed. In addition, the short wavelengths required for direct pumping are not available from diode lasers and absence of high energies can lead to color-center formation in glasses. Many of these problems can be circumvented by up-conversion pumping and operating on long-wavelength transitions terminating on intermediate states, although this approach may exact a high penalty in reduced efficiency. The transitions of potential use for providing gain are discussed in the following subsections organized by the upper state involved. Section 2.4.3 treats the approaches to pumping Tm 3⫹ fiber devices.

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Figure 48

Energy levels of Tm 3⫹ in high fluorine content fluorophosphate glass labeled using Russell–Saunders coupling. The number to the right of each excited state is the wavelength in nanometers of the ground-state absorption transition terminating on it. The solid arrows at left indicate the laser transitions demonstrated for crystalline hosts, and the hatched arrows at right are those reported for glasses.

Table 20 Energy Gap to Next Lower Level for States of Tm 3⫹ State 3

F4 H5 3 H4 3 F3 3 F2 1 G4 1 D2 3

Energy gap (cm ⫺1) 5400 2250 4150 1750 550 5950 6450


93

2.4.2 Emission Properties Transition Originating on the 3 F 4 Level As seen in Figure 49, the 3 F 4 → 3 H 6 transition peaks near 1850 nm and produces an extremely wide, featureless emission band that provides a broad tuning range for lasers and a wide optical bandwidth for amplifiers. Figure 47 shows that the 3 H 6 → 3 F 4 absorption band is similarly broad. A comparison with the 4 I 15/2 ↔ 4 I 13/2 transitions of Er 3⫹ suggests that this is a consequence of the larger number of Stark components in the Tm 3⫹ manifolds and slightly larger splittings. Silica fiber lasers have been operated at wavelengths ranging from 1700 [205] to 2056 nm [206]. The short-wavelength limit is significantly better than what has been achieved with crystalline lasers, possibly because the higher inversions obtainable in a fiber permit a three-level laser to be tuned further into the reabsorbing region. Although silica fiber lasers perform well on this transition, relaxation of the 3 F 4 level is predominantly nonradiative. As seen from Table 21, measured lifetimes τ obs range from 0.2 ms for solution-doped silica fibers [206] to 0.55 ms for a Li–Mg–Al silicate glass [202]. This compares with an estimated radiative lifetime τ rad of 3.4 ms [206]. Table 21 indicates that radiative lifetimes of oxide glasses tend to be shorter than those of fluoride glasses, with values of 1.7 and 3.3 ms for a tellurite and phosphate, respectively, obtained by Judd–Ofelt analysis [207]. The energy gap between the 3 F 4 and the 3 H 6 is in the critical interval for which the radiative and nonradiative rates are of the same order of magnitude for oxide glasses. The quantum efficiency of the 3 F 4 level falls in the 5–15% range for silica. By comparison, relaxation of the 4 I 13/2 state of Er 3⫹ is radiative in almost all glasses as a consequence of the gap being 1000 cm ⫺1 (⬃20%) larger. A further indication of this sensitivity may be the observations that, depending on the synthesis conditions, the 3 F 4 lifetime varies by a factor of 2 for silicate [202] and silica [206] glasses. This may result

Figure 49

3

F 4 → 3 H 6 emission band from Tm3⫹-doped ZBLAN (From Ref. 210.)

94

Table 21

Miniscalco 3

F 4 State Lifetimes Lifetime

Glass

τ obs (ms)

τ rad (ms)

Ref.

Silica Silica Li-Mg-Al silicate Tellurite Phosphate BIZYT ZBLALi ZBLAN ZBLAN ZBLANP

0.20 0.3–0.5 0.55

3.4

206 205 202 207 207 225 203 217 218 209,226

1.7 3.3 9.2 5.8 9.8 10.2 6.4

6.8

from differences in the local environment of the Tm 3⫹ ion, which lead to changes in electron–phonon-coupling strengths or different frequencies for the phonons involved in the relaxation process. In particular, a large reduction in quantum efficiency for some solution-doped silica fibers has been attributed to an oxygen deficiency in the glass [204]. The low quantum efficiency of the 3 F 4 for silica raises the threshold for lasers, but does not impair slope efficiency, because stimulated emission will dominate nonradiative relaxation once the laser has risen above threshold. The high nonradiative rate, however, seriously degrades the performance of small-signal amplifiers, particularly for three-level gain systems. This is confirmed by the extremely low gains obtained in the one amplifier experiment reported [208], and the low inversion is also expected to have a serious influence on the signal-to-noise ratio. As power amplifiers are intermediate between small-signal amplifiers and lasers, they should perform somewhat better if sufficiently saturated by the signal. For fluorides, the only other glass compositions investigated in any detail, the 3 F 4 level decays, radiatively. Table 21 reveals that the measured lifetimes are comparable with, or exceed, the calculated radiative lifetimes. The large variation in observed lifetimes for nearly identical fluorozirconate glasses may be a consequence of radiative trapping, which can occur for the 3 F 4, leading to artificially long lifetimes. Because the decay is completely radiative, a fluorozirconate fiber device directly pumped in the 3 F 4 state (⬃1650 nm) is expected to have a lower threshold as a laser and a higher figure of merit (dB/mW) than a small-signal amplifier compared with one made of silica. Exciting the 3 H 6 → 3 H 5 pump band at about 1200 nm should produce similar results because the 3 H 5 quickly relaxes to the 3 F 4. High-power diode lasers are not currently available for pumping at either of these wavelengths, however. Exciting the 3 H 4 at about 800 nm or any higherlying level will not provide efficient operation because the 3 H 4 is metastable and, as can be seen in Table 22 for ZBLALi, only about 12% of the excitation reaches the 3 F 4 state. This is similar to the situation encountered when pumping the 1500-nm transition of Er 3⫹doped fluorozirconates at the 980 nm or shorter-wavelength bands. Smart et al. obtained a significant improvement using stimulated emission to force the excitation to the 3 F 4 by simultaneously lasing on the 3 H 4 → 3 H 5 (2300-nm) transition, although the slope efficiencies obtained were still lower than those for silica fiber lasers [209]. Simultaneous lasing on the 3 H 4 → 3 F 4 (1480-nm) transition should serve the same purpose, although it was

95


Table 22

Transitions Originating on the 3 H 4 State Branching ratio β Lifetime

Glass Silica Tellurite Phosphate BIZYT ZBLALi ZBLAN ZBLAN ZBLAN ZBLANP

τ obs (ms)

τ rad (ms)

→3 H 6 805 nm

→3 F 4 1470 nm

→3 H 5 2300 nm

0.29 0.77 1.50 1.24

0.89 0.92 0.89 0.88

0.09 0.08 0.08 0.09

0.03 0.00 0.02 0.03

1.30

0.89

0.09

0.03

0.02

1.59 1.42 1.55 1.30 1.61 1.10

Ref. 209 207 207 225 203 216 217 218 209,226

employed by Allain et al. to enhance 1480-nm operation [210]. Smart et al. also proposed using high Tm 3⫹ concentrations to obtain quantum efficiencies greater than 100% through 3 H 4 ⫹ 3 H 6 → 3 F 4 ⫹ 3 F 4 cross-relaxation [209]. This process provides two excited ions for every absorbed pump photon. This technique has been effective for Tm 3⫹-doped crystalline lasers [211]. Ion–ion interactions are not expected to quench the 3 F 4 state unless the material contains impurities or is doped with another ion that serves as a trap. Cross-relaxation cannot occur because the 3 F 4 is the lowest excited state. Cooperative up-conversion is weak because the 3 H 4 level lies at significantly more than twice the energy of the 3 F 4, and it must proceed as a phonon-assisted, thermally activated process. This is confirmed by the effectiveness of the inverse process discussed in the foregoing, 3 H 4 ⫹ 3 H 6 → 3 F 4 ⫹ 3 F 4 cross-relaxation. Transition Originating on the 3 H 4 Level The decay of the 3 H 4 is dominated by nonradiative relaxation for silica because of the small energy gap between it and the 3 H 5 (see Table 20). The measured lifetime for silica is approximately 0.02 ms [209]. Although the radiative lifetime is not available for silica, radiative lifetimes of 0.3 and 0.8 ms have been calculated for a tellurite and a phosphate, respectively [207]. Table 22 indicates a trend similar to that observed in Table 21 for the 3 F 4 in which oxide glasses have significantly shorter radiative lifetimes than fluoride glasses. Because silica and phosphate have similar values of τ rad for the 3 F 4, we adopt the phosphate value for the 3 H 4 and find a quantum efficiency of close to 3%. Such a low number does not promise much gain for transitions originating on this level for silicate glasses at room temperature. In contrast, comparison of the measured lifetimes and the calculated radiative lifetimes in Table 22 indicates that decay is radiative for fluoride glasses. All three of the emission transitions from this state have been successfully lased using fluorozirconate glasses. This level has been efficiently pumped directly at the 800-nm absorption band although the limitations on population inversion discussed earlier for resonant (1480-nm) pumping of Er 3⫹ apply here as well. This level is susceptible to cross-relaxation if the concentration is high. The 3 H 4 → 3 H 6 transition has been operated as a three-level laser [210,212] and amplifier [213,214] over the range from 803 to 825 nm. From Table 22 it is seen that this

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transition dominates the radiative relaxation channels and should provide good performance as a laser or amplifier. By using the emission spectrum of Carter et al. [212] together with the lifetimes and branching ratios in Table 22, the peak stimulated emission cross section for this transition is estimated to be close to 6 ⫻ 10 ⫺21 cm 2 for fluorozirconates. Although the emission and absorption cross sections are comparable with those of Er 3⫹ at 1500 nm, the lifetime of the 3 H 4 is an order of magnitude shorter. Accordingly, one expects similarities between a 790-nm pumped Tm 3⫹ device at 810 nm and a 1480-nm pumped Er 3⫹ one at 1530 nm except that lasing threshold will be considerably higher and amplifier efficiency considerably lower. To date, 23-dB gain has been obtained for 50 mW of pump power [214]. The faster gain dynamics resulting from the shorter lifetime will also make amplifiers somewhat more prone to distortion and cross talk. Emission from the 3 H 4 → 3 H 5 in a ZBLAN glass is illustrated in Figure 50. This transition has been lased by several groups between 2250 and 2400 nm as bulk [215] and fiber [209,210,216] devices. It is of interest for filling in the gap between the 5 I 7 → 5 I 8 (⬇2080 nm) of Ho 3⫹ and the 4 I 11/2 → 4 I 13/2 (⬇2700 nm) of Er 3⫹. Although useful as a four-level laser, the low branching ratio for this transition seen in Table 22 implies that it will have very poor characteristics as a small-signal amplifier. Figure 51 depicts the 3 H 4 → 3 F 4 emission band for ZBLAN. This transition has been operated in the range 1460–1510 nm as a bulk [217] and fiber laser [209,210]. It is of potential use in covering the interval between the 1300-nm emission band of Nd 3⫹ and the 1500-nm band of Er 3⫹. From the low branching ratio for this transition seen in Table 22, one expects relatively low figures of merit for small-signal amplifiers. Because the lifetime of the 3 F 4 terminal level is longer than that of the upper level, this is commonly referred to as a self-terminating transition. It has been pointed out by Quimby and Miniscalco [156] that this does not necessarily preclude cw laser action. If the 3 H 4 is pumped either resonantly or at 660–680 nm using the 3 F 3, 3 F 2 levels above it, the criterion for cw lasing is

Figure 50

3

H 4 → 3 H 5 emission band for Tm3⫹-doped ZBLAN. (From Ref. 210.)


Figure 51

3

97

H 4 → 3 F 4 emission band for Tm3⫹-doped ZBLAN. (From Ref. 210.)

w 32 τ 2 ⬍ 1

(31)

where τ 2 is the lifetime of the 3 F 4 terminal state (level 2) and w 32 is the total spontaneous transition rate, radiative plus nonradiative, from the 3 H 4 upper state (level 3) to the terminal state. The pumping conditions specified ensure that all excitation is initially in level 3. Because every relaxation process from the 3 H 4 populates the 3 F 4 except for radiative decay directly to the ground state (level 1), one finds w 32 ⫽

1 ⫺ β 31 τ3

(32)

where β 31 is the branching ratio to the ground state. In general, the expression for w 32 will depend on the particular energy levels involved. However, if all the excitation originates in level 3 and level 2 is populated by only radiative transitions from level 3, a universal expression can be obtained: w 32 ⫽

β 32 τ3

(33)

By using the branching ratio and measured lifetime for ZBLANP from Table 22 in Eq. (32) and the corresponding observed lifetime from Table 21 for τ 2, one finds w 32 τ 2 ⫽ 0.64 and the criterion is satisfied. Indeed, cw lasing has been reported for this transition despite its apparent self-terminating nature [209,210]. The observations by Smart et al. are particularly convincing because there is no ESA from the 3 F 4 that may depopulate the terminal state for the 790-nm pump used [209]. Although the long lifetime of the 3 F 4 does not preclude cw lasing, it does degrade performance, and various techniques have been used to increase the population inversion. Changing the host to alter the lifetimes cannot improve the situation, for only the nonradiative rate can be significantly affected in this way. Table 20 indicates that the effective

98

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energy gap for the 3 H 4 is smaller than that for the 3 F 4, and thus the lifetime of the 3 H 4 is more sensitive to nonradiative relaxation. Simultaneous operation of the 3 F 4 → 3 H 6 transition removes population from the terminal state and has been successfully used to improve the performance of 1480-nm lasers [210]. Another approach is to co-dope with another ion that acts as a trap and depopulates the 3 F 4 through energy transfer. Improvements in laser performance were obtained by codoping with Tb 3⫹ [217], and Ho 3⫹ has shortened the 3 F 4 lifetime with minimal effect on the lifetime of the 3 H 4 upper state [218]. As discussed earlier, cooperative up-conversion cannot efficiently remove excitation from the 3 F 4 level. A technique that has proved extremely effective for Er 3⫹ in similar situations [162,163] is to pump the device at a wavelength for which there is strong ESA from the terminal state. In Figure 52 the energy levels of Tm 3⫹ are labeled with the wavelengths of the ESA transitions terminating on the energy levels that originate from the 3 F 4 and 3 H 4 states. A comparison of Figures 48 and 52 reveals that there is little possibility of simultaneously pumping the 3 H 4 and depleting the 3 F 4 with a single excitation wavelength. The only practical ESA transitions originating on the 3 F 4 that are not likely to overlap ones from the 3 H 4 are those to the 3 H 4 (⬃ 1410 nm) and 3 F 2 (1050 nm). Neither of these corresponds to a pump band because, as discussed later (see. Sec. 2.4.3), only silica can be pumped at 1050 nm. Nevertheless, a dual-pump wavelength scheme could be applied.

Energy levels of Tm 3⫹ in high fluorine content fluorophosphate glass labeled on the right by the wavelengths of the ESA transition to that level originating on the 3 F 4 and 3 H 4 states.

Figure 52

99


Transition Originating on the 1 G 4 Level Table 23 lists lifetimes and branching ratios from the 1 G 4 level. Comparing the measured lifetimes with the radiative lifetime [219] leads to a quantum efficiency of only 25–30% for silica. There may be a significant uncertainty in the radiative lifetime, however, because only four absorption bands were included in the calculation, and the number is significantly larger than values for the other oxide glasses in Table 23. An alternative procedure for estimating the quantum efficiency relies on a comparison to the 3 F 4 , which is known to have an efficiency of 5–15%. For all glasses, the radiative relaxation rate for the 1 G 4 is roughly an order of magnitude greater than for the 3 F 4 , whereas the larger effective energy gap seen in Table 20 leads to a lower multiphonon emission rate. On this basis, the decay of the 1 G 4 is expected to be completely radiative in fluoride glasses and largely radiative in silica, with a quantum efficiency exceeding 50%. As seen in Table 23, the largest branching ratio is to the 3 H 6 ground state, and this is the only transition for which gain has been reported using glass hosts [220,221]. The 1 G 4 → 3 H 5 (780 nm) might be expected to perform well as a laser or amplifier because it terminates on a short-lived state and has a high branching ratio. However, it overlaps a strong ground state absorption band, and this may explain the absence of any report of lasing on this transition. The 1 G 4 → 3 F 4 (650 nm) and 1 G 4 → 3 H 4 (1175 nm) transitions have branching ratios adequate to obtain good lasing characteristics, and operation has been reported at 650 nm for crystalline hosts [222]. Both transitions are apparently selfterminating for a fluoride glass, although the oversimplified criterion based solely on lifetimes is misleading. Application of Eq. (33) reveals that cw lasing is possible for both, with w 32 τ 2 ⫽ 0.7 and 0.2 for the 1 G 4 → 3 F 4 and 1 G 4 → 3 H 4, respectively. Although branching ratios for the 1 G 4 → 3 F 2 (1650 nm) and 1 G 4 → 3 F 3 (1550 nm) are extremely low, a crystalline laser at 1581 nm has been reported for the latter transition [222]. Because the performance of small-signal amplifiers is more sensitive to the branching ratio, only the transitions terminating on the 3 H 6 (475 nm), 3 H 5 (780 nm), and possibly the 3 H 4 (1175 nm) states are likely to be useful. Transition Originating on the 1 D 2 Level Given the short radiative lifetimes in Table 24 and the large energy gap seen in Table 20, the relaxation of the 1 D 2 is expected to be radiative for most glasses. Nevertheless, the Table 23

Transitions Originating on the 1 G 4 State Branching ratio β

Lifetime Glass Silica Silica Germanate Tellurite Phosphate Borate BIZYT ZBLALi

τ obs τ rad →3H6 (ms) (ms) 475 nm 0.26 0.22

0.67 0.63

0.86 0.57 0.18 0.38 0.38 0.89 0.68

0.50 0.47 0.50 0.47 0.44 0.46

→3 F 4 650 nm

0.07 0.02 0.15 0.07 0.09 0.07

→3 H 5 780 nm

0.30 0.36 0.23 0.33 0.34 0.33

→3 H 4 →3 F 3 →3 F 2 1175 nm 1500 nm 1630 nm

0.10 0.13 0.12 0.10 0.10 0.10

0.02 0.02 0.00 0.02 0.03 0.02

0.01 0.00 0.00 0.01 0.01 0.01

Ref. 221 219 227 207 207 227 225 203

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Table 24 Transitions Originating on the 1 D 2 State Branching ratio β

Lifetime Glass

τ obs τ rad →3 H 6 →3 F 4 →3 H 5 →3 H 4 →3 F 3 →3 F 2 →1 G 4 (µs) (µs) 365 nm 460 nm 515 nm 660 nm 755 nm 790 nm 1500 nm Ref.

Silica 6.5 Germanate 26.4 44.8 Tellurite 13.2 Phosphate 28.2 Borate 14.7 31.8 BIZYT 68.9 ZBLALi 55. 53.7

0.27 0.22 0.26 0.33 0.41 0.38

0.59 0.64 0.61 0.54 0.46 0.48

0.0 0.0 0.0 0.0 0.0 0.0

0.05 0.06 0.05 0.05 0.06 0.05

0.04 0.04 0.04 0.04 0.03 0.04

0.03 0.03 0.03 0.03 0.04 0.04

0.01 0.01 0.01 0.01 0.01 0.01

221 227 207 207 227 225 203

only lifetime measurement reported for silica yielded a surprisingly low value [221], although no calculated radiative lifetimes are available for comparison. The largest branching ratio is to the 3 F 4 (460 nm), a transition that has been lased for a ZBLAN fiber [220] and is classified as self-terminating. Employing Eq. (33), together with the 1 D 2 lifetime (τ 3 ⫽ 0.055 ms) and 1 D 2 → 3 F 4 branching ratio (β 32 ⫽ 0.48) from Table 24 for the similar ZBLALi composition, yields w 32 ⫽ 8700 s ⫺1. With this value and the 3 F 4 lifetime for ZBLANP (τ 2 ⫽ 6.4 ms) from Table 21, one obtains w 32 τ 2 ⫽ 56, indicating that this transition is truly self-terminating. Although the transition to the ground state has an appreciable branching ratio, a three-level ultraviolet laser is a difficult proposition for a crystalline host and is even less promising for a glass. Although the remaining transitions have very low branching ratios, a ZBLAN fiber laser has been reported for the 1 D 2 → 1 G 4 (1510 nm) [220]. Although application of Eqs. (33) and (31) reveals that this is not a true self-terminating transition, the 0.01 branching ratio renders it of little value for small-signal amplification. 2.4.3 Pump Wavelengths As with other rare earth ions that absorb weakly in the visible and near-infrared, significant improvements in performance for lamp-pumped, bulk Tm 3⫹ lasers were realized by codoping with other ions. The use of Yb 3⫹ and Yb 3⫹ /Er 3⫹ as sensitizers was particularly effective for Tm 3⫹-doped glass [202]. Laser excitation, however, largely eliminates the need for energy-transfer pumping. To obtain the best efficiency for directly pumped lasers and amplifiers, pump bands that overlap ESA bands should be avoided. Figure 52 suggests that for gain transitions originating on the 3 F 4 , the 3 F 4 → 3 F 2 , 3 F 3 (1050- to 1120-nm) ESA transitions may interfere with pumping the 3 H 5 at about 1190 nm, whereas the 3 F 4 → 1 G 4 (⬃635-nm) ESA transition may have an effect on pumping through the 3 F 2 , 3 F 3 states at 660-685 nm. The 3 H 4, which is metastable only in fluoride glasses, coincidentally also has ESA transitions at these wavelengths: 3 H 4 → 1 G 4 (⬃1120 nm) and 3 H 4 → 1 D 2 (⬃635 nm). Figure 47 reveals a strong GSA band near 800 nm with cross sections several times larger than those of Er 3⫹ at 800 nm. A further advantage of this band is that Figure 52 indicates it to be completely free from ESA. A variety of excitation sources, including diode lasers, have used this band to pump the 3 F 4 → 3 H 6 transition (1900 nm) for silica and fluorozirconate fiber lasers as well as all transitions originating on the 3 H 4 for fluorozirconate fiber lasers.


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Hanna et al. first demonstrated that a Nd:YAG laser can be used to pump 3 F 4 → H 6 (1900-nm) silica fiber lasers [223]. The moderate threshold, high-slope efficiency, and very high output powers (⬎1 W) obtained in later experiments confirm this as a practical approach to obtaining a high-power laser at about 2000 nm [224]. Although the 1064-nm output from a Nd :YAG laser is far from the 1200-nm peak of the 3 H 6 → 3 H 5 absorption transition, this band is broadened to shorter wavelength for the Ge silica fiber used and still has significant absorption at the excitation wavelength. It is not known, however, whether this technique can be used for any other glasses, because most have narrower pump bands. For Ge silica, the absorption cross section for Nd:YAG is approximately 10% of the peak value for this band [223]. By comparison, it is only about 0.5% for fluorozirconate glasses [203] and the fluorophosphate glass in Figure 47. For these compositions, pumping with Nd 3⫹ lasers is not possible. As expected from the preceding examination of Figure 52, pump ESA is observed, but it does not significantly degrade the performance if the 3 F 4 population is kept low by minimizing resonator losses [204,224]. It is expected to have a more serious effect on amplifiers, for these require higher inversions. From the GSA spectrum, one might expect that Nd 3⫹ lasers operating at longer wavelengths (e.g., 1080 or 1120 nm) might function as more efficient pumps. But Figure 52 suggests that ESA persists to wavelengths greater than 1100 nm, and this is expected to be an equally significant consideration in the choice of pump wavelength. The utility of pumping amplifiers with Nd:YAG lasers has yet to be determined. By using the peak cross section for this band in Figure 47 and the spectrum in [223], the absorption cross section at 1064 nm is estimated to be about 5 ⫻ 10 ⫺22 cm 2 for silica, placing it at the low end of those reported earlier for the weak 800-nm band of Er 3⫹. By analogy with 800-nm pumping of Er 3⫹, any significant amount of ESA would make Nd 3⫹ lasers unattractive as pumps for fiber amplifiers. Although ESA presents a problem for direct pumping, it is a valuable tool for upconversion pumping. Gomes et al. have exploited ESA in the 1000- to 1200-nm region to obtain gain on the 1 G 4 → 3 H 5 (⬇475-nm) transition pumping with a Nd:YAG laser [221]. The 1 G 4 was reached through a three-step process starting with excitation of the 3 H 5, which quickly relaxes to the 3 F 4, followed by an ESA transition to the 3 F 2 (see Fig. 52). The latter decays to the 3 H 4, which absorbs the third photon in the transition to the 1 G 4. Although the fiber was silica, the short lifetimes of the 3 F 4 and 3 H 4 played no role because 150-ns Q-switched pulses were used. The same process was observed by Hanna et al. using a cw Nd: YAG laser, although the up-conversion yield was estimated to be only about 10 ⫺5 for the relatively low powers (⬇1 W) used [219]. The excitation of the 1 G 4 was even more efficient when stimulated Raman generated by Q-switched, modelocked operation of a Nd :YAG laser was also used to pump the fiber [221]. This improvement is due to a better overlap between the Stokes bands at 1120 and 1180 nm and the GSA spectrum [221], as well as the increased ESA for 3 F 4 → 3 F 3 and 3 H 4 → 1 G 4 expected from Figure 52. The Q-switched, mode-locked operation of the Nd:YAG laser is even more important for up-conversion pumping of other glass hosts, because the narrower 3 H 6 → 3 H 5 absorption band renders the Stokes emission essential to the first step of the process. Emission from the 1 D 2 is also observed under both pulsed [221] and cw [219] excitation at 1064 nm. At low powers the intensity varies with the fourth power of the excitation [219], possibly indicating a continuation of the foregoing process through the absorption of a fourth photon in a transition up from the 1 G 4. Because 1064-nm photons have too much energy for the 1 G 4 – 1 D 2 gap and too little to reach the next higher level (1 I 6), the 3

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final step of the process might be expected to have a low probability. For energies above the 1 D 2, however, all glasses have a rising background of absorption from transitions to d levels and charge-transfer states, and these may provide sufficient absorption strength for the fourth photon. At high pump powers, the population of the 1 D 2 varies with the third power of the pump intensity under both pulsed [221] and cw [219] conditions. This behavior has been attributed to the saturation of one of the lower-lying excitation steps [219]. Unlike Er 3⫹, no up-conversion scheme has been found for Tm 3⫹ that provides efficient operation with the use of a single pump wavelength. This requires an overlap between a GSA and an ESA band, and when this condition is satisfied, it usually occurs for ESA transitions originating on both the 3 F 4 and 3 H 4. Accordingly, it is not possible to upconversion pump the 3 H 4 alone, because the process will proceed to populate the 1 G 4 and even the 1 D 2 as well. Allain et al. used a combination of the 647- and 676-nm lines from a Kr ion laser to populate the 1 G 4 and 1 D 2 levels in a ZBLAN fiber by a two-step process [220]. The 676-nm photons contribute most to the GSA transitions to the 3 F 3 and 3 F 2 levels (see Figs. 47 and 48), which decay to the 3 H 4 and 3 F 4 metastable states. As seen from Figure 52, the 647-nm photons are most important in the next step, which populates the 1 G 4 and 1 D 2 levels through ESA transitions from the 3 F 4 and 3 H 4 states, respectively. This process strongly favors excitation of the 1 D 2 , because the 3 H 4 decays radiatively for ZBLAN with only a small branching ratio to the 3 F 4 (see Table 22) and the integrated strength of the 3 H 4 → 1 D 2 transition is an order of magnitude greater than that of the 3 F 4 → 1 G 4 [207]. The actual magnitudes of the ESA cross sections at the excitation wavelengths also play a role. Hanna et al. have up-conversion pumped these levels for a silica fiber using a single excitation wavelength at 660 nm [219]. Despite the rapid nonradiative relaxation of the 3 H 4 , which puts nearly all the excitation in the 3 F 4 , fluorescence from the 1 D 2 still dominated the emission spectrum [219].

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226. Carter, J. N., R. G. Smart, D. C. Hanna, A. C. Tropper. cw diode-pumped operation of 1.97 µm thulium-doped fluorozirconate fibre laser. Electron. Lett. 26:599–601, 1990. 227. Reisfeld, R., Y. Eckstein. Dependence of spontaneous emission and nonradiative relaxations of Tm 3⫹ and Er 3⫹ on glass host and temperature. J. Chem. Phys. 63:4001–4012, 1975. 228. Bruce, A. J., W. A. Reed, A. E. Neeves, L. R. Copeland, W. H. Grodkiewicz, A. Lidgard. Concentration and hydroxyl impurity quenching of the 4 I 13/2 – 4 I 15/2 luminescence of Er 3⫹ doped sodium silicate glasses. In: Optical Waveguide Materials, vol. 244. M. M. Broer, G. H. Sigel, Jr., R. T. Kersten, H. Kawazoe, eds. Materials Research Society, Pittsburgh, 1992, pp 157–161.

3 Continuous-Wave Silica Fiber Lasers MICHEL J. F. DIGONNET Stanford University, Stanford, California

3.1 INTRODUCTION Rare earth doped glass and crystal fiber lasers were first investigated experimentally as early as the 1960s [1–3], then in the 1970s [4,5] and early 1980s [6]. Since their more recent emergence in 1985 [7,8], they have received considerable attention for numerous potential applications in optical communication, sensing, medicine, material processing, imaging, data storage, and laser ranging. The optical confinement provided by the fiber, combined with the excellent laser properties of trivalent rare earth ions, make this type of laser extremely efficient. They can operate with exceedingly low thresholds, as low as 100 µW, and yet can be pumped extremely hard to produce output powers in excess of 100 W, with optical conversion efficiencies greater than 50%. Furthermore, the numerous laser transitions available from trivalent rare earth ions lend them the ability to generate light over a wide selection of wavelengths, from the ultraviolet (UV) to the midinfrared (mid-IR), with broad tuning ranges. Pumped with a laser diode, they retain the advantage of compactness, low cost, and ease of large-scale manufacturing critical for many practical applications. Fiber lasers now compete directly in several domains with semiconductor sources, over which they present the advantage of high brightness, excellent mode quality, highly efficient coupling into a single-mode fiber, and a far superior wavelength stability with temperature. This chapter reviews an important class of fiber lasers, namely continuous-wave (cw) silica-based fiber lasers. The emphasis is placed on resonator configurations, theoretical performance, rare earth ion spectroscopy, and practical characteristics. In this last area, we focus on the wavelengths, tuning ranges, and energy conversions that have been achieved, in particular, the threshold, efficiency, and output power. These properties are reviewed for each of the seven rare earth ions tested to date in silica-based fibers: namely 113

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Figure 1 Wavelength ranges demonstrated in cw rare earth doped silica-based fiber lasers. neodymium (Nd 3⫹), erbium (Er 3⫹), ytterbium (Yb 3⫹), thulium (Tm 3⫹), holmium (Ho 3⫹), samarium (Sm 3⫹), and praseodymium (Pr 3⫹). Fiber lasers based on other glass hosts, in particular heavy metal glasses, are covered in Chapters 4 and 9. Fiber lasers operated in the Q-switched or mode-locked mode are described in Chapters 7 and 8, respectively. Spectral aspects of fiber lasers are reviewed in Chapter 5 (single-frequency fiber lasers) and in Chapter 6 (broadband fiber sources). To illustrate the importance of fiber lasers, Figure 1 shows the wavelength ranges demonstrated to date in rare earth doped silica-based fiber lasers. Samarium has produced the shortest wavelength (650 nm) [9–10], and thulium-sensitized holmium the longest (2260 nm) [11]. Some ions have been operated in several wavelength regions. Each bar in the figure represents the total range of wavelengths achieved with a particular ion, which may have involved different fiber lasers (with different fiber lengths, composition, reflectors, and such); it does not necessarily represent the tuning range demonstrated in a single fiber laser. In a given rare earth ion, fewer transitions are available than in a fluorozirconate glass fiber, and over a narrower range [12]. The reason is the higher phonon energy of silica, which makes low-energy transitions strongly nonradiative and laser operation above approximately 2.3 µm difficult with all rare earths. In spite of this limitation, more than 50% of the 650- to 2260-nm range has now been covered by rare earth doped silica fiber lasers. The broadest tuning range, observed with thulium, approaches 300 nm in a single fiber [13]. 3.2 OPTICAL RESONATORS FOR CW FIBER LASERS Several types of optical resonators have been used in cw rare earth doped fiber lasers, each with its own advantages and disadvantages. The most common resonator is the FabryPerot resonator (Fig. 2a–c). It is typically formed by placing miniature planar dielectric reflectors in intimate contact with the ends of the doped fiber (see Fig. 2a), which are either polished or cleaved perpendicular to the fiber axis. The pump beam is usually focused into the fiber through the high-reflecting mirror, which must be dichroic to transmit the pump.

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Figure 2 Schematics of various fiber resonators: (a) Fabry–Perot with dielectric reflectors; (b) Fabry–Perot with all-fiber reflectors; (c) Fabry–Perot with fiber Bragg gratings; (d) ring; and (e) Fox–Smith.

A variation of this design uses dielectric reflectors deposited directly onto the polished ends of the fiber [14]. The advantages are reduced coupling loss, increased mechanical and thermal stability of the cavity, and consequently, a higher output power stability. In lasers based on a high-gain transition, such as the 1.55-µm transition of Er3⫹, the dielectric reflectors can be eliminated altogether, and the weak Fresnel reflections at the fiber ends can provide sufficient optical feedback to reach oscillation. Another form is the all-fiber Fabry–Perot resonator (see Fig. 2b) [15]. The optical feedback is provided by two Sagnac fiber loops, one at each end of the doped fiber. Each Sagnac loop is made of a length of doped fiber closed by a coupler. The coupler can be

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one of several types of commercial devices, such as a fused fiber coupler. They exhibit a typical insertion loss of less than 0.3 dB, so that the loss of this resonator can be quite low. If the coupling ratio of the coupler is 50% at the laser wavelength, in the absence of nonreciprocal effects laser light entering one port of the loop exits at the same port (i.e., the loop acts as a high reflector). If the coupling ratio differs from 50%, at least some of the light exits at the other port. The loop now acts as a partial reflector, with a reflection coefficient that depends on the coupling ratio [15]. For example, if the coupling ratio is zero, all of the light exits at the other port: the reflection coefficient is equal to zero. Furthermore, if the coupler wavelength dependence is such that its coupling ratio is zero at the pump wavelength, pump light injected into the loop is transmitted by the loop. The device acts as a dichroic high reflector, and it can be used to efficiently inject nominally all of the pump power into the doped fiber. This dichroic character can also be used for laser wavelength discrimination. Other applications of the loop mirror are described in Chapter 8. A Fabry–Perot resonator can also be formed with fiber Bragg grating reflectors (see Fig. 2c) [16]. The grating is selected to reflect the laser light and transmit the pump. It can be either spliced to the fiber ends or, when compatible with the fiber composition, written directly in the doped fiber, which reduces the number of splices and hence the loss. A particular benefit of this configuration, as well as the configuration of Figure 2b, is that a fiber-pigtailed laser diode pump source can be spliced directly to the fiber laser, thereby reducing pump coupling loss. The reader will find discussions of other important aspects of this resonator in Chapter 5. In general, the length of the doped fiber is selected such that a high percentage of the pump power is absorbed. Residual unabsorbed pump power can be reflected back into the doped fiber. It increases the amount of absorbed pump power and the conversion efficiency, especially in three-level lasers. With the foregoing resonators, this can be accomplished by selecting an output coupler (the reflector farthest from the pump source) with a high reflection at the pump wavelength. Another important fiber laser resonator is the all-fiber ring resonator [8,17–21] (see Fig. 2d). It is easy to fabricate in practice by forming a loop with the doped fiber and a coupler, such as a low-loss fused fiber coupler. The pump light can be injected into the resonator either through the coupler, provided its coupling ratio is close to zero at the pump wavelength, or through an auxiliary WDM coupler placed in the loop. Because such a ring laser resonates in both directions and, therefore, has a bidirectional output, its conversion efficiency is only half as high as that of a Fabry–Perot cavity. This limitation can be removed by introducing an optical isolator in the ring, which forces unidirectional operation. Because an isolator adds a small loss, unidirectional ring fiber lasers tend to suffer from a higher threshold. As in a Fabry–Perot resonator, in a ring resonator the two counterpropagating signal waves interfere and produce a standing wave. The latter induces spatial hole burning in the fiber gain, which allows the oscillation of several longitudinal cavity modes. Here again an intracavity isolator can eliminate this effect and help narrow the linewidth. Ring configurations are in fact often used to produce single-longitudinalmode fiber lasers (see Chap. 5). Coupled rings have also been devised to select a single longitudinal mode [19]. A less commonly used, yet interesting fiber interferometer is the Fox–Smith resonator (see Fig. 2e) [22]. It consists of a standard Fabry–Perot resonator coupled, via a fiber coupler, to a third branch with a mirror at its end. The doped fiber is placed in one of the arms and pumped through one of the reflectors. This resonator acts as two coupled Fabry–


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Perot cavities, the first one involving arms 1 and 3, and the second one arms 1 and 4. As in other coupled resonators, this configuration supports enhanced resonance, and higher output power, at the wavelength that is resonant simultaneously with both resonators. Combined with an external grating, it has produced single longitudinal-mode operation in an Er-doped fiber laser [22]. 3.3 THEORY 3.3.1 Formalism Numerous theoretical models have been developed to simulate the gain of fiber amplifiers and the output of fiber lasers [23–32]. The general approach is similar to modeling bulk optic lasers; namely, by combining the laser rate equations, which describe the groundstate and excited-state electronic populations of the laser ions, with the equations of evolution of the pump power and laser signal power along the gain medium (labeled direction z). Consider first the case of a unidirectionally pumped fiber amplifier with a single signal injected into it at the same end as the pump (i.e., the signal co-travels with the pump) (Fig. 3a). This case is modeled by a system of three, coupled first-order differential equations in z: one for the pump power Pp (z), one for the forward signal power P ⫹s (z) (which comprises the signal being amplified and forward amplified spontaneous emission [ASE]), and one for the counterpropagating signal P s⫺ (z) (which comprises only backward ASE) [27,28,32]. This system is subject to three boundary conditions: (1) the pump power Pp (0) at the fiber input (z ⫽ 0) is equal to the known launched pump power P 0P; (2) the forward signal power P ⫹s (0) at the fiber input is equal to the known launched signal power P ⫹0 s ; and (3) the backward signal power P ⫺s (L) at the fiber output (z ⫽ L) is zero (since no signal is injected at this end). These coupled equations are integrated, for example, with the Runge–Kutta method, to obtain the evolution in z of the pump and signal powers. From this solution one obtains such quantities as the amplified signal power P ⫹s (L), the gain and noise figure of the amplifier, and so on. As described in Section 3.12.1, modeling has been further developed to include polarization effects, i.e., to track the evolution of the polarization of the pump and signals along the fiber [33–39]. Integration of the laser equations over the fiber cross section can

Figure 3 Schematic diagram of the pump, signal, and ASE power (a) in a fiber amplifier, and (b) in a fiber laser.

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also be included to take into account the spatial overlap between the optical modes and the dopant [32]. The difficulty in solving these equations exactly is that the boundary conditions apply to different ends of the fiber: two are at z ⫽ 0 and one at z ⫽ L. This is because at the outset the value of the backward ASE power P ⫺s (0) at z ⫽ 0 is unknown: all we know is that P s⫺ (z) starts from zero at z ⫽ L. As a result, to solve these equations one must resort to numerical integration. Furthermore, modeling the spectral dependence of the gain and ASE is essential in both fiber amplifiers and fiber sources. To do so, the gain spectral band is divided into n frequency components, usually equally spaced [32]. There are now two differential equations (one forward, one backward) for each component, or a total of 2n ⫹ 1 differential equations. For faithful spectral modeling, it is not uncommon to require n ⫽ 30 or more. Solving such a large system of coupled equations can be computer time-intensive, unless the root-solving algorithm is carefully optimized. The case of a fiber laser (see Fig. 3b) is treated in a similar manner, except that the boundary conditions are different. At z ⫽ 0, where a mirror of power reflectivity R1 reflects the backward signal in the forward direction, the boundary condition becomes P ⫹s (0) ⫽ R 1 P s⫺ (0). Similarly, at z ⫽ L the output coupler (reflectivity R 2) reflects the forward signal in the backward direction, and the new boundary condition is P ⫺s (L) ⫽ R 2 P ⫹s (L). The laser output P out is the fraction of P ⫹s (L) transmitted by the output coupler, or P out ⫽ (1 ⫺ R 2) P ⫹s (L). In recent years several companies have marketed fiber amplifier and laser computer simulators. These codes use as inputs the fiber, pump, and signal parameters (in particular, the core size; numerical aperture [NA]; dopant concentration; fiber length; signal and pump wavelength and input powers; emission and absorption cross sections; and excitedstate lifetime), and solve the foregoing system of differential equations numerically. Output files typically include the gain, ASE, and noise figure spectra when modeling an amplifier, and the output power curve when modeling a fiber laser. 3.3.2 Approximate Expressions Although powerful simulators are now widespread, approximate closed-form expressions are still beneficial to assess and model the key parameters of doped fiber devices. Such expressions were developed early for four-level fiber lasers [23]. Since then, many models have been published, mostly for amplifiers, with various levels of approximation [24– 32]. This section presents approximate expressions for the threshold and conversion efficiency of a fiber laser. These results are important, as they allow one to predict quickly the pump power required to reach oscillation and how effectively the gain fiber transforms absorbed pump photons into useful output photons. Gain One particular model investigated the simpler case of small-gain fibers [23,28,29]. This regime is adequate to model the threshold of most fiber lasers, because their cavity loss is generally low and the gain at threshold is consequently small. In this case ASE is small, its saturation effect on the gain can be neglected, and the coupled equations can be simplified and solved exactly. The fiber gain is then given by [28] g(L) ⫽ ⫺σ a N 0 η s L ⫹ (1 ⫹ γ s)

σ e τ 2 P abs F ξ ⫽ ⫺α ⫹ κP abs hν p A η p

(1)


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where N0 σe σa γs L τ2 hν p P abs A F ηp ηs ξ

⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽ ⫽

dopant concentration emission cross section absorption cross section σ a /σ e fiber length excited-state lifetime pump photon energy total pump power absorbed by the dopant fiber core area overlap between pump and signal mode profiles and dopant profile overlap between pump mode intensity profile and dopant profile overlap between signal mode intensity profile and dopant profile correction term

Equation (1) is general in that it can be applied to either a three- or a four-level laser by simply adjusting the factor γ s . The first term in Eq. (1), labeled α, represents the unsaturated ground-state absorption (GSA) at the laser wavelength. For a four-level laser, there is no signal GSA (σ a ⫽ 0) and γ s ⫽ 0. For a partially or purely three-level laser, signal GSA is finite and γ s approaches, or even exceeds, unity. The correction factor ξ in Eq. (1) accounts for pump excited-state absorption (ESA), and also contains a small correction term owing to ground-state depletion [28,29]. It can be easily evaluated with a simple analytical expression. In the absence of ESA, under most practical operating conditions ξ is between 1 (when the pump and signal wavelengths are very close) and ⬃1.2 (when they differ markedly; e.g., 1.55 and 0.5 µm) [29]. For all intents and purposes, approximating ξ by 1 introduces only a small error in the gain. For a four-level laser, ξ ⫽ 1 and Eq. (1) takes the simpler form derived earlier [23]. The fact that the laser medium is a waveguide is described mathematically in Eq. (1) by the spatial overlap integrals F, η s , and η p between the dopant distribution, the signal, and/or the pump mode intensity profile. These integrals can be calculated exactly through numerical integration, or approximately with simple expressions based on approximate gaussian modes [28,29]. Threshold At threshold, the round-trip fiber gain 2g(L) is equal to the round-trip loss δ 0 of the fiber laser cavity, which includes such contributions as the fiber scattering loss and the reflector transmission (but not signal GSA). From Eq. (1), the absorbed pump power P th required to reach threshold is thus given by: P th ⫽

α ⫹ δ 0 /2 κ

(2)

where κ is the gain term and α the unsaturated GSA term, defined in Eq. (1), and ξ th is the value of ξ at threshold (which again is close to unity). In a three-level laser with a low cavity loss, the gain must first overcome signal GSA (term α) to produce transparency. Additional upper-state population must also be induced to supply the small gain required to compensate for the remaining cavity losses (term δ 0 /2). In a three-level laser these

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losses are generally small compared with GSA, and most of the pump power required to reach threshold is needed to induce transparency. For a four-level laser, α ⫽ 0 and the threshold power [see Eq. (2)] becomes P th ⫽

δ0 2κ

(3)

The threshold power is simply the single-pass loss δ 0 /2 divided by the gain per unit pump power κ. In both three- and four-level fiber lasers, the threshold power depends on (1) the gain per unit pump power of the laser transition, (2) the round-trip cavity losses δ 0 , and (3) how strongly the pump, signal, and dopant are confined, which is entirely accounted for in κ. Thus, a lower threshold (for a fundamental-mode laser) is produced by reducing the core size and increasing the NA of the fiber [40], and by confining the dopant to the center of the core [31]. Slope Efficiency In a fiber laser operated above threshold, the signal intensity circulating in the cavity is such that it causes just enough gain saturation to reduce the round-trip gain to the value of the cavity round-trip loss. This intracavity signal intensity can be calculated exactly with the formalism outlined in Section 3.3.1. A more physical solution can be obtained by assuming that the intracavity intensity is constant along the fiber [28]. This approximation is excellent in a low-loss cavity, and thus applicable to many fiber lasers. In the absence of pump ESA, the output power P out of the fiber laser is approximately given by [23,28] P out ⫽

T 1 hν s (P abs ⫺ P th) δ 0 hν p

(4)

where hν s is the signal photon energy and T 1 the power transmission coefficient of the output coupler. Equation (4) states that above a sharp threshold, the output power grows linearly with absorbed pump power. The slope efficiency, defined as the output power divided by the power absorbed in excess of threshold P abs ⫺ P th , is simply s⫽

T 1 hν s δ 0 hν p

(5)

Equations (4) and (5) assume that the transition has a quantum efficiency Q of unity. If Q is less than 1, near threshold the slope is approximately multiplied by Q. However, as the laser is pumped higher above threshold, the probability of stimulated emission on the laser transition increases, and the net quantum efficiency increases. When the rate of stimulated emission relaxation becomes much higher than that of all other relaxation mechanisms, Q approaches unity and Eqs. (4) and (5) apply as written. Equation (4) is valid for either a three- or a four-level laser. Note that this approximate form, to first order, does not involve spatial overlaps, a result that has been confirmed by exact solutions for a four-level laser [23]. The slope efficiency is proportional to the ratio λ p /λ s of the pump and signal wavelengths. The physical reason is that the pump photon must be more energetic than the signal photon to be able to excite a laser ion above the upper laser-state level, and the difference in energy between them is wasted (usually in the form of phonons).


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In this chapter we refer to two kinds of laser efficiencies. The first one is the slope efficiency defined in Eq. (5). The second is the conversion efficiency, defined as the ratio of output power to absorbed pump power. This is the overall laser efficiency, which folds in both the threshold and the slope performance. In a fiber laser the slope efficiency is proportional to the ratio T 1 /δ0 of the output coupler transmission to the cavity round-trip loss (which includes T 1). A higher slope efficiency can be achieved by increasing the output coupler transmission [see Eq. (5)] at the cost of an increased threshold [see Eq. (2)]. As in other lasers, for a given pump power there is an optimum output coupler transmission that maximizes the output power, and thus the conversion efficiency. If the fiber loss is negligible, as is usual, most of the cavity loss δ 0 is due to the coupler transmission, i.e., δ 0 ⬇ T 1 and s approaches λ p /λ s. This is the quantum limit: one laser photon is emitted for every absorbed pump photon. Unlike in flashlamp-pumped lasers, such ideal conversions are possible and, in fact, have been demonstrated in fiber lasers. 3.4 SPECIALTY FIBERS FOR HIGH-POWER LASERS 3.4.1 Double-Clad Fibers Principle Silica-based fibers are excellent candidates for high-power fiber lasers for two basic reasons. First, they exhibit an extremely high optical damage threshold, and second, their high surface/volume ratio makes heat dissipation very effective. However, in a conventional fiber laser pumped with a laser diode the pump light is coupled into the fiber core, which imposes a major limitation on the maximum pump power that can be launched into the fiber. The reason is that efficient coupling of the laser diode output into the singlemode fiber core requires the use of a single-mode laser diode. The output power of such pump sources is currently limited by the damage threshold of the semiconductor material to a fraction of a watt, which seriously limits the maximum output power of the fiber laser. Furthermore, the efficiency with which the beam of a laser diode can be coupled into a fiber core is typically about 60% or less because of astigmatism of the laser diode beam, and only a fraction of the available pump power is usable. Because the power conversion of the fiber laser is lower than unity, the brightness of such a fiber laser is typically lower than that of the pump source. Several years ago Snitzer and co-workers demonstrated a clever solution to this problem. It involved what they called a double-clad fiber [41]. As illustrated in Figure 4a, it consists of a single-mode core surrounded by a first cladding of lower refractive index, itself surrounded by a second cladding of still lower index. The first cladding thus forms a second, highly multimoded waveguide. Only the core is doped with a rare earth ion. Pump light is now coupled not in the core but in the first cladding. As it travels down this cladding, pump light, which is distributed over a large number of modes, overlaps spatially with the doped core and is absorbed by the dopant. The outstanding benefit of this design is that because the area of the first cladding is typically 10s to 100 times larger than the core area, and because its NA is large, it becomes possible to inject into it a substantial fraction of the output power of a largearea laser diode, such as a laser diode array. Unlike a single-mode laser diode, a largearea laser diode can emit a very high output power, in excess of 100 W, but it exhibits

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Figure 4 Double-clad fibers: (a) basic configuration and its index profile. Various configurations designed to eliminate helical rays: (b) offset core, (c) rectangular cladding, (d) D-shaped cladding, and (e) scalloped cladding.

a low brightness and cannot be coupled efficiently into a single-mode core. With an efficient laser transition, such as the 4 F 3/2 → 4 I 11/2 transition of Nd 3⫹, a double-clad configuration transforms a substantial fraction of the pump power launched into the first cladding into a highly spatially coherent output, with a brightness that can be thousands of times higher than that of the pump source. The double-clad fiber laser, therefore, acts as a brightness converter: it efficiently converts the low-brightness, multimode light of a high-power laser diode into high-brightness, single-mode laser radiation. Another significant advantage is that the alignment tolerance in coupling to the large-area first cladding is typically tens of microns [42], rather than the submicron tolerance for coupling into a single-mode fiber core. The price for this increased pump coupling efficiency is an increase in fiber length. Because the spatial overlap between the pump and the dopant is small, the pump power absorbed per unit length is reduced compared with a core-pumped fiber, and a longer fiber is required to excite the same total number of dopant ions. This length increase depends on the core/cladding area ratio, and on the design of the fiber profile, but it is typically tenfold or more. In a four-level transition, where GSA is nonexistent, this length increase results in a negligible increase in the laser absorption loss and, therefore, in the threshold. These points are well illustrated by a thorough experimental study of the dependence of the threshold and slope efficiency on fiber length in a double-clad Nd-doped fiber laser


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[42]. However, in a three-level transition GSA is substantial and the fiber length increase results in a large increase in signal absorption loss and threshold. Double-clad fibers, in general, are not effective for three-level transitions. Cladding Shape Optimization A large body of literature now exists on the theoretical investigations and design of doubleclad fiber profiles to optimize power transfer per unit length from the pump to the dopant [43–47]. One of the first difficulties that was encountered is that if the first cladding has a circular cross section, only the HE 1m family of modes has intensity at the center of a fiber [48]. Most of the pump is launched as helical rays, which miss the core. A first solution is to offset the core from the center of the first cladding [41,49], as illustrated in Figure 4b. In one measurement involving an Nd-doped fiber, when the core was centered on the cladding the pump absorption was only 5% of what it would be if the same amount of dopant was uniformly distributed across the first cladding. By offsetting the core to near the edge of the first cladding, the pump absorption increased to 28% [49]. This result emphasizes the importance of a high dopant concentration in a double-clad fiber. If the dopant concentration is too low, the fiber length required to absorb a sizable fraction of the pump power will be hundreds of meters, which means a prohibitively high scattering loss and threshold. By using a core glass composition that tolerates higher quenching-free rare earth concentrations, and by properly designing the cladding/core area ratio, most of the pump power can be absorbed in a few to tens of meters of fiber. A second solution is to alter the shape of the first cladding. Almost any shape but circular supports modes that fill the multimode cladding. Rectangular, D-shaped, and scalloped claddings have been proposed and evaluated (see Figs. 4c–e) [44,47,50]. In a Dshaped cladding, the helical rays are coupled to the meridional rays and all pump rays pass through the core [47]. It was pointed out early that a rectangular shape is particularly attractive because it matches the output pattern of a multiple-stripe laser diode, thereby minimizing the area of the first cladding and thus the required fiber length [49]. Subsequent simulations showed that both a rectangular and a D-shaped cladding can provide a pump absorption in excess of 90%, or over one order of magnitude larger than a circular cladding [47]. Helical pump rays have also been reduced by inducing mode mixing, via bending the fiber [44,45,51,52] or mode scrambling [53]. A particularly effective design involves bending the fiber in a kidney-shaped geometry [45]. Theoretical studies of the absorption efficiency of various double-clad fiber profiles as a function of fiber length and bend radius are available [44,45]. Another important design consideration is the NA of the cladding, which should be as high as possible to capture as much of the high-divergence pump light as possible. For silica-based fibers with a second cladding made of glass, the NA is limited to approximately 0.4. Higher NAs can be achieved if the second cladding is made of a low-refractive–index polymer. NAs as high as 0.6 have thus been achieved [50]. Alternative Pump-Coupling Techniques A few interesting alternative techniques have been developed to couple pump light into a double-clad fiber. One of them is side-pumping with a prism (Fig. 5a) [54,55]. If the second cladding is made of a polymer, such as silicone, it can be locally stripped. A prism of appropriate angle is clamped against the exposed first cladding and pump light is coupled through the prism into the cladding. This method has proved to transfer the pump power to the core quite effectively [54]. It has also been applied to launch pump light at

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Figure 5 Alternative side-coupling methods to inject pump light in a double-clad fiber, using (a) a prism (from Ref. 54); and (b) a V-groove (from Ref. 59).

two different locations simultaneously into the same fiber [55]. However, experimental measurements in a Ho/Tm-doped fiber laser showed that core pumping is still the most efficient method [56]. Cladding pumping produced a higher threshold (by a factor of ⬃2.3) and a lower slope efficiency (by ⬃43%) than core pumping. Side pumping yielded the same threshold as cladding pumping, but a still lower slope efficiency (by ⬃18%). A second method was developed specifically to couple light from a high-power laser diode bar [57,58]. It uses a bundle made of a large number of multimode fibers, arranged at one end into an array shaped to match the laser-diode emitting area; for example, a linear shape for a long and thin laser diode bar. The pump light is coupled into the bundle with a cylindrical lens. At the output end of the bundle, the fibers are arranged into a twodimensional cross section matched to the double-clad fiber pump cladding. A third method, demonstrated with a 1.5-µm Er/Yb fiber amplifier, consists in polishing a V groove into the side of the pump cladding (see Fig. 5b) [59]. Pump light is focused onto a polished face of the groove and reflected by total internal reflection into the pump cladding. Similar to prism coupling, V-groove coupling leaves the fiber ends free (and available, e.g., for splicing). Also, it enables pump injection at multiple points along the fiber. Using a V-groove coupler, as much as 76% of the output power of a laser diode array was coupled into a pump cladding [59]. For reference, side pumping using a multimode fiber coupler has also been reported [60]. Current Status Since their inception, double-clad fibers have produced lasers with several rare earth ions, including Nd 3⫹, Yb 3⫹, and Tm 3⫹, as reviewed in the following sections. This effort has


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resulted in successively more impressive reports of rapidly increasing fiber laser output powers, from the original tens of milliwatts to the current record of 110 W in a Yb-doped fiber laser [61]. Double-clad fiber lasers with output powers in the 10- to 20-W range have already reached the commercial market and are finding practical applications. 3.4.2 M-Profile Fibers Another type of fiber developed more recently to alleviate fiber breakdown and thus increase the output power of fiber lasers is the M-profile fiber. First described by Marcuse and Mammel in 1973 [62], it has a large multimode core, typically tens of microns across, surrounded by a thinner cladding ring, itself surrounded by an outer cladding or a coating. The main difference with a standard fiber is that the core has a lower index than the cladding ring, whereas the outer cladding has a lower index than the core, so that the index profile resembles the letter M, as illustrated in Figure 6. Glas and co-workers were first to report the use of this waveguide as a fiber laser [63]. Only the cladding ring is doped with a rare earth, and the pump light is guided by the highly multimoded core ring, whereas the laser light is guided by the cladding ring alone [63]. With suitable selection of the ring’s thickness and NA, the ring supports only radially fundamental laser modes [62]. The primary benefit of the M-profile fiber laser stems from the fact the laser mode area is considerably larger than in a double-clad fiber. It means that, in principle, a laser output power up to about two orders of magnitude higher than in a double-clad fiber can be accomplished before the onset of damage [63]. For the same reason, the saturation power is comparably higher. A further advantage is that the spatial overlap between the pump modes and the ring (where the signal and the dopant are confined) is quite high for a wide spectrum of pump modes, as shown by theoretical evaluation of modal overlaps [64]. Thus pump absorption is almost complete over much shorter lengths than in a doubleclad fiber. If need be, the dopant profile can also be tailored to reduce this overlap, thus increasing the output power without increasing gain saturation [63]. On the other hand, because of the large diameter of the ring, the output brightness is reduced [64]. An example of an experimental M-profile fiber laser is described in Section 3.5.4. 3.4.3 Other High-Power Fiber Laser Designs Two other approaches for generating high powers in fiber lasers have been reported. The first one utilizes a fiber with multiple cores distributed in a ring along the outer edge of a first cladding of lower index, which is itself surrounded by a cladding of lower index

Figure 6 Schematic diagram of an M-profile doped fiber. (From Ref. 63.)

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[65]. The main geometric difference with the M-profile fiber is that the continuous ring of the latter is replaced by a ring of adjacent single-mode cores. Pump light is coupled into and guided by the first cladding, and absorbed by the rare earth dopant of the core. This design also provides a stronger pump absorption per unit length than a double-clad fiber, and a possibly greater mode stability than the M-profile fiber. It has produced a 1050-nm Nd-doped fiber laser with a 450-mW output and 40% slope efficiency [65]. Another approach, which has not yet produced a diffraction-limited output, involves a bundle of many (100s to over 1000) single-mode or multimode doped fibers [66,67]. It can be either end-pumped with a laser or flashlamp pumped and can produce high cw powers. These two types of fiber lasers may find applications in remote sensing, in power transmission in space, or as high-power, phase-locked lasers. 3.4.5 Thermal Issues With the recent availability of very high power cw laser diode arrays, the output of highpower fiber lasers is often limited by breakdown of the core region due to high laser intensity. This problem can be alleviated by using a larger, slightly multimoded core, which reduces the intensity. Although it is then generally difficult to maintain the fundamental (LP 01) core mode, with special care and design few-mode fibers can carry almost exclusively the fundamental mode over sizable distances. This approach is particularly useful in high-peak–power mode-locked fiber lasers (see Chap. 8). Other solutions are the M-profile and multiple-core fibers described in Sections 3.4.2 and 3.4.3. Another major limitation is heat, which is generated by phonons induced by the pump via at least three mechanisms. First, the difference in energy between a pump photon and a laser photon is dissipated as heat by nonradiative relaxation from the pump band to the metastable level. Second, if the quantum efficiency of the laser transition is less than unity a fraction of the excited electrons decay at least partially by nonradiative relaxation. Third, in the presence of cross-relaxation processes nonradiative relaxation between ions also causes heating. The first mechanism is always present, even under the best possible scenario. The fraction η of absorbed pump power that is turned into heat is, therefore, at least (1 ⫺ λ p /λ s) [43]. The temperature radial distribution in a pumped fiber has been derived theoretically [43,68]. The dynamic regimes of cw and pulsed pumping have also been investigated [68]. The fiber temperature rise can be quite large. For example, in a 1060-µm Nd-doped silica fiber pumped at 800 nm, the fraction η (in the absence of crossrelaxation) is ⬃25%. If a 1-m length of doped fiber absorbs 10 W of pump power, and if it is cooled only by natural convection (i.e., it is just resting in still air), using Eq. (26b) of Ref. [68] the fiber temperature rise at steady state is predicted to be ⬃78°C. In a 1.55µm Er-doped silica fiber laser pumped at 1.48 µm, for which λ p is much closer to λ s and η is thus much smaller (⬃4.5%), for the same length and pump power, this figure drops to 14°C. These thermal effects can be greatly reduced by reducing the dopant concentration and increasing the fiber length, although at some point nonlinear effects become troublesome. If strong enough, pump-induced heating can cause a number of serious problems, from internal stress due to thermal expansion of the glass which, in turn, can result in fractures, to melting of the glass, and thermal lensing. Heating can also decrease the quantum efficiency, although this is generally a smaller effect. For example, for the 4 F 3/2 → 4 I 11/2 transition of Nd 3⫹, the quantum efficiency was predicted to drop by only 6% for a 300°C temperature increase from room temperature. Theoretical models have been devel-


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oped to predict the heat distribution [43,68,69], stress distribution [43,69], and thermal lensing [43] in pumped fibers. They confirm that fiber lasers can operate with negligible to minimal thermal problems up to tens of watts. They also predict that critical attention will need to be paid to fiber design and cooling in upcoming multi–100-W fiber lasers. In high-power lasers, thermal problems can also arise from the material surrounding the fiber, such as polymer jackets or bonding agents (when the fiber is glued into a capillary tube for end-polishing purposes). Under the impact of a multiwatt pump beam, these materials can either suffer thermal damage or simply expand and cause undesirable motion of the fiber and thus spoil the pump input coupling. Care must be taken in practice to select these materials judiciously, or to strip them back a few centimeters from the fiber end [70] to reduce the pump intensity to which they are exposed. 3.5 NEODYMIUM 3.5.1 Absorption Properties Several pump wavelengths have been successfully used to demonstrate cw oscillation in Nd-doped silica fiber lasers, in particular 514.5-nm (Ar-ion laser), 752-nm (Kr-ion laser), around 595-nm (dye laser), and around 810-nm (Tables 1 and 2). The latter wavelength is the most practical because it falls within the emission band of AlGaAs semiconductor lasers. As shown in the energy level diagram of Nd 3⫹ (see Fig. 10 of Chap. 2), this pump band corresponds to the 4 I 9/2 → 4 F 5/2 transition. For an Nd-doped aluminosilicate glass, its absorption spectrum is quite broad (see Chap. 2), a feature that relaxes the requirements on pump wavelength and its stability with temperature over Nd-doped crystals. In a fiber of this material doped with a practical Nd 3⫹ concentration of 9 ⫻ 10 18 /cm 3 (⬃0.11 wt% Nd), the values of the absorption coefficient reported in the literature range from 1.2 [14] to 8 dB/m [75]. It means that a fiber length of only a few meters is sufficient to absorb most of the launched pump power. However, silica fibers containing 28 wt% P 2 O 5 have been doped with as much as 1 wt% Nd. They require about one-tenth the length to absorb the same power [79]. This work shows that Nd-doped silica-based fiber lasers can be made with short lengths of fiber. 3.5.2 Fluorescence Properties Although laser oscillation has been demonstrated for dozens of transitions in many of the trivalent rare earth ions, special attention has been given to Nd 3⫹ and Er 3⫹. This is partly because of the early history of the development of glass lasers, which focused on these efficient ions, and partly because of their laser wavelengths, which coincide with the second and third communication window, respectively. The spectroscopy of Nd 3⫹ is well known, and it has been studied in hundreds of glass compositions [82]. The basic properties of selected Nd-doped glasses are discussed in Chapter 2. The three fluorescence transitions demonstrated in Nd-doped silica fiber lasers are illustrated in Figure 10 of that chapter, including the main 4 F 3/2 → 4 I 11/2 transition near 1.06 µm. The quantum efficiency for fluorescence of rare earths in glasses can be limited by cross relaxation (or up-conversion) between ions. This mechanism, often referred to generically as quenching, is well understood in Nd 3⫹ [83]. As illustrated in Figure 7 of Chapter 2, when an ion in the excited state (the donor) is in close proximity to an ion in the ground state (the acceptor), the donor can give a part of its energy to the acceptor. The donor thus relaxes to the 4 I 15/2 level, whereas the acceptor is excited to the 4 I 15/2 level.

0.5 wt% Nd 2 O 3 50 ppm Nd 300 ppm Nd 300 ppm Nd 1200 ppm Nd 0.5 wt% Nd 2 O 3 300 ppm Nd 0.5 wt% Nd 2 O 3 150 ppm Nd 300 ppm Nd 300 ppm Nd NAc 3 wt% Nd 1 wt% Nd 3 O 3

NAc 514.5 nm 590 nm 590 nm 823 nm 807 nm 822 nm 807 nm 0.83 µm 820 nm 595 nm 514.5 nm 815 nm 752 nm

905nm 980 ⬃920 937 nm 938 nm 1.06 µm 1.06 µm 1.06 µm 1.088 µm 1.088 µm 1.078 µm ⬃1.1 µm 1.363 µm 1.362 µm

b

With respect to absorbed pump power. LD, laser diode. c NA, data not available. i With respect to incident pump power.

a

Neodymium concentration

Pump wavelength

Laser wavelength 5 cm 4m 1m 1m 1.1 m 5 cm NA ⬃14.5 cm 10 m 2m 70 cm ⬍3 m 10 cm 20 cm

Fiber length NAc Ar-ion laser pump Dye laser pump Dye pump LD pump LD pump Dye laser pump Pb-doped/LD pump LD pump LD pump Ring laser/dye pump Ring laser/Ar-laser P-doped/LD pump Kr-ion laser pump

Other features b

Table 1 Characteristics of Representative cw Nd-Doped Silica Fiber Lasers

4.3 mW c 7.5 mW d 8 mW d 8 mW d 1.9 mW d 90 µW d 1.3 mW d 2.15 mW d 1.5 mW d ⬃100 µW d ⬃6 mW d 1.45 mW d 5 mW d 67 mW d

Threshold NAc 2.6% 7.6% 7.1% 36% ⬃29% 59% 59.2% 55% NAc ⬃14% 9.2% 10.8% 0.95%

Slope efficiency a

NAc 0.18 mW @ 14.3 mW 3.4 mW @ 53 mW 3.2 mW @ 53 mW 3 mW @ 10.2 mW 0.2 mW @ 0.84 mW 18 mW @ 32.5 mW 4.6 mW @ 10 mW 4.1 mW @ 8.9 mW NAc 2 mW @ ⬃20 mW 0.47 mW @ 6.5 mW 3.5 mW @ 38 mW 1.9 mW @ 265 mW

Output power at max. absorbed pump power

71 72 73 74 75 71 76 77 14 8 8 17 78 79

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830 nm ⬃807 nm 805 nm 807 nm 808 nm 807 nm 810 nm 815 nm 810 nm 810 nm 809 nm 802 nm 805 nm 804 nm

1087 mn 1.06 µm 1.06 µm 1.06 µm 1057 nm 1.06 µm ⬃1.07 µm ⬃1.06 µm 1.06 µm 1.065 µm 1.06 µm 1054 nm 1050 nm 1050 nm

Fiber length 30 m 6m 11 m 20 m 1.8 m 45 m NA 60 m 10 m 80 m 6m 7 cm 1.9 m 40 cm

Neodymium concentration ⬃700 ppm Nd 0.5 wt% Nd 2 O 3 0.7 mol% Nd 0.26 wt% Nd 3 wt% Nd 0.2 wt% Nd 1300 ppm Nd 0.26 mol% Nd 0.7 mol% Nd 0.13 mol% Nd 0.7 mol% Nd 10 20 Nd/cm ⫺3 0.13% Nd 3 O 3 2 ⫻ 10 19 Nd/cm ⫺3 DCF/LD pump DCF/LD array pump DCF/Ti :sapphire pump DCF/LD pump DCF/LD array pump DCF/LD bar pump DCF/9 LDs pump/MM DCF/LD array pump DCF/LD pump DCF/LD array pump MPF/SP/LD pump MPF/LD array pump MPF/LD array pump Multicore fiber/LD/MM

Other features ⬃27 mW (a) ⬃22 mW (i) 79 mW (a) 70 mW (1) ⬃75 mW (i) ⬃70 mW (i) ⬍10 mW (l) ⬃0.3 W (l) 10.9 mW (a) ⬍2 W (l) 10.4 mW (a) 0.38 W (i) ⬃4 W (l) ⬃0.8 W (i)

Threshold 27% (a) ⬃25% (i) 25% (a) 31% (1) 34.7% (i) 51% (i) 26% (l) 40% (l) 36% (a) 46% (l) 66.3% (a) ⬃3% (i) ⬃54% (l) 39% (i)

Slope efficiency

NA, data not available; DCF, double-clad fiber; LD, laser diode; MM, multimode; MPF, M-profile fiber; SP, side pumped. (i) With respect to incident pump power; (l) with respect to launched pump power; (a) with respect to absorbed pump power.

Pump wavelength

Characteristics of Representative Double-Clad and M-Profile cw Nd-Doped Silica Fiber Lasers

Laser wavelength

Table 2

51 mW @ 215 W (a) 120 mW @ 0.5 W (i) 288 mW @ 1.2 W (a) 0.75 W @ 2.5 W (1) 1.07 W @ 3.16 W (i) 5 W @ 9.8 W (i) 9.2 W @ 35 W (l) 14 W @ 33.5 W (l) 15.9 W @ 55 mW (a) 32.7 W @ 72 W (l) 3.9 mW @ 16.3 mW (a) 10.3 mW @ 0.71 W (i) 9.1 W @ 20.8 W (l) 515 mW @ 2.14 W (i)

Output power @ max. pump power

80 49 54 43 81 58 51 47 42 45 55 63 64 65

Ref.

Continuous-Wave Silica Fiber Lasers 129

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Because the 4 I 15/2 level is strongly coupled to the ground state by nonradiative interaction, both ions then relax quickly to the ground state. This process (energy transfer followed by relaxation) is typically much faster than the radiative lifetime of the excited state 4 F 3/2. Furthermore, because it leads to the loss of one excited electron without the generation of a stimulated photon, it constitutes a pump loss mechanism. In other words, quenching increases the rate of nonradiative relaxation from the excited state; i.e., it reduces the quantum efficiency. The rate of this process increases with increasing rare earth concentration; in heavily doped samples, it can be much faster than the radiative relaxation [84]. In all rare earth doped glass fibers, quenching limits the maximum concentration that can be achieved before a significant reduction in quantum efficiency takes place. For multicomponent silicate or phosphate glasses, the neodymium ions are generally homogeneously dispersed in the host and concentrations in excess of 7 ⫻ 10 19 ion/cm 3 are readily obtainable without concentration quenching. However, for SiO 2 or GeO 2 –SiO 2 hosts the limit of solubility is relatively low, typically 10 17 –10 18 ion/cm 3. The result is a tendency for quenching even at concentrations as low as a few hundred parts per million (ppm). If clustering is important, the transition can be so severely quenched as to generate virtually no fluorescence signal. The addition of P 2 O 5 or Al 2 O 3 substantially improves the solubility of Er 3⫹ and Nd 3⫹ in these glasses. It is a common approach to increase the rare earth concentration in silica-based fibers (without reducing the quantum efficiency) and reduce the fiber length requirement. The fluorescence lineshapes and peak wavelengths of Nd 3⫹ depend strongly on the co-dopants present in the silica host. For low Nd concentrations in silica or germanosilicate glass, the peak wavelength of the 4 F 3/2 → 4 I 11/2 transition is around 1088 nm. The addition of a few mole percent of aluminum shifts this peak down to the vicinity of 1064 nm. It can be shifted even farther, to around 1054 nm, with the addition of a few mole percent of phosphorus. The peak fluorescence shifts also from 1135 nm for pumping at 834 nm to 1064 nm for 806-nm pumping [71,85]. In contrast, with phosphorus co-doping, no shift is observed in peak position or fluorescence lineshape for pump wavelengths between 805 and 850 nm [85]. 3.5.3 Gain Properties of Nd-Doped Fiber Lasers An Nd-doped fiber laser operated around 1.06 µm is a four-level laser; there is no GSA at the laser wavelength. As a result, the internal gain is positive even for a vanishingly small pump power, and the threshold power can be very low. An important parameter for an Nd-doped fiber laser is the gain efficiency κ [see Eq. (1)]. For an Nd-doped silica core co-doped with Al, an NA of 0.15, a core radius a ⫽ 2 µm, and a pump at 807 nm, the measured gain efficiency at 1.06 µm was 0.47 dB/mW [71]. The gain coefficient expected from theory, given by Eq. (1) with, for this fiber, a calculated overlap F/η p ⫽ 0.772, σ e ⫽ 1.0 ⫻ 10 ⫺20 cm 2 [86], and the measured value of τ 2 ⫽ 400 µs, is 0.43 dB/mW, in good agreement with the measured value. In Nd-doped silicate fibers of various compositions pumped at about 830 nm, the measured κ ranged from 0.27 to 0.55 dB/mW [40]. In a fiber with a stronger optical confinement, modeling predicted that the gain efficiency could be as high be 1.1 dB/mW [40]. These values are not nearly as high as for the 1.55-µm transition in Er-doped silica fibers, but they are nonetheless substantial. For threshold to be reached in a fiber laser, the gain needs to equal only the generally low cavity loss. For a typical fiber laser cavity loss of 10% and a κ of 0.5 dB/mW, the absorbed pump power required to reach threshold is about 1 mW.


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3.5.4 Nd-Doped Fiber Lasers at About 1.06 ␮m Single-Mode Fibers The first reported rare earth doped glass fiber device fabricated with MCVD technology was an Nd-doped fiber laser operated at 1088 nm [8]. It consisted in a 2-m germanosilicate fiber doped with about 300 ppm of Nd 3⫹, with ends cleaved and butted against dielectric reflectors. The reflectors had a high reflectivity at 1088 nm and a high transmission at the 820-nm pump. The fiber loss at 1088 nm being only approximately 4 dB/km, the resonator round-trip loss was very small, and the laser could be pumped with a low-power singlestripe AlGaAs laser diode. The threshold was remarkably low, about 100 µW of absorbed pump power [8]. Another 1.06-µm fiber laser with a comparable threshold (90 µW) [71] used the fiber with the gain coefficient of 0.47 dB/mW mentioned in Section 3.5.3. This value suggests a round-trip loss of only ⬃2 ⫻ 0.47 ⫻ 0.09 ⫽ 0.085 dB (⬃2%) probably dominated by the residual transmission of the reflectors. This laser could also oscillate at about 0.9 or 1.4 µm by changing the reflectors [71]. The characteristics (threshold, output power, and slope efficiency) of this laser, as well as other fiber lasers discussed in the rest of this section, are summarized in Table 1. Note that in this table and in all the tables of this chapter, rare earth concentrations are listed as they are found in the original reference. Given that concentration units are often insufficiently specified (e.g., as to whether they refer to the rare earth or to its oxide), no attempt was made to convert them to a common unit. Figure 7 shows the output power curve of a highly efficient 1.06-µm Nd-doped fiber laser pumped at 822 nm [76]. As predicted by theory, above threshold (1.3 mW) the output power grows linearly with absorbed pump power. The slope of this curve, or slope efficiency, was 59%, compared with a maximum possible efficiency of 822/1060 ⬇ 77%.

Figure 7 Output power curve of a 1.06-µm Nd-doped fiber laser pumped with a dye laser at 822 nm. (From Ref. 76.)

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The conversion efficiency was 55.4%, which is the highest reported value for an Nddoped fiber laser. A similar result was obtained by Shimizu et al. in a 1088-nm Nd-doped silica fiber laser, with dielectric mirrors deposited directly on the fiber ends [14], which produced a cavity with a very small excess loss. With an optimized length of 10 m and an 830-nm laser diode pump, their laser exhibited a threshold of 1.5 mW. The output power was 4.1 mW for an absorbed pump power of 9 mW, and the slope efficiency 55% (the maximum possible efficiency was 0.83/1.088 ⫽ 76.3%). (The quantities listed for both lasers refer to absorbed pump power). These high efficiencies show that both fiber lasers operated with a quantum efficiency close to unity, i.e., the number of output photons approached the number of absorbed pump photons per unit time. As pointed out in Section 3.5.2, the laser wavelength is expected to depend on the host composition. One of the first demonstrations of this effect was reported by Stone and Burrus [4]. Since then, the wavelength of a cw Nd-doped silica fiber laser was observed to shift from 1090 nm in a germanosilicate-core fiber to 1057 nm when a high concentration of P 2 O 5 was added to the core [87]. The wavelength also depended on the Nd concentration [88]. This effect points out a useful practical means of tailoring the laser wavelength, as well as the need to control the glass composition to manufacture sources with a reproducible wavelength. Relaxation oscillations are almost a hallmark of the transient response of lasers with long (⬃ms) fluorescence lifetimes [2]. The relaxation oscillation frequency has been used to measure the loss of a fiber laser cavity [89]. The rate at which a fiber laser can be modulated by modulating the pump was shown to be a few megahertz for practical fiber lengths. This rate is limited by the relaxation oscillation frequency [90]. A similar limitation was shown by polarization switching of the pump [33]. The first demonstration of a cw ring fiber laser goes back to the original work of the mid-1980s at the University of Southampton [8]. The ring was made of a 2.2-m Nddoped silica fiber closed with a fused fiber coupler and pumped with a 595-nm dye laser. This device suffered from pump absorption in the lead fibers (which can be avoided by using undoped leads), but it had, nevertheless, a threshold of only about 6 mW and it produced 2 mW of output in each direction for about 20 mW of absorbed pump power. Using a lower loss fiber coupler, Chaoyu et al. demonstrated a ring fiber laser with a threshold comparable with that of a Fabry–Perot fiber laser [17]. The wavelength of Nd-doped fiber lasers has been tuned by incorporating wavelength-selective elements in the cavity. Reported continuous tuning ranges were 1068– 1145 nm (77 nm) with an external grating [91]; 1070–1135 nm (65 nm) with bulk optic birefringent filters [74]; and 1077–1139 nm (62 nm) with a WDM coupler [17]. Ghera et al. introduced a polarizer in their cavity and tuned their laser from 1080 to 1120 nm (40 nm) by adjusting an intracavity polarization controller [92]. It has been predicted that by splicing together fibers with different P and Nd contents, the tuning range can be increased to 93 nm [88]. Other tunable Nd-doped fiber lasers are described in Chapter 5. More recently, a high laser performance was reported in an Nd-doped lead–silicate fiber fabricated by a rod-in-tube method [77]. The presence of Pb 2⫹ in the host is beneficial in several ways. It produces a 1.06-µm fluorescence with a high emission cross section, estimated at 2.4 10 ⫺20 cm 2. The 800-nm absorption cross section is also high, about twice as large as in silica. Importantly, this material is free of concentration quenching up to about 3 wt% Nd 2 O 3. The propagation loss is much higher than in a silica fiber, about 1.5 dB/m at 1.06 µm, but it has a small effect because the Nd concentration is so high that


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a typical device requires only a short length of fiber. A fiber laser fabricated with this fiber and pumped with a laser diode exhibited a threshold of 2.15 mW and a conversion efficiency of 46% [77]. Double-Clad Fibers In recent years, significant efforts have been devoted to increasing the output power of Nd-doped fiber lasers to the 10-W level and higher with double-clad fibers [41– 43,45,47,49,51,54,58,80,81]. The pioneering work carried out by Snitzer and co-workers was unfortunately limited by the low power available from the laser diode arrays of the time. Nevertheless, they greatly exceeded the previous record with a rectangular-cladding double-clad fiber laser pumped with a 500-mW 807-nm laser diode array [49]. The pump coupling efficiency into the first cladding was about 50%. With a 50% output coupler, their laser had a threshold close to 22 mW and a maximum output power of 120 mW. A few years later, Zenteno demonstrated 750 mW with a similar geometry and a 2.5-W laser diode [43], and Po broke the watt barrier with a 5-W Nd-doped fiber laser and a 51% slope efficiency [58]. Two years later, Zellmer and co-workers took the record to 9.2 W by increasing the pump power level to 35 W [50]. Their laser used a circular cladding, and its efficiency was consequently modest (26%). The same research group subsequently improved their result with a 400-µm–diameter D-shaped cladding [47]. This fiber laser was made of a 60-m fiber and produced 14 W of cw power at about 1.06 µm for 33.5 W of power from an 815-nm laser diode, or a conversion efficiency of 40%. A 30-W multimode output power was also reported in a D-shaped fiber with a multimode core [47]. The current published record is held by a double-clad fiber laser in which effective mode mixing was induced by bending the fiber, which allowed power scaling up to more than 30 W [45]. The output polarization properties of high-power Nd-doped fiber lasers have been carefully studied by Zenteno et al. [93]. The test laser used a 6-m double-clad fiber with a fairly high core birefringence, and it was pumped at 807 nm with a 500-mW laser diode. Their study showed that the state of polarization of the output depends strongly on the pump power and externally applied anisotropic stresses. The degree of polarization of the output decreased from near unity (strongly polarized) close to threshold to near zero (strongly unpolarized) far above threshold. This behavior was attributed to a combination of core birefringence and polarization-dependent gain [93]. Such polarization issues need to be addressed for practical devices because many applications critically require a strongly polarized and stable polarization. M-Profile Fibers M-profile fibers offer the promise of a significantly larger laser mode area and substantially higher-output powers than double-clad fibers. In the highest power laser of this kind reported to date, the fiber had a length of 1.9 m, a core diameter of 350 µm, a ring of 5-µm thickness doped with 0.13 mol% Nd 2 O 3, and an undoped outer cladding [64]. It was pumped with a 35-W fiber-coupled laser diode stack, of which up to ⬃21 W was launched. The threshold was ⬃4 W. The laser power emitted at 1050 nm was ⬃10 W, corresponding to a slope efficiency of ⬃54%. The azymuthal distribution of the output power around the ring was relatively uniform, although other M-profile fiber lasers oscillated on a discrete azymuthal mode [63].

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3.5.5 Nd-Doped Fiber Lasers Around 1.3 ␮m The Nd-doped fiber lasers operating near 1.3 µm are potentially very important for optical communication in the second window, and they have stimulated early on a fair amount of research. A strong commercial incentive is that a large number of installed fiber communication systems operate in the 1.3-µm region, and there is a need to supply them with suitable amplifiers and, to a lesser extent, fiber laser sources. Several approaches have being investigated, including Nd-doped and Pr-doped fluoride fiber lasers (see Chap. 12). The earliest attempts involved the 4 F 3/2 → 4 I 13/2 transition of Nd 3⫹ in a silica-based fiber [71,79,78]. Po et al. reported the first Nd-doped silica fiber oscillating at a wavelength as short as 1.36 µm [71]. Although the 4 F 3/2 → 4 I 13/2 fluorescence of the fiber peaked at 1.34 µm, laser emission occurred at 1.40 µm. The reason for this shift is signal ESA to the 4 G 7/2 level. The ESA spectrum is such that losses are much higher in the mid- and short-wavelength range of the gain spectrum, which forces oscillation at the long-wavelength edge of the transition around 1.40 µm. Because the second communication window is generally considered as spanning the 1.28- to 1.33-µm range, following this early result, methods to lower the laser wavelength by reducing signal ESA by altering or changing the glass host were investigated in several laboratories [79,94,95]. The addition of a large amount of phosphorus (14 mol% P 2 O 5) to a silica preform reduced ESA sufficiently for oscillation to take place at the shorter wavelength of 1.363 µm [79]. Signal ESA was reduced in the long-wavelength tail of the transition primarily because phosphorus caused narrowing of the fluorescence line. The fiber laser used dichroic mirrors to suppress laser oscillation on the stronger 1055-nm transition. The threshold was ⬃80 mW and the conversion efficiency ⬃1% (both against absorbed pump power). The threshold was higher than expected from the optical loss alone, perhaps because of gain depletion by ASE at 1055 nm. A similar result was later reported for a commercial phosphate glass fiber heavily doped with Nd 3⫹ (3%) [78]. It was pumped with a Ti: sapphire laser at 815 nm through a dichroic input reflector. A short fiber (10 cm) was sufficient to absorb most of the pump power. Despite an unusually high fiber loss (4 dB at 1.06 µm), the threshold absorbed pump power was reasonably low, about 5 mW. The slope efficiency against absorbed pump power of this 1.363-µm laser was 10.8%, one of the highest in this wavelength range. Although the performance of these fiber lasers was encouraging, their wavelength was still too long for communication purposes. The work on 1.3-µm Nd-doped silica fiber lasers was essentially discontinued after the demonstration of more efficient 1.3-µm sources in Pr-doped fluoride fibers [96,97] (see Chap. 12). These sources are also in competition with more recent cascaded Raman fiber lasers [98]. 3.5.6 Nd-Doped Fiber Lasers Around 0.9 ␮m Silica-based Nd-doped fiber lasers have also been operated on the 4 F 3/2 → 4 I 9/2 transition, which falls around 0.9 µm [71–75]. Since this transition terminates on the ground state 4 I 9/2, it is a partial three-level laser and exhibits a higher threshold. Nevertheless, this transition has been successfully forced to oscillate by using dichroic mirrors with sufficiently low reflections at the other transition wavelengths from the 4 F 3/2 level to suppress oscillation (and reduce ASE) at these wavelengths. The threshold is typically a few milliwatts and the slope efficiency can be reasonably high (see Table 1). This transition was tuned continuously from 900 to 945 nm with bulk-optic birefringent filters [74]. Interesting


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mode competition between 0.9- and 1.1-µm oscillations, including simultaneous oscillation, was also observed [72]. The most efficient 938-nm Nd-doped fiber laser reported to date was pumped at 823 nm with a laser diode [75]. The reflectors, placed against the fiber ends, had a low reflectivity at 1.09 µm and a high reflectivity at the laser wavelength, whereas the input mirror transmission at the pump wavelength was high. The fiber length was optimized to minimize residual ground-state absorption (GSA) at the laser wavelength. This laser exhibited a threshold of 1.9 mW and emitted 3 mW for an absorbed pump power of 10.2 mW, which corresponds to a slope efficiency of 36%. 3.6 ERBIUM Erbium-doped silica fiber lasers have been extensively studied for their potential use as sources in communication systems operating in the third communication window. As discussed in other chapters, they have produced a broad range of broadband and narrowband, cw, and pulses sources, all of them in the ⬃1.5- to 1.62-µm range on the 4 I 13/2 → 4 I 15/2 transition of erbium. In this section, cw Er-doped fiber lasers are distinguished on the basis of their pump wavelength, which strongly affects their performance. The properties of selected Er-doped fiber lasers are summarized in Table 3. 3.6.1 Basic Spectroscopy The main laser transition of interest in Er-doped silica-based fibers is the high-gain 4 I 13/ 4 2 → I 15/2 transition centered around 1.55 µm. It terminates on the ground-state manifold 4 I 15/2; therefore, it is essentially a three-level transition. However, this manifold is broad enough that longer wavelength transitions (⬃1.6 µm and longer) terminate on the lesspopulated upper levels of the manifold and are quasi-four-level transitions. Several pump bands are available to populate the metastable level 4 I 13/2. The bands relevant to pumping are identified on the energy level diagram of Figure 1 in Chapter 10. With current technology, pumping with a laser diode is possible around 810, 980, and 1480 nm. Other useful pump bands include 660 nm (to the 4 F 9/2 level), as well as 532 and 514.5 nm (to the 2 H 11/2 level). Unfortunately, the pump wavelengths of 514.5 nm and ⬃810 nm suffer from strong ESA (see Fig. 35 of Chap. 2), which causes an undesirable waste of pump photons [108]. However, Er-doped silica can be pumped efficiently at several essentially ESA-free wavelengths, including those around 532, 660, 980 [108], and 1480 nm. We refer the reader to Chapter 2 for further details on the spectroscopy of Er-doped glasses, in particular the influence of glass composition on pump ESA. Because of the three-level nature of the 4 I 13/2 → 4 I 15/2 transition, in an Er-doped fiber laser a higher pump power is needed to reach threshold than in a four-level laser [see Eqs. (2) and (3)]. However, thanks to the long lifetime of the 4 I 13/2 level (8–10 ms in silica) and the transition’s fairly high peak emission cross-section (4–7 ⫻ 10 ⫺21 cm 2) [109], in spite of signal GSA the gain efficiency κ near 1.55 µm is quite high. For example, in a 980-nm-pumped Er-doped fiber amplifier (EDFA) a maximum gain efficiency of 11 dB/mW was reported [110], compared with 0.55 dB/mW for Nd-doped fibers [40]. Consequently, Er-doped fiber lasers can exhibit a low enough threshold that they have been generally pumped with a laser diode (see Table 3). As in Nd-doped silica fibers, quenching is a problem in highly doped Er-doped fibers, and it can also be reduced by suitable co-doping. Figure 8 plots the percentage of

514.5 nm 532 nm 532 nm 806 nm 808 nm 980 nm 980 nm ⬃1.46 µm 1.47 µm 1.48 µm 1.48 µm

1.566 µm ⬃1.56 µm 1.535 µm 1.56 µm 1.62 µm 1.56 µm ⬃1.54 µm 1.552 µm 1.552 µm 1.555 µm ⬃1.56 µm 35 ppm Er ion 150 ppm Er 2 O 3 100 ppm Er 500 ppm Er 300 ppm Er 0.08 wt% Er 1100 ppm Er 1370 ppm Er ion 1370 ppm Er ion ⬃45 ppm Er 110 ppm Er 2 O 3

Erbium concentration 13 m 1m 15 m 3.7 m 1.5 m 0.9 m 9.5 m 5m 7m 60 m 42.6 m

Fiber length Ar-ion laser pump Ring laser Doubled Nd :YAG LD array pump LD pump Dye laser Ti : sapphire/Tunable Two LD pumps LD pump LD pump/Ring laser LD pump

Other features 44 mW 10 mW (l) NA 10 mW (l) 3 mW (a) 2.5 mW (a) ⬎10 mW (l) 37 mW (l) 44 mW (a) 6.5 mW (l) 4.8 mW (a)

(l)

Threshold 10% 5.1% (l) 28% (NA) 16% (l) 3.3% (a) 58% (a) ⬎49% (l) 14% (l) 6.3% (a) 38.8% (l) 58.6% (a)

(l)

Slope efficiency

NA, data not available; LD, laser diode. (i) With respect to incident pump power; (l) with respect to launched pump power; (a) with respect to absorbed pump power.

Pump wavelength

Laser wavelength

56 mW @ 0.6 W 1.8 mW @ 45 mW (l) 1 W @ 3.6 W (NA) 8 mW @ 56 mW (l) 0.13 mW @ 7 mW (a) 4.7 mW @ 11.3 mW (a) 260 mW @ 540 mW (l) 8 mW @ 93 mW (l) ⬃1 mW @ 60 mW (a) 3.3 mW @ 15 mW (l) 14.2 mW @ 29 mW (a)

(l)


Table 3 Characteristics of Representative cw Er-Doped Silica Fiber Lasers, Listed in Order of Increasing Pump Wavelength

99 18 100 101 102 103 104 105 106 21 107

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Figure 8 Inferred percentage of erbium pairs in Er-doped fibers of various origins, plotted against the ratio of Al to Er concentration in the core. (From Ref. 111.)

clusters inferred from experimental measurements in Er-doped Al-co-doped silica fibers from various laboratories, plotted as a function of the ratio of Al ion to Er ion concentrations [111]. This plot provides evidence that the percentage of erbium clusters decreases markedly as this ratio increases. The addition of Al reduces the incidence of pairs up to a ratio of ⬃20, beyond which additional Al has minimal benefit. 3.6.2 Er-Doped Fiber Lasers Pumped in the Visible Most of the early Er-doped fiber lasers were pumped with the 514.5-nm line of the Arion laser [99,112–114], then the most common high-power pump source readily available in research laboratories. Because of pump ESA, these fiber lasers exhibited a high threshold, in the range of tens of milliwatts. Their slope efficiencies were generally fairly low, typically of the order of 1% [112–114]. In one report, the slope efficiency was maximized to 10% by optimizing the output coupler transmission, but the threshold was high, about 44 mW [99]. More limited work has been reported with 532-nm pumping [18,115], for which ESA is negligible [108]. Before the advent of 980- and 1480-nm laser diodes, this wavelength was deemed of interest because of the prospect of high-power, laser-diode-pumped, frequency-doubled Nd :YAG lasers as pump sources. The best published result with a 532-nm pump is an output power of 1 W for 3.6 W of pump power, or a conversion efficiency of 28%, in a low-concentration fiber pumped with a frequency-doubled Nd: YAG laser [100]. This early work, as well as parallel research on EDFAs, quickly pointed to the need for reliable and compact light sources around 980 and 1480 nm to pump Er-doped fibers without the penalty of pump ESA. The semiconductor laser industry responded promptly to this need. In just a few years it researched and brought to market strained InGaAs quantum-well lasers operating at about 980 nm and GaInAsP quantum-well lasers at about

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1480 nm. Most of the subsequent research on Er-doped fiber devices used either these semiconductor lasers or ⬃810-nm GaAlAs laser diodes as pump sources. The need for high-power fiber lasers around 1.55 µm has also been driving research in Yb-sensitized Er-doped fibers pumped at 1064 nm. 3.6.3 Er-Doped Fiber Lasers Pumped at About 810 nm The availability of inexpensive, long-lifetime, high-power GaAlAs laser diodes emitting near 0.8 µm has been a strong incentive to investigate this pump wavelength in Er-doped fiber lasers in spite of relatively strong ESA. Early work showed that low thresholds (1–3 mW) were attainable, but that the lasers exhibited a low slope efficiency (1.25– 3.3%) [102,116]. This situation was improved significantly by recognizing that the gain efficiency of an Er-doped fiber is so high that using an output coupler with a fairly high transmission induces only a moderate increase in threshold. By following this approach and pumping an Er-doped fiber with an 806-nm laser diode array, Wyatt and co-workers at British Telecom were able to demonstrate an output power of several milliwatts [101], in part limited by the coupling efficiency of the array beam into the fiber (⬃20%). With a single-pass pump configuration (i.e., an output coupler transparent at the pump wavelength) and a 5-m fiber doped with 500 ppm of Er, the output power was maximum with an output coupler transmission of 50%. This fiber laser had a threshold of 18 mW and produced a maximum output power of 5 mW for a launched pump power of ⬃56 mW, corresponding to a slope efficiency of 13.5% [101]. About 77% of the launched pump power was absorbed by the fiber. This figure could be improved by increasing the fiber length, although as discussed in Section 3.6.5 it would result in an undesirably longer laser wavelength. An appealing alternative was to reflect the unabsorbed pump power back into the fiber with a dichroic output coupler. With this configuration and a 3.7-m fiber, the threshold was reduced to 10 mW and the output power increased to 8 mW [101]. In the early 1990s, several authors reported theoretical investigations of EDFAs pumped in the 800-nm band [117,118]. As expected, their predictions were in quantitative agreement with these experimental observations. One report concluded that for Al–P– silica fibers, approximately five times more pump power is required than when pumping at 980 or 1480 nm [118]. Because of this relatively low performance, and the advent soon after of 980- and 1480-nm laser diodes, 800-nm pumping has not been investigated further, except in Yb-sensitized Er-doped fibers. 3.6.4 Er/Yb-Doped Fiber Lasers Pumped at About 0.8 and 1 ␮m To produce more efficient sources, Er-doped fiber lasers have been co-doped with ytterbium (Yb). The first reported work on Er-doped glasses involved in fact a flashlamppumped Er-doped glass laser in which the upper laser population was increased by using 15 wt% Yb 2 O 3 for 0.25 wt% Er 2 O 3 [119]. The concept is simple: the glass host is doped with a laser ion and co-doped, or sensitized, with a second ion that (1) absorbs strongly in a band not available to the laser ion, and (2) efficiently transfers its energy to the laser ion. The specific mechanism by which Yb 3⫹ accomplishes this function for Er 3⫹ is illustrated in Figure 32 of Chapter 11. Absorption of a pump photon by a Yb 3⫹ ion promotes an electron from the ground state 2 F 7/2 to the 2 F 5/2 manifold, which is followed by efficient energy transfer from this level to the 4 I 11/2 level of erbium and nonradiative decay to the upper laser level 4 I 13/2. This process is efficient, provided the transferred energy remains in the Er 3⫹ ion (i.e., provided the electron relaxes preferentially to the Er 3⫹ upper laser


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state, rather than back to the 2 F 5/2 level of the Yb 3⫹ ion). The energy transfer efficiency can be improved by co-doping with P 2 O 5 [120], which increases the nonradiative relaxation rate from the 4I11/2 level to the 4 I 13/2 level and reduces energy transfer back to the Yb 3⫹ donor [121]. In phosphate glasses, the transfer efficiency can be as high as 85%. Sensitization of Er-doped silica fibers by Yb 3⫹ presents several advantages. First, because silica-based glasses can be heavily doped with Yb 3⫹, it allows a high-concentration species to strongly absorb the pump, thereby greatly reducing the fiber length requirement. Yb 3⫹ does not introduce absorption bands at longer wavelengths, so that a higher concentration does not affect the fiber loss at the laser wavelength. Second, a higher Yb concentration reduces the mean distance between ions and thus facilitates energy transfer between them. Third, the absorption band of Yb 3⫹ is very broad [122] and provides a wide range of possible pump wavelengths, typically about 300 nm centered on 930 nm. As an example, in an Al–P silica fiber doped with 0.055 mol% Er, the addition of 1.8 mol% Yb induced a strong absorption band from 700 to 1115 nm, with a peak of ⬃400 dB/ m and a calculated transfer efficiency of 37% [123]. Er/Yb-doped fibers can be pumped in particular at 1.064 µm [122], a wavelength conveniently available from compact laser– diode-pumped Nd: YAG lasers and high-power Nd:YAG lasers. A fourth benefit is that Yb 3⫹ provides strong absorption in the 820- to 830-nm region, where pump ESA due to Er 3⫹ is significantly smaller, but where GSA due to Yb 3⫹ is strong enough to be of practical use. A final advantage is that Yb is likely to improve the output power stability with temperature of the fiber laser. In unsensitized fibers the pump band is fairly narrow. Because the emission wavelength of a laser diode depends strongly on temperature, stabilization of the diode temperature to a few degrees is expected to be required to keep the fiber laser output power reasonably constant. In contrast, the pump absorption spectrum of Yb 3⫹ is so broad that it should reduce this requirement substantially. Several laboratories have investigated the merits of Yb as a sensitizer in Er-doped fiber lasers [120,122–129]. The performance of some of these lasers are summarized in Table 4. Hanna et al. showed that the threshold presented a minimum, and the slope efficiency a maximum, for pump wavelengths close to 825–830 nm, as expected on the grounds of weaker pump ESA [125]. The fiber laser used a 70-cm fiber containing 1.7% Yb and 0.08% Er. Pumped at the optimum wavelength and with an output coupler transmission of 28%, it exhibited a threshold of ⬃5 mW and a slope efficiency of 8.5%. In comparison, a Yb-sensitized Er-doped fiber tested by the same research group, but pumped at 1064 nm with a Nd:YAG laser, exhibited a poorer performance, namely, an 8-mW threshold and a slope efficiency of 4.2% (all data against absorbed power) [122]. More recently, however, Er/Yb-doped fiber lasers pumped in the same region (1047 nm) have shown much better performance: for example, a threshold of 20 mW and a slope efficiency of 23% [128]. This study concluded that a higher Yb/Er ratio improved both the threshold and the slope efficiency. Interestingly, the residual loss mechanism in this laser originated from the erbium ions, probably from up-conversion to the 4 F 7/2 level when an excited Yb ion (in the 2 F 5/2 level) donated its energy to an erbium ion in the 4 I 11/2 level. The presence of Yb also greatly reduced up-conversion between excited erbium ions [128]. Another report described an Er/Yb-doped fiber pumped at 1064 nm with a transfer efficiency as high as ⬃95% [126]. These results established that optimized Er/Yb-doped silica fibers can be effectively pumped with 1- to 1.1-µm solid-state lasers. Another careful assessment of the effectiveness of Yb 3⫹ as a sensitizer for Er 3⫹ was carried out by Barnes et al., who compared the output power characteristics of an Er/Ybdoped and an Er-doped Al–P–silica fiber laser pumped at 810–826 nm [123]. They found

810 nm 820 nm 832 nm 962 ppm 980 nm 1047 nm 1064 nm 1064 nm 0.98/1.48 µm

1570 nm 1.56 µm 1.56 µm 1537 nm 1545 nm 1535 nm 1.56 µm 1535 nm 1545.6 nm

0.06 wt% 0.08% 0.08% 900 ppm NA 0.06% 0.08% 880 ppm NA

Er conc. 1.3 wt% 1.7% 1.7% 1.1% NA 1.8% 1.7% 7500 ppm NA

Yb conc. 1.45 m 70 cm ⬃0.7 m 1.6 m 7 cm 4m 91 cm NA ⬃7 cm

Fiber length Two LD pumps Dye laser Dye laser pump LD pump/DCF LD pump Nd :YLF pump Nd :YAG pump Nd :YAG pump LD pump/MOPA

Other features 12.7 mW 3.7 mW (a) 5 mW (a) 130 mW (l) 1 mW (i) 20 mW (l) 8 mW (a) 37 mW (a) 10 mW (l)

(l)

Threshold

15.4% 7% (a) 8.5% (a) 19% (l) 25% (i) 23% (l) 4.2% (a) 27%(a) ⬃50%(l)

(l)

Slope efficiency

NA, data not available; DCF, double-clad fiber; LD, laser diode; MOPA, master oscillator power amplifier. (i) With respect to incident pump power; (l) with respect to launched pump power; (a) with respect to absorbed pump power.

Pump wavelength

2.3 mW @ 28 mW NA NA 96 mW @ 620 mW (l) 18.6 mW @ 95 mW (l) 285 mW @ 640 mW (l) 1.3 mW @ 80 mW (a) NA 166 mW @ 340 mW (l)

(l)

Outer power @ max. pump power

Characteristics of Representative cw Yb-Sensitized Er-Doped Silica Fiber Lasers, Listed in Order of Increasing Pump Wavelength

Laser wavelength

Table 4

123 122 125 120 127 128 122 126 129

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that there is an optimum concentration of Yb (Yb/Er ⫽ 20:1 for an Er concentration of 0.06 wt%) that minimizes the threshold. For these concentrations, the fiber laser exhibited a slightly lower threshold and higher slope efficiency (against launched pump power) than the Er-doped fiber laser (after normalization to the same NA) [123]. The general conclusion is that Yb 3⫹ has a small beneficial effect on the fiber laser output power. Using the co-doped fiber and an output coupler reflectivity of 40%, the fiber length that maximized the output power was 1.45 m for the maximum launched pump power of 28 mW available from a pair of 810-nm laser diodes. The threshold launched power was 12.7 mW and the maximum output power at 1.57 µm was 2.3 mW, for a slope efficiency of ⬃15.4% [123]. Another advantage of Yb sensitization, pointed out recently by Taccheo and coworkers, is that because of the energy transfer process the Er/Yb-doped fiber laser exhibits a substantially lower sensitivity to pump power fluctuations [130]. As a result, its intensity noise spectrum is not limited by pump noise, but mainly by fluctuations of the cavity losses. This conclusion was drawn from theoretical considerations and confirmed experimentally in a single-frequency, diode-pumped Er/Yb fiber laser. A theoretical model of laser intensity noise in Er/Yb-doped fiber lasers can be found in Ref. 130. Much of the more recent work on Er/Yb-doped fibers has targeted single-frequency lasers, in particular, distributed feedback (DFB) lasers, a topic covered in detail in Chapter 5. As an example, a DFB fiber laser with fiber gratings fabricated directly on the doped fiber, in a master oscillator power amplifier (MOPA) configuration, was reported [129]. By inducing a π/2 phase shift in the resonator, a highly stable single-frequency output and low RIN noise were achieved, while retaining the low threshold (10 mW) and high slope efficiency (⬃50%) advantage of this type of fiber laser [129]. A tuning range greater than 70 nm was also reported with a WDM fiber coupler in an Er/Yb-doped ring fiber laser [19]. Double-clad fibers (see Sec. 3.4.1) have been used with the Er/Yb system to produce high-power lasers [120]. Although, as discussed earlier, the use of a double-clad fiber is not beneficial with Er 3⫹ alone, it becomes practical in Yb co-doped fibers, because the high concentration and high absorption cross section of Yb 3⫹ compensate for the increased fiber length of a double-clad fiber. As shown in Table 4, this 1.6-m laser produced 96 mW for 620 mW of launched 962-nm pump power [120]. 3.6.5 Er-Doped Fiber Lasers Pumped at 980 nm Pumping Er-doped fiber lasers near 980 nm is appealing because Er-doped silica fibers pumped at this ESA-free wavelength exhibit the highest gain efficiency [110]. One of the highest slope efficiencies reported for an Er-doped fiber laser was in fact in a 980-nm pumped laser [103]. It was made of a 0.9-m Al–P–doped fiber containing 0.08 wt% Er 3⫹. The laser oscillated in one of three discrete wavelengths (around 1.53, 1.56, and 1.60 µm), depending on the output coupler transmission. At all wavelengths the threshold was fairly low and the slope efficiency very high. For example, at 1.56 µm the threshold was 2.5 mW and the slope efficiency 58% (both against absorbed power) [103]. With reference to Eq. (5), because T 1 was large and dominated the cavity loss, T 1 /δ 0 was close to unity, and the slope was expected to be nearly equal to the ratio λ p /λ s, or 0.628. Comparing this value with the measured slope of 58% confirms that the quantum efficiency of this laser was close to unity. The maximum output was only 4.6 mW when pumping with a dye laser [103]. However, with such a slope efficiency and a 100-mW fiber-pigtailed laser

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diode pump source, assuming 80% pump absorption, an output power of 45 mW can be expected. A much higher power was reported by Wyatt at British Telecom, from a fiber laser with a similar conversion efficiency pumped with a 980-nm Ti:sapphire laser [104]. The output power was 260 mW for 540 mW of launched pump power. Using a rotatable grating as a selective back reflector, this power was obtainable from 1.52 to 1.57 µm. In a three-level laser such as the Er-doped fiber laser, the fiber length is an important design parameter that affects the threshold, slope efficiency, and wavelength. Any length of unpumped fiber acts as a strong absorber at the laser wavelength and increases the threshold. Consequently, for a given set of fiber and pump parameters there is an optimum length that minimizes the threshold. Furthermore, increasing the fiber length increases the absorbed pump power, and thus the output power. There is obviously a trade-off between these two effects, which depends on the available pump power. The fiber length also affects the laser wavelength [102,114,123]. If the fiber is too long, the fiber end farthest from the pump source remains unbleached and strongly absorbs the signal, preferentially on the short wavelength side of the gain spectrum where GSA is stronger. As a result, as the fiber length is increased, the laser shifts toward longer wavelengths. Another way to look at it is that at longer wavelengths the laser behaves like a quasi–four-level laser [102], and these wavelengths are favored by a longer fiber. The dependence of the wavelength on fiber length is either smooth [102] or abrupt [123], and it is affected by the spectroscopy. The wavelength shift is always pronounced, as illustrated in Figure 9 [102]. In this example, the laser wavelength shifted from 1555 to 1605 nm by approximately doubling the length. 3.6.6 Er-Doped Fiber Lasers Pumped Around 1480 nm Pumping Er-doped fiber lasers near 1480 nm is also of great interest, because this pump band is essentially free of ESA, and because of the availability of high-power laser diodes at this wavelength. Pumping at 1.48 µm also presents the advantage of close proximity between the pump and laser wavelengths, which implies that the maximum possible laser slope efficiency hν s /hν p [see Eq. (5)] is higher than for 980-nm pumping by a factor of about 1.5. On the other hand, the gain efficiency of Er-doped fibers is generally smaller with 1.48-µm pumping than with 980-nm pumping [110,131]. Everything else being equal, the threshold of 1.48-µm-pumped fiber lasers is thus expected to be higher. However, thresholds are low enough that this difference should be inconsequential. Another difference is that, when pumping near 1.48 µm, stimulated emission at this wavelength reduces the maximum achievable population inversion and slightly increases the required length of fiber. A last minor disadvantage is that 1.48/1.55-µm dichroic dielectric mirrors are somewhat more difficult to fabricate. Several investigations of 1.48-µm pumped Er-doped fiber lasers were carried out at NTT Transmission Systems Laboratories [105,106,132]. Laser diodes in the range of 1.46–1.48 µm were used to pump a fiber doped with 1370 ppm of Er and a moderate optical confinement. One type of fiber resonator was an all-fiber ring made of a 3-m Erdoped fiber loop closed by a 3-dB fiber coupler fabricated with undoped fiber [132]. Pumped with a 1.48-µm high-power laser diode, this laser emitted at 1.553 µm and had a threshold launched power of ⬃14.3 mW. The slope efficiency was not reported. A Fabry–Perot resonator laser was also constructed with the same fiber pumped with two polarization-multiplexed 1.46-µm laser diodes. With a fiber length (5 m) optimized for


143

Figure 9 Measured dependence of the laser wavelength on the fiber length for an Er-doped fiber laser pumped at 808 nm. (From Ref. 102.)

output power at the maximum pump power, they observed a 37-mW threshold and a maximum output power of 8 mW at 1552 nm for 93 mW of launched pump power [105]. A third resonator used a 1.5-m undoped fiber coupled at one end to a 1.47-µm laser diode with a pair of ball lenses, and spliced at the other end to a 7-m length of Er-doped fiber [106]. The cleaved end of the doped fiber acted as the output coupler (⬃96.5% transmission). At the opposite end, the 1.55-µm intracavity signal was coupled into the laser diode waveguide, which is nearly transparent at 1.55 µm so that the back facet of the laser diode acted as the back reflector of the fiber laser cavity. This fiber laser had a threshold of 44 mW and a slope efficiency of 6.3% (both against absorbed power), and a maximum output power of nearly 1 mW [106]. These results raised interesting questions concerning the ultimate performance one may expect from 1.48-µm-pumped Er-doped fiber lasers. From cited data [106], the fraction of launched pump power absorbed by the 5-m–fiber laser was estimated at approximately 53%, and the absorbed pump power at threshold close to 20 mW. Comparing this value with the round-trip cavity loss of 8 dB suggests a gain efficiency of 0.4 dB/mW, in order-of-magnitude agreement with the value measured in this fiber at 1.535 µm [132]. Since this work, a gain efficiency of 5 dB/mW at 1.536 µm has been reported with 1.48-µm pumping [110]. Thus, by optimizing the fiber parameters and reducing the cavity loss, it should be possible to lower the threshold to a few milliwatts. Similarly, from the reported slope efficiency of 14% against launched power, one can infer a slope efficiency against absorbed power of about 27%. A value two to three times higher would have been expected from Eq. (5).

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Since this work, extremely efficient 1.48–µm-pumped Er-doped fiber lasers have in fact been reported by Wagener et al. at Stanford University [107]. This study established that a key factor that needs to be optimized to maximize the conversion efficiency is the erbium concentration. Measurements indicated that fibers with increasingly high Er concentrations have increasingly high thresholds and low slope efficiencies. These two effects were attributed to the presence of an increasing percentage of Er 3⫹ clusters, and to the fact that clusters dramatically reduce the excited lifetime [133], and thereby the quantum efficiency of the transition. The most efficient fiber laser reported in this study used a low-concentration fiber (110 mol ppm Er 2 O 3) and a correspondingly long fiber (42.6 m) [107]. The cleaved fiber ends (⬃3.5% reflections) formed the laser Fabry–Perot resonator. In spite of the high cavity loss (⬃29 dB), the threshold was low (⬃4.8 mW), and the laser was successfully pumped with a low-power laser diode. It emitted simultaneously in the forward and backward direction, with a forward slope efficiency of 58.6% [107]. This is the highest slope efficiency and the highest conversion efficiency reported in an Er-doped fiber laser (see Table 3). The backward slope efficiency was 31.8%. If a dichroic high reflector was placed at the pump input end, a total slope efficiency of approximately the sum of these two figures, or ⬃90.4%, would be expected, as well as a substantial reduction in threshold. This study showed that Er-doped fiber lasers, when pumped near 1.48 µm, can be at least as efficient as 980-nm pumped lasers. The reasons for this high performance were the low Er concentration and the similarity between the pump and laser photon energies [107]. The slope efficiency of 90.4% is, in fact, very close to the quantum limit of 95% predicted for the ratio of pump to signal photon energies. It confirms that the quantum efficiency of this transition can be within a few percent of unity. In this light, concentration quenching may well explain the suboptimal efficiencies and thresholds reported in some Er-doped fiber lasers (see Table 3). It points to the importance of selecting a sufficiently low rare earth concentration to maximize the performance of fiber lasers or amplifiers. This requirement was confirmed in a more recent report of a ring fiber laser that utilized a very low-concentration fiber (see Table 3) [21]. After optimizing the fiber length and output coupler transmission, the laser had a low threshold (6.5 mW) and a fairly high slope efficiency of 38.8%. Tuning from 1525 to 1570 nm was achieved with an intracavity tunable filter. 3.6.8 Summary In summary, Er-doped fiber lasers operating close to 1.55 µm are extremely efficient. When pumped at 1.48 µm, their slope efficiency can be within a few percent of the theoretical limit λ p /λ s ⬇ 95%. Pumping at 980 nm produces a lower, although still substantial, slope efficiency (theoretical limit of ⬃63%). Pumping at about 800 nm is unfortunately less efficient (⬃15%) because of pump ESA, even with Yb co-doping. Er-doped fiber lasers are now almost exclusively pumped close to 980 or 1480 nm. They have also been operated at multiple wavelengths simultaneously. This feature, of great importance for dense WDM systems, is reviewed in Chapter 5. 3.7 YTTERBIUM 3.7.1 Basic Spectroscopy Ytterbium is one of the most versatile laser ions in a silica-based host. It offers several very attractive features, in particular an unusually broad absorption band that stretches


145

from below 850 nm to above 1070 nm because of the 2 F 7/2 → 2 F 5/2 transition, as illustrated with a representative absorption spectrum in Figure 10 [134]. Yb-doped silica fibers can thus be pumped with a wide selection of solid-state lasers, including AlGaAs (⬃800–850 nm) and InGaAs (⬃980 nm) laser diodes, and Nd :YLF (1047 nm) and Nd: YAG (1064 nm) lasers. This broad pump band also relaxes considerably both the requirements for pump wavelength and its stability with temperature. Just as importantly, Yb-doped silica fluoresces effectively over an equally impressive range, from approximately 970 to 1200 nm (see Fig. 10). This is broader than the range available from Nd-doped fiber lasers, which is one of the attractions of Yb 3⫹ over Nd 3⫹. The Yb-doped fiber laser, therefore, can generate many wavelengths of general interest: for example, for spectroscopy or for pumping other fiber lasers and amplifiers. Another well-known advantage of Yb 3⫹ is the simplicity of its energy level diagram. As illustrated in the inset of Figure 10, Yb 3⫹ exhibits only a ground state (2 F 7/2) and a metastable state (2 F 5/2) spaced by approximately 10,000 cm -1. All other levels are in the UV. The radiative lifetime of the 2 F 5/2 state is typically in the range of 700–1400 µs, depending on the host [135]. The absence of higher energy levels greatly reduces the incidence of multi-phonon relaxation and ESA and, therefore, should facilitate the development of high-power lasers. Yet another benefit is the abnormally high absorption and emission cross sections of Yb 3⫹, which are typically several times higher than in multicomponent glasses [136]. These combined features allow for very strong pump absorption and very short fiber lasers.

Figure 10 Ground-state absorption spectrum, emission spectrum, and energy level diagram of Yb 3⫹ in silica. The solid lines identify the radiative transitions responsible for the two features in the emission spectrum. (From Ref. 134.)

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A Yb-doped fiber laser is typically pumped into the higher sublevels of the 2 F 5/2 manifold (see inset of Fig. 10). At wavelengths below about 990 nm, it behaves as a true three-level system (transition A in Fig. 10), whereas at longer wavelengths, from ⬃1000 to ⬃1200 nm (transition B), it behaves as a quasi-four-level system. The literature provides comprehensive descriptions of the spectroscopy of Yb 3⫹, including absorption and emission spectra [134,137] and theoretical gain spectra [137]. Because of the absence of higher energy levels, high concentrations of Yb 3⫹ are possible in silica-based hosts, often up to several thousand ppm (Table 5). However, recent studies have shown that in silica-based hosts a fraction of the Yb ions is strongly quenched, resulting in strong unbleachable absorption around 976 nm and the loss of laser action [135]. This effect was tentatively attributed to color centers. Because energy migrates rapidly between Yb ions, even a small percentage of quenched ions can lead to loss of inversion for most of the Yb population. It means that for practical lasers and amplifiers utilizing Yb as the laser ion or as a co-dopant, the pump must be detuned from 976 nm, while laser action near this wavelength may be extremely inefficient. 3.7.2 Core-Pumped Yb-Doped Fiber Lasers Hanna, Tropper, and co-workers, at the University of Southampton, were first to study the performance of Yb 3⫹ in a silica fiber [137,145,146]. In their original report, they used a pair of prisms as a dispersive element to tune a Yb-doped fiber laser over 152 nm, from 1010 to 1162 nm, across the long-wavelength emission band of Yb 3⫹ [146]. Because of its three-level nature, the Yb-doped fiber laser shifts to longer wavelengths when the fiber length is increased [137]. In one report, the wavelength shifted from 975 nm in a 1-m laser to nearly 1100 nm in a 100-m laser, while a range of lengths supported simultaneous oscillation at two wavelengths [134]. Enough gain is available on the short-wavelength emission band of Yb 3⫹ that the two weak (3.5%) Fresnel reflections from cleaved fiber ends were sufficient to sustain efficient laser oscillation [146]. By proper selection of the fiber length, this fiber laser was also operated at 974 nm. Its characteristics were excellent, including a relatively low threshold of 11.5 mW (in spite of the high transmission of the reflectors), and a maximum output power of 9.3 mW (sum of the outputs from both ends) for 25.3 mW of pump power, or a slope efficiency of 67% (all figures against absorbed power). A 980-nm Yb-doped fiber laser with similar performance was reported soon after by British Telecom [138]. It used a much shorter (8.6 cm), higher-concentration fiber. A summary of the characteristics of these and other Yb-doped silica fiber lasers can be found in Table 5. In another study, Mackechnie et al. used a long Yb-doped fiber (100 m) to force oscillation close to 1115 nm [144]. The resonator utilized a dichroic high reflector butted against one fiber end and the cleaved face of the other fiber end, which acted as the output coupler. When pumped with an Nd: YLF laser (1047 nm), this laser produced a maximum output power of 660 mW, the record at the time. However, the threshold was high (610 mW) and the slope efficiency modest (28%, both figures against incident pump power), partly because the fiber was slightly multimoded at the laser wavelength. Two years later, the same research group reported a similar but improved fiber laser using a single-mode fiber [134]. When free running at 1102 nm, its threshold was 30 mW, its output power was 520 mW, and the slope efficiency was a record 90% (both against launched power). The performance was only slightly lower when pumping at 850 nm with a Ti:sapphire laser (30-mW threshold and 79% slope efficiency, except that the cavity

900 nm 890 nm 869 nm 974 nm 974 nm 915 nm 875 nm 850 nm 915 nm 1047 nm 915 nm 1047 nm 915 nm 1047 nm

974 nm 980 nm 1019 nm 1040 nm 1047 nm 1065 nm ⬃1090 nm 1098 nm 1101 nm 1102 nm 1114 nm 1115 nm 1120 nm 1140 nm

580 ppm 2 10 20 Yb/cm 3 0.11 wt% Yb 500 ppm Yb 1800 ppm Yb NA ⬃600 ppm Yb 550 ppm Yb NA 550 ppm Yb 1.5 wt% Yb 700 ppm NA 550 ppm Yb

Ytterbium conc. 0.5 m 8.6 cm 7m 5m 10 cm NA NA 90 m NA 90 m 50 m 100 m NA 90 m

Fiber length Dye laser pump Dye laser pump Ti : sapphire DCF/Ti :sapphire Single-frequncy DCF/LD bar DCF/LD pump Ti : sapphire pump DCF/LD bar Nd :YLF pump DCF/4 LD bars Multimode DCF/4 LD bars Nd :YLF pump

Other features

Slope efficiency 67% (a) 66% (l) 41% (i) 70% (i) 44% (l) 54% (l) 69% (l) 79% (l) 52% (l) 90% (l) ⬃65% (i) 28% (i) 58.3% (i) 66% (l)

Threshold 11.5 mW (a) 15.8 mW (l) 14 mW (i) 75 mW (i) ⬍230 µW (l) ⬍100mW (l) 5 mW (l) 33 mW (l) 2.2 W (l) 30 mW (l) 0.6 W (i) 610 mW (i) ⬍22 W (i) 6 mW (l)

NA, data not available; LD, laser diode; DCF, double-clad fiber. (i) With respect to incident pump power; (l) with respect to launched pump power; (a) with respect to absorbed pump power.

Pump wavelength

Laser wavelength

9.3 mW @ 25.3 mW (a) 10.6 mW @ 48.4 mW (l) 215 mW @ 550 mW (i) 470 mW @ 750 mW (i) 7.5 mW @ 18 mW (l) 16.4 W @ 32.5 W (l) 51 mW @ 80 mW (l) 410 mW @ 550 mW (l) 20.4 W @ 32.5 W (l) 520 mW @ 600 mW (l) 35.5 W @ 55.4 W (i) 660 mW @ ⬃3W (i) 110 W @ 180 W (i) 330 mW @ 500 mW (l)

Output power @ pump power

Table 5 Characteristics of Representative cw Yb-Doped Silica Fiber Lasers, Listed in Order of Increasing Laser Wavelength

137 138 147 139 140 141 142 134 141 134 143 144 61 134

Ref.


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was formed by the two cleaved fiber ends and the output power was split equally between the two ends). A maximum output of 2 W (1 W at each end) was reported when pumping this laser with a higher-power 1064-nm Nd :YAG laser. The same fiber laser was constrained to specific wavelengths by splicing a narrowband fiber grating at each fiber end (as was also done earlier [147]). The two wavelengths that were selected were 1020 nm (as a potential pump source for Pr-doped fluoride fiber amplifiers and up-conversion lasers) and 1140 nm (to pump blue up-conversion Tm-doped fluoride fiber lasers). Though not quite as efficient as the free-running lasers, these two fiber lasers had a low threshold and a high slope efficiency, as illustrated in Table 5 for the 1140-nm laser. More recent work on Yb-doped fiber lasers has focused on single-frequency operation (see Chap. 5) [134,140,148]. As an example, Asseh et al. described a very short (10 cm) single-frequency fiber laser with a very low threshold (⬍230 µW) owing to the use of a low-loss DFB structure, and a good slope efficiency (44%) [140] comparable with those observed in free-running fiber lasers. 3.7.3 Double-Clad Yb-Doped Fiber Lasers In spite of its important advantages, Yb 3⫹ attracted comparatively little attention in the early years of this field. This was partly because it was largely overshadowed by the more efficient Nd-doped laser, and partly because of the perceived handicap of its three-level nature. More recently, however, and perhaps as a result of the resounding success of the three-level EDFA, a growing number of laboratories have turned to Yb-doped fiber lasers as potential high-power lasers, using in particular double-clad fibers. Gapontsev et al. were first to test cladding-pumped Yb-doped fiber lasers [142]. They reported a very efficient laser at ⬃1090 nm pumped with an 875-nm laser diode (5-mW threshold, 69% slope efficiency), but unfortunately their laser diode power was low and the fiber laser output was limited to 50 mW. It was nevertheless a landmark, and the first laser-diode pumped laser of this kind. Pask et al. improved on this result with a 1040-nm, free-running, double-clad Yb-doped fiber laser pumped at 974 nm with a Ti:sapphire laser [134,139]. The maximum output power was 470 mW at an incident pump power of 750 mW (see Table 5). Since the mid-1990s, high-power Yb-doped fiber lasers have progressed rapidly, from 2 W in 1995 [134], to 20 W [141] and 35 W [143] in 1997, and 110 W in 1999 [61], the published record at the time of this writing. The 20-W fiber laser, reported by Inniss et al., used a Fabry–Perot cavity made with photoinduced gratings formed in a deuterium-loaded fiber [141]. The pump source was a high-power 915-nm InGaAs/AlGaAs laser diode bar. A special optical beam shaper was designed to couple over 50 W into the Yb-doped fiber cladding [149]. The fiber laser emitted 16.4 W at 1065 nm, and 20.4 W at 1101 nm, in both cases for 32.5 W of launched pump power [141]. Both lasers had slope efficiencies in excess of 50%, and a fairly narrow spectrum (0.24 nm and 0.37 nm, respectively). The threshold of the 1.1-µm laser was less than 100 mW. Its output was used to pump a cascaded Raman fiber laser and was efficiently converted to 8.5 W of 1472-nm light [141]. The 35-W fiber laser reported at the same time by Muendel and co-workers of Polaroid Corporation improved on this result in two ways. First, it achieved an even greater slope efficiency of ⬃65% against incident power. Second, it was pumped bidirectionally with two laser diodes in each direction [143]. The cavity was made of a high reflector at one end and the 3.6% Fresnel reflection from the other, polished fiber end. This laser


149

produced as much as 35.5 W at 1114 nm. The spectrum was fairly broad, about 9 nm (FWHM), perhaps as a result of self phase modulation. At high power the output was very quiet (0.2% rms noise) and almost fully unpolarized. Dominic and co-workers, of SDL, Inc., boosted this record by roughly a factor of three by using a similar design; namely, a highly efficient laser (58.3% slope efficiency against incident pump power) made with a high reflector and a 3.6% Fresnel reflector, and pumped with four laser diode bars [61]. The main improvement stems from increasing the incident pump power to 180 W. The Yb-doped fiber was spooled and cooled with a fan. The maximum output power in the recollimated output beam exceeded 110 W. Although the average optical density in the fiber core was ⬃300 MW/cm 2, no catastrophic fiber failure was observed. The output did, however, exhibit some measurable beam steering and a slight degradation of beam quality, worsening with increasing power [61]. These effects were tentatively linked to thermal lensing in the output lens, which was exposed to 190 W of total cw power. Such issues need to be addressed in the future to achieve higher output beam quality, although the double-clad Yb-doped fiber laser has already emerged as a viable alternative to commercial cw Nd-doped crystal lasers. 3.8 THULIUM 3.8.1 Basic Spectroscopy Energy Level Diagram A partial energy level diagram of Tm 3⫹ in silica is shown in Figure 11. Thulium presents three major absorption bands in the IR; namely, from the ground state 3 H 6 to the 3 F 4 level (⬃1630 nm), to the 3 H 5 level (⬃1210 nm), and to the 3 H 4 level (⬃790 nm). Note that, as pointed out in Chapter 9, we use in Figure 11 the correct labeling of the 3 F 4 and 3 H 4 levels, which is reversed from the common usage found in the literature. The 3 F 4 level is the main metastable level. Its measured lifetime ranges from 200 µs [150], to 300 µs [13], 500 µs [13,151], and 600 µs [152]. This wide range reflects variations due to fabrication method (e.g., solution doping versus MCVD) [151] and composition [13]. In particular, Al codoping increases this lifetime [13] to a maximum reported value of 600 µs. [152]. Because of the high phonon energy of silica, this lifetime is mostly nonradiative, although it has a nonnegligible radiative component: its radiative quantum efficiency has been estimated to be approximately 6% in solution-doped fibers [151], and at most ⬃12% in MCVD fibers [153]. This is in sharp contrast with fluoride fibers, in which this quantum efficiency is close to unity. In silica, the 3 H 4 level is nonradiatively coupled to the underlying 3 H 5 level, and it is only weakly metastable. One reference cites its lifetime as ⱕ10 µs [150]. The 3 H 5 level has a short lifetime because it is strongly coupled nonradiatively to the nearby 3 F 4 level. Laser Transitions All Tm-doped silica fiber lasers yet reported have been operated around 1.9 µm on the F 4 → 3 H 6 transition. One of the most beneficial properties of thulium is the enormous bandwidth of this transition: the lasers that have been demonstrated in various compositions range in wavelength from ⬃1.7 to ⬃2.1 µm. Such bandwidth makes Tm-doped silica a great source of coherent radiation at mid-IR wavelengths not available from other rare earths. Because of the strong Stark splitting, this laser is quasi-three-level near 1.9 µm, moving toward a four-level laser at longer wavelengths. The wavelength range of Tm-

3

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Energy level diagram of Tm 3⫹ in silica. Solid lines: radiative transitions. Dashed lines: nonradiative transitions.

Figure 11

doped fiber lasers includes the strong absorption overtone of water around 1.98 µm, a wavelength now used in various developing microsurgical procedures, such as laser angioplasty, blood coagulation, and microsurgery. This laser is also expected to find applications in eye-safe LIDAR and for atmospheric sensing, in particular the detection of CO 2 and methane, which exhibit absorption lines in this range. It may also become an important laser source in ultra-low-loss fiber communication. Stimulated emission arising from up-conversion has also been observed in the blue and UV in Tm-doped fibers pumped in the IR [154]. However, as described in the following these have not yet produced laser oscillation. Pump Wavelengths The 3 H 6 → 3 F 4 absorption band of Tm-doped silica possesses an extremely broad linewidth, close to 130 nm. In fact, it is one of the broadest in any of the trivalent rare earths. This material can thus be pumped in the short-wavelength wing of this transition at 1064 nm. However, as shown in Figure 11 this wavelength suffers from ESA to the 3 F 2 , 3 F 3 levels [153,155,156]. Another possible pump band is at about 670 nm, on the 3 H 6 → 3 F 2 , 3 F 3 transition, although performance is again limited by pump ESA [151,157]. Photochromic effects in Tm-doped fibers pumped with an Ar-ion laser may preclude the use of short pump wavelengths [158]. The pump band most commonly used is the 3 H 6 → 3 H 4 transition at about 800 nm, which fortunately exhibits no significant ESA. This transition is also very broad, and it allows pumping at the strong absorption peak near 790 nm with either a AlGaAs laser


151

diode or a Ti:sapphire laser. Another useful feature is cross-relaxation between Tm 3⫹ pairs, which takes place at higher Tm concentrations [153]. This process leads to energy transfer from a Tm 3⫹ ion in the 3 H 4 level (the donor) to a neighboring Tm 3⫹ ion in the ground state (the acceptor). The latter is thus excited to the 3 F 4 level, whereas the donor drops to the 3 F 4 level, yielding two excited ions for one pump photon, or a quantum efficiency of 2. This effect has been used effectively to pump a fiber laser with a high Tm concentration (7 ⫻ 10 19 cm ⫺3) [153]. It is thought to be responsible for the near-unity quantum efficiency measured in Tm-doped fiber lasers pumped at about 800 nm [151,152]. Tm-doped silica fibers have also been pumped at 1570 nm, which corresponds to the absorption peak of the 3 H 6 → 3 F 4 transition. Because it excites the Tm 3⫹ ions directly into the 3 F 4 level, it produces a higher efficiency [20]. The energy level diagram of Tm 3⫹ (see Fig. 11) suggests ESA at this wavelength, although no mention of it is made in the literature. 3.8.2 Thulium-Doped Fiber Lasers General Properties Table 6 summarizes the properties of representative cw Tm-doped silica fiber lasers. Again most of the early work was carried out at the University of Southampton by Hanna, Tropper, and co-workers, who coauthored nearly two-thirds of all publications on this subject. The threshold of Tm-doped fiber lasers is typically tens of milliwatts, mostly as a result of the low quantum efficiency of the transition. However, by increasing the metastable lifetime with Al co-doping and reducing the cavity loss, a launched pump power threshold of only 4.4 mW (with a moderate slope efficiency of 17%) was reported, which allowed pumping with a laser diode [13]. In contrast, the slope efficiencies are typically fairly high, in the 30% range or higher. The highest reported value, 66% against launched pump power, was obtained with 1.57-µm pumping. Fiber lengths are typically fairly short for a rare earth doped silica fiber laser, from as low as 22 cm to 4 m. As in other quasi-four-level lasers, the laser wavelength can be adjusted by changing the fiber length or the reflectivity of the mirrors [20,70]. Jackson and King reported a detailed experimental analysis of the dependence of the threshold, slope efficiency, and laser wavelength on the fiber length and mirror reflectivity [70]. By varying these two parameters, they could adjust the laser wavelength from 1877 to 2033 nm. Using an intracavity three-plate birefringent filter as a tuning element, a Tm-doped fiber laser was also tuned over 237 nm for a given fiber length, and over 276 nm (1780 to 2056 nm) with two different fiber lengths [151]. The tuning curve is reproduced in Figure 12 [151,153]. In a similar study, a Tm-doped aluminosilicate fiber laser was tuned from 1.71 to 2.0 µm, or a range of nearly 300 nm [13]. This is the widest tuning range achieved in a silica fiber laser. A second laser made with a germanosilicate fiber was tuned over a slightly shorter range (210 nm) shifted 60–80 nm toward shorter wavelengths, showing the considerable influence of the host on the laser wavelength [13]. For reference, Tm-doped fibers have also been used in a ring laser configuration [20] and in a photoinduced Bragg grating cavity [152]. They have been pumped with laser diodes [13,70,152], Q-switched [159], gain switched [160], and mode-locked [161]. The energy budget of cw Tm-doped fiber lasers has been the object of several theoretical studies [162,163] that tend to be rather complex owing to the number of cross-relaxation and ESA processes involved.

660 786 790 790 792 797 808 810 1064 1064 1064 1570

nm nm nm nm nm nm nm nm nm nm nm nm

Pump wavelength 830 ppm Tm 200 ppm Tm ⬃7 10 19 cm ⫺3 1.45 10 20 cm ⫺3 250 ppm Tm 830 ppm Tm ⬃4000 wt. ppm Tm ⬃3000 ppm Tm 840 ppm Tm 840 ppm Tm 840 ppm 320 ppm Tm

Thulium conc. 27 cm 45 cm NA 1.58 m 2.1 m 27 cm 0.5 m 22 cm 1.4 m 70 cm 1.75 m 4m

Fiber length Dye laser pump LD pump/MM Ti: sapphire pump DCF/16 LDs/MM Ti: sapphire pump Dye laser pump/MM Ti: sapphire pump Dye laser pump/MM Nd: YAG pump/MM Nd: YAG pump/MM Nd: YAG pump/MM EDFL/MM

Other features 50 mW (a) 4.4 mW (l) ⬃32.5 mW (l) 3.3 W (l) 36 mW (l) 21 mW (a) 15 mW (l) 44 mW (a) ⬃900 mW (a) NA 60 mW (a) 95 mW (l)

Threshold 1.3% (a) 17% (l) 49% (l) 31% (l) 30% (l) 13% (a) 36% (l) 36% (l) 37% (l) NA 30% (a) 66% (l)

Slope efficiency

NA 1 mW @ 11.5 mW (a) NA 5.4 W @ ⬃20.5 W (l) 8.5 mW @ 65 mW (l) 2.7 mW @ 42 mW (a) 0.2 W @ ⬃0.59 W (l) 44 mW @ 167 mW (a) 1.05 W @ 3.8 W (a) 1.35 W @ ⬃4.5 W (a) 51 mW @ 230 mW (a) 21 mW @ 127 mW (l)


Characteristics of Representative cw Tm-Doped Silica Fiber Lasers, Listed in Order of Increasing Pump Wavelength

NA, data not available; LD, laser diode; DCF, double-clad fiber; MM, multimode at the laser wavelength; EDFL, Er-doped fiber laser. (i) With respect to incident pump power; (l) with respect to launched pump power; (a) with respect to absorbed pump power.

⬃1.96 µm 1.94 µm 1.9 µm 1980 nm 1945 nm 1.96 µm 2102 nm 1900 nm 2.01 µm 2.0 µm 2038 nm 1.9 µm

Laser wavelength

Table 6

157 13 153 70 159 150 152 151 156 156 155 20

Ref.

152 Digonnet


153

Figure 12

Experimental tuning range of two Tm-doped silica fiber lasers of different fiber lengths. (From Ref. 151.)

High-Power Lasers The Tm-doped silica laser system is efficient enough that core-pumped fiber lasers with output powers in excess of 1.3 W were achieved very early on [156]. Higher powers, in the 5-W range, were later observed in double-clad fibers [70]. Although many of the lasers listed in Table 6 had a cutoff wavelength below 1.9 µm, they were probably oscillating in the fundamental mode [151]. In spite of ESA at 1064 nm, Tm-doped fiber lasers have been essentially as efficient when pumped at this wavelength [155,156]. For 1064-nm pumping to be efficient, it is essential to maintain the cavity loss as low as possible to minimize the population in the 3 F 4 level, and thus minimize the loss of pump photons through ESA. In spite of ESA, the output power grows linearly with absorbed pump power, because above threshold the laser population is clamped [155], and the relative pump power lost to ESA does not change. Tm-doped fiber lasers pumped at 1064 nm have produced up to 1.35 W of output power for 4.5 W of absorbed pump power [156]. Up-Conversion In fluorozirconate fibers, Tm 3⫹ has produced efficient up-conversion fiber lasers (see Chap. 4). In silica fibers, however, up-conversion is expected to be hindered by short nonradiative lifetimes. In spite of this shortcoming, fluorescence caused by frequency up-conversion has been observed near 370 and 460 nm in Tm-doped silica fibers excited at 660 nm [154]. The 460-nm fluorescence is thought to arise from two-photon absorption, a first photon from the 3 H 6 level to the 3 F 2 / 3 F 3 levels, which rapidly decay to the underlying 3 H 4 level, followed by absorption of a second photon to the 1 D 2 level (see Fig. 11). Decay from this level to the ground state produces fluorescence at 460 nm. Fluorescence was also observed at 370 and 467 nm under 1064-nm pumping [154]. The latter was attributed to three-photon absorption to the 1 G 4 level followed by fluorescence to the ground state (see Fig. 11). Yb-sensitized Tm-doped silica fibers pumped at 1064 nm also produced blue fluorescence by multiple energy transfers from the excited Yb ions to the Tm ions

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[154]. These up-conversion processes were too inefficient (only ⬃10 ⫺5 of the ground state was depleted) to produce a useful laser, largely because of the short nonradiative lifetime of the levels involved. The observation of photodarkening in Tm-doped silica fibers exposed to strong 475-nm light, attributed to the formation of color centers [158], points to another difficulty with the operation of this host as a blue laser. 3.9 HOLMIUM Figure 13 shows a partial energy level diagram of Ho 3⫹. This ion exhibits strong GSA bands centered around 450, 540, and 650 nm. Laser emission has been observed at about 2 µm from the 5 I 7 level to the ground state 5 I 8. It is typically centered between 1.9 and 2.0 µm and exhibits a FWHM bandwidth of about 200 nm [11,137,164,165]. Therefore, this laser is potentially useful for some of the same applications as the Tm-doped laser, in particular for medical applications. When pumped on any of the foregoing pump bands, it is a quasi-three-level transition. The lifetime of the 5 I 7 level in silica has been measured to be 600 µs [164]. A quantum efficiency was inferred [165] for the 5 I 7 → 5 I 8 transition of 0.11, which is lower than in fluoride fibers, perhaps as a result of nonradiative relaxation from the 5 I 7 level. The earliest Ho-doped silica fiber laser was pumped at 457.9 nm with an Ar-ion laser, and it had a relatively high threshold of 46 mW and a low slope efficiency of 1.7% [137,164] (Table 7). Most of the subsequent work used Ho 3⫹-doped silica fibers sensitized with Tm 3⫹ [11,56,162,165,166] which present the advantage that they can be pumped between 800 and 830 nm and at 1064 nm. As illustrated in Figure 13 for 0.8-µm pumping, a pump photon excites a Tm 3⫹ ion to the 3 H 4 level. This level decays nonradiatively to the metastable level (3 F 4) of Tm 3⫹, and its energy is transferred to an Ho 3⫹ ion in the ground state, which is thus excited to the metastable level 5 I 7. To achieve high pump absorption, especially when pumping in the wings of the Tm 3⫹ absorption band, the Tm concentration is generally chosen to be very high, typically 5–40 times larger than the Ho concentration

Figure 13 Energy level diagram of Ho 3⫹ in silica, showing sensitization with Tm 3⫹. Solid lines: radiative transitions. Dashed lines: nonradiative transitions.

Pump wavelength 457.9 nm 809 nm 1064 nm 820 nm 786 nm 488 nm 590 nm 590 nm 590 nm 592 nm

Laser wavelength

2.04 µm 2.04 µm 2023 nm 2076 nm ⬃2 µm 650 nm 888 nm 1048 nm 1080 nm 1047 nm 200 ppm Ho 0.02 wt% Ho 0.13 wt% Ho 600 ppm Ho 0.02% mol% Ho 250 ppm Sm ⬃10 19 Pr/cm 3 ⬃4.8 10 18 Pr/cm 3 ⬃10 19 Pr/cm 3 6 10 18 Pr/cm 3

Rare-earth concentration Ar-ion laser 0.2 wt% Tm 0.8 wt% Tm 2.3% Tm 0.2% mol% Tm Ar-ion laser Dye laser Dye laser Dye laser Dye laser

Other features 17 cm 30 cm 57.4 cm 22 cm 36 cm NA 1.3 m 1.08 m 1.3 m 1.05 m

Fiber length 46 mW 77.5 mW (a) 625 mW (l) 214 mW (a) 625 mW (i) 20 mW (a) ⬃10 mW (a) 4 mW (a) 16 mW (a) 23 mW (a)

(a)

Threshold 1.7% 13.5% (a) 1.8% (l) 4.2% (a) 17.5% (i) 12.7% (a) NA 18% (a) 2.7% (a) 4.7% (a)

(a)

Slope efficiency

0.67 mW @ 85 mW 5.8 mW @ 147 mW (l) 11 mW @ 1.25 W (l) 12.5 mW @ 510 mW (a) 71 mW @ 1.03 W (i) 28 mW @ 250 mW (a) NA NA 1.6 mW @ 75 mW (a) 4.3 mW @ 115 mW (a)

(a)


Characteristics of Representative cw Silica Fiber Lasers Doped with Ho 3⫹, Pr 3⫹, and Sm 3⫹, Listed in Order of Increasing Output Power

NA, data not available. (i) With respect to incident pump power; (l) with respect to launched pump power; (a) with respect to absorbed pump power.

Ho Ho 3⫹ Ho 3⫹ Ho 3⫹ Ho 3⫹ Sm 3⫹ Pr 3⫹ Pr 3⫹ Pr 3⫹ Pr 3⫹

3⫹

Rare-earth ion

Table 7

164 68 166 165 56 10 167 168 167 169

Ref.


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(see Table 7). High energy transfers have been reported [11]. For a given fiber length, the pump wavelength must be carefully selected to optimize the fiber laser output power. If the pump wavelength is such that the pump is absorbed too strongly, more power is absorbed per unit time by the Tm ions than can be transferred to the Ho ions. If the pump is absorbed too weakly, the inversion drops and the output power is reduced [11]. As in any quasi-three-level laser, the wavelength can be adjusted by changing the fiber length. In Ho/Tm-doped silica fiber lasers, oscillation was thus demonstrated from 2037 to 2096 nm (length change from 13 to 35 cm) [165], from 1960 to 2032 nm (1–35 cm) [162], and from 1960 to 2170 nm (23–124 cm) [166]. Several laser peaks have been observed between 1840 and 2260 nm in a free-running Ho/Tm-doped silica fiber laser, indicating a potentially much broader tuning range [11]. This last wavelength is the longest reported for a doped silica fiber laser. Ho/Tm-doped fiber lasers have been pumped with Ti:sapphire lasers [56,162,165], dye lasers [11], Nd: YAG lasers [166], and AlGaAs laser diodes [11]. As can be seen in Table 7, all pump bands have produced relatively high thresholds and low to modest slope efficiencies. Pumping in the 800-nm band of Tm is more efficient than pumping Ho at 1064 nm. The highest reported output power (71 mW) and highest conversion efficiency (17.5%) were obtained with a double-clad Ho/Tm-doped fiber [56]. A theoretical model of the Ho/Tm-doped fiber laser in Ref. 166. 3.10 PRASEODYMIUM One of the most interesting features of Pr 3⫹ is that it possesses several metastable levels, in particular 3 P 0 , 1 D 2 , and 1 G 4 (see Fig. 36 of Chap. 9); and thus, it offers a broad range of fluorescence bands that have produced laser oscillation in crystalline hosts. For example, spontaneous emission from the 1 D 2 level has been observed at close to 630 nm (to the 3 H 4 level), 890 nm (3 F 2 / 3 H 6 levels), 1050 nm (3 F 3 / 3 F 4 levels), and ⬃1550 nm (1 G 4 level) [167,170]. Pr-doped silica also exhibits several pump bands, from the ground state 3 H 4 to the 3 P 0 (⬃488 nm), 1 D 2 (⬃590 nm), and 1 G 4 (⬃970 nm) levels. The lifetime of the 1 D 2 level has been measured to be ⬃120 µs. Most Pr-doped silica fiber lasers have been pumped directly to the 1 D 2 level with a dye laser at about 590 nm, and operated on the 1 D 2 → 3 F 3, 3 F 4 transition in the 1050to 1080-nm range (see Table 7) [137,167–169]. Pumping at 488 nm to the higher energy 1 P 0 level also induced lasing on this transition, but with an order-of-magnitude higher threshold [167]. It suggests that, at least in that fiber, relaxation from the 3 P 0 level was not dominantly radiative to the 1 D 2 level, but perhaps involved cross-relaxation. Lasing has also been observed at 888 nm [167]. Early lasers had a relatively high threshold (as high as 23 mW) and a slope efficiency of only a few percent (see Table 7). This was tentatively attributed to a low quantum efficiency, estimated to ⬃2% for the 1050-nm transition and ⬃0.7% for the 890-nm transition [167]. However, more recently, Shi and Poulson reported a 1048-nm Pr-doped silica fiber laser with a much lower threshold (4 mW) and higher slope efficiency (18%) [168]. This laser was also successfully mode-locked into 45-ps, 9-W pulses at 100 MHz, at a pump power of only 216 mW. As the cavity round-trip loss was at least 30% [168], the gain efficiency at 1048 nm in this fiber was at least ⬃0.4 dB/mW, which suggests a substantial quantum efficiency. This result was confirmed soon after by the same group, with the demonstration of a highly efficient superfluorescent fiber source (SFS) constructed with nominally the same Pr-doped fiber [171]. The SFS emitted 60 mW of broadband


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ASE for an absorbed pump power of 185 mW. Its slope efficiency was ⬃43%. When compared with the ratio of signal to pump photon energy of 592/1049 ⫽ 56.4%, this result suggests that the quantum efficiency of the 1050-nm transition in this fiber was ⬃76%. This is in approximate agreement with an independent measurement of a branching ratio of 56% for this transition in this fiber [172]. A Pr-doped silica fiber laser has been tuned over a broad range of 86 nm, from 1000 to 1086 nm [169], suggesting that if the efficiency can be further improved, as may be anticipated from the foregoing results, this laser may become competitive with the Nddoped fiber laser. 3.11 SAMARIUM Samarium has produced the shortest wavelength in doped silica fibers (650 nm) [9,10,173]. Such a short wavelength is of interest in particular for optical data storage applications. As shown in Table 7, a relatively low Sm 3⫹ concentration was used to avoid quenching effects. Pumped at 488 nm, the laser had a threshold of 20 mW and a slope efficiency of 12.7% with a 60% output coupler. Its maximum output power was 28 mW. This laser was also Q-switched (10-W peak, 300-ns pulses) and self-mode-locked [10]. 3.12 POLARIZATION PROPERTIES The state of polarization (SOP) and degree of polarization of a fiber laser output are important parameters in most applications. Some sensor systems, for example, utilize polarization-sensitive components and benefit from a linearly polarized fiber laser. Other systems operate best with an unpolarized source. How these parameters vary with laser design—in particular, with pump power, pump polarization, fiber characteristics, and environmental parameters, is therefore of great interest. Unfortunately, polarization properties are among the least extensively studied characteristics of fiber lasers, and they are generally poorly known. However, the polarization properties of fiber amplifiers, in particular EDFAs, has received a lot of attention because of the need for a time-invariant gain in communication links. This section first summarizes the main results reported in this field, then describes the various approaches reported to produce highly polarized fiber lasers. 3.12.1 Polarization of Fiber Lasers Basic Concepts One of the key phenomena that affects the polarization of a fiber laser is polarizationdependent gain (PDG). This effect stems from the fact that rare earth ions in a glass do not absorb or emit isotropically: each ion can be thought of as an anisotropic absorber and emitter, with a certain spatial orientation. In an amorphous host such as a glass, the ions are randomly oriented. The cross-section anisotropy is generally assumed to be siteindependent, and to be identical for absorption and emission (theoretical models based on these hypotheses yield predictions consistent with experimental observations). The anisotropy can thus be characterized by a single anisotropy parameter ε ⫽ σ m /σ M , where σ m and σ M are the minimum and maximum cross sections of the ions, respectively [38,174]. In a rare earth doped fiber pumped with linearly polarized light, which is almost always the case, ions oriented roughly parallel to the pump polarization absorb more strongly than ions oriented roughly perpendicular to it, and they are thus excited in greater numbers.

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In addition, they have a higher emission cross section in the direction of the pump. Consequently, the gain is higher for a signal polarized parallel to the pump than for a signal polarized perpendicular to it. The gain difference depends strongly on the degree of anisotropy. For erbium, it can be as large a 2 dB when ε ⫽ 0 [38], but it has been measured to be less than 0.1 dB in practical fibers [35,38]. Although small, this effect has a strong influence on fiber lasers: as described further on, it can cause single-polarization oscillation. Most fiber lasers use a low-birefringence fiber. The two eigenpolarizations are then nearly degenerate and easily coupled by mechanical perturbations. Consequently, independently of the internal effects of PDG, the output polarization also strongly depends on (1) how the pump is launched into the fiber, and (2) the fiber environment, in particular external perturbations (tension, pressure, twists, bends, and such) applied to any low-birefringence fiber link between the pump source and the doped fiber. PDG in EDFAs has been studied both theoretically [33,37,38] and experimentally [35,38]. Following earlier studies of Nd-doped glass lasers [174], Lin and co-workers were first to model PDG in doped fibers [33]. They derived simple expressions for the degree of polarization and the dependence of the slope efficiency on the pump polarization. Subsequently, Falquier et al. modeled PDG by integrating the rate equations over all possible orientations of the erbium ions, and derived closed-form expressions for the gain [36]. Wysocki and Mazurczyk used a similar approach; they grouped the ions in a large, but finite, number of subsets, each one oriented at a different angle [37]. They also provided approximate expressions for PDG in an EDFA. The foundations and predictions of this model are described in Chapter 11. Wagener et al. followed a different approach and used a Mueller matrix formalism to describe the state of polarization of both the pump and signals at any point along the doped fiber [38]. The rate equations are rewritten in a matrix form and integrated numerically. This matrix formalism can easily take into account such effects as fiber birefringence and polarization-dependent loss in the fiber and fiber components. It has accurately predicted the behavior of EDFAs and fiber lasers [38], as well as polarized and depolarized superfluorescent fiber sources [39,175]. Experimental Observations An example of polarization effects in a fiber laser is shown in Figure 14. This laser consisted in 90-m of polarization-maintaining (PM) fiber lightly doped with erbium and pumped with linearly polarized light at 980 nm [38]. As the orientation of the pump polarization at the fiber input is varied, the fiber laser polarization varies substantially. When the pump polarization is aligned with the x axis of the PM fiber, the x-polarization power grows linearly above a certain threshold (see Fig. 14a). The y-polarization power, on the other hand, grows much more slowly. It is, in fact, due entirely to ASE. The reason is gain competition: the x polarization is parallel to the pump and experiences a higher gain than the y polarization. It begins to oscillate first, and through saturation leaves too little gain for the y polarization to reach threshold. The behavior of the x- and the ypolarized outputs is reversed when the pump was launched into the y axis. Thus, PDG can be strong enough to produce a single-polarization fiber laser. When the pump is launched with its polarization at 30° to the x axis (see Fig. 14b), the laser starts oscillating with an x polarization at a pump power threshold of ⬃10 mW. Because the pump is now partially polarized along y, at higher pump power (⬃15 mW), the y polarization sees enough gain to start oscillating too. Above this power level, both output polarizations continue to grow, and the output polarization depends in a complex manner on their rela-


159

(a)

(b)

Figure 14

Output power versus launched pump power measured in a fiber laser made with a polarization-maintaining Er-doped fiber, shown for the x-polarized and the y-polarized output polarizations. The pump light is linearly polarized, and launched (a) along the x axis of the fiber, and (b) at 30° to the x axis. (From Ref. 38.)

tive phase and power. As shown by others [33,34,176,177], the polarization of a fiber laser generally depends on the pump power and polarization. The solid curves in Figure 14 are theoretical predictions based the Mueller matrix formalism [38]. They are in good agreement with experimental observations, and predict an anisotropy parameter ε for this fiber between 0.6 and 0.7. From other measurements a value of ε ⫽ 0.01 was inferred for an Nd-doped fiber, and ε ⫽ 0.11 for an Er-doped

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fiber [33]. These results indicate that dipole transitions in both Nd and Er ions in a silicabased host can exhibit a strong anisotropy. They also suggest that this anisotropy depends on the ion, the composition of the host, or both. A discussion of experimental values of ε can be found in Ref. 37. Another noteworthy polarization effect is frequency splitting of the two polarization components, which has been observed in an Er-doped [177] and a Yb-doped [178] fiber laser. This intensity-dependent splitting, on the order of a few nanometers, has been attributed to gain competition between the two polarization modes. It can lead to undesirable spectral instabilities, especially in low-birefringence fibers. Although this effect has been used for low-power polarization switching [34], in general, it is detrimental. A singlepolarization fiber offers a simple solution to this problem. 3.12.2 Single-Polarization Fiber Lasers As mentioned earlier, the output polarization of a low-birefringence fiber laser is generally not linear, possibly unstable, and pump-power-dependent. However, a stable, highly polarized output is desirable for many applications. In addition to the approach based on PDG described in the previous section [38], several schemes have been developed to produce such a fiber laser [34,179,180]. The first scheme involves an intracavity polarizer to increase the cavity loss preferentially for one of the polarization modes, which thus experiences a higher threshold and does not oscillate. Ideally, the polarizer should exhibit a high loss for the undesired mode, a negligible loss for the desired mode, and be easy to align with the fiber birefringence axes. In-line fiber polarizers meet all of these requirements and are ideal for this purpose. Three basic types of fiber polarizers have been implemented to this end [34,179]. The first type was a fiber with a metal-filled hole parallel and very close to the fiber core [34], developed to produce fiber polarizers with high extinction ratios. The metal induces attenuation through ohmic losses for the polarization component orthogonal to the metal surface, while leaving the other component essentially unaffected. In one implementation, an Nd-doped fiber with a D-shaped gallium-filled core was placed in a Fabry–Perot cavity and pumped at 825 nm with a laser diode [34]. With 10 mW of absorbed pump power it produced a 2.1-mW–output power at 1088 nm with a 23-dB extinction ratio. An earlier version of this device, pumped at 514.5 nm, produced 20 mW of output power with a 35-dB extinction ratio [179]. A 1.54-µm single-polarization, Er-doped fiber laser based on the same principle was also demonstrated, with a 22-dB extinction ratio at an output power of 1.2 mW [34]. The third type of fiber polarizer implemented in this context is a metal-film polarizer, which is based on the same principle of differential ohmic loss. The fiber is polished on its side until the polished surface is within a wavelength or so of the fiber core. A metal film is then evaporated on the polished surface. This approach was applied to an Nddoped fiber laser pumped with an 825-nm laser diode [34]. With 10 mW of absorbed pump power, an output power of 3 mW at 1080 nm was produced, with a polarization extinction ratio of 25 dB. These approaches are fairly general and can be applied to fiber lasers utilizing other rare earths. The extinction ratio is expected to be ultimately limited by the residual ASE building up in the unwanted polarization, which should remain negligible up to fairly high pump power levels if the polarizer has a reasonably high rejection ratio.


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Another approach to produce a single-polarization fiber laser is to form a Fabry– Perot cavity with a high-birefringence doped fiber and two anisotropic fiber gratings [180]. This work, carried out by Pureur and co-workers, relied on two effects. First, the reflection coefficient of a photosensitive grating written in a high-birefringence fiber depends on polarization. Second, when gratings are written under different conditions, the Bragg wavelengths for the two eigenpolarizations are spaced by different amounts for the two gratings. By stretching one of the gratings, one can force the two Bragg wavelengths to overlap for one polarization only. By combining these two effects, the differential mode attenuation is strong enough to force single-polarization oscillation. Applied to an Nddoped fiber laser, this technique produced a linearly polarized output with an extinction ratio of 28 dB and an improved power and frequency stability against stresses applied to the fiber [180]. 3.13 SUMMARY AND FUTURE DIRECTIONS Rare earth doped silica fiber lasers have produced a large number of efficient light sources in the near- and midinfrared, with high spatial and temporal coherence. Many of them exhibit a low threshold and a high slope efficiency and can be pumped with a laser diode to produce a high output power, with a current record in excess of 100 W. Research has established that several parameters must be selected judiciously to accomplish such high performance, in particular the pump wavelength (to avoid ESA), the dopant concentration (which must generally be kept very low to eliminate quenching), the fiber length (to minimize GSA loss in three-laser systems), and the mode confinement (to reduce the threshold). Seven rare earth ions have produced laser emission from 650 to 2260 nm. Among them they cover more than 50% of this wavelength range. Many fiber lasers are tunable over wide wavelength ranges, the record being 300 nm with the Tm-doped fiber laser. The most efficient ions are Yb 3⫹ (974–1162 nm), Nd 3⫹ (900–945 nm, 1055–1145 nm, and 1360–1400 nm), Er 3⫹ (1535–1620 nm), and Tm 3⫹ (1710–2170 nm). These properties make fiber lasers particularly attractive for a broad range of applications, including optical communication, sensing, and medicine. For a few fiber lasers, development is sufficiently advanced that they have reached the commercial market. Compared with conventional bulk-optic lasers, they offer the benefits of ease of manufacturing, considerably reduced size, and substantial reduction in cost. Subpicosecond mode-locked Er-doped fiber lasers the size of a shoe-box and miniature Yb-doped fiber lasers putting out tens of watts are prime examples of sources that now compete with traditional lasers. As the needs of the communication industry and other industries evolve and their requirements become better defined, other commercial products are expected to be developed. Several research issues remain to be addressed. Studies of the polarization properties of fiber lasers have been limited and need to be expanded. Of particular importance is the need to produce a stable linearly polarized output, with a high extinction ratio, without jeopardizing the efficiency, which means combining high-efficiency fiber laser designs with low-loss polarizing schemes, both of which exist. Such improvements must be made, in particular, for high-power double-clad fibers. Further work is also needed to optimize the energy budget of double-clad fiber lasers, in particular the pumping efficiency. Research has often focused, as it should in early stages, on optimizing one parameter. Consideration should be given to optimizing simultaneously all parameters known to affect effi-

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ciency to produce optimum output powers. Another area of research in need of attention is the output stability and noise spectrum of fiber lasers (low-frequency power stability, relative intensity noise, and so on). To become competitive with solid-state lasers, in particular high-power laser-diode-pumped solid-state lasers, it is critical to develop fiber lasers with a comparable stability. Finally, the search for exotic glasses as alternative to silica-based hosts, such as sulfides and chalcogenides, must continue in an attempt to broaden the range of available wavelengths and laser characteristics, and to further optimize performance. REFERENCES 1. E. Snitzer. Proposed fiber cavities for optical masers. J. Appl. Phys. 32:36–39, 1961. 2. C. J. Koester, E. Snitzer. Amplification in a fiber laser. Appl. Opt. 3:1182–1186, 1964. 3. G. C. Holst, E. Snitzer, R. Wallace. High-coherence high-power laser system at 1.0621 µ. IEEE J. Quant. Electron. 5:342, 1969. 4. J. Stone, C. A. Burrus. Neodymium-doped silica lasers in end-pumped fiber geometry. Appl. Phys. Lett. 23:388–389, 1973. 5. J. Stone, C. A. Burrus. Neodymium-doped fiber lasers: room temperature CW operation with an injection laser pump. Appl. Opt. 13:1256–1258, 1974. 6. M. J. F. Digonnet, C. J. Gaeta, H. J. Shaw. 1.064- and 1.32-µm Nd :YAG single crystal fiber lasers. J. Lightwave Technol. 4:454–460, 1986. 7. S. B. Poole, D. N. Payne, M. E. Fermann. Fabrication of low-loss optical fibres containing rare earth ions. Electron. Lett. 21:737–738, 1985. 8. R. J. Mears, L. Reekie, S. B. Poole, D. N. Payne, Neodymium-doped silica single-mode fibre lasers. Electron. Lett. 21:738–740, 1985. 9. M. C. Farries, P. R. Morkel, J. E. Townsend. Samarium 3⫹-doped glass laser operating at 651 nm. Electron. Lett. 24:709–711, 1988. 10. M. C. Farries, P. R. Morkel, J. E. Townsend. The properties of the samarium fibre laser. In: Fiber Laser Sources and Amplifiers. Proc. SPIE 1171:271–278, 1991. 11. C. Ghisler, W. Luthy, H. P. Weber, J. Morel, A. Woodtli, R. Da¨ndliker, V. Neuman, H. Berthou, G. Kotrotsios. A Tm 3⫹ sensitized Ho 3⫹ silica fibre laser at 2.04 µm pumped at 809 nm. Opt. Commun. 109:279–281, 1994. 12. M. Monnery. Status of fluoride fiber lasers. In: Fiber Laser Sources and Amplifiers III. Proc. SPIE 1581:2–13, 1992. 13. W. L. Barnes, J. E. Townsend. Highly tunable and efficient diode pumped operation of Tm 3⫹ doped fibre lasers. Electron. Lett. 26:746–747, 1990. 14. M. Shimizu, H. Suda, M. Horiguchi. High-efficiency Nd-doped fibre lasers using directcoated dielectric mirrors. Electron. Lett. 23:768–769, 1987. 15. I. D. Miller, D. B. Mortimore, P. Urquhart, B. J. Ainslie, S. P. Craig, C. A. Millar, D. B. Payne. A Nd 3⫹-doped cw fiber laser using all-fiber reflectors. Appl. Opt. 26:2197–2201, 1987. 16. G. A. Ball, W. W. Morey, W. H. Glenn. Standing-wave monomode erbium fiber laser. IEEE Photon. Technol. Lett. 3:613–615, 1991. 17. Y. Chaoyu, P. Jiangde, Z. Bingkun. Tunable Nd 3⫹-doped fibre ring laser. Electron. Lett. 25: 101–102, 1989. 18. P. L. Scrivener, E. J. Tarbox, P. D. Maton. Narrow linewidth tunable operation of Er 3⫹doped single-mode fibre laser. Electron. Lett. 25:549–550, 1989. 19. J. Peng, Y. Chaoyu, H. Yidong, Z. Bingkun. All-fiber tunable and composite cavity ring fiber lasers using ultra low loss fiber couplers. Fiber Integrat. Opt., 12:31–38, 1993. 20. T. Yamamoto, Y. Miyajima, T. Komukai. 1.9 µm Tm-doped silica fibre laser pumped at 1.57 µm. Electron. Lett. 30:220–221, 1994.


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151. D. C. Hanna, R. M. Percival, R. G. Smart, A. C. Tropper. Efficient and tunable operation of a Tm-doped fibre laser. Opt. Commun. 75:283–286, 1990. 152. S. Boj, E. Delevaque, J. Y. Allain, J. F. Bayon, P. Niay, P. Bernage. High efficiency diode pumped thulium-doped silica fibre lasers with intracore Bragg gratings in the 1.9–2.1 µm band. Electron. Lett. 30:1019–1020, 1994. 153. A. Tropper, R. Smart, I. Perry, D. Hanna, J. Lincoln, B. Brocklesby. Thulium-doped silica fiber lasers. In: Fiber Laser Sources and Amplifiers II. Proc. SPIE 1373:152–157, 1991. 154. D. C. Hanna, R. M. Percival, I. R. Perry, R. G. Smart, J. E. Townsend, A. C. Tropper. Frequency upconversion in Tm- and Yb: Tm-doped silica fibers. Opt. Commun. 78:187– 194, 1990. 155. D. C. Hanna, M. J. McCarthy, I. R. Perry, P. J. Suni. Efficient high-power continuous-wave operation of monomode Tm-doped fibre laser at 2 µm pumped by Nd :YAG laser at 1.064 µm. Electron. Lett. 25:1365–1366, 1989. 156. D. C. Hanna, I. R. Perry, J. R. Lincoln, J. E. Townsend. A 1-watt thulium-doped cw fibre laser operating at 2 µm. Opt. Commun. 80:52–56, 1990. 157. D. C. Hanna, R. M. Percival, I. R. Perry, R. G. Smart, P. J. Suni. and A. C. Tropper. Continuous-wave oscillation of a monomode thulium-doped silica fiber laser. Conf. Tunable Solid State Lasers. OSA Proc. Ser. 5:Paper WE3, 350–353, 1989. 158. C. A. Millar, S. R. Mallinson, B. J. Ainslie, S. P. Craig. Photochromic behaviour of thuliumdoped silica optical fibres. Electron. Lett. 24:590–591, 1988. 159. P. Myslinski, X. Pan, C. Barnard, J. Chrostowski, B. T. Sullivan, J.–F. Bayon. Q-switched thulium-doped fiber laser. Opt. Eng. 32:2025–2030, 1993. 160. S. D. Jackson, T. A. King. Efficient gain-switched operation of a Tm-doped silica fiber laser. IEEE J. Quant. Electron. 34:779–789, 1998. 161. R. C. Sharp, D. E. Spock, N. Pan, J. Elliot. 190-fs passively mode-locked thulium fiber laser with a low threshold. Opt. Lett. 21:881–883, 1996. 162. C. Ghisler, W. Luthy, H. P. Weber. Tuning of a Tm 3⫹ :Ho 3⫹ :silica fiber laser at 2 µm. IEEE J. Quant. Electron. 31:1877–1879, 1995. 163. S. D. Jackson, T. A. King. Theoretical modeling of Tm-doped silica fiber lasers. J. Lightwave Technol. 17:948–956, 1999. 164. D. C. Hanna, R. M. Percival, R. G. Smart, J. E. Townsend, A. C. Tropper. Continuous-wave oscillation of holmium-doped silica fibre laser. Electron. Lett. 25:593–594, 1989. 165. K. Oh, T. F. Morse, A. Kilian, L. Reinhart, P. M. Weber. Continuous-wave oscillation of a thulium-sensitized holmium-doped silica fiber laser. Opt. Lett. 19:278–280, 1994. 166. S. D. Jackson, T. A. King. CW operation of a 1.064-µm pumped Tm-Ho-doped silica fiber laser. IEEE J. Quant. Electron. 34:1578–1587, 1998. 167. R. M. Percival, M. W. Phillips, D. C. Hanna, A. C. Tropper. Characterization of spontaneous and stimulated emission from praseodymium (Pr 3⫹) ions doped into a silica-based monomode optical fiber. IEEE J. Quant. Electron. 25:2119–2123, 1989. 168. Y. Shi, C. V. Poulsen, M. Sejka, O. Poulsen. Mode-locked Pr 3⫹-doped silica fiber laser with an external cavity. J. Lightwave Technol. 12:749–753, 1994. 169. Y. Shi, C. V. Poulsen, M. Sejka, M. Ibsen, O. Poulsen. Tunable Pr 3⫹-doped silica-based fibre laser. Electron. Lett. 29:1426–1427, 1993. 170. B. J. Ainslie, S. P. Craig, S. T. Davey. The absorption and fluorescence spectra of rare earth ions in silica-based monomode fiber. J. Lightwave Technol. 6:287–293, 1988. 171. Y. Shi, O. Poulsen. High-power broadband singlemode Pr 3⫹-doped silica fibre superfluorescence light source. Electron. Lett. 29:1945–1946, 1993. 172. Y. Shi, O. Poulsen, B. Palsdottir. Stimulated emission characterization of Pr 3⫹-doped silica fiber. Proc. Conf. Lasers and Electro-Optics, CLEO ‘94 8:388–389, 1994. 173. M. C. Farries, P. R. Morkel, J. E. Townsend. Spectroscopic and lasing characteristics of samarium doped glass fiber. IEE Proc. 137(pt. J):318–322, 1990.

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4 Visible Fluoride Fiber Lasers* D. S. FUNK National Institute of Standards and Technology Boulder, Colorado J. G. EDEN University of Illinois Urbana, Illinois

4.1 INTRODUCTION The advent of low-loss fluoride fibers has led to the demonstration of numerous roomtemperature lasers based on rare earth transitions at wavelengths ranging from 0.38 to 3.45 µm. Fluoride fiber lasers are of interest because they provide a means of generating laser output at wavelengths for which there are currently few or no solid-state laser sources, particularly in the spectral regions lower than 0.63 µm and higher than 2.0 µm. As nearly all rare earth doped fluoride fiber lasers have been pumped in the 0.63- to 1.2-µm region, they can take advantage of the relatively mature AlGaInP (0.63–0.69 µm), InGaAlAs/ GaAlAs (0.78–0.88 µm), and InGaAs (0.90–1.2 µm) semiconductor laser technologies, as well as diode-pumped, solid-state lasers, such as the Nd 3⫹-doped YAG laser (1.064, 1.112, 1.116, and 1.123 µm) and the Yb 3⫹-doped silica fiber laser (1.1–1.2 µm). Thus, the potential for the development of all–solid-state laser sources based on fluoride fiber exists. Many applications, including laser projection displays, reprographics, optical data storage, semiconductor manufacture and inspection, biology, and medicine benefit from the availability of completely solid state lasers operating in the visible and ultraviolet (UV) spectral regions. Solid-state lasers are preferred because relative to their gas or dye

* This work is a contribution of the U. S. Government and is not subject to copyright.

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counterparts emitting in the visible or UV, they are generally more efficient, compact, robust, less expensive, and have considerably longer lifetimes. They also often exhibit lower-output power noise. Impressive progress in the development of short-wavelength semiconductor lasers emitting in the violet (405–410 nm) [1], blue (444 and 450 nm) [2,3], blue-green (514 and 529 nm) [4,5], and red (635–640 nm) [6,7] has been made in the last few years. These devices are expected to dominate in applications that require lowcost, compact, short-wavelength sources providing tens to hundreds of milliwatts (mW) of continuous wave (CW)-output. However, it will likely be years before semiconductor lasers are capable of producing diffraction-limited, CW output powers greater than 1 W across the visible and into the near ultraviolet spectrum. This situation has prompted continued research into alternative methods of generating visible laser output that can be driven by existing high-power diode lasers or diodepumped solid-state lasers. Techniques such as intracavity, frequency-doubling of diodepumped, infrared (IR), solid-state lasers [8,9] and external resonant cavity frequency doubling [10–12], or resonant cavity frequency summing [13–15] of the output of semiconductor lasers and solid-state lasers have been developed that utilize bulk nonlinear crystals to generate output in the green or blue. These methods involve placing the nonlinear crystal within a cavity that is resonant with the pump wavelength(s), thereby generating infrared laser powers within the crystal that are close to 100 times higher than those available outside the cavity. These approaches typically exhibit optical conversion efficiencies from the IR to the visible, ranging from several percent to as high as 70%. Efficient single-pass frequency conversion can also be achieved using quasi–phase-matching in periodically poled ferroelectrics. Periodically poled lithium niobate (PPLN) and lithium tantalate have been used in single-pass configurations to double near-infrared and red laser light to the green, blue, and UV [16–22]. Conversion efficiencies from the IR to the green and blue are typically about 1–10%, whereas conversion efficiencies from the red to the UV are substantially lower (⬃0.01–0.1%). Recently, 2.5 W of CW output power in the red has also been demonstrated by intracavity sum-frequency generation in a PPLN optical parametric oscillator (OPO) [23]. Despite the success, and even commercialization, of many of these nonlinear devices, there are several drawbacks associated with nonlinear frequency conversion. Tight tolerances for the pump wavelength and the nonlinear crystal temperature require active stabilization of both of these parameters. In addition, the incorporation of bulk elements into the cavity complicates automated manufacture. Intracavity-doubled lasers are also susceptible to amplitude fluctuations, which can require complex stabilization schemes. All of these factors increase the size and cost of the laser. Upconversion pumping of short-wavelength rare earth doped fluoride fiber lasers is a relatively straightforward means of converting the output of an IR solid-state laser to the visible. Upconversion is a term that has come to be associated with a variety of processes by which trivalent rare earth ions in a crystal or glass absorb two or more photons to populate high-lying electronic states (typically ⬎20,000 cm⫺1 above ground state). Upconversion exploits the long excited-state lifetimes (⬎100 µs) of rare earths in a host that allows substantial excited-state populations to be produced. Ions in these excited states can undergo further excitation by the absorption of a second or third pump photon or by receiving energy nonradiatively from a neighboring excited ion. Upconversion lasers, therefore, are capable of operating at wavelengths shorter than that of the pump laser. Nonlinear frequency doubling and upconversion differ in that the pump photons are absorbed by the ions through transitions between real electronic states of the ions, rather than between virtual states. Upconversion is discussed in more depth in Section 4.2.

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Visible fluoride fiber lasers are similar to silica fiber lasers in the sense that they consist of a relatively simple optical cavity, which makes them attractive from a manufacturing standpoint. Dielectric mirrors coated directly onto the fiber end facets, or photoinduced Bragg gratings written in the fiber core, can form the fiber laser cavity [24–26]. In addition, no thermoelectric or water cooling of the fiber is required, even for highpower fiber lasers, because the cross-sectional area of the fiber is sufficiently small that heat is rapidly transferred from the pumped core region to the cladding and into the surrounding air. Because the absorption bands of rare earth ions have a large bandwidth (typically ⬎ 5 nm), inexpensive, broad-linewidth pump sources can be used and pump wavelength stabilization is not required. The confinement of both the pump and signal within the fiber core over the long distances available with fiber lasers make these devices quite efficient. Consequently, sufficient gain for lasing on transitions with low emission, or pump absorption, cross sections can often be obtained by increasing the fiber-laser cavity length. High pump intensities are achievable even with modest pump powers by using fiber with a small core diameter and a high numerical aperture (NA). For example, 100 mW of power circulating within a fiber having a 2 µm diameter core corresponds to pump intensities greater than 3 MWcm⫺2. These high intensities, coupled with the long interaction lengths, result in opticalto-optical conversion efficiencies frequently greater than 20% and thresholds below 10 mW. One of the main advantages of the confinement properties inherent to single-mode fiber lasers is the ability to produce high-output powers (tens of watts) while maintaining a diffraction-limited circular transverse mode. Simply increasing the fiber length can increase the attainable fiber laser power, provided that sufficient pump power can be coupled into the fiber core to fully pump the available gain volume. Initially, the output powers of fiber lasers were limited by the scarcity of high-power pump sources at appropriate pump wavelengths with a transverse intensity profile of sufficient quality to obtain efficient coupling into single-mode fiber cores. However, the development of the double-clad fiber geometry in silica fiber [27,28], which allows efficient coupling of the output of highpower diode laser bars into a single-mode fiber core, has led to the demonstration of a Yb 3⫹-doped silica fiber laser producing 110 W of single–transverse-mode CW output at 1120 nm [29] (see Chap. 3). The double-clad fiber geometry has been implemented in fluoride fibers as well, resulting in a diode-pumped fluoride fiber laser producing 1.7 W of output power at 3 µm [30]. A cladding-pumped, Yb 3⫹-sensitized, Pr 3⫹-doped fluoride fiber laser based on upconversion and operating at 635 nm has also been reported [31]. It produced 440 mW, limited only by the available 3 W of 850-nm Ti:sapphire pump power. These results demonstrate the feasibility of cladding-pumped upconversion fiber lasers. Higher output powers from the 635-nm fiber laser should be obtainable using pump sources currently under development [31]. Over 1 W of 635-nm output has also been demonstrated from a Yb 3⫹-sensitized, Pr 3⫹-doped fluoride fiber laser with 3.4 W of Ti: sapphire pump power launched directly into the single-mode fiber core [32]. The singlemode IR output of cladding-pumped fiber lasers, as well as other high-power diodepumped solid-state lasers, can also be coupled efficiently into single-mode fluoride fiber to pump upconversion visible lasers. Compared with silica fiber lasers, fluoride fiber lasers offer a wider range of wavelengths, spanning the spectral range from the near-UV to the mid-IR, because of the low phonon energy and the extended IR transparency range of fluoride glass. The fluoride glass typically used for the fabrication of fluoride fiber lasers is known as ZBLAN, an acronym derived from the constituents of the glass, namely ZrF4 (53% nominal concentra-

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tion by weight), BaF2 (20%), LaF3 (4%), AlF3 (3%), and NaF (20%). A more in-depth discussion of the properties of ZBLAN glass is given in Chapter 9. Only a few of the properties of ZBLAN pertinent to the performance of rare earth doped fiber lasers are reviewed here. The most important of these is the phonon energy spectrum of the glass which has a maximum energy of ⬃600 cm⫺1, compared with a value of ⬃1100 cm⫺1 for silica. As a consequence, in silica at room temperature, multiphonon decay begins to quench rare earth levels that are separated in energy from the next lowest level by less than ⬃5000 cm⫺1. In contrast, in ZBLAN, quenching of an excited state by multiphonon relaxation does not become appreciable until the energy separation between the state of interest and the next lowest level is less than ⬃3000 cm⫺1. This leads to higher radiative efficiencies in the 2- to 4-µm spectral region, as well as the existence of more trivalent ion metastable levels in ZBLAN than in silica. The presence of numerous metastable levels makes possible the efficient upconversion pumping of high-energy levels that emit visible and uv radiation. Another consequence of the low-phonon energy of ZBLAN is that the IR transparency range of this glass, which is limited by the onset of multiphonon absorption, occurs beyond 4 µm. However, unlike other low-phonon–energy glasses, such as the chalcogenides, the short-wavelength transparency range in ZBLAN extends throughout the visible and into the UV, cutting off at ⬃300 nm. Thus, the low-phonon energy and short-wavelength transparency, coupled with the ability to fabricate optical fiber, make ZBLAN an excellent host for lasers in the visible as well as the IR. Figures 1 and 2 illustrate the impact of these characteristics of ZBLAN on its utility as a host for visible and IR lasers, respectively, by providing a comparison between the laser transitions demonstrated in rare earth doped ZBLAN fibers and silica fibers. The aim of this chapter is to provide an overview of the current status of upconversion-pumped visible fiber lasers. In the next section, a general description of several up-

Figure 1 Wavelengths of visible and near-ultraviolet laser transitions demonstrated to date in rare earth doped ZBLAN and silica fiber.


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Figure 2 Wavelengths of infrared (0.8–4.0 µm) laser transitions demonstrated to date in rare earth-doped ZBLAN and silica fiber.

conversion-pumping processes common to visible fiber lasers is presented. In the following five sections, upconversion-pumped visible and ultraviolet lasers in Pr 3⫹-, Nd 3⫹-, Ho 3⫹-, Er 3⫹-, and Tm 3⫹-doped ZBLAN fiber are described. The specific-pumping processes and a summary of the laser characteristics reported in the literature for each visible fluoride fiber laser demonstrated to date are provided. The only visible laser to operate in a silica fiber, a Sm 3⫹-doped fiber laser operating at 650 nm, is described in Chapter 3. 4.2 UPCONVERSION-PUMPING PROCESSES Upconversion pumping is the process of exciting, optically or through the exchange of energy between two ions, a state of a rare earth ion that lies at an energy higher than that of the pump photons. It occurs as a series of sequential excitation steps. In each step, the ion is excited to a higher energy level than in the previous step by the absorption of a pump photon or by the transfer of energy from a neighboring excited ion. Nonlinear simultaneous absorption of multiple photons is a relatively weak process and generally plays a negligible role in upconversion pumping. Upconversion pumping is most efficient in rare earth doped hosts that have a low-energy phonon spectrum, such as ZBLAN glass and, consequently, numerous metastable levels. Excited states with long lifetimes are more likely to undergo further excitation to even higher-energy metastable levels before they decay. Although some radiative transitions from high-energy states populated by upconversion pumping may produce photons with a lower energy than that of the pump photons, the focus of this chapter is on laser transitions that produce output wavelengths shorter than that of the pump source.

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Upconversion pumping of rare earth ions doped into bulk crystals and glass fiber has been demonstrated to be an efficient means of converting IR light to the visible. Originally proposed as a method for IR photon counting in 1959 [33,34], upconversion was eventually recognized as a potential means to pump visible rare earth doped solid-state lasers. The first upconversion-pumped laser was reported in 1971 by Johnson and Guggenheim, who obtained stimulated emission at 551 nm from a Ho 3⫹ /Yb 3⫹-co-doped BaY2 F8 crystal and at 670 nm in an Er 3⫹ /Yb 3⫹-co-doped BaY2 F8 crystal [35]. Both crystals were cooled to 77 K and flashlamp pumped. In 1989, Allain and co-workers demonstrated the first upconversion-pumped visible fiber laser, which emitted at 455 or 480 nm when pumped simultaneously at 647 and 676 nm, in Tm 3⫹-doped ZBLAN fiber cooled to 77 K [36]. The following year, they reported the first room-temperature upconversion-pumped fiber laser in Ho 3⫹-doped ZBLAN fiber, which lased at 550 nm when pumped at 647 nm [37]. Since then, numerous room-temperature rare earth doped fiber and bulk crystal lasers have been reported. Some of these devices generate coherent radiation at frequencies more than twice that of the pump [38,39]. Such systems rely on the ability of a rare earth ion or ensembles of rare earth ions in a solid to store the energy of more than two pump photons and release that energy as a single, higher-frequency photon. Upconversion pumping can be achieved by the sequential absorption of multiple pump photons by a single ion. The process (Fig. 3), begins with the absorption of a pump photon, of wavelength λ 1 , by an ion in its ground state, a process termed ground-state absorption (GSA). The ion may be promoted directly to a metastable level, or it may be excited to a state that decays rapidly, through multiphonon or radiative relaxation, to a metastable level. The next step is the absorption of a second pump photon at wavelength λ 2 by the excited ion, known as excited-state absorption (ESA). Again, the ion may be excited to a metastable level or to a state that subsequently undergoes rapid decay to a lower metastable level. Additional ESA steps may also follow. In this example, laser oscillation occurs from the final excited metastable level down to the ground state (see Fig. 3). Because of the broadening of rare earth ion transitions in glass at room temperature,

Figure 3 Upconversion laser pumped by sequential two-photon absorption. Dashed arrows represent multiphonon relaxation.


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overlapping GSA and ESA spectra are quite common and have led to the demonstration of numerous upconversion-pumped fiber lasers pumped at a single wavelength (λ 1 ⫽ λ 2 ). Optical fiber offers the additional advantage of producing high pumping intensities over a long interaction length, so even when one pump absorption process is substantially weaker than the other, pumping rates sufficiently high to achieve gain can be obtained. In contrast, in rare earth doped crystals, the rare earth absorption spectra are significantly less broadened owing to interactions with the host. The absorption spectral profiles exhibit fine structure, and it is much less likely that the GSA and ESA spectra overlap. Consequently, the pump schemes used in many upconversion-pumped rare earth doped crystalline lasers have either required two pump wavelengths or relied on various mechanisms involving transfer of energy from neighboring excited ions. Energy transfer (ET) involves the nonradiative transfer of energy from a donor ion to an acceptor ion. In the context of ET-pumped rare earth lasers, the acceptor is usually the ion that provides gain for the laser; here, it is also known as the activator. In general, the donor and acceptor ions can be the same or different species. For rare earth doped fiber lasers, the donor is most often a rare earth species different from the acceptor, and it is added as a sensitizer to improve the pumping efficiency into the upper-laser level of the activator. A sensitizer is added (1) because it absorbs at a desirable pump wavelength more effectively than does the activator, and (2) it is capable of efficiently transferring the absorbed energy to the activator. In upconversion pumping, a sensitizer can provide energy to promote the activator from the ground state to an excited state or from an excited state to a higher-energy state and, occasionally, multiple steps in an upconversion process may occur by ET. In general, the upconversion process may involve a combination of GSA, ESA, and ET steps. Several examples of ET-assisted upconversion using a sensitizing ion are illustrated in Figure 4. In Figure 4a, the GSA and the ESA wavelengths of the activator do not coincide. The GSA of the sensitizer does overlap, however, with the ESA spectrum of the activator. In addition, the sensitizer has a metastable level at the same energy as the first excited state of the activator. In this case, a single pump wavelength can be used. The metastable excited state of the sensitizer is populated by the absorption of a pump photon, followed by rapid nonradiative decay. The sensitizer transfers its energy to an activator in the ground state, promoting this ion to its first excited state. Pump ESA excites the upper laser level of the activator, and lasing occurs from this level to the ground state. This example illustrates the requirement that, for ET, the donor and acceptor transitions must overlap energetically. Small energy defects between the transitions may be overcome through energy transfer between the ions and the vibrational modes of the host lattice in a process known as phonon-assisted ET [40]. In Figure 4b, ET serves to promote the activator from its first excited state to the upper laser level. Figure 4c shows the case in which multiple ET transfer steps lead to population of the upper-laser level. When GSA is very weak, ET can lead to an enhanced-pumping efficiency above a critical pumping threshold in a process known as photon–avalanche upconversion [41]. Figure 5 depicts the three steps of a simple example of photon–avalanche upconversion in a system involving a single rare earth ion species, in which the GSA and ESA steps of the initial two-photon absorption-pumping process do not overlap well. As a result, GSA is substantially weaker than ESA, and the pumping rate into the upper laser level (see level 3 in Fig. 5a) is limited by the GSA step. However, a small population in level 3 can be produced, possibly through phonon-assisted GSA. If the concentration of the ions is sufficiently large, cross-relaxation between the ion in level 3 and an ion in level

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Figure 4

Three examples of energy-transfer (ET) upconversion where the upper laser level is pumped by (a) ET followed by ESA, (b) GSA followed by ET, and (c) two successive ET steps. MPR: multiphonon relaxation.

1 can occur (see Fig. 5b), resulting in two ions in level 2. These two ions can then be promoted to level 3 by resonant ESA (see Fig. 5c) where they can undergo further crossrelaxation steps with neighboring ions in the ground state. At some threshold pumping level, the density of ions in level 3 becomes large enough that the pumping rate of level 2 by ET begins to exceed the pumping rate by GSA. Above this pump power, level 3 is pumped primarily by ESA and ET, circumventing the GSA ‘‘bottleneck’’ of step a, and resulting in an avalanche effect. The larger the population of level 3, the more efficient becomes the pumping process. One of the most commonly used rare earth ions for ET upconversion pumping in fiber lasers is Yb 3⫹. The trivalent Yb ion is an effective sensitizing ion for several reasons. First, Yb 3⫹ has only one excited 4f level, lying ⬃1000 cm⫺1 above the ground state, so quenching of high energy levels in the acceptor by ET to Yb 3⫹ is not as likely as with ions having high energy levels. Also, because there is only one excited state, cross-relaxation between two Yb 3⫹ ions does not result in a net loss of energy available for upconversion pumping. Consequently, large concentrations of Yb 3⫹ can be used to increase both the pump absorption and the ET efficiency from the Yb 3⫹ ion to the acceptor. In addition, Yb 3⫹ has broad absorption and emission bands, which has two favorable consequences. First, Yb 3⫹ has a wide excitation band, spanning the ⬃800- to 1064-nm region [42], that allows a wide choice of pumping wavelengths. Second, the broad emission band of Yb 3⫹ at room temperature, stretching from ⬃970 to ⬃1200 nm [42], means that ET can occur


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Figure 5 Photon-avalanche upconversion. (a) Weak non-resonant GSA followed by ESA leads to a small population in level 3 of ion A. (b) ET from of ion A in level 3 to ion B in level 1 produces two ions in level 2. (c) The two ions in level 2 are promoted to level 3 by ESA where they can each promote two more ions in the ground state to level 2 via ET. MPR: multiphonon relaxation.

for a wide range of acceptor-transition energies. An added benefit is that the pump band lies at wavelengths accessible to semiconductor laser sources. The efficiency of the ET process, which is highly dependent on the average distance between the rare earth ions, increases rapidly with increasing ion concentration. Most upconversion-pumped visible fiber lasers have been demonstrated in ZBLAN fiber doped with a single species of rare earth ion. In such systems, the ion concentration typically lies in the 500- to 2000-wt ppm range, corresponding to a density in the range of ⬃1- to 4 ⫻ 10 19 ions/cm 3. At this doping level, the energy-transfer efficiency is low, and these systems rely on ESA by single ions to achieve upconversion pumping. Low concentrations are used because cross-relaxation ET processes between ions of the same species tend to lower the excited-state lifetime of the higher energy levels. In co-doped systems such as the Yb 3⫹-sensitized, Pr 3⫹-doped ZBLAN fiber lasers described in Section 4.3, the concentration of the activator is typically in the 500–to 2000-wt ppm range, but the sensitizer concentration is substantially higher, usually by a factor of ⬃10–20. In Yb 3⫹-sensitized systems, the high Yb 3⫹ concentration is desirable because cross-relaxation between neighboring Yb 3⫹ ions enables energy migration to the activator ion. Given that, in upconversion-pumped fiber lasers, multiple pump photons are re-

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quired to produce a short-wavelength photon, a nonlinear dependence of fiber laser output power on pump power is expected. Indeed, the dependence of fluorescence power on pump power generally does show the expected superlinear behavior for low pump powers [36]. However, in nearly all upconversion fiber lasers, the output power is linearly dependent on pump power, which is generally attributable to saturation of one or more of the upconversion-pumping steps as a result of the high pump intensities present in the fiber core for pump powers above threshold [36,37]. 4.3 VISIBLE PRASEODYMIUM-DOPED ZBLAN FIBER LASERS 4.3.1 Laser Transitions and Upconversion-Pumping Mechanisms The upconversion-pumped praseodymium-doped fluoride fiber laser has received considerable attention because it offers laser transitions in the blue, green, orange, and red that operate at room temperature. Some of these transitions have even operated simultaneously [43], suggesting that a single laser source could provide output in the blue, green, and red for projection display applications. Lasing in the visible occurs on transitions originating from the 3 P0 , 3 P1 , and 1 I 6 levels of Pr 3⫹, which are thermally coupled at room temperature [44]. The 3 P1 and 1 I 6 levels are nearly degenerate, so these two levels will be referred to collectively as the 3 P1 level in the discussion to follow. The lifetime of the 3 P1- and 3 P0-coupled manifold of Pr 3⫹ in ZBLAN has been reported to be in the range of 40–50 µs [45,46]. The partial energy level diagram of Pr 3⫹ in Figure 6 illustrates the transitions on which visible lasing has been obtained. Room-temperature lasing has been observed in Pr 3⫹-doped ZBLAN fiber at about 490, 520, 605, 635, 695, and 715 nm [44,47]. The

Upconversion-pumping process and visible laser transitions in Pr 3⫹-doped ZBLAN fiber. All of the wavelengths are expressed in nm.

Figure 6


181

490-, 605-, 635-, and 715-nm laser transitions all originate from the 3 P0 level and terminate on the 3 H 4 , 3 H 6 , 3 F2 , and 3 F4 levels, respectively. The 520-nm–laser transition originates from the 3 P1 level and terminates on the 3 H 5 state. Despite that, at room temperature, only ⬃5% of the population of the 3 P0- and 3 P1-coupled manifolds resides in the 3 P1 level, the 3 P1 → 3 H 5 transition dominates over the 3 P0 → 3 H 5 transition, centered at ⬃540 nm, because the latter is nominally forbidden and, therefore, much weaker [47]. A similar situation exists for emission near 695 nm. The 3 P1 → 3 F4 transition is predicted to be much stronger than the 3 P0 → 3 F3 transition, because the latter is nominally forbidden. However, as the two transitions overlap spectrally, the transition that is primarily responsible for lasing at 695 nm has not been determined [44]. Most of the published research has focused on the 490-, 520-, 605-, and 635-nm transitions because they lie in the spectral region of interest for most visible laser applications. To date, only these transitions have been upconversion-pumped, and further discussions are limited to these transitions. The first demonstrations of lasing in the red, orange [44], and, subsequently, the green and blue [47], in Pr 3⫹-doped ZBLAN fiber were reported in 1991. In these initial experiments, the 3 P0 and 3 P1 upper laser levels were populated by direct excitation from the ground state using the 476.5-nm line of an argon ion laser. In that same year, two methods for upconversion pumping of the visible lasers were demonstrated. Smart and co-workers reported a Pr 3⫹-doped ZBLAN fiber oscillator that operated at 491, 520, 605, or 635 nm when pumped simultaneously at 1.01 and 0.835 µm with two CW Ti:sapphire lasers [48]. The pump scheme is shown in Figure 6. In this dual-wavelength pump scheme, GSA at a wavelength of 1.01 µm populates the 1 G 4 level, which has a lifetime of ⬃110 µs. ESA from the 1 G 4 level to the 3 P1 level at ⬃0.835 µm populates the 3 P1 and 3 P0 levels, the latter by nonradiative relaxation. Tropper and co-workers [45] have measured the GSA cross section at 1.01 µm to be 5.7 ⫻ 10⫺26 m 2, and the ESA cross section at 835 nm to be 1.0 ⫻ 10⫺24 m 2. Because the GSA cross section is substantially weaker than the ESA cross section, GSA is the rate-limiting step in this pumping process, resulting in a lower saturation pump power for the ESA process than for the GSA process, as observed by Smart et al. [48]. Allain and co-workers reported the first upconversion-pumped 635-nm laser in Pr 3⫹ / 3⫹ Yb -co-doped ZBLAN fiber pumped at a single wavelength [49]. The fiber laser was pumped by a CW Ti: sapphire laser in the 800- to 870-nm-wavelength range. The core of the fiber contained 0.1 wt% Pr 3⫹ and 2.0 wt% Yb 3⫹. The authors proposed two pumping pathways for the Pr 3⫹ /Yb 3⫹-co-doped visible laser system (Fig. 7). Both pumping schemes share a common first step (see step 1, Fig. 7), which is as follows. Weak absorption of the ⬃840-nm pump in the short-wavelength wing of the Yb 3⫹ absorption band, which extends to ⬃800 nm in fluoride fibers containing high Yb 3⫹ concentrations [50], populates the 2 F5/2 level of Yb 3⫹. ET from the excited Yb 3⫹ ion to a neighboring Pr 3⫹ ion residing in the ground state results in simultaneous occurrence of the Pr3⫹ 3 H 4 → 1 G 4 and Yb 3⫹ 2 F5/2 → 2 F7/2 transitions. Allain and co-workers suggested two possible mechanisms for Pr 3⫹ ions in the 1 G 4 level to be promoted to the 3 P0 level. The first is that ET from a Yb 3⫹ ion in the 2 F5/2 level to a Pr 3⫹ ion in the 1 G 4 level excites the 2 F5/2 → 2 F7/2 and 1 G 4 → 3 P0,1 transitions (see step 2a, Fig. 7). The second mechanism is pump ESA from the 1 G 4 level to the 3 P0,1 levels at close to 840 nm (see step 2b, in Fig. 7). The authors decided that, based on two observations, the latter process is primarily responsible for pumping the 3 P0 level. First, as the pump wavelength was varied, local maxima in the pumping efficiency of the red transition were observed, which corresponded to ESA resonances out of the 1 G 4 level. Second, the authors noted that only Yb 3⫹ ions in the higher-lying Stark sublevels of the 2 F5/2 manifold have sufficient energy to excite the Pr 3⫹ 1 G 4 → 3 P0 transition by ET.

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Figure 7

Two-step upconversion-pumping processes for the visible lasers in Pr 3⫹ /Yb 3⫹ co-doped ZBLAN fiber. Step 1: Weak GSA excites a Yb 3⫹ ion, which transfers its energy to a neighboring Pr 3⫹ ion. Step 2: Two possible paths: (a) a second ET step from a Yb 3⫹ ion to a Pr 3⫹ ion in the 1 G 4 state (unlikely, due to the energy mismatch between the 2 F5/2 → 2 F7/2 and 3 P 0,1 ← 1 G4 transitions), or (b) pump ESA from the Pr 3⫹ 1 G 4 state.

However, at room temperature, thermal relaxation within the Yb 3⫹ 2 F5/2 manifold leads to negligible population in these higher-lying Stark sublevels. A third upconversion-pumping mechanism, photon–avalanche upconversion, has also been reported in the Pr 3⫹ /Yb 3⫹-co-doped upconversion fiber laser [51]. Previously, in Pr 3⫹ /Yb 3⫹-co-doped ZBLAN glass, quenching of the visible emission from the 3 P0 level of Pr 3⫹ by ET to Yb 3⫹, resulting in the Pr 3⫹ 3 P0 → 1 G 4 and Yb 3⫹ 2 F7/2 → 2 F5/2 transitions, had been observed [52]. This cross-relaxation process is summarized in Figure 8. Xie and Gosnell [51] noted that each such cross-relaxation process generates one Pr 3⫹ ion in the 1 G 4 level and one Yb 3⫹ ion in the 2 F7/2 level (see step 1, Fig. 8), which can generate a second Pr 3⫹ ion in the 1 G 4 level through ET to a Pr 3⫹ ion in the ground state (see step 2, Fig. 8). These two Pr 3⫹ ions can then be excited by pump ESA to the 3 P0 level (see step 3 of Fig. 8), where they can each undergo the same process again (see steps 4 and 5, Fig. 8). The result of this process is that, as the population of the 3 P0 level increases, the dependence of the 1 G 4 population on Yb 3⫹ pump GSA decreases. When pumping in the 800- to 870-nm range where the absorption of Yb 3⫹ is weak, circumventing the Yb 3⫹ GSA step increases the upconversion-pumping efficiency, resulting in a photon–avalanche upconversion process.


183

Figure 8 Photon avalanche upconversion in Pr 3⫹ /Yb 3⫹-co-doped ZBLAN fiber pumped at 850 nm. Step 1: A Pr 3⫹ ion in the 3 P0 level transfers its energy to a Yb 3⫹ ion in the ground state. Step 2: ET from the Yb 3⫹ ion to a Pr 3⫹ ion in the ground state leaves two Pr 3⫹ ions in the 1 G 4 level. Step 3: ESA promotes both Pr 3⫹ ions to the 3 P0 level. The Pr 3⫹ ions in the 3 P0 level can participate in further ET steps with Yb 3⫹ ions, shown in steps 4 and 5.

The simplified photon–avalanche upconversion scheme (see Fig. 8) neglects the ET that occurs between Yb 3⫹ ions. Because the typical dopant concentrations of Pr 3⫹ and Yb 3⫹ used in visible fiber laser applications are about 1000 and 10,000 ppm, respectively, it is unlikely that any given Yb 3⫹ ion will be located near two Pr 3⫹ ions, assuming the doping to be spatially uniform. Generally, the energy from an excited Yb 3⫹ ion may migrate through one or more nearby Yb 3⫹ ions until a Yb 3⫹ ion that lies near a Pr 3⫹ ion is excited, at which point a Yb 3⫹ –Pr 3⫹ interaction can take place. The photon–avalanche upconversion process in Pr 3⫹ /Yb 3⫹-co-doped ZBLAN glass has been experimentally verified by Gosnell [53], who reported a highly nonlinear increase in pumping efficiency at 800 or 840 nm of fluorescence emerging from the Yb 3⫹ 2 F5/2 level and the Pr 3⫹ 3 P0 level as the pump power is increased above a threshold level. At

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pump powers higher than this threshold, the Pr 3⫹ emission intensity at 635 nm was observed to increase by nearly four orders of magnitude when the pump power was increased by only one order of magnitude. A similar increase in emission intensity was observed at 980 nm from the Yb 3⫹ 2 F5/2 → 2 F7/2 transition. These experiments were conducted using a bulk ZBLAN sample doped with 0.3 wt% Pr 3⫹ and 2.0 wt% Yb 3⫹. The dramatic dependence of pumping efficiency on pump power, as well as the fact that the pump wavelength band extends to 800 nm, at which the Yb 3⫹ GSA is very weak, indicates that the photon–avalanche upconversion process is likely a dominant pumping mechanism for visible lasers in Pr 3⫹ /Yb 3⫹-co-doped ZBLAN fiber pumped with a single wavelength near 840 nm. A fourth pumping scheme has also been realized in a Pr 3⫹ /Nd3⫹-co-doped ZBLAN fiber pumped at 796 nm. Goh and co-workers reported the observation of stimulated emission, indicated by spectral line narrowing, at 488, 635, and 717 nm in a fiber doped with ⬃0.2 mol% Pr 3⫹ and 0.2 mol% Nd 3⫹ [54]. The proposed pump scheme is depicted in Figure 9. A GSA step, followed by an ESA step, at 796 nm in Nd 3⫹ pumps the 2 D 5/2 level. Rapid multiphonon decay from the 2 D 5/2 state populates the 4 G 11/2 and 4 G 9/2 levels of Nd 3⫹, which lie at energies close to those of the 3 P0,1 levels of Pr 3⫹. ET from an excited Nd 3⫹ ion to a Pr 3⫹ ion in the ground state then populates the Pr3⫹ 3 P0,1 levels through the 4 G 11/2 ⫹ 4 G 9/2 → 4 I 9/2 and 3 H 4 → 3 P0,1 transitions. 4.3.2 Laser Performance A summary of the laser characteristics of the Pr 3⫹-doped ZBLAN fiber lasers reported in the literature is given in Table 1. All results discussed in this section were obtained at

Figure 9 Upconversion-pumping at 796 nm of the Pr 3⫹ visible laser transitions in Pr 3⫹ /Nd3⫹ codoped ZBLAN fiber. Dashed arrows represent multiphonon relaxation.


185

room temperature. Despite that most of these Pr 3⫹-doped fiber lasers have not yet been optimized, several examples of high-power operation and impressive efficiencies exist. The highest output powers and efficiencies have been obtained from the 635-nm 3 P0 → 3 F2 transition, largely owing to the truly four-level nature of this transition. The 605-nm 3 P0 → 3 H 6 and 520-nm 3 P1 → 3 H 5 transitions behave less like four-level lasers because of the larger energy gap between the lower laser level and the next lower-lying level; consequently, they are less efficient than the 635-nm transition. In addition, the 520-nm transition originates from the 3 P1 level, which contains only ⬃5% of the total population of the 3 P0 and 3 P1 thermally coupled manifolds (at room temperature), so the 520-nm transition is generally less efficient than the 605- and 635-nm transitions. The 491-nm 3 P0 → 3 H 4 transition terminates on the higher-lying Stark levels of the ground-state manifold and acts as a quasi–three-level laser [55]. Consequently, this transition suffers GSA loss at the laser wavelength, which makes it less efficient than the other visible transitions. Also, the efficiency of this laser is highly sensitive to fiber length, for unpumped regions at the end of a fiber can substantially increase the laser cavity loss. Several of the most efficient and highest-power upconversion-pumped fiber lasers have been observed in the Pr 3⫹ /Yb 3⫹-co-doped system pumped at about 850 nm. Sandrock and co-workers [32] demonstrated a 635-nm Pr 3⫹ /Yb 3⫹-co-doped ZBLAN fiber laser that produced 1.02 W of CW output power. The fiber had a core diameter of 5 µm, an NA of 0.2, and Pr 3⫹ and Yb 3⫹ concentrations of 3,000 and 20,000 ppm, respectively. The fiber length was 51 cm. A flat mirror having a high reflectivity at 635 nm was butt-coupled against one cleaved fiber end facet, and the cavity was completed with the Fresnel reflection from the second end facet. Therefore, the cavity output coupling was 96%. The laser was pumped by two CW Ti: sapphire lasers operating at 852 and 826 nm, which provided a maximum combined power of 5.51 W incident on the pump-coupling optics. The authors estimated an efficiency for launching pump power into the fiber core of 40%, yielding an optical conversion efficiency against launched pump power of 46%. They reported a launched threshold pump power of 81 mW and a slope efficiency of 54%. Xie and Gosnell [51] also reported efficient and high-power operation of the 635nm transition, as well as the 615-, 520-, and 490-nm transitions, in a Pr 3⫹ /Yb 3⫹-co-doped ZBLAN fiber containing 3,000 wt ppm Pr 3⫹ and 20,000 wt ppm Yb 3⫹. The fiber, which had a core diameter of 3.0 µm and an NA of 0.3, was pumped by a CW Ti: sapphire laser. The fiber laser cavity was formed by butt-coupling bulk dielectric mirrors against the fiber end facets. For a fiber length of 60 cm and a cavity output coupling of 96% (provided by the Fresnel reflection from one end facet), 300 mW of output power at 635 nm was generated for 760 mW of launched Ti:sapphire pump power, yielding an optical conversion efficiency of 39%. The threshold launched pump power was 42 mW, which is lower than that reported by Sandrock et al., possibly because of the higher degree of pump power confinement produced by the smaller core size and higher NA of the fiber of Ref. 51. For the 3 P0 → 3 H 6 transition, using a cavity output coupling of 5% and a fiber length of 60 cm, 44 mW of output at 615 nm and an optical conversion efficiency of 10% were obtained for 430 mW of launched pump power. For the 615-nm laser, the dielectric mirror coatings had an appreciable reflectivity at 635 nm, so an intracavity collimating optic and prism had to be placed between the output end of the fiber and the output coupler to suppress lasing at 635 nm. This may explain why the reported 615-nm–output wavelength differs from the 605-nm wavelength typically reported for this transition. At 520 nm, 20 mW of output power and a conversion efficiency of 10% were obtained for 200 mW of pumplaunched power using a cavity output coupling of 3% and a fiber length of 42 cm. Finally,

0.3 0.3 0.39

3.0 3.0 1.7

0.2

3000/20,000 3000/20,000 1000/10,000

480/ –

0.3 0.3 0.39

0.15

3.25

3000/20,000 3000/20,000 1000/10,000

0.6 0.25 0.98

1.2

0.51 3.0

5.5

0.60 0.25 1.1

1.0

⬃0.18

4.6

3.0 3.0 1.7

2000/4000 ns

0.75 ⬃10

Length (m)

⬃0.17 0.15

0.2 0.15

4.0

635-nm fiber lasers 0.1/2.0 (wt.%) 560/ –

NA

5.0 5.0/30

5.7 4.6

[Pr 3⫹ ]/[Yb 3⫹] (wt ppm)

3000/20,000 ns 3000/20,000 ns 605-nm fiber lasers 560/ –

Core size (µm)

5 5 n.a.

60

96 70

96

96 96 96

23

40 96

Cavity output coupling (%)

860 t 860 s 860 s

835 t /1010 t

850 t 840 t,cp

840 t /1020 f

860 t 860s 860 s

833 s /1016 s

849 t 835 t /1010 t

Pump λ (nm)

Table 1 Summary of the Characteristics of Visible Pr 3⫹-Doped ZBLAN Fiber Lasers

30 in /1000 in l.e.⫽ 30–40% 29 36 130 in l.e. ⫽ n.a.

125 ⬃100/1000 in or 700/⬃200 in l.e. ⫽ 30–40% 112 in /9 in l.e.⫽ 30–40% 42 44 69 in l.e. ⫽ n.a. 120 in (total from both pump λs) l.e. ⫽ 60% 81 700

Launched threshold pump power (mW)

11.5 10 n.a.

7 in /3 in

54 17

23 in

52 49 n.a.

n.a./8.7 in

10 14 in /9.6 i

Slope efficiency (%)

44 5 0.2

30

1020 440

54

300 20 3.9

6.2

24 185

Max. output power (mW)

51 57 60

48

32 31

58

51 57 60

50

49 48

Ref.

186 Funk and Eden

0.15

5/30 4.6 3.0 3.0 3.0 1.7 1.7 1.7 3.25 3

3000/20,000 ns 490-nm fiber lasers 560/ –

500/ – 3000/20,000 3000/20,000 1000/ – 1000/10,000 1000/ – 480/ –

3000/20,000

0.3

0.21 0.3 0.3 0.39 0.39 0.39 0.2

0.3 0.3 0.39 0.2

0.23

0.85 0.26 0.25 0.48 1.7 0.68 2.0

1.2

3.0

0.42 0.25 1.7 5.7

1.5

t

845 t

835 t /1017 t 860 t 860 s 830 s /1017 s 858 s 835 s /1017 s 840 t /1020 f

835 t /1010 t

⬍1 10 3 3 7 10 ⬃10 6

840 t,cp

860 t 860 s 858 s 840 t /1020 f

833 s /1016 s

835 t /1010 t

n.a.

3 3 20 8

4

⬍1

wt ppm or molar ppm not specified. Pumped by a Ti 3⫹ :sapphire laser. s Pumped by a semiconductor laser. f Pumped by a Yb 3⫹-doped silica fiber laser. cp Cladding pumped. in Incident pump power threshold/slope efficiency relative to incident pump power. l.e., estimated launch efficiency provided by authors. n.a., information not available.

ns

0.15

3.0 3.0 1.7 3.25

3000/20,000 3000/20,000 1000/10,000 480/ –

1.0

⬃0.18

4.0

2000/4000 ns

1.2

0.15

4.6

520-nm fiber lasers 560/ –

200 in /280 in l.e. ⫽ 30–40% 65/40 60 56 29/24 ⬃90 8/42, or 28/28 260 in (total from both pump λs) l.e. ⫽ 60% ⬃100 in l.e. ⫽ 40%

160 in /160 in l.e. ⫽ 30–40% 138 in /36 in l.e. ⫽ 30–40% 21 32 55 180 in (total from both pump λs) l.e. ⫽ 60% n.a.

n.a.

n.a./13 3 6 n.a. n.a. n.a./8.5 6 in

n.a.

n.a.

12.4 16 n.a. 8.5 in

n.a./1.6 in

n.a.

16

9 4 2 1.2 0.7 1.2 7

⬃1

⬎100

20 10 0.7 18

0.7

⬃1

56

59 51 57 61 43 62 58

48

31

51 57 43 58

50

48

Visible Fluoride Fiber Lasers 187

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4 mW were obtained from a 26-cm–long fiber for 3% cavity output coupling with 200 mW of launched pump power, corresponding to an optical conversion efficiency of 2%. With a 23-cm length of the same type of fiber and dielectric mirrors coated directly onto the fiber end facets, Xie et al. [56] subsequently obtained 16 mW of blue output with 850 mW of incident 845-nm–pump power. These results represent the highest output powers and efficiencies yet reported for the Pr 3⫹-doped ZBLAN fiber lasers. Both Sandrock et al. and Xie and Gosnell reported that photon–avalanche upconversion plays an important role in the pumping process. Gosnell and Xie 57 also reported the highest output powers yet obtained from diodepumped visible Pr 3⫹-doped fiber lasers using the same fiber described in the foregoing. An AlGaAs semiconductor laser operating at 860 nm provided a maximum launched pump power of 88 mW. The cavity configurations and output couplings used for each wavelength were the same as those discussed earlier. A fiber length of 25 cm was used for all wavelengths. Maximum output powers of 20, 5, 10, and 2 mW were obtained at 635, 615, 520, and 490 nm, respectively. More recently, an output power of 2.6 mW has been observed for 290 mW of incident diode laser pump power from a fiber laser with dielectric mirrors deposited directly onto the fiber end facets [56]. For visible lasers in Pr 3⫹ singly doped ZBLAN fiber pumped simultaneously at 0.84 and 1.01 µm, some of the highest efficiencies have been realized in a system pumped with a silica fiber laser. The two pump sources used [58] were the 1020-nm laser output of a Yb 3⫹-doped silica fiber laser and its copropagating 840-nm unabsorbed pump. The silica fiber laser was pumped with a CW Ti: sapphire laser, and the fiber length was chosen such that approximately equal amounts of 1020-nm fiber laser output power and unabsorbed 840-nm pump emerged from the output end of the fiber. The ZBLAN fiber had a Pr 3⫹ concentration of 480 wt ppm, a core diameter of 3.25 µm, and an NA of ⬃0.2. For a 5.5-m length of fiber and a cavity output coupling of 96%, a maximum output power of 54 mW at 635-nm was obtained for 380 mW of total incident power (at both wavelengths). The estimated pump launching efficiency was 60%, yielding an optical conversion efficiency of ⬃24%. At 520 nm, 20 mW of output power and a ⬃9% optical conversion efficiency were obtained using a 5.0-m length of fiber and an 8% cavity output coupling. A maximum output power of 7 mW at 491 nm and a conversion efficiency of ⬃3% were obtained from a 2.0-m fiber and a 6% cavity output coupling. The highest conversion efficiency yet reported for the blue transition has been obtained using the dualwavelength-pumped Pr 3⫹-doped ZBLAN fiber. Zhao and Poole [59] reported 9 mW of output power at 492 nm with 65 mW of launched pump power at 835 nm, and 100 mW of launched pump power at 1017 nm. The fiber had a Pr 3⫹ concentration of 500 wt ppm, a core diameter of 3 µm, and an NA of 0.21. The fiber length was 85 cm and the output coupling was 10%. At this point, the efficiencies available using the single–wavelength-pumped Pr 3⫹ / 3⫹ Yb -co-doped system and the dual–wavelength-pumped Pr 3⫹-doped system are comparable. Neither system has been fully optimized, so it remains to be seen whether one method offers fundamentally better performance than the other. However, the co-doped system has the important advantage of requiring only a single pump wavelength. The 635-, 605-, 520-, and 490-nm transitions exhibit various degrees of tunability. Allain et al. [44] reported tuning ranges for the 3 P0 → 3 H 6 and 3 P0 → 3 F2 transitions of 601–618 and 631–641 nm, respectively. The tuning spectra contained fine structure, attributed to structure in the fluorescence curve or Fabry–Perot cavity resonances caused by polarization effects. Xie and Gosnell [51] reported tuning ranges of 635–637, 605–622,


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517–540, and 491–493 nm for the 3 P0 → 3 F2 , 3 P0 → 3 H 6 , 3 P1 → 3 H 5, and 3 P0 → 3 H 4 transitions, respectively. They also examined the pump band for the Pr 3⫹ /Yb 3⫹-co-doped system, and reported a pump excitation spectrum that extends over the ⬃820- to 880-nm region (full width at half maximum) and is relatively flat over the ⬃840- to 870-nm region. 4.3.3 Fiber Lasers Producing Simultaneous, Multicolor, Visible Output The Pr 3⫹-system offers the advantage of having a single manifold ( 3 P0,1 ) that undergoes several radiative decay processes to produce emission across the visible spectrum. This is advantageous because a single upconversion-pumping scheme, and in the case of Pr 3⫹ / Yb 3⫹-doped ZBLAN fiber, a single pump wavelength, can potentially be used to simultaneously produce laser output at widely spaced, multiple wavelengths in the visible spectrum. Baney et al. [43] demonstrated a Pr 3⫹ /Yb 3⫹-co-doped ZBLAN fiber laser that simultaneously produced up to 0.7 mW of output at 521 nm, and 0.7 mW of output at 492 nm, when pumped at 856 nm by a laser diode. The fiber contained 1,000 wt ppm Pr 3⫹ and 10,000 wt ppm Yb 3⫹. The core diameter and NA were 1.7 µm and 0.39, respectively. Dielectric mirrors were coated onto the cleaved fiber end facets. The coatings on both ends had reflectivities of 90% at 492 nm and 80% at 521 nm. The fiber length was 1.7 m. The green laser reached threshold first, at ⬃55 mW of launched pump power. As the pump power was increased, the green output power increased to a maximum of ⬃0.7 mW. At this point, the blue laser reached threshold, and further increases in pump power primarily increased the blue output power, whereas the green output power remained relatively constant. The authors suggest that further optimization of the fiber length and cavity output coupling could make it possible to achieve simultaneous blue, green, and red output using a single semiconductor pump laser [43]. 4.3.4 Cladding-Pumped Visible Fiber Lasers The most significant advance in the last several years in the field of fluoride fiber lasers is the development of dual-clad fluoride fiber for cladding-pumped lasers. The recent demonstration of a cladding-pumped, visible, upconversion fiber laser is the first step toward the development of high-power (⬎ 1 W), diode-pumped, visible fiber lasers. Zellmer et al. [31] demonstrated a cladding-pumped upconversion fiber laser in Pr 3⫹ /Yb 3⫹-co-doped ZBLAN fiber. The fiber had dopant concentrations of 3,000 ppm Pr 3⫹ and 20,000 ppm Yb 3⫹. The fiber geometry consisted of a 5-µm-diameter core in the center of a 25-µmdiameter inner cladding, which was surrounded by a 125-µm-diameter outer cladding. The core had an NA of 0.15 and the inner cladding had an NA of 0.35. The fiber length was 3 m, and the cavity output coupling was 30%. Cladding pumping is advantageous primarily when the pump source is a non–diffraction-limited, low-brightness source, which generally has a large aspect ratio. To simulate such a source, the output of a CW Ti:sapphire pump laser was first coupled into a multimode silica fiber with a core diameter of 30 µm and an NA of 0.22. The output of this intermediate fiber was then coupled into the dual-clad ZBLAN fiber. Up to 440 mW of output power was obtained for a maximum launched pump power of ⬃3 W. More than 100 mW at 520 nm was also realized using the appropriate mirrors. The authors predict that commercially emerging, fiber-coupled diode lasers that produce 5–10 W should make possible the scaling of the fiber laseroutput power to more than 1 W [31].

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4.4 ULTRAVIOLET AND VIOLET NEODYMIUM-DOPED ZBLAN FIBER LASERS 4.4.1 Laser Transitions and Upconversion-Pumping Mechanisms The shortest wavelengths yet generated from a glass fiber laser are those available from Nd 3⫹-doped ZBLAN. In 1994, Funk et al. [63] reported the first UV fiber laser, operating at 381 nm and room temperature. When pumped at ⬃590 nm, fibers ⬃40 cm in length, and installed in a resonator having a low output coupling, produced more than 70 µW of output power. Subsequently, lasing was also observed at 412 nm [64]. This section describes the properties of these oscillators and discusses the potential for other UV and visible laser transitions in Nd 3⫹-doped ZBLAN fibers. Emission in the violet and UV has been observed from the 4 D 3/2 and 2 P3/2 levels of Nd 3⫹ in several hosts. These states are illustrated in Figure 10. In Nd 3⫹-doped BaY2 F8 [67], the 4 D 3/2 level exhibits strong emission bands at 357 and 380 nm, corresponding to the 4 D 3/2 → 4 I 9/2 and 4 D 3/2 → 4 I 11/2 transitions. Weaker emission is also observed from the 4 D 3/2 → 4 I 13/2 transition in the 415- to 420-nm region. Radiative decay from the 2 P3/2 level produces intense emission at λ ⬃ 380 and 413 nm, corresponding to the 2 P3/2 → 4 I 9/2 and 2 P3/2 4 I 11/2 transitions, respectively. Although the 4 D 3/2 → 4 I 11/2 and 2 P3/2 → 4 I 9/2 transitions overlap, lasing is attributed to the former transition, because it terminates on a relatively short-lived excited state, rather than the ground state; consequently, inversion on this transition is more easily obtained. It has been noted earlier in this chapter that the fiber geometry is particularly beneficial for a laser when the pump absorption is weak or the stimulated emission cross section for the rare earth ion transition of interest is small. In the preponderance of cases, transitions that have been demonstrated to lase at room temperature in ZBLAN fibers have required cooling for lasing to occur in a crystal. This statement is particularly true for the 4 D 3/2 → 4 I 11/2 and 2 P3/2 → 4 I 11/2 transitions of Nd 3⫹. For example, the ⬃380-nm transition, which originates from the 4 D 3/2 level at 28,400 cm⫺1 and terminates at the 4 I 11/2 state at

Figure 10

Upconversion-pumping at 590 nm of the ultraviolet (381-nm) and violet (412-nm) Nd 3⫹-doped ZBLAN fiber lasers. Dashed arrows represent multiphonon relaxation.


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2100 cm⫺1, has a stimulated emission cross section that is estimated to be less than 10⫺19 cm 2 [65]. Macfarlane et al. [65] found that obtaining lasing at 380.1 nm from Nd 3⫹-doped LaF3 entailed cooling the crystal to a temperature lower than 90 K. Similarly, Tong and co-workers [66] demonstrated a 413-nm laser in Nd 3⫹-doped YLiF4 crystals cooled to less than 40 K. The processes responsible for pumping the 4 D 3/2 and 2 P3/2 excited states of Nd 3⫹ are also shown in the partial energy-level diagram of Nd 3⫹ in Figure 10. GSA by an Nd 3⫹ ion at 590-nm (បω ⬃2.1 eV) populates the 4 G 5/2 level. Subsequently, the excited ion decays to the 4 F3/2 state by multiphonon emission. Joubert and co-workers [67] have measured the spontaneous emission lifetime of the 4 F3/2 level for Nd 3⫹-doped BaY2 F8 to be 470 µs at 300 K. ESA of a second pump photon excites states lying above the 4 D 3/2 level at ⬃3.5 eV. Both the 4 D 3/2 and 2 P3/2 states are populated by phonon emission and, although they are separated in energy by only a few hundred per centimeter, the lifetime of the 2 P3/2 state against multiphonon emission in ZBLAN is roughly an order of magnitude larger than that for the 4 D 3/2 state. As a consequence, inversion is expected to be easier to achieve and maintain for the 412-nm transition than for the 381-nm transition. Furthermore, to obtain lasing at 381 nm, the dominant 412-nm transition must be suppressed since lasing on the violet transition populates the lower level of the 381-nm laser. 4.4.2 Laser Spectra, Excitation Spectra, and Output Power To date, all instances of ultraviolet and violet lasing in Nd 3⫹-doped ZBLAN fiber lasers have been realized in single-mode ZBLAN fiber having core and cladding diameters of 2.2 and 125 µm, respectively, and a Nd 3⫹ concentration in the core of 1000 wt ppm. Because the NA of the fiber was 0.15, the single-mode cutoff wavelength was 400 nm. For these experiments, fiber lengths of 38–45 cm were investigated. Two mirrors, butted directly against the polished ends of the fiber, formed the optical cavities. One of the mirrors was dichroic, and the pump radiation was launched through this mirror into the fiber with a 10⫻ microscope objective. The estimated launching efficiency was 30%. For the 381-nm laser, both mirrors were flat and had reflectivities greater than 99.8% at 380 nm. The transmission of the dichroic mirror at 590 and 412 nm was greater than 95% and 59%, respectively. The latter was necessary to suppress oscillation on the 2 P3/2 → 4 I 11/2 transition at 412 nm, which competes with the 380-nm laser. The fiber laser output was collected with a second 10⫻ microscope objective and a glass filter removed the unabsorbed pump radiation. For the 412-nm laser, a similar optical cavity and the same piece of fiber were used. The pump laser beam was launched into the fiber core with a 10⫻ microscope objective through a flat mirror with a transmission of ⬃0.3 and ⬃95% at 412 nm and 590 nm, respectively. The second mirror had a radius of curvature of 10 cm and a transmission of ⬃0.1% at 412 nm. This mirror was used, as opposed to a flat mirror, only because it was readily at hand. Therefore, the total cavity output coupling was ⬃0.4%. Because the second cavity mirror had a thickness of ⬃4 mm, a 5⫻ microscope objective, which did not collect all of the light emitted from the end of the fiber because of its low NA, was required to collimate the fiber laser output. The laser output from this end of the fiber was separated from the pump radiation with a glass filter. At the pump input end of the fiber, the 412-nm laser power was separated from the incoming pump using a dichroic beamsplitter and a color filter. The total output power from the violet fiber laser is taken to be the sum of the powers emerging from both ends of the resonator.

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The spontaneous emission and laser spectra for the Nd 3⫹-doped ZBLAN fiber are shown in Figure 11. To avoid distortion caused by absorption and stimulated emission, the spontaneous emission spectrum was recorded by collecting the fluorescence emitted orthogonal to the fiber axis. Intense fluorescence bands, peaking at 381 and 412 nm and associated with the 4 D 3/2 → 4 I 11/2 and 2 P3/2 → 4 I 11/2 transitions of Nd 3⫹, respectively, are observed when the fiber is pumped by a CW ring dye laser operating at ⬃590 nm (see Fig. 11, trace a). When the appropriate optical cavity is installed, lasing occurs at either 381 nm or 412 nm, and spectral narrowing is apparent (see Fig. 11, traces b and c). The widths (FWHM) of the 381- and 412-nm fluorescence bands are ⬃4 and 6.5 nm, respectively, whereas the linewidths of both laser transitions are less than 0.1 nm. The dependence of the 381-nm laser-output power on pump power is shown in Figure 12 for Nd 3⫹-doped ZBLAN fiber lengths of 45 and 39 cm. A maximum output power of 76 µW was obtained from the 45-cm-long fiber for 275 mW of incident pump power at 590 nm. The estimated incident threshold pump power (indicated by the dashed line in Fig. 12) is 130 mW, which, for an estimated launching efficiency of 30%, corresponds to 39 mW of launched pump power. Defects in the fiber, presumably induced by the high intracore laser intensities (1–10 MW/cm 2 at the pump wavelength, 10s of kW/ cm 2 at 381 nm) resulted in degradation of the UV laser performance. Deterioration of the laser output power correlated with an increase in pump light-scattering at distinct points along the fiber, as well as an increase in the UV laser threshold over the course of several hours. The observation of distinct scattering centers is indicative of local imperfections in the fiber, such as inclusions or microscopic crystalline domains. It is also possible that, in addition to the development of local-scattering centers, photodarkening processes, such as those observed in Tm 3⫹-doped ZBLAN fiber, were occurring (see Sec. 4.7.3). ESA at the signal or pump wavelengths from the 4 D 3/2 or 2 P3/2 levels could lead to the population of high-energy levels of Nd 3⫹ that could emit mid- to deep-UV photons, thereby causing either the formation of color centers or a change in the oxidation state of the Nd 3⫹ ion. Alternatively, two-photon absorption at 380 nm (បω ⫽ 3.26 eV), or 412 nm by the impuri-

Figure 11

Fluorescence (a) and laser spectra (b, c) of the Nd 3⫹-doped ZBLAN fiber laser.


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Figure 12 Output power characteristics of the 381-nm Nd 3⫹-doped ZBLAN fiber laser for a cavity output coupling of ⬍0.2% and fiber lengths of 45 and 39 cm.

ties in the glass host, enhanced by the high intracore intensities present in the fiber lasers, could also lead to the formation of color centers. The apparent saturation of the output power in Figure 12 for pump powers higher than 220 mW is due to the formation of defects in the fiber as the pump power was increased, rather than a saturation of the laser transition. One particularly noticeable localized defect in the 45-cm–long fiber was removed, resulting in a 39-cm fiber. As illustrated in Figure 12, the incident pump power threshold for this shorter fiber was much lower, namely 75 mW, which corresponds to a launched power threshold of ⬃25 mW. The slope efficiency relative to launched pump power was ⬃0.07%. If we recall that the transmission of the output coupler in these experiments is under 0.1%, it is likely that higher cavityoutput couplings will significantly improve the output power and, hence, the slope efficiency of this laser. Figure 13 shows analogous data for the 412-nm–fiber laser, which used a 38-cm– long fiber. Despite the cavity loss introduced by the use of a curved, rather than flat, mirror at one end of the resonator, a maximum output power of 0.47 mW was obtained for 320 mW of incident pump power (again for λ ⫽ 590 nm). The threshold launched pump power was 67 mW. The dashed line in Figure 13, which represents the least-squares fit to the data acquired for incident pump powers less than 300 mW, has a slope of 1.7% relative to the launched pump power. Excitation spectra for the 381- and 412-nm lasers are presented in Figures 14 and 15. Recorded by measuring the fiber laser output power as the pump wavelength is scanned, the excitation spectra illustrate the broad pump bands for each laser. Lasing at 381 nm, for example, is obtained for pump wavelengths ranging from 582 to beyond 597 nm (see Fig. 14). Because the laser was operated near threshold, its performance was somewhat erratic for pump wavelengths lower than 593 nm, but was stable for pump wavelengths between 593 and 597 nm. In addition, interference effects caused by the

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Output power characteristics of the 412-nm Nd 3⫹-doped ZBLAN fiber laser for a fiber length of 38 cm and a cavity output coupling of ⬃0.4 %.

Figure 13

Figure 14

Excitation spectrum of the 381-nm Nd 3⫹-doped ZBLAN fiber laser. Inset shows modulation of pump power reflected off of pump coupling optics, indicating a modulation of launched pump power of several percent as the pump wavelength is scanned.


Figure 15

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Excitation spectrum of the 412-nm Nd 3⫹-doped ZBLAN fiber laser.

pump-coupling optics and the dichroic mirror of the laser resulted in a periodic modulation of the launched pump power of a few percent, which resulted in a corresponding modulation of the fiber laser output power as the pump wavelength was changed. This is illustrated by the inset to Figure 14. Similar results were obtained for the 412-nm laser. The modulation of the excitation spectrum in Figure 15 is an artifact of the pump-coupling optics, but the optimal pumping wavelengths are clearly seen to lie between ⬃587 and 592 nm. 4.4.3 Temporal Behavior The 412-nm laser exhibited CW operation, whereas the 381-nm laser operated in a selfpulsing mode [68]. Oscilloscope traces depicting the temporal behavior of the 412-nm laser as the pump beam was chopped are shown in Figure 16. The unchopped incident pump power was 450 mW for this trace. The laser output was detected with a photomultiplier tube and recorded with a digital oscilloscope having a bandwidth of 400 MHz. The onset of lasing occurred ⬃400 µs after the pump beam was turned on. After the onset of lasing, the output power of the fiber decayed to a value two to three times smaller than its initial value, presumably owing to a buildup of population in the lower laser level. Figure 17 shows a waveform for the 412-nm laser on an expanded time scale. Initially, relaxation oscillations having a periodicity of ⬃15 µs (⬃67 kHz) were observed, but after ⬃200 µs, the device was operating CW. In contrast, the 381-nm laser exhibited erratic, pulsing behavior indicative of a selfterminating laser transition. Pulsed operation of this transition is not surprising, as the 4 D 3/2 level has a larger multiphonon emission rate—therefore, a shorter lifetime—than the 2 P3/2 level so that a continuous inversion is more difficult to maintain. From the con-

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Figure 16 Time dependence of the 412-nm Nd 3⫹-doped ZBLAN fiber laser output (top waveform) as the pump laser is chopped (bottom waveform).

Figure 17

Expanded waveform showing the relaxation oscillations of the output power of the 412-nm Nd 3⫹-doped ZBLAN fiber laser immediately after pump power is applied.


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stants proposed by Joubert et al. [67] for ZBLA glass, the multiphonon decay rates for the 4 D 3/2 and 2 P3/2 upper laser levels and the 4 I 11/2 lower level are ⬃3.0 ⫻ 10 5, 2.6 ⫻ 10 4, and 3.7 ⫻ 10 6 s⫺1, respectively. Radiative lifetimes of the 4 D 3/2 and 2 P3/2 states in LaF3 have been reported to be approximately 42 and 421 µs, respectively [69]. These values yield overall upper-state lifetimes for the 4 D 3/2 and 2 P3/2 levels of approximately 3.1 and 35 µs, respectively. The decay of the 4 I 11/2 lower level is dominated by multiphonon decay and has a corresponding lifetime of ⬃0.3 µs. The strong 2 P3/2 → 4 I 11/2 and 4 F3/2 → 4 I 11/2 (1.06 µm) transitions feed directly into the lower level of the 381-nm laser, making an inversion even more difficult to maintain. 4.4.4 Prospective Nd 3ⴙ-Doped ZBLAN Fiber Laser Transitions: Upconversion-Pumped Emission from Nd 3ⴙ 2 F(2) in the Near UV and Visible Because pumping at 590 nm is currently impractical, new one-color or two-color schemes for exciting both the 381- and 412-nm lasers in the deep red or near-infrared are desirable. Figure 18 shows the absorption spectrum (resolution ⬃0.25 nm) for a bulk sample of Nd 3⫹-doped ZBLAN glass, 2.6 cm in length and having a Nd 3⫹ concentration of 1.8 ⫻ 10 19 cm⫺3. Note the UV absorption edge of the glass below 300 nm and the presence of several strong absorption features in addition to the 4 I 9/2 → 4 G 5/2 , 2 G 7/2 transition at ⬃580 nm. The 4 I 9/2 → 4 F9/2 , 4 I 9/2 → 4 F7/2 ⫹ 4 S 3/2 , and 4 I 9/2 → 4 F5/2 ⫹ 2 H(2) 9/2 pump bands, peaking at ⬃680, ⬃740, and ⬃800 nm, respectively, are of particular interest because of the commercial availability of high-power laser diodes at these wavelengths. Pumping an Nd 3⫹-doped ZBLAN fiber simultaneously at 805 and 690 nm generates side fluorescence in the ⬃370- to 430-nm region, as illustrated in Figure 19. For these experiments, the 805- and 690-nm beams were combined using a polarizing beam splitter and launched into one end of the fiber. Weak emission on the 2 P3/2 → 4 I 11/2 transition (412

Absorption spectrum of bulk ZBLAN glass with an Nd 3⫹ concentration of 1.8 ⫻ 10 19 cm⫺3. The terminal Nd 3⫹ electronic state(s) associated with these GSA transitions are indicated near the corresponding peak.

Figure 18

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Comparison of fluorescence spectra of an Nd 3⫹-doped ZBLAN fiber co-pumped at 805 nm and 690 nm with that obtained by pumping at 590 nm.

Figure 19

nm) is observed, but the 381-nm ( 4 D 3/2 → 4 I 11/2 ) transition is absent and new features at 390, 400, and 420 nm appear. In addition to these violet and near-UV bands, several strong features in the 445- to 530-nm interval are observed. The visible and UV bands produced by this two-color excitation scheme are illustrated in Figure 20. All bands originate from the 2 F(2) 5/2 state of the Nd 3⫹ ion, lying at ⬃38,700 cm⫺1, which bears a remarkable resemblance to the 3 P0,1 states of Pr 3⫹ in the sense that numerous transitions in the visible and violet originate from one level. Emission from the 2 F(2) 5/2 state of Nd 3⫹ has been observed previously, but only by direct photoexcitation in the UV in fluoride and oxide crystals (LaF3 , LiYF4 , YAG, and BaY2 F8 ) [67,69]. Because the onset of UV absorption by the ZBLAN glass host occurs close to 300 nm, access to the 2 F(2) state requires multiple photon excitation, as the wavelength for single-photon excitation would necessarily be less than 260 nm. The spectroscopic assignments for the transitions identified are given in Figure 21. Spectra virtually identical to those of Figure 20 are observed when the fiber is excited at 680 and 740 nm simultaneously, 800 and 590 nm simultaneously, or with 740 nm alone. Each of the four schemes for pumping the Nd 3⫹ 2 F(2) 5/2 state is illustrated in Figure 22. Clearly, all of the multistep processes of Figure 22 are unsuitable for exciting the 412nm laser transition because, in each case, the population of the upper laser level ( 2 P3/2 ) is depleted through ESA at one of the pumping wavelengths. In the 740-nm excitation scheme, ESA originating from the 4 F5/2 ⫹ 2 H(2) 9/2 level must be the mechanism responsible for populating the 2 P3/2 state. This is a surprising result, since the energy gap between the 4 F5/2 ⫹ 2 H(2) 9/2 and 4 F3/2 levels is ⬃1000 cm⫺1 (in LaF3 ) so that de-excitation of the 4 F5/2 ⫹ 2 H(2) 9/2 state by multiphonon emission is rapid. Nevertheless, the 2 P3/2 → 4 F5/2 ⫹ 2 H(2) 9/2 line strength is known to be large [70] and the 4 F5/2 ⫹ 2 H(2) 9/2 state is fed continuously by GSA and by radiative decay of the 2 F(2) 5/2 level. As far as prospective lasers are concerned, an attractive characteristic of the 2 F(2) 5/2 state is its high radiative efficiency. Because this level lies ⬃5000 cm⫺1 higher than the


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Figure 20 Fluorescence emission spectra of an Nd 3⫹-doped ZBLAN fiber pumped at 740 nm. Similar spectra are obtained with dual-wavelength pumping at 680 nm and 800 nm, or at 590 nm and 800 nm. The transition assignments are indicated in parentheses next to the corresponding peaks.

next highest state, its multiphonon emission rate, from known constants for ZBLA glass, is estimated to be on the order of 10 s⫺1. The radiative lifetime for the 2 F(2) 5/2 state, in contrast, is relatively short (23 µs at T ⫽ 6 K for 0.1 wt% of Nd 3⫹ in LaF3 ) [69] as a result of the strong-emission line strengths in the visible and UV. The short upper-state lifetime does not necessarily preclude lasing from this level, however, because the lower levels of the 390-, 420-, 445-, and 470-nm transitions are deactivated rapidly by phonon relaxation. Clearly, selection of a pumping process that does not populate these lower levels would be desired to increase the likelihood of obtaining lasing on transitions originating from the 2 F(2) 5/2 level. Thus, one would want to avoid pumping at 590 nm, as strong GSA at this wavelength feeds the lower levels of all of the transitions in the 390-

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Figure 21 Partial energy-level diagram of Nd 3⫹ illustrating the violet and visible transitions observed in Nd 3⫹-doped ZBLAN fiber under dual wavelength pumping at 580 nm and 800 nm at room temperature.

to 470-nm region that originate from the 2 F(2) 5/2 level. Similarly, pumping at 740 nm populates the lower levels of the 390- and 400-nm transitions, but it may be suitable for pumping the 2 F(2) 5/2 transitions at wavelengths longer than 420 nm. The Nd 3⫹-doped ZBLAN fiber laser at 381 nm is the first ultraviolet fiber laser to be demonstrated. However, now that the threshold of the UV has been crossed, it is inevitable that other, shorter-wavelength UV fiber lasers will follow. Indeed, Thrash and Johnson [39] have reported room-temperature, single-pulse lasing at 347.9 nm from BaY2 F8 crystals co-doped with Yb 3⫹ and Tm 3⫹. Consequently, as the quality of ZBLAN fibers continues to improve, one might expect that lasing on the 355-nm transition of Tm 3⫹ in ZBLAN will also be demonstrated, for it lies above the UV absorption edge of ZBLAN glass.


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Upconversion-pumping mechanisms for the population of the 2 F(2) 5/2 level in Nd 3⫹doped ZBLAN fiber. 1) co-pumping at 800 nm and 680 nm, 2) pumping at 740 nm, 3) co-pumping at 740 nm and 680 nm, and 4) co-pumping at 800 nm and 590 nm.

Figure 22

Other near-UV and visible laser transitions in Nd 3⫹-doped ZBLAN fibers also appear to be achievable by one-color or two-color pumping schemes. The current availability of high-power semiconductor laser diodes in several wavelength regions between 0.65 and 1 µm suggests that multiple laser transitions can be excited simultaneously in Nd 3⫹ by diode laser pumping. 4.5 GREEN HOLMIUM-DOPED ZBLAN FIBER LASER The first upconversion-pumped operation of the holmium green laser (λ ⬃0.55 µm) was reported in 1971 by Johnson and Guggenheim [35], who obtained stimulated emission

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from a flashlamp-pumped BaY2 F8 crystal co-doped with Ho 3⫹ and Yb 3⫹ and cooled to 77 K. Lasing at 550 nm in a Ho 3⫹-doped ZBLAN fiber at room temperature and pumped at 647.1 nm was first reported by Allain et al. in 1990 [37,71]. 4.5.1 Excited-State Kinetics and Multiphonon Relaxation Figure 23 shows a partial energy level diagram for Ho 3⫹, limited to the states most relevant to this upconversion laser. The proposed pumping scheme is a two-step resonant process. The absorption of a red (λ ⬃645-nm) pump photon by the ground-state ion ( 5 I8 ) populates Stark sublevels of the 5 F5 excited state, which subsequently relax nonradiatively to the lower-energy 5 I 6 and 5 I 7 levels. It has previously been shown [72–75] that the excited states of Ho 3⫹ in fluorozirconate glass adhere to the phenomenological energy gap law, which expresses the nonradiative decay rate for a given state as W ⫽ C exp(⫺∆E/aបω), where ∆E is the energy separation between the excited state of interest and the next lowestlying state, C and a are constants, and បω is the highest phonon energy in the host spectrum (see Chap. 2). For fluorozirconate glass, C and aបω have been determined to be 1.88 ⫻ 10 10 s⫺1 and 173.3 cm⫺1, respectively [73,75], and radiative relaxation of a Ho3⫹ excited state dominates decay of that state by multiphonon emission when ∆E is greater than ⬃2100 cm⫺1 [74]. The rate for deactivation of the 5 F5 state (∆E ⬃ 2200 cm⫺1 ) by multiphonon emission is ⬃5.8 10 4 s⫺1, which gives rise to a nonradiative lifetime of ⬃17 µs. The lifetimes of both the 5 I 6 and 5 I 7 states are 3–13 ms, making these levels well-suited as intermediate or ‘‘platform’’ states for the upconversion-pumping process. The absorption of a second pump photon by the ion in either the 5 I 6 or 5 I 7 levels accesses (as indicated in Fig. 23) either the 5 G 5 or 5 F3 states which also relax nonradiatively to the comparatively

Partial energy-level diagram for Ho 3⫹ illustrating the pumping scheme for the green Ho 3⫹-doped ZBLAN fiber laser. Solid arrows represent the emission or absorption of a photon, and dashed arrows represent multiphonon relaxation of the ion.

Figure 23

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long-lived 5 F4 and 5 S 2 levels (τ ⬃ 100–300 µs) [74,76]. Because the energy gap ∆E between the lowest Stark sublevel of the 5 F4 manifold and the highest level of the 5 S 2 manifold is ⬃90 cm⫺1 in LaF3 [77] and 114 cm⫺1 in YAG [78], these states are coupled thermally at room temperature (kT ⬃ 200 cm⫺1 ). Recent measurements of fiber laser spectra [79] indicate that the 5 F4 – 5 S 2 energy defect for the Ho 3⫹ ion in ZBLAN glass is ⬃74 cm⫺1 (⬃10 meV). Lasing occurs on the 5 S 2 → 5 I 8 transition (λ ⬃550 nm) which was calculated to have a peak stimulated emission cross section at 300 K of (0.78–1.75) ⫻ 10⫺20 cm 2 [74,80]. Note that the theoretical maximum photon efficiency for this system is 2.25 eV/ (2 ⫻ 1.92 eV) ⬃ 59%. Absorption at the laser wavelength by the ground state ( 5 I 8 ) and, possibly the 5 I 7 excited state, as well as other excited states, introduces loss to this system. Furthermore, depletion of the ground-state population at the pumping intensities present within the fiber core during normal operation of the laser has a strong influence on the spectral and temporal characteristics of this laser. 4.5.2 Laser Experiments The fiber used in the laser experiments described by Allain and co-workers [37,71] had a core diameter of 2.7 µm and a single-mode cutoff wavelength of 550 nm, so that the fiber guided a single transverse mode at both the pump and laser wavelengths. The holmium ion concentration in the fiber core was 1200 wt ppm ([Ho] ⬃ 2 ⫻ 10 19 cm⫺3 ). The pump was provided by either a CW dye laser or a krypton ion laser. A maximum green output power of 12 mW and a launched threshold pump power of 24 mW were measured for a fiber 45-cm long. A prism was placed within the cavity for tunability. The tuning range was reported to be dependent on the fiber length, with shorter fibers favoring shorter wavelengths. An overall tuning range of 538–553 nm was obtained from three separate fibers, ranging in length from 45 to 121 cm. CW operation was reported, although continuous spiking, with a peak amplitude ⬃20% of the CW level, was observed. The Ho 3⫹-doped ZBLAN, 550-nm upconversion laser has also been driven by a pump laser operating at either 750 or 890 nm [81]. Although the pumping scheme is similar to the two-step resonant pumping process at 645-nm described in the foregoing (see Fig. 23), the laser efficiency is considerably lower because of smaller GSA and ESA cross sections at 750 and 890 nm. A series of experiments designed to examine the dependence of the Ho 3⫹-doped ZBLAN fiber laser parameters on the core diameter, length, and NA of the fiber have recently been carried out at the University of Illinois [79,82,83]. The main characteristics of the three types of fibers used in these experiments are described in Table 2. Although the fibers were obtained from two vendors, the nominal composition of the Table 2 Characteristics of Fibers Used in the Ho 3⫹-Doped ZBLAN Fiber Laser Experiments

Fiber number

Core diameter (µm)

1 2 3

11 3 1.7

Numerical aperture

Number of LP modes supported at λ ⫽ 550 nm

Number of LP modes supported at λ ⫽ 645 nm

0.15 0.2 0.39

24 3 3

17 3 3

Source: Refs. 79, 82, and 83.

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glass host (ZrF4 [53% by weight]–BaF2 [20%]–LaF3 [4%]–AlF3 [3%]–NaF[20%]) was the same. The fiber cores included a small percentage of PbF2 to raise the glass refractive index. The core Ho 3⫹ dopant concentration (⬃0.1 wt%) corresponds to an ion concentration in the core of ⬃1.8 ⫻ 10 19 cm⫺3. As indicated in Table 2, all of the fibers supported multiple guided modes at both the pump (⬃645-nm) and fiber laser (⬃550-nm) wavelengths. For several of the experiments, the fibers were pumped by a CW scanning-ring dye laser capable of producing more than 400 mW of output power over the 630- to 660-nm region. The linewidth of the dye laser (without etalons) was 20 GHz (⬃0.7 cm⫺1 ). The studies described in Section 4.5.3, however, involved pumping the fiber with an InGaAlP diode laser operating at ⬃643 nm. Output power (slope efficiency) and temporal waveform data were obtained for the Ho 3⫹-doped ZBLAN fiber laser, operated in a Fabry–Perot cavity configuration with the fiber ends polished and butted directly against two flat mirrors. Measurements were made for the three types of fibers listed in Table 2, with lengths ranging from 12.5 to 86 cm. Several output couplers, with transmission characteristics described in Table 3, were used. Details of the fiber laser configurations are available [79,82,83]. Either a Brewster-angle prism or short-pass and long-pass filters were used to separate the residual pump from the green-output laser beam. 4.5.3 Slope Efficiency and Threshold Pump Power The values for launched pump power threshold and slope efficiency for the 11-µm–core diameter fiber and fiber lengths of 21 and 86 cm are summarized in Table 4. Results for cavity output couplings as large as 24% are presented. The dependence of the Ho 3⫹-doped ZBLAN fiber laser output power on the launched pump power (at 643.2 nm) is shown in Figure 24 for a 21-cm long fiber. The lines represent the linear least-squares fit to the data for each value of output coupling. Threshold pump powers as small as ⬃85 mW (launched) were measured for cavity output couplings of 1.5 and 3%, and the slope efficiency increased monotonically with output coupling, up to almost 17% for an output coupling of 24%. Expressed relative to the absorbed pump power, the slope efficiency for 24% output coupling rises to 30%. Because of GSA losses at the laser wavelength, the same laser cavities made with an 86-cm length of fiber exhibited considerably higher

Table 3 Transmittances of Output Couplers Used in the 550-nm Ho 3⫹-Doped ZBLAN Fiber Laser Experiments Transmittance of output coupler at 550 nm (%) 1.5 3 7 12 24 60 96.5 (Fresnel reflection) Source: Refs. 79, 82, and 83.

Transmittance at 645 nm (%) 34 43 95 85 72 0.2 96.5 (Fresnel reflection)

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Table 4 Summary of Threshold Pump Powers and Slope Efficiencies, Both Relative to Launched Pump Power, for the Ho 3⫹-Doped ZBLAN Upconversion Fiber Laser Core diameter (µm)/NA 11/0.15 11/0.15 11/0.15 11/0.15 11/0.15 11/0.15 11/0.15 11/0.15 11/0.15 11/0.15 3/0.2 3/0.2 3/0.2 3/0.2 3/0.2 3/0.2 3/0.2 3/0.2 1.7/0.39 1.7/0.39 1.7/0.39 1.7/0.39 1.7/0.39

Length (cm)

Output coupling (%)

Threshold pump power (mW)


21 21 21 21 21 86 86 86 86 86 12.5 27.5 27.5 27.5 27.5 67 67 67 21 21 21 21 21

1.5 3 7 12 24 1.5 3 7 12 24 1.5 1.5 7 24 96 1.5 24 96 1.5 3 7 24 60

91 86 116 122 156 198 182 209 205 251 6.2 7.9 9.8 10.5 27 13 22 79 3.6 4.0 4.9 5.6 5.3

2.6 3.4 9.1 11.1 16.8 1.2 2.9 4.5 7.4 11.4 0.4 (0.7) a 0.6 (2.4) a 3.1 (5.1) a 2.9 (5.5) a 11.5 0.7 6.5 (19.0) a 22.4 1.1 1.9 7 12.7 —

a

For slope efficiency data displaying clear dual slope characteristics, both efficiencies are given.

pump power thresholds (⬎180 mW), a maximum slope efficiency of ⬃11% (see Table 4), and a maximum output power of 14 mW. Similar data for fiber with a 3-µm-core diameter were gathered for fiber lengths of 12.5, 27.5, and 67 cm. Because of the high gain of this laser system [10], Fresnel reflection from one end of the fiber provided sufficient feedback for lasing to occur. Consequently, data were obtained for output couplings as high as 96%. Table 4 lists the launched threshold pump power and slope efficiencies observed for lasers formed using the fiber with a 3-µm-core diameter. For most of the output curves, two distinct slopes were observed, with a higher slope being associated with higher pump powers. This is illustrated in Figure 25 for the 24% output coupling. The solid lines represent the least-squares fit to each of two distinct slopes. At lower pump powers, the laser spectrum consists of one or more lines lying at about 550 nm. The emergence of the higher slope with increasing pump power coincides with the onset of lasing on transitions at slightly shorter wavelengths in the 545- to 548-nm range and the suppression of transitions close to 550 nm. The laser lines near 550 nm are attributed to 5 S 2 → 5 I 8 transitions, whereas those at wavelengths less than 548 nm primarily result from 5 F4 → 5 I 8 transitions. The dynamics behind the

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Figure 24 Output power of the green Ho 3⫹-doped ZBLAN fiber laser as a function of the launched pump power at 643.2 nm, measured for several values of cavity output coupling, a fiber core diameter of 11 µm and a fiber length of 21 cm. The linear least-square fit to each set of data is also shown.

shift in output wavelength are not fully understood. One possibility is that a change in strength of one or more ESA processes as the pump power is changed leads to a wavelength shift of the gain peak and, consequently, the fiber laser spectrum. This dual-slope behavior of Fig. 25, for example, was not observed with the 11-µm core diameter fiber experiments because the pump intensities required to drive these shorter-wavelength tran-

Figure 25

Measured output power curve of the green Ho 3⫹-doped ZBLAN fiber laser for a fiber 67-cm in length with a core diameter of 3 µm, and two values of output coupler transmission.


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sitions above threshold could just be reached with only the maximum available pump power. The early stages of the effect can be seen in the 24%-output coupling data of Figure 24: for example, for pump powers ⬃325 mW. Figure 25 shows that slope efficiencies as large as ⬃22% (for launched power) and output powers up to 20 mW were obtained from the 67-cm fiber laser with 96% output coupling. In addition, threshold pump powers (again, relative to launched pump power) of less than 6.5 mW were measured from a 12.5-cm fiber laser with an output coupling of 1.5%. The output power versus launched pump power curves for a fiber with a 1.7-µm– core diameter and a length of 21 cm was measured for several values of the output mirror transmission, and the results are depicted in Figure 26 and summarized in Table 4. Because of the small core diameter and high NA of this fiber, the pump intensity was sufficiently large to cause the fiber to operate on the 5 F4 → 5 I 8 transitions at pump powers just higher than threshold. As an example, Figure 27 shows the fiber laser spectra observed for a cavity output coupling of 24% for two values of pump power. Between 9 and 12 mW of launched pump power, the free-running laser switches from operating on transitions in the vicinity of 549.1 nm to oscillating near 544 nm. Consequently, the dual-slope behavior was not observed with the fiber with a 1.7-µm core diameter. Saturation of the gain medium is evident for all of the output coupling values, although its onset increases with increasing output coupling. The deviation of the slope efficiency data for 60% output coupling from the behavior observed for the other output-coupling values is likely due to an inadvertent misalignment of the fiber laser cavity during this particular set of measurements. With this core diameter, the pump power threshold was less than 6 mW for all of the output couplings studied, and the slope efficiency below saturation for the 24%-output coupling data was ⬃12.7%. To compare the efficiencies of the short- and long-wavelength transitions directly, the 21-cm–long, 1.7-µm–core-diameter fiber was installed in a tunable resonator having two intracavity prisms and an output mirror with a transmittance of 7% over the 540- to

Figure 26 Same as Fig. 25, but obtained for a Ho :ZBLAN fiber 21 cm in length with a core diameter of 1.7 µm.

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Figure 27

Laser spectrum of the green Ho 3⫹-doped ZBLAN fiber laser (22-cm length, 1.7-µm core diameter, 3% output coupling) measured at two pump powers. The resonator is ‘‘free-running’’ (i.e., untuned).

550-nm region. After tuning the laser to either 544.1 or 549.1 nm, output power versus pump power data were recorded. At both wavelengths, the laser operated on a single line for all pump powers investigated. The results are illustrated in Figure 28. For launched pump powers greater than 7 mW, the 544.1-nm transition was more efficient than the 549.1-nm transition because the latter saturates at a lower pump power (⬎10 mW). This result is somewhat surprising because the emission and absorption cross sections at 544.1 nm are higher than those at 549.1 nm, so one would expect that the shorter-wavelength transition would saturate at a fiber laser intensity lower than that of the longer-wavelength transition. However, an ESA transition rate that increases in strength with increasing pump power, and has a larger cross-section at 549.1 than at 544.1 nm, could result in the observed saturation of the 549.1-nm transition at a lower fiber laser intensity as well as a lower pump power than for the 544.1-nm transition. Several states, including the 5 I 7 , 5 I 6 , 5 I 5 , and 5 S 2-5 F4 levels, could be responsible for such an ESA process. 4.5.5 Excitation Spectra and the Pumping Window The 5 F5 ← 5I8 absorption spectrum of Ho 3⫹ in ZBLAN is broad, with a full width at half maximum (FWHM) of 12.5 nm, and it does not exhibit fine structure at a resolution of 0.25 nm. However, because of the existence of numerous absorption steps at the pump and signal wavelengths from the ground state and several excited states, which either beneficially or adversely affect the pumping efficiency as well as the cavity loss, the dependence of the green laser efficiency on pump wavelength is both intricate and informative. Excitation spectra, which depict the variation of laser output power (or, for example,


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Figure 28

Comparison of the measured output power dependence on launched pump power of a Ho 3⫹-doped ZBLAN fiber laser tuned to either the 544.1-nm or the 549.1-nm line.

fluorescence intensity) with pump wavelength from an ionic excited state of interest, have been recorded for a fiber 21 cm in length and having a core diameter of 11 µm [84]. Typically, the laser operated on two or more transitions in the 547- to 550-nm region, and excitation spectra were recorded by selecting a particular line with a 0.25-m monochromator (resolution ⬃0.2 nm) and monitoring the relative output power as the pump (dye laser) wavelength was scanned. An excitation spectrum for the Ho 3⫹-doped ZBLAN fiber laser, obtained by observing the output power at 549.4 nm, is shown in Figure 29. Fluorescence excitation spectra, which were acquired by monitoring the fluorescence power from the 3 P1 (358, 408 nm), 5 G 4 (385 nm), and 5 F3 (486 nm) states of the ion as the pump wavelength was varied, are also included in Figure 29. The partial energy-level diagram in Figure 30 illustrates the transitions that produce the monitored emission bands. Several distinct suppressions or dips in the spectra, which are not due to experimental artifacts, lie at ⬃644, 645.5, 646, 647.5, 648.5, and 650 nm. Notice the strong correlation between the structure of the excitation spectra for the laser and that for of all of the fluorescence bands, despite that some of the fluorescence bands are associated with Ho 3⫹-excited states lying well above the upper levels for the green laser (5 S 2 , 5 F4 ). Laser emission from the 5 S 2 and 5 F4 levels, as well as fluorescence from the 5 F3 state, is driven by GSA at ⬃645 nm, followed by ESA of the pump by the 5 F 3 ← 5 I7 or 5 G 5 ← 5 I 6 transitions. In contrast, pumping the 3 P1 and 5 G 4 levels with 645-nm light requires the absorption of a third pump photon, presumably by the 5 S 2 or 5 F4 metastable levels (see Fig. 30). If this was the primary mechanism that pumped the 3 P1 and 5 G 4 levels, one would expect minima in the excitation spectra of emission from the 5 S 2 and 5 F4 levels to correspond to maxima in the excitation spectra of emission from the 3 P1 and 5 G 4 levels, as pumping the latter removes population from the 5 S 2 and 5 F4 levels. The strong correlation of the intensity maxima of fluorescence from the 3 P1 and 5 G 4 levels with the intensity maxima of the laser emission from the 5 S 2 and 5 F4 levels, and the fluorescence from the 5 F3 level, strongly suggests that the emission

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Figure 29

Laser and fluorescence excitation spectra from a Ho 3⫹-doped ZBLAN fiber pumped in the 640–654 nm range. The laser excitation spectrum was obtained by measuring the relative fiber laser power while varying the pump wavelength and maintaining a constant pump power of 180 mW. For the fluorescence excitation spectra, the pump power was kept at 250 mW, and emission was collected from the fiber end while the fiber was lasing at λ ⬃ 549 nm. (After Ref. 84.).

from the 3 P1 and 5 G 4 levels is enhanced by the presence of the intense ⬃550-nm radiation within the fiber core while the fiber is lasing. That is, ESA near 550 nm, presumably from the 5 S 2 and 5 F4 levels, pumps the 3 P1 and 5 G 4 levels (see Fig. 30). This ESA process is detrimental to the performance of the ⬃550-nm–fiber laser because it both introduces an absorption loss at the laser wavelength as well as reduces the population of the upperlaser level. A lower pump power was used for the laser excitation spectrum than for the fluorescence spectra in Figure 29, so the fluorescence excitation spectra are broader than the laser excitation spectrum. This laser excitation spectrum is shown for illustrative purposes because, at higher pump powers, the structure in the spectrum becomes less pronounced. Other laser and fluorescence excitation spectra obtained at the same pump power show the same spectral width. The structure in the excitation spectra in Figure 29 is likely due to the overlap of several pump ESA transitions originating from the 5 I 7 , 5 I 6 , and 5 F4 , 5 S 2 levels, and possibly even higher-energy states. The result of this overlap is a complicated dependence on pump wavelength of the pumping efficiency of the 550-nm laser. Because of the breadth of the 5 F 5 ← 5 I8 absorption transition, low pump power thresholds are observed over a broad band. Figure 31 shows the launched threshold pump power as a function of pump wavelength for fibers of different lengths and core diameters. For all of the data, the transmission of the output mirror at 550 nm was fixed at 1.5%. Over most of the pump band (637–653 nm), the pump power threshold for the 3-µm– core fiber dropped monotonically with decreasing fiber length to the shortest fiber exam-


211

Partial energy-level diagram of Ho 3⫹ illustrating the transitions for which the excitation spectra in Fig. 29 were collected (arrows pointing down) and the potential pumping paths of those transitions (arrows pointing up).

Figure 30

ined (12.5 cm). This result is a consequence of lower GSA losses at the fiber laser wavelength for shorter fiber lengths. Continuing to decrease the fiber length would eventually result in an increase in the threshold pump power, as stronger pumping would be required to obtain sufficient gain to overcome cavity losses (mirrors, scattering, and such). For pump wavelengths outside of the 637- to 653-nm region, the pump power threshold is lower for the 27.5-cm fiber than for the 12.5-cm fiber. In this wavelength region, the pump absorption is lower—hence, the optimal fiber length is longer—because of the need to absorb a sufficient amount of pump power to achieve threshold. In addition, because the pump absorption is smaller, the fiber is pumped more uniformly, and GSA losses at the end of the fiber are reduced. The lowest threshold pump power was measured for a 21cm length of the fiber with a 1.7-µm core diameter, because of the higher pump intensities produced in this small core. The threshold launched pump power for this fiber was less than 6 mW for a pump wavelength range of 645–651 nm (see Fig. 31). These results have significant positive implications for diode-laser pumping of the Ho 3⫹-doped ZBLAN fiber laser. The threshold pump powers of Figure 31 are well within the capability of commercially available, single-mode red diode lasers, and the breadth of the pumping window dramatically relaxes the constraint on diode wavelength; therefore, it alleviates the cost associated with wavelength control. 4.5.6 Laser Spectra and Tuning Characteristics The free-running Ho 3⫹-doped ZBLAN fiber laser typically operates simultaneously on several transitions at wavelengths between 545 and 550 nm. The laser spectra are generally complex and often congested, partly because of the multiple sites occupied by the rare earth ion in the glass. Two main groups of lines have been observed [79]. One group,

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Figure 31

Threshold pump power as a function of pump wavelength for the green Ho 3⫹-doped ZBLAN fiber laser, measured for various fiber core sizes and lengths.

lying in the ⬃548- to 550-nm interval, is observed at low pump intensities and, as discussed previously (see Fig. 27), this is attributed to transitions originating from the 5 S 2 level. Under intense pumping, the spectrum is dominated by a second group of lines at wavelengths ranging from 543 to 548 nm, which arise from transitions from the higherenergy 5 F4 state. These assignments are based partially on the observed dependence of the laser spectrum on pump power and temperature [79]. Spectra obtained from a fiber laser made with a 19.5-cm length of 11-µm core diameter fiber and a 1.5% output coupling are shown in Figure 32 for two values of incident pump power (170 and 350 mW) and fiber temperature (77 and 300 K). At room temperature and for lower pump power, the fiber laser spectrum consists of several lines between 549.1 and 549.6 nm. When the pump power is increased to 350 mW, lines lying between 547.2 and 547.6 nm dominate the spectrum. As discussed previously in Section 4.5.3, the reason for the change in the fiber laser spectrum has been tentatively attributed to a shift in the gain-peak wavelength as a result of pump intensity-dependent ESA. When the fiber is cooled to 77 K, the longer-wavelength transitions between 549.6 and 550.4 nm appear (see Fig. 32). This is because the 5 F4 and 5 S 2 levels are no longer thermally coupled, and the population resides mostly in the 5 S 2 level. Consequently, the population of the 5 F4 level is insufficient to support a significant inversion, even at high pump powers, and the lines between 547 and 547.5 nm are not observed.


213

Comparison of the laser emission spectra of the green Ho 3⫹-doped ZBLAN fiber laser for a fiber 19.5 cm in length with an 11-µm core diameter, measured for two incident pump powers and two fiber temperatures.

Figure 32

With the tunable fiber laser cavity with two intracavity prisms, described earlier, a 40-cm–long fiber with an 11-µm–core diameter has been tuned over an ⬃11-nm range [79]. The results of several experiments are summarized in Figure 33 for an incident pump power of 450 mW at 645 nm. The top portion of the figure shows the superposition of several representative spectra recorded over the full-tuning range of the fiber laser. Lasing was obtained at wavelengths ranging from ⬃539 to 550 nm. The lower portion of the figure gives the dependence of output power on fiber laser wavelength. The output power peaks at 544.8 nm. Tuning over the 11-nm region was not continuous; that is, lasing could be obtained only at discrete wavelengths across the tuning spectrum. Also, in a few wavelength regions, single-wavelength operation was not observed, and the fiber laser operated on two transitions simultaneously. Usually, however, single-wavelength operation (linewidth ⬍ 0.1 nm) could be obtained. Also, that tuning the cavity did not shift the position of the laser lines indicates that the wavelengths at which the fiber laser operates are dictated by the emission properties of the ion, rather than by polarization or mode effects associated with the cavity. This supports the assertion that the rare earth ion occupies only a few sites in fluorozirconate glass [85]; consequently, Ho 3⫹ transitions suffer less inhomogeneous broadening than is observed in silicate glasses. 4.5.7 Diode–Laser-Pumped Ho 3ⴙ-Doped Fiber Laser Diode laser excitation of the green Ho 3⫹-doped ZBLAN fiber laser has been realized [82]. The pump source was an InGaAlP laser diode that produced ⬃30 mW of diffractionlimited output power at 643 nm for a drive current of 80 mA. The diode laser was kept at a temperature of 17°C. Its output was collimated with an aspheric lens, passed through

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Figure 33

Representative laser spectra observed from the tunable Ho 3⫹-doped ZBLAN fiber laser (top) and output power as a function of fiber laser wavelength across the tuning range (bottom). The fiber laser was tuned with two intra-cavity prisms. The incident pump power was 450 mW, and the pump wavelength was 645 nm. The top curve also shows the relative emission and absorption cross-section spectra of Ho 3⫹-doped ZBLAN glass in this spectral region (530–560 nm).

a 6⫻ anamorphic prism pair to produce a more azimuthally symmetric beam, and launched into the fiber with a 20⫻, 0.4-NA microscope objective. The dichroic mirror through which the pump beam was launched had a transmittance of 74% at the pump wavelength and a reflectance greater than 99.8% at 549 nm. The measured launching efficiency was ⬃43%, the same as that for dye laser pumping. Care was taken to align the dichroic mirror to prevent reflection of the pump back into the diode, which might otherwise damage the diode laser’s end facet or increase the diode output power. Monitoring the pump power reflected from the fiber laser front mirror and off of a microscope slide placed between the diode and fiber lasers revealed no increase in diode laser output power when the fiber laser cavity and diode were coupled. Output coupling mirrors with a transmittance at 550 nm of 1.5 and 24% were tested. Figure 34 illustrates the dependence of the fiber laser output power on launched pump power for a cavity output coupling of 24%. With a 1.5%-output coupling (not shown), the threshold power was 1.9 mW, which is the lowest of any upconversionpumped fiber laser reported to date. This value is also significantly lower than the threshold observed with dye laser pumping. The same is true for the fiber laser that used the 24%output coupling mirror. This could be partly due to a better overlap of the focused beam spot of the corrected diode laser with the LP01 fiber mode. The dye laser beam is somewhat


215

Figure 34

Measured output power of the diode-pumped green Ho 3⫹-doped ZBLAN fiber laser as a function of launched pump power for an output coupler transmission of 24% using a 21-cmlong fiber with a core diameter of 1.7 µm.

elliptical and not perfectly collimated; hence a substantial percentage of its power may have been coupled into the less effective LP11 fiber modes. Also, the 643-nm diode laser wavelength lies closer to the peaks of the GSA and 5 F 3 ← 5 I7 ESA spectra than does the 645-nm wavelength used for dye laser pumping, which could lead to more efficient absorption of the pump. More than 1.2 mW of output power was produced for 10.5 mW of launched pump power (see Fig. 34), which corresponds to a 12% optical conversion efficiency relative to launched pump power (20% relative to absorbed power) and a slope efficiency of 18%. 4.5.8 Temporal Behavior The green Ho 3⫹-doped ZBLAN fiber laser exhibits several regimens of temporal behavior that are associated with specific pump power ranges. Immediately above threshold, the laser operates in a pulsed mode with a repetition frequency of ⬃50–75 kHz. As the pump power is increased, the repetition frequency also rises. For pump powers greater than two to three times the threshold value, the laser operates CW, but the signal contains an AC component with a frequency and amplitude that are proportional and inversely proportional, respectively, to the pump power. Figures 35–37 display the laser waveforms recorded for a 22-cm–long fiber laser with a core diameter of 1.7 µm. For the data of Figure 35, the pump power is 1.2 times the launched pump power threshold (⬃5 mW). Figure 35a shows the temporal dependence of the fiber laser output, and Fig. 35b its Fourier transform. The fundamental frequency component of the laser’s output is ⬃70 kHz, but six harmonics are also observed. CW operation was observed for a pump power ⬃2.5 times the threshold value (15 mW; see Fig. 36). The AC portion of the signal contains two primary frequency components. The low-frequency component, ⬃25 kHz, is accompanied by its second and third harmonics.

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Figure 35 Measured temporal behavior of the Ho 3⫹-doped ZBLAN fiber laser output for a launched pump power of 6 mW (1.2 times threshold). (a) Variation of fiber laser output with time and (b) Fourier transform of the waveform shown in (a).

The high-frequency component is at ⬃265 kHz. Note that the upper and lower sidebands, caused by the 25-kHz modulation, also appear at ⬃290 kHz and ⬃240 kHz, respectively. For a launched pump power of 20 mW (see Fig. 37), the amplitude of the AC component has decreased noticeably and its frequency has risen to ⬃300 kHz. The lower-frequency component (fundamental at ⬃45 kHz) has virtually disappeared. To explore further the nature of the higher-frequency oscillations, the dependence of the oscillation frequency was recorded as a function of the pump power. The laser, which was operated on a single line for all pump powers studied, was tuned to either 544.1 or 549.1 nm by using two intracavity prisms as previously described (refer back to Fig. 28). The cavity output coupling was 7% over the 540- to 550-nm–frequency range. Figures 28 and 38a present the dependence of the fiber laser output power and the oscillation frequency for the ac component, respectively, on the launched pump power. Although, for a given pump power, the frequency associated with the 544.1-nm transition is higher than that for the 549.1-nm transition, Figure 28 shows that the output (and intracavity) intensity for the shorter wavelength line is also higher than that for the 549.1-nm line. If the ac frequencies associated with the laser output at the two wavelengths are now plotted as a function of the fiber laser-output power at that wavelength, as shown in Figure 38b, the two curves are virtually identical. One concludes that the frequency of the ac component depends only on the intracavity intensity of the green laser, and not on the laser wavelength. It suggests that the ac modulation originates from a loss mechanism, which is similar at both fiber laser wavelengths, that is modulated by the intracavity green laser intensity. Both GSA, and ESA originating from the Ho 3⫹ 5 I 7 level are candidate mechanisms.


Figure 36

Same as Fig. 35, for a launched pump power of 15 mW.

Figure 37


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Figure 38

The dependence of the frequency of the ac component of the green Ho 3⫹-doped ZBLAN fiber laser output for two fiber laser wavelengths on (a) launched pump power and (b) green laser output power.

Two differences in the behavior of the ac component are observed when pumping with the laser diode as opposed to the dye laser. First, its amplitude decreases more rapidly with increasing pump power under diode pumping. The diode-pumped fiber achieves CW operation immediately above threshold, whereas with the dye laser pump, the pump power must be more than twice the threshold value. Furthermore, the AC component frequency rises more quickly with increased diode laser power than does its dye laser counterpart. For a launched pump power of ⬃10 mW, for example, the frequency of the AC component of the output signal is 230 kHz for diode laser pumping, as opposed to 156 kHz for dye laser pumping. This agrees with the previously discussed dependence of the AC component frequency on fiber laser power because, for this pump power, the fiber laser output was 1.2 mW under diode pumping and only 0.6 mW under dye laser excitation. The improved fiber laser performance observed under diode pumping is likely due to the lower noise in the output of the diode compared with the dye laser. 4.5.9 Competition Between ⬃544- and ⬃549-nm Transitions In an effort to gain further insight into the dynamics of the upper states for the green Ho 3⫹-doped ZBLAN fiber laser transitions, the waveforms for the short (λ ⬇544 nm) and long (λ ⬇ 549 nm) wavelength transitions were monitored simultaneously over the pump power range in which the laser switches to operation on the 544 nm ( 5 F4 → 5 I 8 ) transitions.


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For these experiments, the fiber laser was constructed using a Fabry–Perot cavity with an output coupling at 550 nm of 7%, and at least two laser lines could be observed simultaneously using separate monochromators and photomultipliers. The spectral resolution of each detection system was ⬃0.5 nm. Figures 39–41 summarize the temporal history of the 544.2 and 548.7-nm laser lines as the launched laser pump power is increased from 10 to 41 mW. The waveforms in each of these figures were recorded simultaneously over the same time period. The side graph in each figure displays the laser spectrum observed at the indicated pump power. For a launched pump power of 10 mW (see Fig. 39), which is about twice the threshold value, the laser operates at a single wavelength (548.7 nm). When the launched pump power is increased to 16 mW, new laser lines appear at ⬃544 nm in the laser spectrum (see Fig. 40). The waveforms for the 548.7- and 544.2-nm laser lines clearly show that the laser is switching between the two lines at a frequency of 26 ⫾ 2 kHz. Since these two lines originate from the 5 S 2 and 5 F4 levels, respectively, which are thermally coupled at room temperature, one concludes that the observed temporal behavior is determined by competition between the upper laser levels for the available population. As the pump power is increased further, the duty cycle of the 544.2-nm transition increases, whereas that for the 548.7-nm transition decreases. For example, for a launched pump power of 19 mW (not shown), duty cycles for the two transitions are almost equal, and the frequency of oscillation between them is ⬃16 kHz. At a launched pump power of 41 mW (see Fig. 41), the laser operates solely on several short-wavelength (544.1– 546.6 nm) transitions, all of which originate from the 5 F4 level.

Figure 39

Temporal waveforms, recorded simultaneously, of the 548.7-nm and 544.2-nm laser lines during free-running operation of a Ho 3⫹-doped ZBLAN fiber laser at a launched pump power of 10 mW. The frame to the right shows the laser spectrum.

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Figure 40


Figure 41



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4.6 GREEN ERBIUM-DOPED ZBLAN FIBER LASER The room-temperature, upconversion-pumped green Er 3⫹-doped ZBLAN fiber laser attracted much attention when it was first demonstrated by Whitley and co-workers in 1991 [86] because it required only a single pump wavelength, typically 800 or 970 nm, which was conveniently accessible by existing laser diodes. The only other room temperature, solid-state, CW lasers that had been demonstrated at the time were the 550-nm Ho 3⫹doped ZBLAN fiber laser [37] and the 520-nm Pr 3⫹-doped ZBLAN fiber laser [47]. However, both of these lasers have disadvantages. The Ho 3⫹ laser requires a pump wavelength near 650 nm, a spectral region for which semiconductor laser technology was not well developed at the time, whereas the Pr 3⫹ 520-nm laser had been demonstrated only by dual-wavelength pumping at ⬃830 nm and ⬃1.01 µm. Single-wavelength pumping at 800 nm of the Er 3⫹ 540-nm laser had been demonstrated in a bulk LiYF4 crystal, but cryogenic cooling was required [87]. Lasing at 470 and 560 nm on the 2 P3/2 → 4 I 11/2 and 2 H 9/2 → 4 I 13/2 transitions, respectively, pumped at either 797 or 969 nm, had also been reported in Er 3⫹-doped LiYF4 at low temperatures [88]. 4.6.1 Laser Transitions and Upconversion-Pumping Mechanisms Under excitation at either ⬃800 or ⬃970 nm, Er 3⫹ ions in ZBLAN glass exhibit two strong emission peaks at about 540 ( 4 S 3/2 → 4 I 15/2 ) and 850 nm (4 S 3/2 → 4 I 13/2 ). These transitions are illustrated in the Er 3⫹ partial energy-level diagram of Figure 42. The ratio of the line strength of the 540-nm transition to that of the 850-nm transition has been reported to be ⬃2.5 in ZBLA glass [75]. However, because the 4 S 3/2 → 4 I 15/2 transition

Figure 42 Upconversion-pumping mechanisms of the 540-nm Er 3⫹-doped ZBLAN fiber laser. Solid arrows represent the emission or absorption of a photon and dashed arrows represent multiphonon relaxation.

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terminates on the ground state and, therefore, suffers from GSA loss, the 540-and 850nm transitions can compete, and colasing at 850 nm can limit the efficiency of the green laser. Millar and co-workers [89] reported the first demonstration of upconversion-pumped lasing at 850-nm in Er 3⫹-doped ZBLAN fiber in 1990. Population of the upper laser level was accomplished by the sequential absorption of two 801-nm photons. The pumping mechanism is depicted in Figure 42. Initially, an Er 3⫹ ion in the ground state is promoted to the 4 I 9/2 level by the absorption of an 801-nm pump photon. The lifetime of the 4 I 9/2 level in ZBLAN is ⬃0.12 ms [90]. Ions in this level decay by multiphonon and radiative emission to the 4 I 11/2 and 4 I 13/2 metastable levels, which have lifetimes of 7 and 9 ms, respectively [90]. Ions in the 4 I 11/2 and 4 I 13/2 levels are promoted to the 4 F5/2 or 4 F7/2 levels, respectively, by the absorption of a second 801-nm pump photon. Multiphonon relaxation from these levels populates the 4 S 3/2 level, which has a lifetime of ⬃0.45 ms in ZBLAN. ESA from the 4 I 9/2 level also occurs, but it is much weaker (by a factor of ⬃2.2) [89] than ESA from the 4 I 11/2 level. Lasing then occurs on the 4 S 3/2 → 4 I 13/2 transition. The fiber used in this demonstration had an Er 3⫹ concentration in the core of 500 ppm by weight, which is low enough that ET upconversion processes are thought to be negligible compared with ESA upconversion. Because the lifetime of the 4 I 13/2 level is long compared with that of the 4 S 3/2 state, the 850-nm transition is normally self-terminating. However, ESA at 801 nm rapidly removes population from the 4 I 13/2 level, allowing the 850-nm transition to operate CW, and possibly dominate over lasing at 540 nm. When using the same pumping mechanism, Whitley and co-workers [86] demonstrated, in 1991, an 801-nm–pumped 540-nm laser in Er 3⫹-doped ZBLAN fiber. The fiber had an Er 3⫹ concentration in the core of 500 wt ppm, a single-mode cutoff wavelength of 790 nm, and an NA of ⬃0.15. A 2.4-m length of fiber was placed in a Fabry–Perot cavity, formed by butting the two fiber ends against two flat mirrors, with a total output coupling of 35%. Both mirrors had a high transmittance at 800 and 850 nm. The fiber laser was pumped with a CW Ti: sapphire laser. The fiber laser threshold was 100 mW of absorbed pump power. Despite the high transmissions of the mirrors at 850 nm, for absorbed pump powers above 250 mW colasing at 850 nm occurred, which caused saturation of the 540-nm laser for higher pump powers and limited the obtainable green output power to less than 25 mW. Despite the detrimental effects of encouraging lasing at 850-nm, removing population from the 4 I 13/2 level by ESA at 800-nm has the beneficial effect of reducing ESA loss at 540 nm. Whitley and co-workers [86] discovered evidence of such ESA loss in a study of the dependence of the 540-nm laser threshold on pump wavelength. As the pump was tuned from the minimum threshold wavelength of 801 nm, the threshold increased more rapidly as the pump was tuned to 810 nm than when it was tuned to 790 nm. The wavelength for the peak of ESA from the 4 I 13/2 level lies at ⬃790 nm, whereas the peak of ESA from the 4 I 11/2 level is centered at 810 nm. Thus, as the pump wavelength is tuned away from the pump ESA resonance associated with the 4 I 13/2 level, the population of the 4 I 13/2 level increases, presumably increasing the ESA loss at 540 nm, as well as the threshold pump power. In 1992, Allain and co-workers [91] reported pumping of the green Er 3⫹-doped ZBLAN fiber laser at 970 nm. The partial energy level diagram in Figure 42 illustrates the pump and laser transitions. Pump absorption from the ground state at 970 nm excites the 4 I 11/2 level, which is subsequently promoted to the 4 F7/2 level by the absorption of a second pump photon. This state then relaxes nonradiatively to the upper laser level ( 4 S 3/2 ), and lasing takes place to the 4 I 15/2 level. This pump scheme discourages lasing at 850 nm


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because there is no pump ESA from the 4 I 13/2 level and, consequently, an inversion on the 850-nm transition cannot be maintained. However, the accumulation of population in the 4 I 13/2 level adversely affects the performance of the green laser, both because of ESA loss from the 4 I 13/2 level at 550 nm, and because the ions in this state are largely excluded from participating in the pumping and lasing processes. To explore the effect of population buildup in the 4 I 13/2 level, Allain and co-workers placed a fiber 1.2 m in length in a cavity incorporating an intracavity prism [91]. The cavity was made doubly resonant at 540 nm and 1.55 µm so that colasing at 1.55 µm could be established, thereby draining population from the 4 I 13/2 level back into the 4 I 15/2 ground state. The fiber had a core diameter of 5.5 µm, an NA of ⬃0.1, and its core contained 500 wt ppm of Er 3⫹. The pump source was a CW Ti:sapphire laser. For low pump powers, it was observed that when lasing at 1.55 µm was allowed to occur simultaneously with lasing at 540 nm, the performance of the green laser improved. At higher pump powers, the upconversion-pumping process becomes more efficient, reducing the population in the 4 I 13/2 level, so that the presence of colasing at 1.55 µm makes less of a difference. The tunable cavity prevented lasing at 850 nm, which would have also been encouraged by colasing at 1.55 µm. 4.6.2 Laser Performance In the first demonstration of 540-nm lasing in Er 3⫹-doped ZBLAN fiber pumped at 801 nm, colasing at 850 nm limited the performance of the green laser, as discussed previously. Subsequently, Allain and co-workers [91] reported 970-nm–pumped operation of the 540nm transition. Using the cavity arrangement described in the foregoing, which included an intracavity prism that prevented lasing at 850 nm, they obtained up to 50 mW of green output power for ⬃850 mW of launched pump power, corresponding to a ⬃5.9% optical conversion efficiency. The threshold launched pump power was ⬃100 mW, and the slope efficiency relative to launched pump was 15%. The authors obtained a tuning range of 540–545 nm for the green transition. The pump band extended from 965 to 975 nm for a pump power of twice the minimum threshold value. Since these first demonstrations of a green laser in Er 3⫹-doped ZBLAN fiber, fluoride fiber manufacturing technology has improved, making possible the fabrication of low-loss (⬃0.05 dB m⫺1 ), small-core–diameter (1–2 µm), high NA (⬃0.39) fibers. This improvement has led to a dramatic drop in the pump power thresholds of upconversion-pumped fiber lasers, including the 540-nm Er 3⫹-doped ZBLAN fiber laser, which has made feasible diode pumping of most upconversion fiber lasers. In 1993, Massicott and co-workers [92] reported on experiments with fiber having an NA of 0.4 and core diameter of 1.1 µm. The Er 3⫹ concentration in the core was 500 ppm, and the fiber length was 3 m. The pump source was a semiconductor laser operating at ⬃800 nm and providing a maximum launched pump power of ⬃40 mW (100-mW incident). Butting a flat mirror having a high reflectance at 540 nm against one fiber end facet and an output coupler against the other end formed the cavity. Output couplers ranging in transmittance from 35 to 96% were investigated. For the lowest cavity-output coupling, the threshold was under 10 mW of launched pump power. For an output coupling of 96%, a maximum output power of 3 mW was obtained for the maximum available pump power, which corresponds to an optical conversion efficiency of 7.5%. A slope efficiency and threshold pump power of 16% and 14 mW, respectively, were also observed with 96% output coupling. No competitive lasing at 850 nm was observed. The pump band of this laser extended over the range ⬃798–808 nm for launched pump powers greater than 30 mW. Piehler and Craven [93] also reported low-threshold operation of a 540-nm Er 3⫹-

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doped ZBLAN fiber laser pumped with a 970-nm InGaAs diode laser. The fiber core was doped with 1000 ppm of Er 3⫹, and the fiber core diameter, NA, and length were 2.1 µm, 0.31, and 1.5 m, respectively. The cavity was formed by butting a bulk mirror against each fiber end facet, or by depositing dielectric mirrors directly onto the fiber end facets. The best performance was obtained for a cavity-output coupling of 29%. The semiconductor pump laser provided a maximum pump power of 150 mW for a drive current of 230 mA, or a maximum launched pump power of ⬃52 mW. At the maximum pump power, 11.6 mW of 540-nm output was produced, corresponding to an optical conversion efficiency of 22%, and a wall-plug efficiency of 2.7%. The launched pump power threshold and slope efficiency were 18 mW and 29%, respectively. With use of a fiber length of 2.2 m and a cavity output coupling of 77%, the authors obtained a slope efficiency of 51%, a threshold pump power of 31 mW (both relative to the launched pump power), and a maximum output power of 14 mW for 59 mW of launched pump power [90]. This corresponds to an optical conversion efficiency of ⬃24%. Table 5 summarizes the fiber laser characteristics of the 540-nm Er 3⫹-doped ZBLAN fiber lasers demonstrated to date. The green Er 3⫹-doped ZBLAN fiber laser has exhibited one of the highest efficiencies and lowest thresholds of any of the upconversion-pumped fiber lasers. With the emergence of dual-clad ZBLAN fiber, and the abundance of commercial, high-power, 980nm–diode laser pump sources, the 540-nm Er 3⫹-doped ZBLAN fiber laser offers the potential of producing in excess of 1 W of CW output power in the green when pumped with a diode laser. 4.6.3 Warm-up Effect Some authors have reported a ‘‘warm-up’’ effect in the erbium green laser. Whitley and co-workers [86] observed that when the fiber laser had not been operated for more than a few hours, the threshold of the 546-nm laser was high, exceeding 1 W of absorbed pump power, and the 850-nm transition dominated. Once lasing at 546 nm was established by increasing the pump power, however, the pump power required to maintain lasing for this transition dropped to about 100 mW and the 850-nm transition was suppressed. A similar effect was described by Piehler and Craven [93] for a fiber laser pumped at 970 nm with a diode laser. From the time pumping of the fiber began, several minutes passed while the green fluorescence power emerging from the fiber end gradually increased. Then, over a period of ⬃30 s, the green power increased by an order of magnitude while the transmitted 971-nm–pump power dropped by a factor of 2. At this point, lasing at 546 nm occurred, and within a few minutes the output power at this wavelength would stabilize at the maximum value. Once lasing in the green had occurred, the pump could be shut off and turned back on, and the green laser would reach full power immediately. After a period of 8–12 h without operation, the warm-up effect would reoccur. This warm-up effect is currently not well understood. One possible cause is the formation of color centers by highly excited Er 3⫹ ions that can subsequently be bleached by circulating large intensities of 540-nm light within the fiber core. A similar, but more severe, effect has been observed in Tm 3⫹ and is discussed in Section 4.7.3. Piehler and Craven [93] also point out several observations showing that the presence of green radiation in the fiber reduces the warm-up effect, possibly by bleaching the absorption of color centers. Launching several hundred milliwatts of 515-nm light into the fiber before pumping at 970 nm eliminated the transient increase in pump threshold for the 546-nm laser. In addition, reducing the cavity losses, which increased the power of the green amplified

3.4 5.5 1.1 2.1 2.1

Fiber core size (µm) 0.18 0.18 0.4 0.31 0.31

NA 2.4 1.2 3.0 1.5 2.2

Fiber length (m)

ns

35 35 96 29 77

Output coupling (%)

Pump power threshold/slope efficiency relative to absorbed pump power. Wt ppm or molar ppm not specified. t Pumped with a CW Ti :sapphire laser. s Pumped with a semiconductor laser.

ab

500 500 500 ns 1000 ns 1000 ns

Er 3⫹ concentration (wt ppm)

Table 5 Characteristics of 540-nm Er 3⫹-doped ZBLAN Fiber Lasers

801 970 t 801 s 970 s 970 t

t

Pump wavelength (nm) 160 100 14 18 31

ab

Launched pump threshold (mW) 11 15 16 29 51

ab


23 50 3 11.7 14

Output power (mW)

86 91 92 93 90

Ref.


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spontaneous emission (ASE) circulating within the fiber when the laser was below threshold, reduced the amount of time required to achieve lasing, presumably because the ASE bleached the defects more rapidly. The cavity losses were reduced by using mirrors with lower transmission values at 546 nm, or by depositing dielectric coatings directly onto the fiber end facets, which reduced the scattering losses associated with butt coupling of bulk mirrors to the fiber ends. 4.7 BLUE THULIUM-DOPED ZBLAN FIBER LASERS In 1990, the first upconversion-pumped visible fiber laser was realized in a Tm 3⫹-doped ZBLAN fiber cooled to 77 K [36]. When pumped simultaneously at 647.1 and 676.4 nm, it emitted at 480 or 455 nm. Upconversion-pumped pulsed emission at 450 nm had been reported previously in Tm 3⫹-doped YLiF4 at 75 K when pumped simultaneously with two pulsed pump sources operating at 648.8 and 780.8 nm [94]. Subsequently, lasing on the 450-nm transition was obtained under CW pumping at 648 and 780 nm in a Tm 3⫹-doped YLiF4 crystal [95]. In 1992, the first room temperature operation of the 480-nm Tm 3⫹-doped laser in any host was demonstrated in a ZBLAN fiber. It was pumped with a Nd 3⫹-doped YAG laser emitting simultaneously at 1112, 1116, and 1123 nm [38], although only a single pump wavelength in the 1.1 to 1.2-µm region is required. Subsequently, the 480-nm Tm 3⫹ laser attracted much attention because the only other room temperature blue fiber laser, the 490-nm transition in Pr 3⫹-doped ZBLAN, required a two-wavelength pump scheme. Another advantage of the 480-nm Tm 3⫹ laser is that its pump band lies conveniently at wavelengths accessible by diode lasers as well as high-power, diode-pumped, solid-state lasers such as the Nd :YAG and the cladding-pumped Nd 3⫹-doped and Yb 3⫹-doped silica fiber lasers. Because of this situation, the Tm 3⫹ :ZBLAN fiber laser could potentially provide high CW output powers in the blue spectral region where few solid-state sources exist. 4.7.1 Laser Transitions and Upconversion-Pumping Mechanisms The first upconversion-pumped visible fiber laser was demonstrated in a Tm 3⫹-doped ZBLAN fiber by Allain and co-workers [36]. Two visible laser transitions were observed—namely, at 455 ( 1 D 2 → 3 F4 ) and 480 nm ( 1 G 4 → 3 H6 )—along with infrared transitions at 1.48 ( 3 H 4 → 3 F4 ) and 1.51 µm ( 1 D 2 → 1 G 2 ). The fiber, which had a core diameter of 3 µm and an NA of ⬃0.15, was cooled to 77 K for these experiments. The pump source was a krypton ion laser operating simultaneously at 676.4 and 647.5 nm. The pump and laser transitions are shown in the partial-energy–level diagram of Tm 3⫹ in Figure 43. The thulium ion concentration in the fiber core was 1250 wt ppm, so that ET played a negligible role in the upconversion process. The authors proposed a sequential two-photon absorption pumping mechanism, as illustrated in Figure 43. First, a thulium ion in the ground state is excited to the 3 F2 or 3 F3 levels by the absorption of a 676.4-nm pump photon, and then decays to the 3 H 4 state by multiphonon relaxation. The 3 H 4 level has a long lifetime (⬃1.4 ms) [36]. An ion in this level can be promoted to the 1 D 2 state by the absorption of a 647.5-nm photon, or it can undergo radiative decay or multiphonon relaxation to the 3 F4 level, which has a lifetime of 6 ms [36]. The 1 G 4 level, which has lifetime of ⬃0.6 ms [36], is populated either by multiphonon and radiative decay from the 1 D 2 state, or by ESA at 647.5 nm from the 3 F4 level. Lasing at 455 nm occurs from the 1 D 2 level down


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Figure 43

Pumping mechanism employed in the first upconversion-pumped visible fiber laser demonstrated in Tm 3⫹-doped ZBLAN fiber at 77 K. The excited-state lifetimes are indicated in parentheses next to the metastable levels of the ion.

to the 3 F4 state. Because the lifetime of the 1 D 2 level is only ⬃0.05 ms [36], the 455-nm transition terminates on a state with a substantially longer lifetime (⬃6 ms) than the upper laser level. Consequently, cooling of the fiber to cryogenic temperatures is required to reduce the population of the high-lying Stark sublevels in the 3 F4 state to achieve inversion. Even at low temperatures, this laser was self-terminating and operated only in a pulsed mode, with the pump laser beam being chopped. The authors reported that, immediately after the pump shutter opened, the 455-nm laser would reach threshold, emit a pulse and self-terminate. The onset of lasing at 455 nm rapidly introduces population into the 3 F4 level, which increases ESA from this state into the 1 G 4 level. Thus, after a time delay, lasing at 480 nm out of the 1 G 4 level would begin. The 480-nm laser operated continuously, but spiking behavior of the output was reported. The laser cavity consisted of a 170-cm length of fiber and flat mirrors, designed to have a peak reflection at 488 nm, butted against each of the fiber ends. Except for the fiber ends, the fiber was immersed in liquid nitrogen to maintain it at a temperature of 77 K. A maximum output power of 400 µW was obtained at 480 nm. Grubb and co-workers reported room temperature operation of the 480-nm Tm 3⫹doped ZBLAN fiber laser 2 years later [38]. This laser was pumped with a Nd :YAG laser, simultaneously operating at 1.112, 1.116, and 1.123 µm, using an efficient sequential three-photon absorption process. The pump and laser transitions are depicted in Figure 44. GSA at all three of the pump wavelengths excites the 3 H 5 level, which can relax to the 3 F4 state. The 3 H 4 level is then populated by pump ESA from the 3 F4 to the 3 F3 level, followed by multiphonon relaxation from that level. A second pump ESA step from the 3 H 4 state populates the 1 G 4 upper laser level. Pumping in this fashion results in more efficient, as well as room temperature, operation of the 480-nm laser, compared with dualwavelength pumping in the red, because it avoids pumping into the 1 D 2 level. Pumping a Tm 3⫹-doped ZBLAN fiber laser at 676 and 647 nm initially populates the 1 D 2 level. The primary mechanisms for the relaxation of ions in this state are radiative decay to the

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Upconversion pumping mechanism in the room-temperature 480-nm Tm 3⫹-doped ZBLAN fiber laser pumped in the 1.1–1.2-µm region. Dashed arrows represent multiphonon relaxation.

Figure 44

3

F4 (455-nm) or 3 H 6 (357-nm) levels. Consequently, these ions must lose most or all of their energy through radiative decay before they can be pumped into the 1 G 4 level. In fact, because the radiative decay rates for the 1 D 2 → 3 F4 and 1 D 2 → 3 H 6 transitions are ⬃9 ⫻ 10 3 s⫺1 and ⬃7 ⫻ 10 3 s⫺1, respectively [96], over 40% of the ions in the 1 D 2 level decay to the ground state where they must start over in the pumping process. The fiber used by Grubb and co-workers had an NA of 0.21 and a core diameter of ⬃3 µm. The Tm 3⫹ concentration in the core was 1000 ppm. A launched threshold pump power of 46 mW, a maximum output power of 57 mW, and a slope efficiency of 18% were measured from a 2-m length of fiber in a Fabry–Perot cavity configuration with 10% output coupling. Lasing at 650 nm on the 1 G 4 → 3 F4 transition was also observed in a similar fiber codoped with 4000 ppm of Yb 3⫹. This transition was not observed in the fiber doped only with Tm 3⫹. The authors hypothesized that ET to Yb 3⫹ ions is required to remove the lower laser level population by the 3 F4 → 3 H 6 and 2 F7/2 → 2 F5/2 transitions, as the 650-nm laser is self-terminating. Given that these transitions differ in energy by ⬃20% or more, the ET efficiency is probably low. Alternatively, ET from excited Yb 3⫹ ions might remove population from the lower level of the 650-nm laser by promoting Pr 3⫹ ions in the 3 F4 state to the 3 F2 level. In this case, ET from excited Tm 3⫹ ions would most likely be the mechanism for exciting Yb 3⫹ ions, because the absorption of Yb 3⫹ in the 1.1- to 1.2-µm– region is weak. Although Grubb and co-workers used a three-wavelength pump source for their initial work, the 480-nm Tm 3⫹-doped ZBLAN fiber laser is generally pumped by a singlewavelength source operating in the 1.1- to 1.2-µm region. For example, it has been pumped with an Nd :YAG laser producing single-wavelength output at 1.112 [97] or 1.123 µm [98] with a tunable diode laser operating in the 1.11- to 1.14-µm region [99], and with a


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Yb 3⫹-doped silica fiber laser emitting in the 1.10- to 1.14-µm region [100]. In addition, a Yb 3⫹-sensitized, Tm 3⫹-doped ZBLAN fiber has been pumped with a diode-pumped Nd 3⫹-doped silica fiber laser operating at 1.065 µm [101]. Other dual-wavelength pump schemes have been reported to improve the efficiency of the 480-nm laser. The peak of thulium 3 H5 ← 3 H6 GSA in ZBLAN lies close to 1.2 µm [102], whereas the peaks of the 3 F3 ← 3 F4 and 1 G 4 ← 3 H 4 ESA transitions lie in the 1.12- to 1.16-µm range [38,104]. Thus, using a single-wavelength source to pump all of these transitions does not result in optimal efficiency. Tohmon et al. [102] reported increased efficiency of the 480-nm laser with the addition of 680-nm pumping in a 1.1µm–pumped system. The pumping mechanism is shown in Figure 45. The 680-nm pump, provided by a CW dye laser, takes advantage of large Tm 3⫹ GSA at 680 nm, which is approximately two orders of magnitude stronger than GSA at 1.1 µm [102]. The addition of the 680-nm pump greatly increases the pumping rate into the 3 H 4 level compared with pumping at 1.1 µm, and, thus enhances the ESA at 1.1 µm from the 3 H 4 level to the 1 G 4 state. Tohmon and co-workers used a 1.8-m length of fiber with a core diameter of 4 µm, an NA of 0.22, and a Tm 3⫹ concentration in the fiber core of 1000 ppm. The laser cavity, formed by butting a flat mirror against each fiber end facet, had an output coupling of 90% at 480 nm. The 1.1-µm pump was provided by a diode-pumped Nd :YAG laser. The addition of ⬃20 mW of incident 680-nm pump power reduced the 1.1-µm pump power threshold by more than a factor of three, and with 60 mW of incident 680-nm pump power, the slope efficiency relative to absorbed 1.1-µm pump power nearly doubled. However, the enhanced pumping into the 3 H 4 level owing to the additional 680-nm pump, coupled with a small amount of reflection from the mirrors at 800 nm, led to competitive lasing at 800 nm on the 3 H 4 → 3 H 6 transition, which increased the ground-state population and,

Figure 45

Pumping mechanism for the 480-nm Tm 3⫹-doped ZBLAN fiber laser co-pumped at 1.1 µm and 0.68 µm. Dashed arrows represent multiphonon relaxation.

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hence, the GSA loss at 480 nm. This loss reduced the improvement in the performance of the 480-nm laser expected from copumping at 680 nm. A second dual-wavelength pumping scheme for the 480-nm Tm 3⫹-doped ZBLAN fiber laser, which also utilized a red and an infrared pump wavelength, has been realized by Tohmon and co-workers [103]. This scheme is shown in Figure 46. A laser diode emitting at 1.2 µm, near the peak of the Tm 3⫹ 3 H 5 ← 3 H 6 GSA transition, was used to pump the 3 F4 level. A 650-nm dye laser was then used to pump the Tm 3⫹ ions via the ESA transition between the 3 F4 level and the 1 G 4 state. A secondary pumping pathway is also shown in Figure 46. Weak GSA in the 630- to 650-nm region to the 3 F2,3 levels, followed by multiphonon decay, populates the 3 H 4 state. ESA from this level at 1.2 µm then populates the 1 G 4 state. The efficiency of the 480-nm laser peaks sharply when the red wavelength is tuned to 650 nm, which Tohmon and co-workers attributed to the peak of the ESA originating from the 3 F4 level, which also lies at 650 nm. The range of red pump wavelengths, over which the threshold of the 480-nm laser is lowered considerably, extends from 630 to 650 nm. For this work, Tohmon and co-workers used a ZBLAN fiber with a core diameter of 3 µm, an NA of 0.2, and a Tm 3⫹ concentration in the fiber core of 1000 wt ppm. In a 1.3-m fiber laser with a cavity output coupling of ⬃4%, increasing the incident pump power at 650 nm from 40 to 120 mW resulted in more than a fivefold increase in blue output power. Dual wavelength pumping at 1135 and 1220 nm has also been reported by Boothe et al. [104]. The 1220-nm pump is resonant with GSA in Tm 3⫹-doped ZBLAN, whereas the 1135-nm pump lies near the peaks of both the 3 F 2,3 ← 3 F4 and 1 G4 ← 3 H 4 ESA transitions. Introduction of a 1220-nm pump at low powers resulted in a decrease in the threshold of the 1135-nm–pumped 480-nm laser [104]. As the 1220-nm power increased, however, the threshold rose above the value for single-wavelength pumping at 1135 nm because

Figure 46

Pumping mechanism for the 480-nm Tm 3⫹-doped ZBLAN fiber laser co-pumped at 1.2 µm and 0.65 µm. Dashed arrows represent multiphonon relaxation.


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stimulated emission from the 1 G 4 level, which has a cross section peak at 1190 nm, reduced the efficiency of the upconversion-pumping process. The slope efficiency increased with increasing 1220-nm power, but eventually saturated because of stimulated emission from the 1 G 4 level. Researchers have sought to improve the performance of the 455-nm fiber laser, since this wavelength is closer to the optimal range of 460–470 nm for a blue light source for video displays than the 480-nm Tm 3⫹-doped fiber laser and the 490-nm Pr 3⫹-doped fiber laser. Tohmon et al. [105] reported enhanced efficiency of the 455-nm transition in Tm 3⫹ / Eu 3⫹-co-doped fluorozirconate fiber pumped simultaneously at 645 and 780 nm. The pumping process is illustrated in Figure 47. The fiber was doped with 1000 ppm Tm 3⫹ and 5000 ppm Eu 3⫹. The europium removes population from the ground state of the 455nm transition through ET from the 3 H 4 level of thulium to the 7 F6 level of a neighboring europium ion. Decreasing the population of the 3 H 4 level also decreases the pumping rate into the upper level of the 480-nm laser as a result of the 1 G 4 ← 3 H 4 transition at 645 nm. In the co-doped fiber, lasing occurred only at 455 nm, whereas for the same pump powers, lasing occurred solely at the 480-nm wavelength in the fiber doped only with 1000 ppm Tm 3⫹. For both lasers, the fiber was cooled to 77 K. Room temperature, CW laser operation at 455 nm in a Tm 3⫹-doped fluorozirconate fiber was first obtained by Le Flohic et al. [106] using a dual-wavelength pump scheme (645 nm and 1.06 µm). The pump and laser transitions are shown in Figure 48. The GSA bands that excite the 3 F2 and 3 F3 levels peak at 660 and 690 nm, respectively, so the absorption at the 645-nm–pump wavelength is relatively weak. However, population can slowly build up in the 3 F4 state, from which excitation to the 1 D 2 level occurs through ESA at 645 nm. The 455-nm laser transfers population from the 1 D 2 level to the longlived 3 F4 state, normally causing the laser to self-terminate. However, absorption at 1.06 µm efficiently pumps population out of the 3 F4 level and into the 3 F2 state where it decays

Pumping mechanism for the 455-nm Tm 3⫹ /Eu 3⫹-co-doped ZBLAN fiber laser. ET from Tm 3⫹ to Eu 3⫹ removes population from the lower level of the 455-nm laser transition. Dashed arrow represents multiphonon relaxation.

Figure 47

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Pumping mechanism for the room-temperature 455-nm Tm 3⫹-doped ZBLAN fiber laser co-pumped at 645 nm and 1064 nm. Excited-state lifetimes for several metastable levels are indicated in parentheses. The short dashed arrow represents multiphonon relaxation.

Figure 48

to the 3 H 4 level. ESA at 645 nm again promotes this population to the upper laser level. Aside from emptying the lower laser level so that room-temperature CW lasing can occur, this pumping scheme also effectively recycles population from the lower laser level without requiring a GSA step, so that this laser works despite the weak GSA at 645 nm. 4.7.2 Laser Performance Table 6 lists the fiber and output power characteristics of the room temperature upconversion-pumped Tm 3⫹-doped ZBLAN fiber lasers demonstrated to date. The availability of high-power pump sources for the 480-nm transition has led to the demonstration of numerous fiber lasers producing more than 100 mW in the blue. Paschotta and co-workers [98] have demonstrated a Tm 3⫹-doped ZBLAN fiber laser producing a maximum of 230 mW of CW output power for ⬃0.8 W of launched 1123nm pump power from a diode-pumped Nd 3⫹-doped YAG laser. The fiber had a core diameter of 3 µm, an NA of 0.2, and a Tm 3⫹ concentration in the core of 1000 wt ppm. The laser cavity was formed by butting the end facets of a 2.3-m–long fiber against two flat dielectric mirrors. The maximum blue output power was obtained using a cavity output coupling of 37%. For an output coupling of 50%, the launched threshold pump power was ⬃50 mW and the slope efficiency (relative to launched pump power) was 50%, which is the highest yet observed. Paschotta and co-workers reported a reversible photoinduced loss that occurred under high-pumping intensities. The result of this loss was a rapid drop in output power over a period of a few seconds when the fiber laser was operated at output powers above 100 mW. An increase in threshold and decrease in slope efficiency were also observed. When the laser was subsequently operated at a lower power (⬃40 mW),

0.21

3.0 3.5 2.6 n.a. 3.0 3.0

1000 wt 1500 ns (⫹5000 Yb 3⫹)

2500 ns 1500 ns (⫹5000 Yb 3⫹) 1000 wt 455-nm laser 1000 ns

0.2 0.19

0.21 0.2

1.5

0.38 n.a. n.a.

1.3 1.0

1.6 2.2

2.5

2 1.8

Fiber length (m)

wt

Wt ppm or molar ppm not specified. Wt ppm. mo Molar ppm. la Pump power threshold/slope efficiency relative to launched pump power. ab Pump power threshold/slope efficiency relative to absorbed pump power. in Pump power threshold/slope efficiency relative to incident pump power. s Pumped by a semiconductor laser. f Pumped by a fiber laser. l.e., launch efficiency. n.a., information not available.

ns

0.21 n.a. 0.21

3.0 3.0

1000 ns 1000 wt

0.2

3.0

1000 mo

0.21 0.22

3.0 4.0

NA

480-nm lasers 1000 ns 1000 ns

Fiber core size (µm)

20

20 n.a. 37

5 30

28 50

20

10 10

Cavity output coupling (%)

0.645/1.064

1.112 1.07 f 1.141

0.65/1.21 s 1.065 f

1.13 s 1.123

1.13 s

⬃1.1 0.68/⬃1.1

Pump wavelength (µm)

Characteristics of the Room-Temperature Blue Tm 3⫹-Doped ZBLAN Fiber Lasers

Tm 3⫹ concentration (ppm)

Table 6

200/230

46 la 60 in /33 ab l.e. ⫽ n.a. 80 in l.e. ⫽ 60–65% 22 ab 100 in l.e. ⫽ 50% 10 la /8 la ⬃400 in l.e. ⫽ 50% 21 ab n.a. 100 in

Threshold pump power (mW)

1.5/n.a.

3

72 375 23

2.7 106

⬃1.6 la /n.a. 6.6 in 24 ab n.a. 10 in

33 230

106

57 14.8

Output power (mW)

34.6 ab 25 in

13 in

18 n.a./18.9 ab


106

97 107 100

103 101

104 98

99

38 102

Ref.


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the loss was bleached and the threshold and slope efficiency returned to their initial values. This loss has been attributed to the formation of color centers in the glass host (see Sec. 4.7.3). Laperle and co-workers [97] were able to obtain 70 mW of output power, which remained stable over an 8-h period, by pumping at 1112 nm with pump powers similar to those used by Paschotta and co-workers [98]. A 38-cm fiber, with a core diameter of 2.6 µm, an NA of 0.2, and a Tm 3⫹ concentration in the core of 2500 ppm, was used in a Fabry–Perot cavity with an output coupler with 20% transmission. High output powers in the blue have also been obtained by Zellmer and co-workers [101] who used a Yb 3⫹-sensitized Tm 3⫹-doped ZBLAN fiber pumped with a diodepumped, Nd 3⫹-doped, dual-clad, silica fiber laser. The ZBLAN fiber had a core 3.5 µm in diameter doped with 1500 ppm Tm 3⫹ and 5000 ppm Yb 3⫹, and the fiber NA was 0.19. Mirrors glued to the polished fiber end facets, which remained fixed in SMA connectors, formed the laser cavity. The fiber length was 1 m and the optimized cavity output coupling was 30%. Up to 106 mW at 480 nm was obtained for 2.8 W of incident 1065-nm power (⬃1.4 W coupled). Further optimization of the fiber geometry and dopant concentration has led to a Yb 3⫹-sensitized, Tm 3⫹-doped ZBLAN fiber laser producing up to 375 mW of 480-nm output for ⬃2 W of launched pump power [107]. High output power at 480 nm has also been obtained by Sanders and co-workers from a direct diode-pumped Tm 3⫹-doped ZBLAN fiber laser [99]. By combining the power of two diode lasers operating at 1130 nm to produce a total incident pump power of 900 mW, 106 mW of blue output was obtained. The fiber laser consisted of a 2.5-m–long fiber placed in a Fabry–Perot cavity, with an output coupling of 20%. The fiber core contained 1000-mol ppm Tm 3⫹, and the core diameter and NA were 3 µm and ⬃0.2, respectively. Up to 72 mW of output power was obtained for 550 mW of incident 1130nm pump power provided by a single-laser diode. The launching efficiency was estimated to be ⬃50%, resulting in a 26% optical conversion efficiency. Conversion efficiencies greater than 30% were observed when the pump wavelength was tuned to 1137 nm. There have been no reports of attempts to tune Tm :ZBLAN fiber lasers operating on the 455- or 480-nm transitions, although the wavelength of the 4 G 1 → 3 H 6 transition has been reported to vary from 478 to 483 nm, depending on output coupling. 4.7.3 Photodarkening in Tm 3ⴙ-Doped ZBLAN Fiber Several authors have reported an absorption band extending from the near-IR to the UV, induced by pumping at 1.1–1.2 µm, in Tm 3⫹-doped ZBLAN fibers [108–110]. This photodarkening has been attributed to the formation of color centers in the glass, which absorb in the visible and UV, resulting from the excitation of high-energy states of Tm 3⫹. The induced loss causes an increase in the threshold of the 480-nm fiber laser and a decrease in its output power and slope efficiency over time as the fiber is pumped [97,98,110]. Usually, the loss can be removed almost entirely by circulating blue light through the fiber core. When pump light in the 1.1- to 1.2-µm region is launched into a nondarkened, Tm 3⫹doped ZBLAN fiber, the fiber transmission in the visible and UV decays to an equilibrium value, which is dependent on pump power and pump wavelength. Barber and co-workers [108] measured the dependence of transmission spectra on pump power in Tm 3⫹-doped ZBLAN fiber pumped at about 1.12 µm. They found that the time required for the photodarkening effect to reach equilibrium varied from ⬃30 s for 77 mW of pump power to 10–20 min for several milliwatts of power, and that the equilibrium value of the induced


235

loss increased with increasing pump power. The loss spectrum extended from ⬃1 µm into the UV. A 60-s exposure to 77 mW of pump power in a 50-cm fiber doped with 3000 wt ppm Tm 3⫹ resulted in an increase in loss of ⬃8 dB at 500 nm. They also found that lowering the pump power to a few milliwatts could restore the fiber to the nondarkened state. The loss could be repeatedly introduced and removed by adjusting the pump power, and the equilibrium loss level did not show any noticeable dependence on photodarkening history. Barber and co-workers suggested that the reversibility of the process indicates that pumping the Tm 3⫹-doped ZBLAN fiber in the 1.1- to 1.2-µm region drives two competing processes, one that creates absorbing defects and another that bleaches these defects. The equilibrium loss is reached when the rates of these two processes are equal. The rate of defect formation increases more rapidly with pump power than the rate of bleaching, which leads to the observed increase in equilibrium loss with increasing pump power. Photodarkening had been observed previously in Tm 3⫹-doped silica fiber pumped at either 475 or 1064 nm [111–113]. Broer et al. [112] reported a photoinduced decrease in transmission at 600 nm with a decay time on the order of seconds in a Tm 3⫹-doped aluminosilicate fiber pumped with a mode-locked 1064-nm Nd:YAG laser. The photodarkening rate varied with pump power P as P 4.7, suggesting that the creation of the absorbing color centers is the result of a five-photon absorption process, which possibly results in the photoionization of Tm 3⫹ ions. It was hypothesized that the absorption of two 1064-nm photons from the 1 G 4 level populates states lying at energies above ⬃35,000 cm⫺1, which may overlap with the conduction band of the glass or charge-transfer bands. At this energy, electron migration between Tm 3⫹ ions and nearby ligand ions may induce electronic defects in the surrounding glass. The excitation of the high-energy states initially involves the sequential absorption of three 1064-nm photons by a Tm 3⫹ ion in the ground state, leading to excitation of the 1 G 4 level. If the ion can subsequently be excited to the 2 D 1 state, then a single photon is sufficient to excite the ion from the 2 D 1 level to the 1 I 6 level (35,000 cm⫺1 ). However, the energy gap from the 1 G 4 state to the 1 D 2 level is only 6000 cm⫺1 (1670 nm), so the absorption cross section at 1064 nm is extremely low. Broer and co-workers suggested two pumping pathways that could lead to excitation from the 1 G 4 state to the 1 I 6 state. The first one is two-photon absorption from the 1 G 4 level, which could possibly be enhanced by the presence of the 1 D 2 state. The second pathway is ET from a Tm 3⫹ ion in the 3 F4 level to a Tm 3⫹ ion in the 1 G 4 level, resulting in one ion in the ground state and one ion in the 1 D 2 level, followed by the absorption of a pump photon by the ion in the 1 D 2 level. Both pathways would lead to a fifth-power dependence on pump power, but the second would also lead to a dependence of the photodarkening rate on Tm 3⫹ concentration. However, the dependence of photodarkening on the concentration of Tm 3⫹ ions in silica fiber was not investigated in this study. In experiments with a Tm 3⫹-doped ZBLAN fiber pumped at a wavelength ranging from 1.1 to 1.14 µm, Laperle and co-workers [109] observed a fourth-power dependence of the photodarkening rate on pump power, suggesting that a four-photon absorption process might be responsible for the formation of color centers in ZBLAN. They proposed that photoionization is not responsible for the creation of absorbing defects in ZBLAN, as hypothesized by Broer et al. [112] in the case of Tm 3⫹-doped silica fiber, because five 1.1-µm photons are required for photoionization of Tm 3⫹. Laperle and co-workers proposed that the color centers were created by the absorption of UV photons emitted from the 1 D 2 level by other defects or impurities already present in the glass. They hypothesized that ET from a Tm 3⫹ ion in the 3 F4 level to one in the 1 G 4 level pumps the 1 D 2 level. Each Tm 3⫹ ion promoted to the 1 D 2 level requires the absorption of four pump photons, which

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is consistent with the observed fourth-power dependence. The hypothesis that an ET process plays a role in the photodarkening in ZBLAN is supported by the observation, made by several groups, that the photodarkening rate, as well as the magnitude of the induced loss, increases with increasing Tm 3⫹ concentration. For example, Barber et al. [108] reported that the induced loss in a 10,000 wt ppm Tm 3⫹-doped ZBLAN fiber was 2.5 times that in a fiber with a Tm 3⫹ concentration of 3000 wt ppm, whereas no photodarkening was observed in a fiber doped with 1000 wt ppm Tm 3⫹. However, Laperle and co-workers observed photodarkening in ZBLAN with Tm 3⫹ concentrations as low as 500 wt ppm [109], which indicates that the Tm 3⫹ concentration may not be the only determining factor in the photodarkening process. Some researchers have observed that the photodarkening effect is larger for fiber with a higher NA, suggesting that chemicals used to adjust the refractive index of the core glass may also be a factor [109,110]. Despite the fourth-power dependence of the photodarkening rate on the pump power, emission has been observed from the Tm 3⫹ 1 I 6 level at 290 nm, which requires the energy of five 1140-nm photons, in ZBLAN fiber [108]. The 1 I 6 level could be populated by pump ESA from the 1 D 2 level or by ET from nearby excited Tm 3⫹ ions. That the expected fifth-power dependence of the photodarkening rate is not observed could be due to saturation of one or more of the absorption steps in the upconversion-pumping process. Booth et al. [110] observed that emission from the 1 D 2 state exhibited a dependence on pump power that was less than the expected fourth-power dependence, suggesting the saturation of at least one of the pumping steps. Since the 1 I 6 level is being populated, photoionization of Tm 3⫹, as suggested by Broer et al. [112], as well as UV emission from the 1 I 6 and 1 D 2 levels, may play a role in the formation of color centers. Visible emission from the 1 G 4 level appears to be able to bleach the absorbing centers. Booth and co-workers [110] reported that Tm 3⫹-doped ZBLAN fiber lasers that had lased several times showed an increase in threshold when they had not been operated for several hours. However, once lasing began, the pump power required to maintain lasing would drop to the initial threshold level. They attributed the transient rise in threshold pump power to the accumulation of photoinduced loss during each period of operation. Once lasing was established, the intense blue light circulating in the fiber laser cavity could, at least temporarily, bleach the absorption loss. Even when lasing threshold could not be reached with the available pump power, the blue ASE produced by pumping the fiber below threshold bleached the absorption loss sufficiently for lasing to occur. Once the fiber laser was turned off, however, the loss caused by the absorbing centers would begin to recover [110]. The recovery rate was largest during the first few hours and gradually slowed down, eventually reaching equilibrium after hundreds of hours. The absorption recovery did not exhibit a well-defined exponential time constant, suggesting that absorption is produced by defects with a range of activation energies. Furthermore, heating the fiber to 50°C greatly increased the absorption recovery rate [110]. Barber et al. [108] also found that the induced absorption could be bleached faster when pumping at low powers by heating the fiber to 49°C. In addition, annealing the fiber at temperatures greater than 100°C completely removed the color centers, returning the fiber to its initial (unpumped) state [110]. As described previously in this chapter, the 550-nm Er 3⫹-doped ZBLAN fiber laser exhibits similar behavior, although not as severe as that observed for Tm3⫹. Photodarkening has also been observed in Tm 3⫹-doped silica fibers, Tb 3⫹-doped phosphosilicate fiber [114] as well as in Tb 3⫹-doped, Eu 3⫹-doped, or Pr 3⫹-doped silicate glass [115]. The photodarkening observed in most rare earth doped oxide glasses has been attributed to oxidation


237

of the rare earth ion, resulting in nearby trapped charges. The details of the process are still unknown in oxide and fluoride glasses. 4.8 CONCLUSIONS Since the first demonstration of an upconversion-pumped visible fiber laser in 1989, improvements in the manufacture of low-loss fluoride fiber have resulted in the demonstration of many efficient fiber lasers that produce tens to hundreds of milliwatts of output power in the visible spectrum. With the development of dual-clad ZBLAN fiber, diode-pumped fluoride fiber lasers producing greater than 1 W in the IR (2.7 µm) are now available, and it is expected that diode-pumped visible fiber lasers with multiwatt output powers will soon be demonstrated. Several materials problems, such as photodarkening, must be addressed before visible ZBLAN fiber lasers become a viable commercial technology. However, the strong and increasing interest in optical fiber fabricated from low-phonon–energy glasses, such as ZBLAN, for medical, sensing, and telecommunications applications will accelerate the development of ZBLAN glass and other hosts, which will also lead to the improvement of visible fiber lasers. Improvements in ZBLAN fiber as well as the development of new materials, such as oxyfluoride glass ceramics [116–118], which have an even lower maximum phonon energy than ZBLAN as well as transparency into the UV, will likely lead to the demonstration of new and shorter-wavelength transitions from rare earth doped fibers. REFERENCES 1. S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Yamada, T. Matsushita, H. Kiyoku, Y. Sugimoto, T. Kozaki, H. Umemoto, M. Sano, K. Chocho. High-power, long-lifetime InGaN/ GaN/AlGaN-based laser diodes grown on pure GaN substrates. Jpn. J. Appl. Phys. 37:L309L312, 1998. 2. J. H. Chang, M. W. Cho, K. Godo, H. Makino, T. Yao, M. Y. Shen, T. Goto. Low-threshold optically pumped lasing at 444 nm at room temperature with high characteristic temperature from Be-chalcogenide-based single-quantum-well laser structures. Appl. Phys. Lett. 75:894– 896, 1999. 3. S. Nakamura, M. Senoh, S. Nagahama, N. Iwasa, T. Matsushita, T. Mukai. Blue InGaNbased laser diodes with an emission wavelength of 450 nm. Appl. Phys. Lett. 76:22–24, 2000. 4. E. Kato, H. Noguchi, M. Nagai, H. Okuyama, S. Kijima, A. Ishibashi. Significant progress in II–VI blue-green laser diode lifetime. Electron. Lett. 34:282–284, 1998. 5. K.–K. Law, P. F. Baude, T. J. Miller, M. A. Haase, G. M. Haugen, K. Smekalin. Roomtemperature continuous-wave operation of blue-green CdZnSSe/ZnSSe quantum well laser diodes. Electron. Lett. 32:345–346, 1996. 6. B. Lu, J. S. Osinski, R. J. Lang. 400 mW continuous-wave diffraction limited flared unstable resonator laser diode at 635 nm. Electron. Lett. 33:1633–1634, 1997. 7. B. Lu, J. S. Osinski, E. Vail, B. Pezeshki, B. Schmitt, R. J. Lang. High power 635 nm lowdivergence ridge waveguide singlemode lasers. Electron. Lett. 34:272–273, 1998. 8. L. R. Marshall. Passively stabilized CW doubling. Conf. Lasers and Electro-Optics, paper CFB2, 1997, p. 464. 9. D. G. Mathews, R. S. Conroy, B. D. Sinclair, N. MacKinnon. Blue microchip laser fabricated from Nd:YAG and KNbO 3 . Opt. Lett. 21:198–200, 1996. 10. G. J. Dixon, C. E. Tanner, C. E. Wieman. 432-nm source based on efficient second-harmonic

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5 Narrow-Linewidth Fiber Lasers NIGEL LANGFORD University of Strathclyde Glasgow, Scotland

5.1. INTRODUCTION Rare earth doped optical fibers are now a well-established class of gain media with many diverse applications that extend far from the original conceived application; namely, inline amplifiers [1]. Erbium-doped silica fiber lasers have been used, for example, for distributed sensing applications [2], remote sensing of magnetic fields [3], and as sources of optical solitons for all-optical fiber-based communications networks [4]. Many of these applications have evolved because of the advantages accrued from placing the rare earth ion in the optical fiber host lattice. As described in Chapter 2, the interaction between the rare earth ion and the intrinsic electric field associated with the host results in a broadening of the absorption and emission lineshapes associated with the rare earth ion. It is fortuitous that the absorption bands associated with many of the rare earth ions occur at wavelengths that are common to well-established laser diodes. The broadening of the absorption bands removes some of the wavelength-tailoring problems encountered with rare earth doped crystalline materials [5]. In fact, the ability to convert the output radiation from low-cost laser diodes, which generally occurs in a low-quality output mode with a poor frequency definition, into a high-brightness coherent source, is beneficial to applications, such as remote sensing and fiber-based communications systems, because it results in compact systems with low power requirements. The broadband emission of trivalent rare earth ions allows the development of sources emitting either broad continuous-wave (CW) spectra (see Chap. 6) or ultrashort pulses (see Chap. 8), as well as widely tunable narrow-linewidth operation, as described in this chapter. The core diameter of a standard single-mode fiber can vary from 3 to 10 µm, so that a significant intensity can be developed with a modest average power. A signal with 243

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an average power of 10 mW coupled into a fiber with a core diameter of 6 µm will result in an intensity of ⬃35 kW/cm 2. A consequence is that the intensities necessary to reach the continuous-wave oscillation threshold for both three-level and four-level systems can be achieved with modest input powers. This feature has been exploited extensively in the design of short-cavity diode-pumped single-frequency neodymium (Nd)-, erbium (Er)-, and ytterbium (Yb)-doped fiber lasers [6–8]. The inherent waveguiding property associated with the fiber ensures that the intensity is maintained over long distances, thereby providing long interaction lengths between the rare earth dopant and the pump field. Hence, a significant intracavity gain can be developed, and a small-signal gain of 25 dB is not uncommon. A small-signal gain of this magnitude enables elements with a comparatively high insertion loss, such as optical isolators, frequency modulators, and integrated interference filters, to be inserted in the cavity of a fiber laser without significantly increasing the oscillating threshold or reducing the output power. We will see later in this chapter that these devices have been used to force single-longitudinal-mode operation in a range of rare earth doped fiber lasers [9–11]. Furthermore, the flexibility of the fiber enables long cavity lengths to be established while taking up a small volume of space. A fiber laser using a trivalent rare earth as the active element has the potential for very narrow linewidth operation compared with other sources that oscillate in the same spectral regions (e.g., semiconductor lasers). The output radiation from a single-frequency laser is not monochromatic, but has a finite bandwidth. The theoretical limit for the bandwidth is known as the Schalow–Townes limit and depends on both the linewidth of an individual longitudinal mode of the cavity and the amount of amplified spontaneous emission coupled to the oscillating longitudinal mode [12]. The cavity linewidth, as is discussed further on, scales inversely with the cavity length of the laser, and the waveguiding nature of a fiber allows cavity lengths of many meters to be established. In comparison, the cavity length of semiconductor lasers is typically a fraction of a centimeter. The coupling of amplified spontaneous emission to the oscillating mode is determined by the gain cross section of the transition [12]. For most rare earth ions, this cross section is of the order of 10 ⫺21 cm 2 [13], whereas for a semiconductor laser it is typically 10 ⫺16 cm 2. This means that the optimum linewidth that can be expected from a fiber laser is significantly smaller than that of a semiconductor laser, making the fiber laser a suitable tool for narrow-linewidth applications. For many applications, such as high-resolution spectroscopy, it is necessary to make sensitive heterodyne measurements [14]. To do this successfully it is best to operate at frequencies for which the relative intensity noise of the laser does not add significantly to the noise generated by the detection system [15]. For many types of single-frequency laser, such as semiconductor lasers, this occurs several 100 MHz away from the center frequency, and complicated high-frequency detection systems are needed to make the measurement [15]. The long upper-state lifetimes and the high intracavity losses that can be tolerated by fiber lasers means that the noise arising from relaxation oscillations peaks at frequencies ⬃100 kHz away from the center frequency [16]. Single-frequency fiber lasers are attractive because they can offer shot-noise-limited operation in the megahertz frequency range [17]. Noise-free measurements can thus be made at substantially lower frequencies than those possible with alternative lasers. In this chapter I discuss recent advances that have been made toward the realization of narrow-linewidth fiber lasers, covering the initial attempts aimed at the development

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of line-narrowed lasers through the attainment of ultranarrow single-frequency systems. A range of cavity configurations extending from short-cavity lasers to complex multicavity ring lasers are described and their relative advantages and disadvantages highlighted. An outline of the various applications of these laser systems is also provided. 5.2. BASIC CONCEPTS ASSOCIATED WITH NARROW LINEWIDTH OPERATION Consider the generalized two-mirror fiber-based resonator illustrated in Figure 1a, which has a round-trip optical path length ᐉ, an intrinsic electric-field loss α, and mirrors with electric-field reflection coefficients r 1 and r 2, respectively. If a field E in oscillating at a frequency ν is injected into this cavity, it is straightforward to show that, in the absence of birefringence, the intracavity field E cav is given by [18] E cav (ν) ⫽ φ⫽

E in (ν) 1 ⫺ r 1 r 2 exp(iφ ⫺ αᐉ)

2πνᐉ c

(1a) (1b)

with φ the intracavity phase shift and c the speed of light. Analysis of Eq. (1a) shows that E cav is maximum when φ is an integer multiple of 2π, as shown in Figure 1b. These

Figure 1 (a) Schematic of a two-mirror laser cavity; (b) the intracavity light intensity | E(ν)| 2 as a function of the cavity phase shift φ, where E(ν) is defined in Eq. (1a).

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maxima correspond to the longitudinal or axial modes of the cavity and occur periodically with a frequency spacing ∆ν given by ∆ν ⫽

c ᐉ

(2)

The round-trip optical path length for a typical fiber laser may range from 1 cm to 50 m, giving a longitudinal mode spacing from 30 GHz to 6 MHz. Because rare earth dopants such as Er 3⫹ and Nd 3⫹ exhibit fluorescence spectra that extend over hundreds of terahertz, the gain medium can support many longitudinal modes of the cavity. It is accepted that the spectral broadening for a rare earth dopant in an amorphous host is a result of both homogeneous and inhomogeneous broadening mechanisms [19]. For a purely homogeneously broadened gain medium, standard theoretical treatments predict that the longitudinal mode that experiences the highest small-signal gain will be the first mode to oscillate and saturate the gain. Gain saturation depletes the gain and prevents neighboring modes from oscillating. Thus, the output is single-frequency, and in an ideal system the linewidth is imposed by the Schalow–Townes limit. In practice this does not occur. The output from a fiber laser can contain many longitudinal modes oscillating simultaneously. There are several reasons why this happens. For a homogeneously broadened system, the excited ions exhibit the same frequency response as the intracavity signal. The effect of inhomogeneous-broadening mechanisms is to destroy this frequency behavior. For example, the local environment experienced by the ions may alter their frequency response. Thus, different groups of ions will respond to the intracavity field in a different way, and although one longitudinal mode may saturate the gain associated with one particular group of ions, gain may still be available from a different group of ions that will enable a different longitudinal mode to oscillate. Consequently, many different frequencies may oscillate in an inhomogeneously broadened gain medium. This feature has been exploited to allow multiple wavelength operation of rare earth doped fiber lasers [20]. Another factor that inhibits single-longitudinal-mode operation from bidirectional fiber lasers is spatial hole burning. For an ideal homogeneously broadened saturable gain medium with an intracavity signal of frequency ν and intensity I propagating through it, the gain coefficient γ(ν,I ) obeys the following relationship: γ(ν,I) ⫽

γ 0 (ν) 1 ⫹ I/I sat

(3)

with γ 0 (ν) the small-signal gain coefficient and I sat the saturation intensity. For a bidirectional laser the intensity I in the gain medium takes the form of a standing wave described by I ⫽ I r ⫹ I l ⫹ 2I r I l cos(kz)

(4)

with I r the intensity propagating right to left, I l the intensity propagating left to right, k the wave vector, and z the position along the gain medium. An intensity distribution of the form described by Eq. (4) results in a periodic spatial modulation of the gain coefficient, with a periodicity of λ/2, where λ is the oscillating wavelength. This periodic gain modulation can be considered a grating. In an amplifying medium, the presence of this grating is problematic. When light interacts with this grating it is scattered back on itself. Thus, a fraction of the light propagating left to right is scattered into the opposite direction, right to left. The scattered light superimposes with light already propagating in that direc-


247

tion, but there is a 180° phase difference between the scattered and nonscattered signals, so the two signals destructively interfere. This effect lowers the intracavity intensity, and thus reduces both the grating strength and the coherence of the waves that produced the grating. The reduction in grating strength produces a more uniform gain distribution, which favors incoherent multimode operation, rather than coherent single-mode operation. There are several ways to overcome these deleterious effects of spatial hole burning and inhomogeneous broadening. Spatial hole burning can be eliminated by ensuring that a standing-wave intensity distribution is not established in the gain medium. There are several different ways to accomplish this, described later in this chapter. An alternative way of eliminating spatial hole burning is to ensure that the frequency spacing between longitudinal modes is greater than the fluorescence linewidth, so that only one mode experiences gain. This method can also be used to eliminate the effects of inhomogeneous broadening. Another effective scheme for eliminating multilongitudinal mode operation arising from inhomogeneous broadening is to introduce some form of frequency control into the cavity, which offers a frequency discrimination that is greater than the frequency response of the inhomogeneous process. In fact, limiting the number of oscillating modes is the key to obtaining a narrow-linewidth output from a fiber laser. The simplest way to restrict the number of modes is to include a bandwidth-limiting element in the cavity. This element can be a wavelength-selective mirror, such as a Bragg reflector or a diffraction grating, a tunable filter, such as an interference filter or a Fabry– Pe´rot filter, or an optical e´talon. The wavelength-selective mirror reflects light back only into the cavity, with frequencies that fall within the reflection bandwidth, whereas the filter transmits only certain frequency components, thereby reducing the number of modes that can access the optical gain. If the wavelength selective device allows a few longitudinal modes to oscillate, the output from the fiber laser is described as being line-narrowed. On the other hand, when the frequency restriction is strong enough that only one longitudinal mode oscillates, the laser output is quantified as single-frequency. The laser output then exhibits a high degree of temporal coherence and can be used for a wide range of applications. The broad fluorescence spectra of trivalent rare earth ions offer the potential for wavelength tunability. For a laser to reach threshold, the round-trip phase shift must be an integer multiple of 2π, as shown by Eq (1b). From this equation it is evident that the simplest way of varying the oscillating frequency is to vary the optical path length of the cavity. To exploit the full potential of the narrow-linewidth fiber laser, it is important that the oscillating frequency must vary continuously relative to any perturbation applied to the laser. In general, however, this does not occur. It can be understood by considering two neighboring cavity modes with oscillating frequencies ν n and ν n⫺1 , respectively. As shown in Figure 2a, mode ν n coincides with the minimum loss of the spectral filter, whereas mode ν n⫺1 experiences a higher loss. As the cavity length changes, the oscillating frequency varies, the loss of mode ν n increases, whereas the loss of the neighboring mode ν n⫺1 decreases. The situation may arise whereby the loss of mode ν n exceeds that of mode ν n⫺1 (see Fig. 2b), at which point mode ν n⫺1 becomes the dominant mode. This will induce a discrete change in the oscillating frequency (i.e., a mode hop). The simplest way to avoid mode hops is to ensure that the oscillating mode remains coincident with the minimum loss of the spectral filter at all frequencies. Then the oscillating frequency can be tuned continuously without a longitudinal mode hop. A variety of schemes have been developed to prevent longitudinal mode hopping. Their relative merits are discussed in this chapter.

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Figure 2 Effects of perturbing the optical path length of a resonator on the oscillating longitudinal

mode: (a) The oscillating mode ν n coincides with the frequency of minimum loss of the frequencyselective element; (b) the loss experienced by the oscillating mode increases and the neighboring mode (ν n⫺1 ) dominates.


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5.3 LINEWIDTH MEASUREMENT TECHNIQUES Once the fiber laser output has been line-narrowed, its linewidth must be measured. The electric field E(t) produced by a single-frequency laser oscillating at a central angular frequency ω 0 is given by E(t) ⫽ A(t) exp(i[ω 0 t ⫹ φ N (t)])

(5)

where A(t) is the time-varying instantaneous field amplitude and φ N (t) the time-varying random phase factor that determines the degree of coherence of the laser light. Measuring the laser linewidth in essence measures the instantaneous frequency of the laser over the time scale of the measurement. The instantaneous frequency ω(t) is given by [21] dφ (t) ω(t) ⫽ ω 0 ⫹ N d(t)

(6)

For a perfectly coherent source, φ N (t) is time-independent, and the instantaneous linewidth is equal to the central oscillating frequency. In general, this is not true, as many factors influence the laser resulting in a time-dependent value of φ N (t). Thus, if the degree of coherence can be determined, then an estimate of the linewidth is possible. The coherence of a light source can be measured using either homodyne or heterodyne measurement techniques. A homodyne measurement involves mixing the signal with a time-delayed replica of itself at a photodetector, which essentially determines the autocorrelation function of the light. Heterodyne measurements involve mixing the signal with either a frequency-shifted time-delayed replica of itself or another laser on a photodetector and observing the beat note. Figures 3 and 4 illustrate some of the experimental configurations used in both homodyne and heterodyne linewidth measurements. The simplest homodyne measurement uses a fiber-based Michelson interferometer (see Fig. 3a), whereby the fringe visibility at a given optical path difference provides information about the coherence length of the laser [22]. For ultranarrow linewidth lasers this approach is not ideal because long lengths of fiber (⬎10 km) are required. The interferometer is then susceptible to environmental perturbations that can distort the measurement, and the intrinsic loss of the fiber must be taken into account when the fringe visibility is measured. A more effective approach is to use either a ring geometry [23,24] (see Figs. 3b and 3c), or a Fabry–Pe´rot geometry [25] (see Fig. 3d). These configurations require much shorter fibers while achieving the same resolution as the Michelson interferometer. The resonator can be constructed with fused fiber couplers and a length of fiber. By varying the optical path length of the resonator, light will couple to the resonator, and a fringe pattern will be observed at the output. If the loop has a free spectral range (FSR) and a finesse ℑ, the minimum linewidth ∆ν that can be resolved is given by ∆ν ⫽

FSR ℑ

(7a)

c nᐉ

(7b)

FSR ⫽

where ᐉ is the length of fiber in the loop and n the fiber refractive index. For the single coupler resonator it is straightforward to show that the parameter ℑ is given by

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Figure 3 Schematics of the various interferometers used for homodyne measurements of the oscillating linewidth: (a) unbalanced Michelson interferometer; (b) single-coupler fiber loop; (c) dual-coupler fiber loop; (d) a fiber Fabry–Pe´rot filter (PZT: piezoelectric transducer).

251


Figure 4

Schematics of the various configurations used to make self-heterodyne measurements of the oscillating linewidth: (a) an unbalanced Mach–Zehnder interferometer; (b) a fiber loop (AOM: acousto-optic modulator).

ℑ⫽

冤冢√

π sin ⫺1 2

(1 ⫺ bL) 2 4bL

冣冥

⫺1

(8a)

b ⫽ (1 ⫺ k) 1/2 (1 ⫺ δ) 1/2

(8b)

L ⫽ exp ⫺ (αᐉ ⫹ s)

(8c)

where k is the intensity coupling ratio of the coupler, δ the excess intensity loss of the coupler, α the electric-field loss coefficient of the fiber, and s the loss experienced by the electric field at the splices. For the twin coupler system it can be shown that ℑ takes the form ℑ⫽

冤冢√

π sin ⫺1 2

1 ⫺ b 1 b 2 L) 2 4b 1 b 2L

b i ⫽ (1 ⫺ k i) 1/2 (1 ⫺ δ i ) 1/2

冣冥

⫺1

i ⫽ 1,2

L ⫽ exp ⫺ (αᐉ ⫹ s) where k i and δ i are the coupling ratio and excess loss of each coupler, respectively.

(9a) (9b) (9c)

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If the coherence time of the laser is greater than the storage time of the resonator, then resolution-limited fringes are observed from the resonator. From Eqs. (7) through (9) it is evident that the resolution of the resonator is influenced by the coupler strength, the excess loss introduced by the couplers, the fiber and the splices. Yue et al. [23] have shown that if a low-loss polished fiber coupler (coupling ratio of 0.25% and insertion loss of 0.006 dB) is used to form a resonator, a finesse of 1260 is possible, but to achieve this finesse the length of fiber was kept short (60 cm), so that the excess loss was minimal. Hence, the effective resolution was only 270 kHz. To measure ultranarrow linewidths it is best to use a longer fiber and accept a lower finesse owing to the increased loss in the fiber. This excess loss can be compensated by placing an amplifier in the fiber loop. For a single-coupler resonator the amplifier gain G modifies the finesse of the resonator in the following way ℑ⫽

冤冢√

π sin ⫺1 2

(1 ⫺ bGL) 2 4bGL

冣冥

⫺1

(10)

Equation (10) states that as the gain increases, compensating the losses, ℑ approaches the value determined by the coupling coefficient k. Using a ring resonator with a free spectral range of 8.5 MHz, Okamura et al. [24] were able to measure a linewidth of 100 kHz, corresponding to a finesse of 85. This finesse was limited by the linewidth of the available light source, not by the resonator. This means that long fibers (⬎100 m) can be used in the resonator. There is, however, a drawback with using long fibers [25]. To observe fringes from the ring resonator, the optical path length of the resonator must be modulated to take the incident signal in and out of resonance with a resonator mode. When the incident signal is resonant with a resonator mode, the signal couples to the resonator and a fringe forms as a result of interference between the incident signal and light that has made several transits through the resonator. There is a finite time required to reach the maximum fringe intensity, determined by the storage time of the resonator. If the cavity length is modulated on a time scale comparable with the storage time, the fringe will not reach maximum intensity and will appear distorted, which affects the linewidth measurement. Hsu et al. [25] showed that for a fiber Fabry–Pe´rot e´talon the minimum linewidth ∆ν that can be measured for a fiber length ᐉ and modulation time T f is

冢冣

c ∆ν ⫽ 2nT f ᐉ

1/2

(11)

For a ring resonator the factor of 2 in the denominator should be dropped. A more effective way of measuring the linewidth is to use a heterodyne technique, which can be done in two ways. The simplest one is shown in Figure 4a. An asymmetric Mach–Zehnder interferometer is formed with one arm significantly longer than the other. An amplitude modulator is placed in the long arm so that the light in that arm is frequencyshifted. The time-delayed frequency-shifted signal is then recombined with the light that propagated through the short arm and a beat note is generated at the modulation frequency of the amplitude modulator. This beat note is detected using a fast photodiode and radio frequency (rf ) spectrum analyzer combination [26]. For this type of measurement to give a true representation of the laser linewidth, the time delay imposed by the long length of fiber must be significantly greater than the coherence time of the laser, so that the two fields incident on the detector are not coherent. If this condition is satisfied the beat note


253

displayed on the spectrum analyzer has a Lorentzian frequency distribution [27]. If the delay time imposed by the fiber and the coherence time are comparable, the output observed on the spectrum analyzer comprises a delta function superimposed on a broadband modulated pedestal, and linewidth information can be derived only by careful numerical analysis and complex shape fitting of the pedestal [28]. Hence, long fibers are preferable, which can be impractical in some cases. As with the homodyne measurements, the effective fiber length can be increased by forming a ring resonator [29] (see Fig. 4b). The amplitude modulator is placed inside the resonator, and for each transit of the resonator the light is frequency-shifted. Linewidth information is provided by monitoring the beat note between the frequency-shifted time-delayed field and the field that is not coupled to the resonator. The output on the rf spectrum analyzer contains discrete frequency components at harmonics of the modulation frequency. Each harmonic corresponds to a different delay time, and once the delay time exceeds the coherence time the desired Lorentzian profile is observed. Although this approach is effective, the number of transits and, hence, the ultimate resolution of the system, is limited by the loss of the modulator. A typical amplitude modulator can introduce a loss of 5 dB. Vahala et al. [30] showed that this loss could be overcome by introducing a fiber amplifier in the resonator and carefully biasing its gain. With this approach they were able to measure the 30th harmonic of their resonator, which provided information not only on the linewidth of their single-frequency laser but also the degree of frequency jitter in the system [30]. The final and most precise method for measuring the linewidth of the radiation is to mix the output from two different lasers. If both lasers are stabilized to the same frequency reference source this approach provides a detailed measure of the linewidth and relative frequency jitter between the two sources [21]. In the remainder of this chapter I will describe the evolution of narrow-linewidth fiber lasers from the initial studies of line-narrowed lasers to the complex cavity configurations that are used for stable-frequency, tunable single-frequency operation. 5.4. LINE-NARROWED FIBER LASERS As mentioned in the previous section, a free-running fiber laser can have a bandwidth exceeding several terahertz and cover many thousands of longitudinal cavity modes. Some form of bandwidth restriction, therefore, must be used to prevent most of these modes from oscillating. The boom in all-fiber-based sensing and communication networks has seen significant research aimed at the development of suitable fiber-compatible, frequencyselective devices. These include integrated versions of bulk-optic components such as interference filters [32] and Fabry–Pe´rot filters [33], as well as structures that can be created directly in the fiber, such as fiber Bragg reflectors [34] and overlay filters [35]. Initial studies made on line narrowing of fiber lasers concentrated on the fixed wavelength operation of the fiber laser, rather than exploiting its full tuning potential [6,36,37]. The oscillating wavelength is controlled by a filter with a fixed wavelength response, such as a distributed Bragg structure. These are reflective devices, with a center wavelength determined by the periodicity of the Bragg grating and a reflection bandwidth defined by the length of the periodic structure. The Bragg structure is either etched close to the core of a polished fiber [38] or, if the fiber is photosensitive, written directly into the fiber core [34] using an ultraviolet (UV) laser. Because a distributed Bragg reflector can have a very narrow reflection bandwidth (⬍0.5 nm), they have been used to great effect for narrowing the linewidth of a selection of fiber lasers.

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Neodymium- [39], erbium- [36], and ytterbium-doped [40,41] standing-wave linearcavity fiber lasers have been operated in a line-narrowed fashion using fiber Bragg reflectors to define the oscillating wavelength. The first report of a line-narrowed Nd 3⫹-doped fiber laser used an etched Bragg reflector as one of the reflectors. Figure 5 shows a schematic of the cavity configuration. The reflector was designed to coincide with the peak of the emission spectrum of the Nd 3⫹ ions [39]. A dichroic mirror completed the cavity. The pump light was coupled into the Nd 3⫹-doped germanosilicate fiber through this mirror. The Bragg reflector had a peak reflectivity of ⬃75% at 1.084 µm (the emission peak of the gain fiber was 1.088 µm). This fiber laser oscillated at 1.084 µm and had a measured linewidth of 16 GHz. A similar design of resonator was used to force line-narrowed operation from an Er 3⫹-doped fiber laser [36]. Again the Bragg reflector was etched onto a polished fiber. An oscillating linewidth of 4.9 GHz was observed at 1.551 µm. The linewidth attainable from this type of laser is frequently, limited by the interaction length between the evanescent field coupled from the fiber core and the Bragg structure. A modular grating filter was designed to increase this interaction length [42]. A diffraction grating was placed in contact with the flat surface of a D-shaped fiber, which increased the interaction length between the evanescent field and the diffraction grating; thereby, resulting in a significantly narrower reflection linewidth. In this case the reflection bandwidth was 13 GHz. Incorporating this device into a standing-wave Er 3⫹-doped fiber laser with a 7-m–long gain fiber resulted in a linewidth of 20 MHz at 1.542 µm. The bulk diffraction grating allowed the wavelength to be tuned by 0.6 nm. The fabrication of either the etched-fiber Bragg reflectors or the modular D-shaped fiber grating filter is difficult and time-consuming. A more attractive method is to write the Bragg structure directly into the core of a photorefractive fiber. Kashyap et al. [43] used such a filter to narrow the linewidth of an Er-doped fiber laser. The oscillator utilized a 30-m standing-wave cavity. The Bragg reflector had a reflectivity of 0.5% at 1.538 µm, with a reflection bandwidth of 1 nm, and it acted as one mirror of the cavity. The resonator was completed by a high reflector at 1.55 µm and oscillated at 1537.5 nm, with a timeaveraged linewidth of 1.0 GHz. Although a line-narrowed output was obtained from this fiber laser, the laser itself was a rather cumbersome device, containing a Bragg grating and a butted mirror as the cavity reflectors. This design was effectively simplified by using a fiber Bragg reflector at each end of the cavity. This approach was first demonstrated by Ball et al. [37]. A Bragg reflector was written holographically into each end of a 4-m Nd 3⫹-doped fiber [44]. The Bragg reflectors had a peak reflectivity at 1.085 µm and a bandwidth of 0.1 nm. The intensity reflection coefficients of the two reflectors were 10.8 and 5.6%, respectively. At

Figure 5 Diagram of the cavity used to force line-narrowed operation of a Nd 3⫹-doped fiber laser. (Courtesy of D. N. Payne.)


255

the maximum pump power of 265 mW (at 830 nm), a fiber laser output power of 12 mW was obtained, corresponding to a slope efficiency of 7%. By temperature tuning the Bragg reflector, the laser wavelength could be tuned by 0.012 nm/K. Intracore fiber Bragg reflectors have also been used to force narrow linewidth operation from Yb 3⫹-doped fiber lasers [40,41], which were subsequently used to pump upconversion Tm 3⫹-doped fluorozirconate fiber lasers. The main reason why rare earth doped fibers are attractive compared with their bulk crystal counterparts, is their broad tuning range, which arises from the interaction of the rare earth dopant and the crystal field of the glass fiber host. Because the line-narrowed lasers using fixed wavelength Bragg reflectors described in the foregoing do not exploit this feature fully, there have been extensive studies aimed at the development of tunable line-narrowed lasers. Aside from varying the temperature of the Bragg reflector, tuning can be achieved by placing the grating under tensile [45] or compressive [46] stress. These approaches are discussed in greater detail in subsequent sections. Research in Bragg reflectors has provided many types of Bragg structures, which have been used to tune rare earth doped fiber lasers. One such advance is the sampled grating, a device in which the phase or amplitude of a standard grating is modulated along the grating. This modulation induces additional peaks in the reflection profile of the Bragg structure [47]. If two sampled gratings are used as the end reflectors of a fiber laser, and one of them is placed under tensile strain, the laser can be tuned as the successive peaks of each sampled grating are brought into resonance with each other. Ibsen et al. [48] tuned an Er-doped fiber laser over 16.7 nm, either discretely by straining one grating, or continuously by straining both gratings. Although fiber Bragg reflectors have proved to be reliable components to define the wavelength of rare earth doped fiber lasers and induce narrow-linewidth operation, there are other ways of achieving this goal. One method is to introduce an e´talon in the cavity. The spectral transmission profile of the e´talon superimposes on the mode distribution and thus increases the loss experienced by some of the cavity modes. O’Sullivan et al. [49] used this approach in an Er-doped fiber laser. A 13-m length of germanosilicate fiber was placed between two dielectric mirrors and optically excited with the 514-nm line of an argon ion laser. The high-reflecting mirror was butt-coupled to the gain fiber, whereas the output coupler was placed close to, but not in contact with, the other fiber end. This fiber end and the output coupler, therefore, formed an e´talon, which ensured line-narrowed operation. A linewidth of 620 MHz was measured for this laser. The high optical gain that can be established inside a rare earth doped fiber laser means that lossy elements, such as birefringent filters and bulk diffraction gratings, can be used as cavity components without affecting the overall operating characteristics of the laser. One of the first demonstrations of tunable line-narrowed operation was made by Alcock et al. [50] in a standing-wave Nd 3⫹-doped fiber laser (Fig. 6a). A birefringent filter was used to define the oscillating wavelength. With careful adjustment of this filter, the laser was tuned on the 4 F 3/2 → 4 I 11/2 transition from 1070 to 1135 nm (see Fig. 6b), with a resolution-limited linewidth of 0.1 nm. This laser was also made to oscillate on the three-level 4 F 3/2 → 4 I 9/2 transition with a tuning range of 45 nm (from 900 to 945 nm) and a resolution-limited output of 0.1 nm. Asymmetries in the fiber core induced during fabrication make standard rare earth doped fibers weakly birefringent. For a fiber laser, the polarization state at any given point in the cavity must be the same after one round-trip of the cavity. The fiber birefringence can also be controlled by applying stress to the fiber [51]. Also, because the fiber is disper-

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Langford

(a)

(b) (a) Schematic of a Nd 3⫹-doped fiber laser resonator containing a birefringent filter for wavelength selection (a, microscope objective; b, high reflector; c, doped fiber; d, waveplates; e, birefringent filter; f, output coupler); (b) typical tuning range from this fiber laser. (Courtesy of A. I. Ferguson.)

Figure 6

sive, different wavelengths experience a different birefringence. Thus, if a linear polarizer is inserted in the cavity and the polarization state of the laser is adjusted with polarization controllers, a wavelength-dependent loss can be introduced in the cavity, which can be utilized for wavelength tuning. This effect has been used to tune both linear [52] and unidirectional ring [53] cavities. For example, Ghera et al. [52] introduced a polarizer in the cavity of an Nd-doped fiber laser and, by varying the cavity polarization controllers, observed discrete tuning from 1080 to 1120 nm, with a resolution-limited linewidth of 0.1 nm. Humphrey et al. [53] extended this technique to an Er-doped ring fiber laser and observed a 33-nm tuning range with a resolution-limited linewidth of 0.1 nm. Although the laser was a unidirectional ring, multimode operation was observed instead of the expected single-mode operation. The high gain available in a rare earth doped fiber, combined with the low dispersive power of a birefringent filter, means that achieving single-longitudinal-mode operation in a fiber laser containing such a filter is difficult. On the other hand, diffraction gratings have a much greater dispersive power, and they have been used effectively to induce linenarrowing in a variety of rare earth doped fiber lasers [54–56]. The standard cavity design is shown in Figure 7. The bulk optic grating is used in the Littrow configuration. The


257

Figure 7 Fiber laser operated with a Littrow bulk-optic diffraction grating.

fluorescence from one end of the doped fiber is collimated onto the grating and the firstorder diffracted spot is coupled back into the cavity. Varying the angle of incidence on the grating defines the laser wavelength. With this approach, a Nd 3⫹-doped fiber laser was tuned from 1.07 to 1.14 µm, with a linewidth of 0.25 nm [54]. Erbium-doped fiber lasers have also been operated in a similar mode [55]. Wyatt optically excited a 9.5-m gain fiber with the output from a 980-nm Ti:sapphire laser. The wavelength of the fiber laser was tunable from 1.51 to 1.58 µm. The laser linewidth was determined to be ⬃2 GHz. By including an e´talon with a free spectral range of 50 GHz in the cavity, the linewidth was reduced to 100 MHz. This is substantially greater than the longitudinal mode spacing of the cavity, which was 10 MHz, indicating that, in spite of the narrow linewidth, the laser was oscillating on several longitudinal cavity modes. This was attributed to the adverse effects of spatial hole burning. Methods of negating and eliminating the effects of spatial hole burning are discussed later in this chapter. This technique was also applied to Tmdoped fiber lasers with a tuning range, depending on the composition of the host fiber, extending from 1.65 to 2.05 µm [56]. For example, in a fiber with a GeO 2 –SiO 2 core tuning over the 1.65 to 1.85-µm range was possible, whereas for an Al 2 P 3 –SiO 2 core the wavelength was tunable from 1.77 to 2.05 µm. Traveling-wave fiber lasers have also been studied as sources of line-narrowed laser light. A simple Nd 3⫹-doped ring laser was constructed by Chaoyu et al. [57]. The ring structure was formed by making a polished dichroic fiber coupler from the ends of a 3-m Nd 3⫹-doped fiber. For this laser to operate effectively, the coupling coefficients at the pump and laser wavelengths had to be significantly different. The coupling coefficients were measured to be 11% at the pump wavelength and 99.58% at the laser wavelength. Thus at the laser wavelength the cavity acted as a high-finesse resonator. Because coupling in the polished fiber coupler is wavelength-dependent, this device can be used for tuning. Adjusting the coupling between the two fibers permitted the laser wavelength to be tuned by 60 nm with a narrow-linewidth output of ⬃0.1 nm. A similar approach was used to obtain narrow-linewidth operation from an Er 3⫹-doped fiber laser [58]. A tunable coupler was used to tune the laser and a resolution-limited linewidth of 0.1 nm was observed. The laser wavelength was tunable over three discrete wavelength bands, one centered around 1530 nm, another one on 1570 nm, and a third one on 1585 nm. The origin of these three bands was attributed to the substantial Stark splitting of the 4 I15/2 ground state of the laser transition [59]. Line-narrowed operation of an Er-doped ring fiber laser containing an overlay filter has also been reported [60]. The overlay filter is formed by side polishing a length of optical fiber so that the fiber core is exposed. As a result the lowest order fiber mode is taken below cutoff and the fiber no longer acts as a waveguide. A thin (⬍10-µm) planar multimode lithium niobate waveguide is placed in contact with the exposed core. When

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the fiber mode is resonant with a mode of the planar waveguide, the field in the fiber core couples to the waveguide and propagates over the exposed core region, which restores the guiding properties of the fiber. As lithium niobate is dispersive, the fiber mode is resonant only with a given mode of the planar waveguide at a given frequency. This effect results in discrete transmission bands. The bandwidth and periodicity of the transmission maxima are determined by the thickness of the planar waveguide [35]. Also, because the planar waveguide is birefringent its TE and TM modes have different resonance frequencies, which increase the tuning range. By using a filter with a 5-µm–thick planar overlay, Gloag et al. [60] observed line-narrowed operation from an Er-doped ring fiber laser. The output was oscillated on several longitudinal cavity modes, with a linewidth of 100 MHz. By applying a selection of index-matching oils to the exposed surface of the overlay, the output wavelength could be tuned discretely from 1539 to 1560 nm for the TE mode, and from 1560 to 1575 nm for the TM mode. Er-doped fiber lasers have attracted significant commercial interest because their wavelength coincides with the minimum loss window of standard telecommunications fiber. For sensing and wavelength-sensitive time-domain reflectometry applications, a tunable line-narrowed Er-doped fiber laser would be ideal. The tuning approaches described in the foregoing, however, are not ideal, and alternative mechanisms have been investigated. Electronic tuning of Er-doped fiber lasers has been achieved in a variety of ways. One of the first demonstrations was by Wysocki et al. [61], who incorporated a bulk-optic acousto-optic (AO) modulator in a linear cavity Er-doped fiber laser. The 5-m doped fiber was excited by the 514-nm line of an argon ion laser. One fiber end was polished to act as a 4% output coupler. The cavity was completed by the modulator and high reflector at the other end. A radio frequency signal coupled to the modulator induces a phase grating in the modulator that diffracts the light. The angle of diffraction is determined by the periodicity of the phase grating, and thus by altering the drive frequency the laser frequency can be tuned. Line-narrowed operation was observed in two discrete bands, extending from 1.53 to 1.535 µm and from 1.545 to 1.564 µm, with linewidths varying from 0.3 to 1.0 nm. The laser could be tuned electronically with a tuning coefficient of 3.7 nm/MHz for the 1.53-µm band, and 15 nm/MHz for the 1.55µm band. An interesting feature of this laser is that the continuous change in laser frequency prevents the buildup of the longitudinal mode structure, and the laser appears ‘‘modeless.’’ Yun et al. [62] extended the work of Wysocki et al. [61] to the ring geometry using a bulk AO tuning filter. They achieved a continuously tunable laser with a tuning range of 38 nm centered around 1550 nm, a tuning rate of ⫺20.6 nm/MHz, a linewidth of 9 GHz, and an output power of 100 mW. The cavities constructed by Wysocki et al. [61] and Yun et al. [62] contained bulkoptic AO modulators, that required the light to be coupled out of the fiber, through the modulator and back into the fiber. A more practical approach would use an integrated tunable AO filter, which works by converting TE-polarized light into TM-polarized light. However, this type of device suffers from a Doppler shift introduced by the interaction of the light with the acoustic field, which prevents narrow-linewidth operation [61]. This frequency shift can be eliminated by using two filters in series [11], as described in Section 5.6, or by passing twice through a single-stage device [63]. This last approach was developed by Doughty et al. [63], whereby a single tunable AO filter was placed in a cavity, and the cavity was terminated by Faraday rotating mirrors. These structures ensured that no matter in which direction the intracavity field propagated through the modulator the polarization change induced by the filter was TE–TM (or vice–versa). The frequency


259

shift imposed on the field in the modulator in one direction was removed when the light counterpropagated through the modulator. With this approach, the frequency of the fiber laser could be tuned over 20 nm, with a wavelength change of 8.65 nm/MHz. Narrowlinewidth operation was observed, but the laser showed a tendency to undergo random longitudinal mode hops, which affected its overall frequency stability. This approach was extended by Frankel et al. [64] to allow rapid tuning of the laser wavelength. A ‘‘σ’’ cavity configuration was used, in which the integrated AO filter was placed in a polarization-sensitive unidirectional ring and the tail section of the ‘‘σ’’ contained an Er-doped amplifier terminated with a Faraday mirror. The filter was driven at two discrete frequencies—173.1 and 170.7 MHz—and to allow rapid switching between them they were modulated by a square wave at a frequency of 420 Hz. The laser changed wavelength from 1552.3 to 1572.3 nm in 50 µs, indicating that rapid tuning of the wavelength was possible. However, as the wavelength changed the laser output exhibited severe relaxation oscillations. These oscillations were minimized by using a suitable electronic-feedback scheme. Chieng et al. [65] developed a similar laser using a nonlinear loop mirror [66] to eliminate the relaxation oscillations. The laser wavelength was tuned from 1537 to 1561 nm in ⬃20 µs. Because the laser operated in a bidirectional manner, spatial hole burning was a major problem and the linewidth ranged from 0.15 to 2.0 nm. The integrated-optic AO filters used in the foregoing studies relied on coupling between two orthogonal polarization modes to achieve the desired tuning. Yun et al. [67] showed that it was possible to make an all-fiber AO tunable by exciting and transferring energy between two spatial optical modes. The energy exchange is induced by the interaction of the fiber-guided light and a flexural acoustic wave. The all-fiber filter was fusion spliced to a 4-m length of Nd-doped fiber and a tuning rate of 0.5 nm/kHz was observed over a 20-nm band, with a laser linewidth less than 0.2 nm. This tuning rate was an order of magnitude greater than that of the bulk and integrated polarization-converter AO filters. A line-narrowed output was also obtained from an Er-doped ring fiber laser containing an electro-optic polarization converter [68,69]. This device is more attractive than the AO tuners described in the foregoing because they are free of Doppler shift. Chollet et al. [68] were able to tune the laser over 10 nm, with a tuning rate of 0.05 nm/V and a linewidth of 0.06 nm. Electro-optic rotation of the polarization is possible using liquid crystals. Mollier et al. [69] placed a liquid crystal cell between two crossed polarizers to form a simple tuning element that was subsequently inserted into the linear cavity of an Nd-doped fiber laser. By varying the voltage applied to the liquid crystal cell the laser could be tuned over 17 nm at a rate of 8 nm/V; the linewidth was 1.0 nm. Liquid crystals have also been used in a spatial light modulator to tune an Er-doped ring fiber laser [70]. 5.5 SINGLE-FREQUENCY STANDING-WAVE FIBER LASERS Although a line-narrowed fiber laser may be of benefit to sensing applications for highresolution spectroscopy or nonlinear frequency conversion studies, it is essential that the output oscillates only on one longitudinal mode. As discussed in Section 5.2, spatial hole burning can prevent a standing-wave laser from oscillating on a single longitudinal mode. Several approaches have been applied to fiber lasers to eliminate the effects of spatial hole burning. Some of them are discussed in this section. The simplest approach for overcoming spatial hole burning is to increase the frequency spacing between the cavity longitudinal modes. This can be done by reducing the optical path length of the cavity. For example, a fiber laser with a round-trip optical path

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length of 10 m has a free spectral range of 30 MHz, whereas, with a round-trip path length of 1 cm, the free spectral range is 30 GHz. Shortening the cavity length means that, for a given gain bandwidth, the number of modes that experiences optical gain is reduced. For rare earth doped fiber lasers, this is an attractive approach, as the confinement of both the pump and the laser enables low-threshold operation to be achieved even in short (⬍10 cm) cavities. This technique has been applied successfully to many fiber lasers, as discussed in the following. Single-longitudinal-mode operation was observed by Jauncey et al. [6] from an Nddoped fiber laser. The cavity was similar to that shown in Figure 5. A polished fiber Bragg reflector was formed directly on the core of the doped fiber. It had a peak reflectivity of 80% at 1082 nm and a reflection bandwidth of 0.8 nm. For a cavity length of 50 cm the laser had a linewidth of 2 GHz and the laser oscillated on about ten cavity modes. By reducing the cavity length to 2.7 cm, the laser was then observed to oscillate on only one longitudinal mode. The laser threshold was 6 mW, and the average output power was 0.8 mW for a 40-mW pump power. A delayed self-heterodyne interferometer containing a 2-km delay fiber gave a value of 1.3 MHz for the laser linewidth. A similar approach was adopted by Gilbert [71] to demonstrate a short-cavity, single-longitudinal-mode Er-doped fiber laser. The cavity configuration is shown in Figure 8. It had an optical path length of 40 cm, corresponding to a free spectral range of 375 MHz. The key to obtaining single-longitudinal-mode operation from this cavity was as follows. The wavelength definition was provided by a Littrow-mounted diffraction grating, with a measured reflection bandwidth of 5 GHz. Additional spectral filtering was provided by the gain medium. Two lengths (2.8 and 1 cm) of Er-doped fiber were used as the active medium. Because the ends of the fibers were not antireflection coated, the fibers acted as intracavity e´talons, with free spectral ranges of 3.6 and 10 GHz, respectively. The overlap of the transmission spectra of these two e´talons increased the spectral filtering and forced the laser to oscillate on a single longitudinal mode. Coarse frequency tuning was achieved by rotating the diffraction grating, and fine tuning was accomplished by stretching the 2.8-cm fiber with a piezoelectric transducer and tilting the grating using another piezoelectric transducer. The short-term root-mean-square (RMS) frequency jitter of the laser was determined to be less than 1 MHz. It was reduced to less than 500 kHz by locking the laser frequency to an overtone transition of acetylene. The composite nature of this cavity meant that continuous tuning of the laser was difficult. To minimize the loss experienced by the oscillating mode, the transmission maxima of the various e´talons in the cavity must be kept in resonance. If this condition is not satisfied, the net loss experienced by the oscillating mode may exceed that of a nearby

Figure 8 Pictorial representation of an Er 3⫹-doped fiber laser using an external grating. (Courtesy of S. L. Gilbert.)


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mode (see Fig. 2b). This nearby mode will then oscillate, thus inducing a mode hop rather than the desired continuous-frequency change. Larose et al. [72] overcame this problem by introducing a single length of Er-doped fiber in their cavity. The basic cavity design was similar to that of Gilbert, but tuning was achieved using a grating–mirror combination in the Littman configuration (Fig. 9a). This combination acted as a tunable filter with a transmission bandwidth of 7.6 GHz. Fine-tuning of the laser frequency was achieved by adjusting the incident angle of the light on the grating. A tilted e´talon was included in the cavity to ensure single-longitudinal-mode operation. Subsequent frequency stabilization relative to the R(10) line of acetylene resulted in a resolution-limited linewidth of 70 kHz and an RMS jitter of 2 MHz.

(a)

(b)

Figure 9 (a) Diagram of a linear cavity used to obtain narrow-linewidth operation from a Tm 3⫹-

doped fluorozirconate fiber laser; (b) the absorption spectrum of methane at about 2.3 µm and the associated tuning range of the laser. (Courtesy of J. Hegarty.)

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Many molecular transitions exhibit strong vibrational or rotational absorptions in the mid-IR region. For example, methane exhibits absorptions in the 2.2–2.4-µm range, which coincides with the 3 H 4 → 3 H 5 transition in Tm-doped fluorozirconate fibers [56]. McAleavey et al. [73] constructed a linear cavity Tm-doped fiber laser and tuned it using a grating–mirror combination in the Littman configuration. A linewidth of 207 MHz was observed, which was narrow enough to probe the methane transitions at about 2.3 µm. Figure 9b shows the tuning range of the fiber laser and the absorption spectrum of methane in the vicinity of 2.3 µm. The work of Gilbert [71] and Larose et al. [72], described in the foregoing demonstrated that single-longitudinal-mode operation was attainable in fiber lasers by introducing additional spectral filtering with an intracavity e´talon. Barnsley et al. showed that it was also possible to achieve single-longitudinal-mode operation in an Er-doped fiber laser with a Fox–Smith resonator [74]. This resonator (Fig. 10), is a composite cavity that contains a beamsplitter used to form two separate Fabry–Pe´rot cavities coupled by a common gain medium [75]. The two cavities are arranged to have different optical path lengths. This mismatch introduces sufficient additional spectral filtering in the composite cavity to induce single-longitudinal-mode operation. The development of low-loss fused fiber couplers that can be spliced to the gain fiber means that the Fox–Smith geometry can be implemented easily. The cavity layout used by Barnsley et al. [74] is shown in Figure 11a. One cavity was formed by butt-coupling mirrors to the fiber ends. The other one was completed with a diffraction grating, which allowed tuning of the laser wavelength. Singlelongitudinal-mode operation was observed with a resolution-limited linewidth of 8.5 MHz (see Fig. 11b). The inherent complexity of the various resonators, outlined in the foregoing, means that these lasers may not be suitable for applications outside the laboratory. As already demonstrated by Jauncey et al. [6], the simplest way of eliminating the effects of spatial hole burning in a standing-wave geometry is to use a short cavity with narrowband reflectors. The advances made in fiber Bragg-grating reflectors have enabled the realization of a range of compact and environmentally robust short-cavity single-frequency lasers that can be used in diverse practical applications [76–78]. The first report of an integrated single-frequency fiber laser using intracore Bragg reflectors was made by Ball et al. [76]. They wrote two 12.5-mm–long Bragg reflectors separated by 50-cm in an Er-doped germanosilicate fiber. It is difficult to fabricate two

Figure 10

Simplified diagram of a Fox–Smith resonator.


263

(a)

(b)

Figure 11

(a) Fiber-based Fox–Smith resonator laser; (b) the output obtained from a 300-MHz confocal e´talon. (Courtesy of P. Urquhart).

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identical gratings, because the Bragg wavelength varies slightly from grating to grating. This problem can be overcome by monitoring the reflectivity profile of the Bragg grating as it is formed. In the designed by Ball et al. the two gratings had the same Bragg wavelength when the reflectivities of the two gratings were 72 and 80%, respectively. When pumped with 980-nm light from a Ti:sapphire laser, the laser oscillated at 1548 nm, corresponding to the selected Bragg wavelength. For low pump powers, a slope efficiency of 27% was observed. For high pump powers, this efficiency was reduced owing to saturation of the pump absorption. By monitoring the output of this laser on a fast photodiode– rf spectrum analyzer combination, no evidence of a beat note at the longitudinal-mode spacing of the cavity (180 MHz) was observed, indicating that the laser was oscillating on a single longitudinal mode. This was further verified by measuring the laser linewidth with an asymmetric Michelson interferometer, which gave a linewidth of 47 kHz. This work showed that this method of obtaining stable single longitudinal mode is an extremely powerful technique. It has since then been refined, for example, to allow the use of very short cavities [77], or to enable narrow-linewidth multiple-wavelength operation [78]. For many applications it is imperative that the laser frequency does not change randomly; therefore it is essential that these short-cavity lasers are robust against longitudinal-mode hopping. The most obvious answer is to shorten the cavity length still further, so that the longitudinal-mode spacing is comparable with the grating bandwidth. This implies that for a reflection grating with a bandwidth of 0.2 nm the cavity mode spacing should be of the order of 10 GHz, or a length of 1 cm for a standing-wave fiber laser cavity. Zyskind et al. [77] constructed several Er-doped fiber lasers with cavity lengths of the order of a centimeter. Single-longitudinal-mode operation was indeed observed with resolution-limited linewidths of 6 MHz. In a 2-cm laser pumped either at 1480 or at 980 nm, output powers of 122 µW for 34 mW of 1480-nm pump power, and 181 µW for 61 mW of 980-nm pump power, were observed. The threshold power for each pump wavelength was 5 mW. In a 1-cm cavity pumped at 980 nm the laser reached threshold for a pump power of 15 mW, and a maximum output power of 57 µW was observed for a pump power of 66 mW. The high threshold powers and the low output powers can be attributed to the design of the cavity and the gain fiber. With such short-cavity-length lasers a high concentration of active ions must be introduced into the fiber core so that the laser can absorb sufficient pump power to reach threshold. In the lasers developed by Zyskind et al. [77] the erbium-concentration was 2500 ppm. The use of such high concentrations results in ion–ion interactions, such as concentration quenching [79], twoparticle upconversion [80], and self-pulsing [81], which have serious effects on the performance of the laser. Concentration quenching and two-particle upconversion result in increased threshold powers and reduced output powers, whereas self-pulsing leads to amplitude instabilities in the output of the laser. The laser constructed by Zyskind et al. [77], indeed, did exhibit marked amplitude fluctuations. Subsequent studies showed that the amplitude instabilities caused by self-pulsing can be eliminated by applying an appropriate feedback control signal to the pump laser diode [82]. An alternative way of inhibiting random mode hopping is to ensure that the differential loss between the dominant cavity mode and neighboring modes is sufficient enough that all but the dominant mode are below threshold. This can be achieved by careful engineering of the narrowband reflectors. Ball et al. [83] modeled the transient evolution of the energy density of two cavity modes in the presence of modal gain and modal loss. For the short-cavity fiber lasers considered, the modal loss is dominated by the reflectivity profile of the Bragg gratings, and it is given by


γ ⫽ ⫺ln[R 1 (δβ)R 2 (δβ)]

265

(12)

where δβ is the complex propagation constant, which assumes that the Bragg reflector is written in the rare earth doped fiber, and R 1 and R 2 are the intensity reflection coefficients of the two reflectors. If γ 1 is the modal loss of the dominant mode and γ 2 that of the neighboring mode, the analysis developed by Ball et al. [83] showed that provided the condition γ2 ⬎

1 2 α0 L ⫹ γ1 3 3

(13)

is satisfied, where α 0 is the small-signal gain of the doped fiber and L the resonator length, then the laser will oscillate on a single longitudinal mode. Equation (13) indicates that single-mode operation depends on both the gain and the loss experienced by the twocavity modes. As the homogeneous linewidth of the Er ions in a GeO 2 :SiO 2 based fiber core is of the order of 5 nm [19], then the gain experienced by both modes is equal over the narrow bandwidth of the cavity reflectors. Thus, in this system, mode discrimination must be provided by the wavelength variation of the narrow-bandwidth Bragg reflectors. The results of modeling indicated that for small-signal gains between 2.5 and 4.0 dB/m, single-frequency operation of short-cavity lasers could be achieved only with Bragg reflectors with reflection coefficients close to unity. For example, in a 5-cm cavity with a small-signal gain coefficient of 3.0 dB/m, single-frequency operation requires Bragg reflectors with reflectivities of 98%. The short cavity lasers developed by Ball et al. [83] Zyskind et al. [77], and Mizrahi et al. [82] had Bragg reflectors written into the active fiber. Consequently, the reflectors experienced gain, a fact ignored by Ball and Glenn in their initial numerical analysis [83]. Ball et al. [84] extended their analysis to include the effects of gain on the reflection profile of Bragg gratings and found that the presence of gain increased the peak reflectivity of the Bragg structure, but had minimal effect on the wings of the reflection profile. The significance of this point can be understood with reference to Eqs. (12) and (13). If it is assumed that the oscillating mode coincides with the peak wavelength of the Bragg reflector, then an increase in the reflection coefficient of the Bragg reflector means that γ 1 decreases [see Eq. (12)], which allows an increase in the small-signal gain, while satisfying the condition given in Eq. (13). One of the key requirements of single-frequency fiber lasers is the ability to frequency tune them without inducing mode hopping. As discussed earlier, mode hopping occurs when the loss experienced by the oscillating mode exceeds that of a neighboring mode, at which point the laser frequency changes abruptly to this neighboring mode. Continuous tuning of the laser frequency is normally achieved by changing the optical path length of the cavity. For a laser to oscillate the round-trip phase change imposed on the oscillating mode must satisfy the following condition: nνL ⫽ mc

(14)

where ν is the resonance frequency, L the length of the resonator, and m an integer. Thus a change in length δL with result in a corresponding change in frequency δν given by δν δL ⫽⫺ ν L

(15)

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Numerical simulations [83] indicated that if the reflectivity spectrum of the Bragg reflector does not follow the frequency change induced by the cavity-length variation, the laser can then be tuned by up to one-half a cavity free-spectral range before undergoing a mode hop. This is because the loss experienced by the oscillating mode exceeds that of the neighboring mode. If, on the other hand, the reflection peak of the Bragg reflector tracks the frequency change, the laser can be continuously tuned without mode hopping. This can be understood as follows. If the optical path length is altered either by heating or strain, the change in resonance frequency δν is given by [45]

冢

冣

δn δL δν ⫽ (1 ⫺ ρ)ε ⫹ (α ⫹ ζ)∆T ⫽⫺ ⫹ ν n L

(16)

with δn the change in refractive index, ρ the photoelastic coefficient, ε the applied stress, α the coefficient of linear expansion, ζ the thermo-optic coefficient, and ∆T the temperature change. For a Bragg reflector with a grating period Λ, the reflected frequency ν b is determined by the Bragg condition: νb ⫽

c 2nΛ

(17)

and the change in wavelength δν b due to either strain or thermal variation is given by [45]

冢

冣

δν b δn δΛ ⫽⫺ ⫽ (1 ⫺ ρ)ε ⫹ (α ⫹ ζ)∆T ⫹ νb n Λ

(18)

It is clearly evident from Eqs. (16) and (18) that if an equal strain and/or thermal variation is applied to both the cavity fiber and the Bragg reflector, the change in resonance frequency, as the laser is perturbed, will be followed by the Bragg reflector. Thus, the oscillating mode and the Bragg reflector remain in resonance, thereby eliminating mode hops. Ball and Morey [45] demonstrated that a short-cavity fiber laser could be tuned by applying a strain to it. They attached the fiber to a piezoelectric translator and stretched the cavity by 90 µm, which induced a change in laser wavelength of 0.72 nm. The maximum tuning range that can be achieved by using tensile strain is limited by the fiber strength. Simple calculations have shown that a maximum stain of 1% can be applied to the fiber before it will deform [46]. Silica fiber, however, is much more robust under compressive strain. This feature has been exploited to allow continuous tuning of a 4-cm– long Er-doped fiber laser over 32 nm without a mode hop [46]. The cavity configuration is shown in Figure 12a. The laser was mounted in a series of precision ground ferrules to prevent the fiber from buckling when the compressive strain was applied. One ferrule was attached to a fixed support, whereas the other was mounted on a translation stage that was driven by a stepper motor to compress the fiber. The translation stage had a linear translation resolution of ⫾50 nm, which gave a frequency step of ⫾250 MHz. Figure 12b shows the measured variations in laser wavelength versus the applied compression. When the cavity length was compressed by 2.5%, a linear wavelength change of 32 nm was recorded. This tuning range approaches that achieved in semiconductor devices operating in the same wavelength region, which makes this type of integrated fiber laser suitable for many applications.


267

(a)

(b)

Figure 12

(a) Schematic of the compression-tuned Bragg-grating fiber laser; (b) the measured dependence of the laser wavelength on the compressive strain applied to the cavity. (Courtesy of W. W. Morey.)

For this type of fiber laser to compete with the semiconductor laser in high-resolution spectroscopy or communication applications, its output power and noise characteristics must be comparable with, or better than, those of semiconductor lasers. A detailed knowledge of the noise characteristics therefore, is essential. In digital communication applications, the noise spectrum can mix with the carrier frequency to produce noise at high frequencies. Similarly, the noise characteristics of the laser can limit the overall sensitivity of a sensing system. The intensity noise characteristics of a light source can be obtained by analyzing its power spectrum on a photodiode–rf spectrum analyzer. Frequency noise characteristics are determined by placing a suitable frequency discriminator, normally a Fabry–Pe´rot e´talon, between the light source and the photodetector. The low-frequency noise characteristics (⬍1 MHz) of short-cavity laser systems have been studied by several research groups [82,85,86]. Mizrahi et al. [82] showed that the noise spectrum lower than 1 MHz was dominated by a peak corresponding to the relaxation oscillation frequency of the laser. By monitoring the output power from the fiber laser and by deriving an error signal to control the pump diode current supply, this noise feature could be eliminated. Ball et al. [85]. showed that with a similar control system applied to their fiber laser the

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intensity noise could be reduced from ⫺82.1 dB/Hz to ⫺112.1 dB/Hz below the DC level. Svalgaard and Gilbert [86] monitored both the intensity noise and frequency noise characteristics of a Bragg–reflector-based short-cavity fiber laser and found that, in the absence of the relaxation oscillation peak, the frequency jitter approached the limit imposed by the phase noise caused by thermal fluctuations of the laser cavity. Mixing the output from two lasers oscillating at different frequencies results in the generation of a beat note. The rf spectrum of this beat note reveals not only information about the linewidth of the lasers, but also about their intensity noise. By mixing the output from two relaxation–oscillation-stabilized Bragg reflector fiber lasers frequency detuned by 1 GHz, Ball et al. [87] determined that, for frequencies higher than 50 kHz, the output from the lasers was dominated by white noise. The white noise characteristics were consistent with those expected for a system in which the noise is dominated by spontaneous emission [88]. The Lorentzian linewidth of the white noise spectrum, 6.2 Hz/Hz 1/2, enabled a linewidth of 62 Hz to be assigned to the fiber lasers. The absorption and emission cross sections of the 4 I 13/2 → 4 I 15/2 transition are small, of the order of 10 ⫺20 cm 2, which results in low pump-power absorption and low output powers in short-cavity fiber lasers. For example, the 1–cm long laser developed by Zyskind et al. [77] generated an average output power of 50 µW for a pump power of 66 mW. There are several ways of overcoming this problem. Because only a small fraction of the pump power is absorbed by the active fiber, an additional length of doped fiber can be placed after the laser and pumped by the residual pump power to act as an amplifier. This configuration is known as a master oscillator power amplifier (MOPA). Ball et al. [89] were able to generate output powers of 60 mW from their single-frequency, stabilized erbium laser using a simple one-stage bidirectional pumped erbium amplifier. The relative intensity noise of the laser was approximately 110 dB/Hz less than the DC laser level over the 0.1- to 2-MHz frequency range. Taylor et al. [90] have used a series of preamplifiers and power amplifiers to generate output powers of 1 W from their single-frequency light source. Another approach for high-power operation of narrow-linewidth Er-doped fiber lasers is to optically excite the gain medium at wavelengths other than 980 and 1480 nm. The erbium ion exhibits strong absorptions at 650 and 528 nm that are free from ESA [91,92]. In fact, the absorption cross sections are significantly larger at these wavelengths than at 980 and 1480 nm [13]. Recently, high-power laser diodes at 650 nm have become available, and Giles and Mizrahi [93] used such a source to excite a 1-cm fiber laser. They observed an output power of 34 µW at a pump power of 6 mW, which is an order of magnitude more efficient than with a 980-nm pump. The numerical modeling of distributed Bragg reflector fiber lasers, developed by Ball et al. [83], showed that the lasers were immune to multiple-longitudinal-mode operation provided that the inequality given in Eq. (13) was satisfied. This shows the benefits of using a gain fiber with a large small-signal gain. In the case of short-cavity laser, to achieve this requires significant pump absorption and necessitates the use of a high dopant concentration, which makes the lasers susceptible to relaxation oscillations owing to ion–ion interactions [81]. An alternative approach to a high concentration is to co-dope the fiber. For Er 3⫹, ytterbium is the ideal co-dopant. Yb 3⫹ exhibits only two energy levels, so that very high concentrations can be introduced in a fiber without problems associated with ion–ion interactions [79–81]. If a fiber is co-doped with both Er 3⫹ and Yb 3⫹ and the Yb 3⫹ is excited at 980 nm, an Yb 3⫹ ion will absorb the pump radiation and will transfer it to an erbium ion. By careful control of the core dopants this energy transfer can be made


269

nearly 100% efficient, as demonstrated for an aluminophosphate fiber [94]. Kringlebotn et al. [95] investigated the potential of an Er :Yb co-doped fiber for high-power operation of a short-cavity fiber laser using the cavity configuration shown in Fig. 13a. It comprised a high reflector butt-coupled to one end of the co-doped aluminophosphate fiber, and a narrowband Bragg reflector (peak wavelength of 1545 nm, linewidth of ⬃0.09 nm) at the other end. The laser oscillated at a wavelength of 1544.8 nm. The output spectrum and the fringes obtained from a scanning e´talon are shown in Fig. 13b. Because the aluminophosphate fiber is not photosensitive, the Bragg reflector had to be written in a short length of undoped fiber, which was then fusion spliced to the active fiber; the cavity had a path length of 10 cm. When optically excited at 980 nm, the laser reached threshold at an incident pump power of 7 mW and produced an output power of 7.6 mW for ⬃100 mW of incident pump power, which is a significant advance over that obtained by Zyskind et

(a)

(b)

Figure 13

(a) Diagram of a high-power Er :Yb co-doped fiber distributed Bragg reflector laser; (b) the output obtained from the laser. (Courtesy of D. N. Payne).

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al. [77] with their fiber laser without amplification. Subsequent refinements to this laser [96], namely, reducing the loss of the grating-to-doped–fiber splice and matching the reflectivity peak of the Bragg reflector to the gain peak of the fiber, resulted in an output power of 19 mW for 40 mW of pump power incident on the gain fiber. The laser linewidth was measured to be 300 kHz. In some instances dual–longitudinal-mode operation has been observed from distributed Bragg reflector lasers [97]. This effect has been attributed to the intrinsic birefringence associated with the laser cavity, which allows two orthogonally polarized modes to satisfy the cavity round-trip phase criterion [see Eq. (14)] and, thereby, reach threshold. These lasers have been used as polarimetric sensors, as described in Section 5.8. The cavity design used by Kringlebotn et al. to demonstrate efficient narrow-linewidth operation in Er: Yb-co-doped fiber lasers has one major drawback that makes it unsuitable for practical applications; namely, it uses a bulk-optic mirror butted to one end of the cavity. The ideal cavity configuration is similar to the ones developed by Ball et al. [76] and Zyskind et al. [77] wherein Bragg reflectors are used as both cavity reflectors. The aluminophosphate host fibers used by Kringlebotn et al. [94,95] were not photosensitive, so that the Bragg gratings had to be written in photosensitive fibers that were then spliced to the active fiber. The physical dimensions of most fusion splicers means that the cavity length can then not be much smaller than about 5 cm. Such a length places tight constraints on the reflectivity profiles of the Bragg reflectors, as described by Eqs. (12) and (13). An aluminophosphate fiber can be made photosensitive if it is ‘‘loaded’’ with hydrogen. By this process, Archambault et al. [98] were able to write gratings with intensity reflection coefficients of 100% in aluminophosphate fibers. By writing a 2-cm long Bragg grating in a 3-cm Er: Yb-doped aluminophosphate fiber, Kringlebotn et al. [99] were thus able to produce the first fiber laser variant of a distributed-feedback laser. When a distributed-feedback laser is formed with a uniform grating and no end reflectors, it oscillates simultaneously on two wavelengths spaced symmetrically about the Bragg wavelength of the grating. This is a consequence of the round-trip phase criterion associated with a distributed-feedback laser [100]. Single-frequency operation can still be obtained from a distributed-feedback laser by introducing an additional phase shift in the cavity, which forces the laser to oscillate at the Bragg wavelength. This can either be done by either perturbing the Bragg structure that forms the cavity, or by using an end reflector to change the cavity round-trip phase shift. Both approaches were studied by Kringlebotn et al. [99]. Initially a high reflector was placed close to the end of the gain fiber, as depicted in Figure 14a. As the separation between the fiber and the reflector was varied, the laser was observed to make the transition from dual-mode operation to singlemode operation. Here, an output power of 3.4 mW was obtained for a pump power of 120 mW, and the linewidth, measured with a delayed self-heterodyne interferometer, was 60 kHz. A more effective way of ensuring single-mode operation is to introduce a π/2 phase shift into the grating. This was accomplished by locally heating the grating with a resistance wire (Figure 14b). The output power from the phase-shifted distributed-feedback laser was optimized by precise positioning of the heater. Once the optimum position was located, an output power of 3.0 mW was observed with an associated linewidth of 300 kHz. This work represented a major breakthrough in fiber laser technology, as only a single grating has to be written into the fiber to form the cavity. However, the short length of the grating limits the available gain length. Furthermore, in this first distributed-feedback fiber laser, the method used to induce the π/2 phase shift was cumbersome. A major


Figure 14

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Erbium-doped distributed-feedback fiber lasers. (Courtesy of D. N. Payne.)

technological advance in the fabrication of distributed Bragg reflectors has been the use of phase masks, which allow gratings up to 10-cm long to be written in doped fibers [101]. A clear advantage derived from such long gratings is that more pump light can be absorbed, thereby yielding greater gain and hence a higher output power. Furthermore, it is possible to induce a permanent phase shift in Bragg gratings, either by dithering the fiber while the grating is being written [102], or by exposing a short section of the grating to UV light after it has been written [47]. This postprocessing technique effectively alters the refractive index of the region exposed to the UV, thereby altering the optical path length at that point. By controlling the UV light exposure time the refractive index can be modified such that a specific wavelength within the reflectivity spectrum of the grating experiences the required phase shift. The first report of an all-fiber distributed-feedback fiber laser containing a permanent phase shift was made by Asseh et al. [8]. The Bragg grating was 10-cm long and was written into a length Yb 3⫹-doped fiber, and the phase shift was induced using the UV postprocessing technique. The grating was designed to have a reflectivity of 99% and a bandwidth of 0.05 nm at the Bragg wavelength of 1047 nm. When excited with light from a 974-nm laser diode, the laser had a launched pump power threshold of 230 µW and an output power of 7 mW for 18 mW of launched pump power. A fortuitous feature of this laser is that all the output power was coupled from one end of the laser. The reason for this is not fully understood, but was attributed to an asymmetry in the refractive index profile of the grating. Following this report, Er-doped distributed-feedback fiber lasers have been fabricated with permanent phase shifts [103,104]. Sejka et al. [103] formed a 25-mm-long Bragg reflector in a length of Er-doped fiber. Before inducing the phase shift, the laser oscillated on two modes, with a launched pump power threshold of 70 mW. After generat-

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ing the phase shift, it oscillated on a single mode with a threshold reduced to 10 mW. An interesting extension of this work was to incorporate the distributed-feedback structure in a power amplifier system [103]. The grating was 36-mm long and slightly chirped, so that the phase shift was distributed over the entire grating and there was no need for UV postprocessing. For a launched pump power of 50 mW this MOPA delivered an average output power of 5.4 mW and had a measured linewidth of 15 kHz. Loh and Laming [104] also constructed an Er-doped distributed-feedback fiber laser. The grating was written into the Er-doped fiber using a 10-cm–long phase mask, and the π/2 phase shift was introduced by translating the fiber during the writing process. Because of imperfections in the phase mask, the π/2 phase shift was not written precisely at the center of the grating, but was distributed over its center. Spectral analysis of the output from this laser with a scanning e´talon revealed that it oscillated on two longitudinal modes separated by 400 MHz. As only one frequency can satisfy the Bragg condition in this type of distributed-feedback laser, dual-mode operation was not expected. In general, rare earth doped fibers exhibit a weak linear birefringence. Analysis of the polarization properties of this laser showed that the two modes were indeed orthogonally polarized. Using a linear polarizer the two modes were separated and the linewidth of each was measured to be 13 kHz. Although the total output power from the laser remained constant, the intensity of each polarization mode fluctuated as a function of time, owing to random exchange of energy between the two polarization modes induced by external perturbations, such as temperature fluctuations. If these all-fiber distributed-feedback lasers are to find widespread use in communications and sensing applications, this random exchange of energy between polarization modes must be eliminated. Harutjunian et al. [105] showed that by introducing a slight twist in the fiber of the distributed-feedback laser, one of the polarization modes could be eliminated. The exact reason why twisting the cavity should eliminate one of the oscillating modes is not yet fully understood, but it has been attributed to an interplay between the elliptical birefringence induced by the twist and the distributed feedback introduced by the grating. A more straightforward way of forcing single-polarization operation in a distributedfeedback laser was developed by Storoy et al. [106], who used the UV postprocessing technique to create the necessary quarter-wave phase shift in the Bragg structure. They found that the intrinsic birefringence of the fiber causes the transmission dip associated with the phase shift to appear at different wavelengths for each of the orthogonal polarization states. Furthermore, by controlling the exposure time of the UV postprocessing light, one of the transmission dips could be tuned to the reflection edge of the Bragg reflector. Consequently, one of the polarization modes experiences a greater loss than the other and cannot reach threshold, and the laser oscillates on a single longitudinal mode. As with the distributed Bragg-reflector lasers described earlier in this section, the output power obtained from Er-doped distributed-feedback fiber lasers is low owing to either low, pump power absorption or the ion–ion interactions that occur in high-concentration Er-doped fibers. Attempts have been made to increase the output power of distributed-feedback fiber lasers by modifying the gain fiber. The most logical approach is to use an Er: Yb co-doped aluminosilicate fiber that has been photosensitized with hydrogen, such that the grating can be written into the fiber. This approach resulted in an increase in the output power of distributed-feedback fiber lasers to the 1-mW level [107]. This power level has been further increased by placing the distributed-feedback laser within an Yb 3⫹ laser cavity. Two 975-nm Bragg reflectors were written on either side of the codoped distributed-feedback fiber laser. This allowed the Yb 3⫹ ion to reach threshold and


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oscillate, which increased the energy transfer between the Yb 3⫹ ions and the Er 3⫹ ions. When the Yb 3⫹ ions were excited at their peak absorption of 924 nm, an output power of 3 mW was obtained at 1549 nm for 110 mW of launched pump power. Although photosensitizing the aluminophosphate Er :Yb-doped fiber with hydrogen enables Bragg structures to be written into the fiber core, the presence of hydrogen increases the intrinsic loss of the host fiber. Germanosilicate fibers are inherently photosensitive, so it is better to use this fiber host for the erbium dopant, but the Er :Yb co-doping approach cannot be used to achieve efficient operation because the energy transfer between the Yb ions and the Er ions is not efficient. A solution is pumping Er 3⫹ on its very strong 520-nm absorption band, which is made possible by the development of efficient frequency-doubled diode-pumped all–solid-state lasers emitting in the 520-nm region. Loh et al. [108] have obtained output powers of 16 mW directly from a distributed-feedback fiber laser pumped at 523 nm. Propagating green light through a germanosilicate fiber results in the formation of color centers that absorb at the pump wavelength. So even though pumping Er 3⫹ at close to 520 nm is efficient, the output power gradually degrades. Hence, the best approach to achieve high-output powers from Er-doped distributed-feedback fiber lasers is to co-dope the fiber. However, this approach requires that the fibers be photosensitized with hydrogen, which increases the fiber loss. Aluminosilicate fibers can be photosensitized by co-doping with Sn [109]. Sn co-doping is attractive compared with hydrogenization because Sn can be incorporated in the fiber core directly during fabrication without any additional processing. More importantly the inclusion of Sn in the fiber core does not increase the excess loss of the fiber at 1550 nm. Using an Sn :Er :Yb co-doped fiber, output powers as high as 10 mW for 100 mW of 980-nm pump power have been observed [110], although the laser oscillated on two orthogonally polarized modes. This power level is comparable with that observed from semiconductor-based distributed-feedback laser, making this fiberbased laser an attractive alternative as a source of narrowband light. The narrow-linewidth lasers described in the foregoing use either short cavities with narrowband reflectors or distributed-feedback structures to force single-longitudinal-mode operation. In these lasers the length of the gain fiber ranged from 1 to 10 cm. Bulk solidstate gain media, such as Nd :YAG or Er: Yb-phosphate glass, oscillate on a single longitudinal mode in a microchip cavity configuration [111]. Their cavity length is much shorter, of the order of 200 µm, so that their free spectral range is comparable with, or greater than, the gain bandwidth of the laser transition, which automatically ensures a single longitudinal mode. For bulk gain media it is straightforward to form the microchip cavity because the active medium is large enough for high-quality dielectric coatings to be deposited directly on its faces. On the other hand, for short lengths of fiber, preparing the ends so that high-quality dielectric coatings can be deposited on them is a nontrivial matter. However, fiber Fabry–Pe´rot devices with very small spacings (⬍100 µm) between the dielectric mirrors have been developed [33] and can be used as the cavity of a fiber-based micro-laser. Hsu et al. have developed such a laser [112]. A short length of Er :Yb-doped phosphate glass fiber (⬍50 µm) was placed inside the air gap of a fiber Fabry–Pe´rot filter such that it was in contact with one of the coated fiber ends. Single-frequency oscillation was observed for cavity lengths ranging from 100 to 500 µm. For lengths more than 200 µm, the single-frequency operation was unstable. With the 100-µm cavity, the 980-nm pump power threshold was 1.5 mW, the maximum output power was 19 µW, and the linewidth was ⬃500 kHz. This work was extended to allow continuous and discrete tuning of the wavelength [113]. Continuous tuning over 3.33 nm was observed for a single-cavity

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system. For a coupled-cavity laser, in which one end of the Er: Yb-doped fiber had a highreflectivity coating so that the gain medium acted as an intracavity e´talon, discrete tuning was observed over 10 nm. The overall performance characteristics of this type of laser are poor, with slope efficiencies of 0.07% and broad linewidths (typically 500 kHz). When combined with the difficulties encountered in constructing the laser, these properties make this type of lasers an unattractive source of single-mode radiation. Besides the short optical path length approaches outlined in the foregoing, there are many other ways of alleviating the problems associated with spatial hole burning in standing-wave laser geometries. One of them is to use the modified Sagnac cavity geometry illustrated in Figure 15. The two outputs from a 50% fused fiber coupler are spliced together to form a fiber Sagnac loop. Light launched into one of the coupler’s input ports propagates in both directions around the loop and recombines at the coupler. For a lossless 50% coupler and no loop birefringence, all the light is coupled back to the arm into which light was launched [114]. In other words, the loop acts as a mirror with a reflection coefficient of 100%; hence, its name of loop mirror. This Sagnac geometry can be modified by placing a length of gain fiber and an optical isolator inside the fiber loop (see Fig. 15). The isolator ensures that light travels only in one direction around the loop, and spatial hole burning is eliminated. If one of the input arms of the loop is spliced to a length of standard communication fiber containing a reflective device, for example, a bulk-optic mirror, a bulk diffraction grating, or a Bragg reflector, a linear cavity can be configured in which the gain medium is accessed by a traveling wave, which eliminates the problems associated with spatial hole burning. The remaining port of the coupler then acts as an output for the cavity. This modified loop mirror approach was first applied to Er-doped fibers by Cowle et al. [115] using a cavity similar to that depicted in Figure 15. A polished fiber Bragg reflector was used to complete the standing-wave portion of the cavity and define the laser wavelength. A narrow linewidth of 9.5 kHz was observed. The laser was optically excited at 980 nm, and for 40 mW of pump power the laser emitted an average power of 10 mW. It was pointed out that it should be possible to increase this output power by using a fused fiber coupler with a higher coupling ratio, although it would also increase the loss and, hence, the threshold. This work was extended by O’Cochlain and Mears [116], who used a bulk diffraction grating to tune the output from the laser over 43 nm (1525–1568 nm). Pan and Shi [117] used the same cavity geometry but replaced the bulk grating with an intracore Bragg reflector. The laser was tuned from 1518 to 1535 nm by compression tuning of the Bragg reflector. Guy et al. [118] configured a similar cavity using an intracore Bragg grating as

Figure 15

Diagram of a unidirectional Sagnac loop fiber laser.


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the wavelength-selective element, but found that the laser oscillated on several longitudinal modes. This problem was rectified by introducing a phase-shifted Bragg grating into the loop section of the cavity. Once the peak wavelength of the fiber Bragg reflector was tuned to the passband wavelength of the phase-shifted Bragg grating, single-mode operation was observed because the increased spectral filtering provided by the phase-shifted Bragg structure ensured that the other modes would not reach threshold. The linewidth was 2 kHz. Gloag et al. [119] also investigated the single-frequency characteristics of a modified Sagnac cavity laser. This laser showed a tendency to mode hop, but the rate of random mode hopping was greatly reduced by increasing spectral filtering in the loop. In contrast to Guy et al. [198], who included a filter in the cavity, Gloag et al. [119] butt-coupled a mirror to the free port of the cavity to reflect light back into the cavity (Fig. 16a), which resulted in a coupled-cavity geometry. The mismatch in path length between the two cavities provided a 1-GHz frequency modulation (see Fig. 16b). The depth of modulation was optimized by matching the reflectivity of the butt-coupled mirror with that of the Bragg reflector used to define the laser wavelength. A resolution-limited linewidth of 37 kHz was observed. Although the use of either bulk gratings or fiber Bragg reflectors to define the laser wavelength of modified Sagnac loop lasers has been effective, alternative tuning filters have been developed, such as the reflection Mach–Zehnder interferometer [120]. In this device the two arms of the Mach–Zehnder interferometer have different optical path lengths, which gives the interferometer wavelength-dependent transmission maxima. Thus, the device acts as a filter, which can be tuned by varying the path length difference. Chieng and Minasian [121] used a fiber-based reflection Mach–Zehnder interferometer as the end reflector in a modified Sagnac loop laser. Its path difference was 33.5 µm, yielding a wavelength separation of 40 nm between successive transmission maxima. The laser was tuned over 40 nm and exhibited single-longitudinal-mode operation, but as the laser was exposed to environmental fluctuations it exhibited random mode hops. The laser also exhibited a tendency to oscillate on two orthogonally polarized cavity modes. Although this modified loop mirror approach produces single-frequency operation in a linear cavity geometry, there is a power penalty to pay. The isolator, which is necessary for unidirectional propagation in the loop, adds spurious cavity loss. The origin of this loss is that the light that arrives at the coupler from the standing-wave section of the cavity (see Fig. 15) is split into two components that propagate around the loop in opposite directions, one of which is eliminated by the isolator (a 3-dB loss). The isolator is also somewhat lossy. This power penalty can be reduced by using a different coupling ratio, at the expense of a higher pump power threshold. This is because the threshold scales inversely with the product α(1 ⫺ α), where α is the power-coupling ratio of the coupler. Pan and Shi [117] overcame this power penalty by using an optical circulator instead of a 50% coupler. The circulator allows a traveling wave to be established in the gain medium without the need for an optical isolator. The output power obtained from the fiber laser formed with a circulator was 22 mW for 80 mW of pump power. In comparison, the authors observed an average power of 20 mW for a modified Sagnac loop laser utilizing a 50% coupler. Another way to prevent spatial hole burning is to ensure that circularly polarized light counterpropagates through the gain medium. This is known as the twisted mode technique, which has been successfully applied to bulk solid-state lasers [122]. In general, a standard rare earth doped fiber is weakly birefringence. By applying the correct strain

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(a)

(b)

Figure 16

(a) Cavity layout of a modified Sagnac loop mirror with additional spectral filtering; (b) the frequency modulation introduced on the laser output by this additional filtering.

to such a fiber, any desired state of polarization can be generated at a given point [51], in particular a circular polarization, and the twisted mode technique can be easily implemented. Chang et al. [123] applied this technique to a linear-cavity Er-doped fiber laser. The cavity comprised a polarization-sensitive fused fiber coupler, which defined the polarization state of the cavity, and a length of Er-doped fiber placed between two polarization controllers. The inset in Figure 17 shows the transmission spectrum of the polarization splitter for two orthogonal polarizations. The cavity reflectors were provided by either a butt-coupled high reflector, as shown in Figure 17, or an intracore Bragg reflector at one end and the 4% Fresnel reflection from the cleaved end of one of the arms of the coupler at the other end. With suitable adjustment of the polarization controllers, two counterprop-


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Figure 17 Schematic of a twisted-mode fiber laser cavity; the inset represents the wavelength transmission response of the polarization splitter. (Courtesy of J. R. Taylor.)

agating waves with the same circular polarization state were generated. As a result, they did not interfere, which eliminated spatial hole burning. This laser generated an output power of 0.6 mW with a measured linewidth of 10 kHz. One of the major problems associated with both the modified Sagnac loop lasers and the twisted-mode laser is that they are sensitive to environmental perturbations, which can induce random frequency changes and mode hopping. Horowitz et al. [124] developed a very simple approach to eliminate mode hopping. It relies on exploiting spatial hole burning in a saturable absorber. In stark contrast to an amplifier, as described in Section 5.2, the presence of a grating in a saturable absorber is beneficial. In an absorber, the light scattered by the grating is in phase with that transmitted by the grating, and constructive interference, rather than destructive interference, occurs [125]. This means that the loss induced by the absorber at the laser frequency is lower than that experienced by other frequencies, and single-longitudinal-mode operation is favored. Up to a wavelength of about 1570 nm the 4 I 13/2 → 4 I 15/2 transition of Er 3⫹ is a three-level transition. Consequently, the doped fiber can act either as either a saturable amplifier or a saturable absorber, depending on whether it is optically excited or not. Horowitz et al. [124] exploited this feature by configuring a simple linear cavity. The gain medium was placed between two wavelength division multiplexers (WDM). The first WDM was used to couple the 980nm pump light into the cavity, and the second one to remove it from the cavity. An additional length of Er-doped fiber was spliced after the second WDM. As the pump light was removed from the cavity by the second WDM this additional length of fiber acted as a saturable absorber. The cavity was completed by butt-coupling mirrors to each fiber end. To eliminate the effects of spatial hole burning, polarization controllers were used to generate circularly polarized fields in the gain medium. After optimization of the polarization state in the cavity, a resolution-limited linewidth of 20 kHz was observed. This approach has also been applied to the modified Sagnac geometry by Cheng et al., who reported a linewidth of 0.95 kHz [126]. In the Er-doped fiber lasers described in the foregoing, spatial hole burning was avoided by either ensuring that the counterpropagating fields in the linear cavity were orthogonal or using a modified Sagnac cavity in which a unidirectional traveling wave

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propagated through the gain medium. The reason why spatial hole burning in a laser is a problem is because the grating established in the gain medium reduces the coherence of the light circulating in the cavity and destabilizes the cavity. It has been pointed out that the stabilizing effect of spatial hole burning in an absorber can overcome this destabilizing effect, provided that the pump transition rates are greater than the signal transition rates [127]. Each of these rates is proportional to the corresponding cross-section [128]. Thus, if the gain medium exhibits a pump absorption cross section larger than the signal emission cross section, the destabilizing effect of spatial hole burning can be minimized. Paschotta et al. [127] demonstrated this principle in a Yb-doped standing-wave fiber laser. This rare earth is essentially a two-level system and its pump absorption cross-section in silica (2.6 ⫻ 10 ⫺20 cm 2 at 975 nm) exceeds the signal emission cross section (5.13 ⫻ 10 ⫺21 cm 2 at 1040 nm). A 6-m, highly doped fiber was used so that the pump was completely absorbed in the first few meters of fiber, and the rest of the fiber acted as a saturable absorber. A fiber Bragg reflector was used to define the laser wavelength. Single-longitudinal-mode operation was observed when the pump power was 1.5 times above the threshold power (70 mW). For power levels higher than this value the laser oscillated on several longitudinal modes. When the laser oscillated on a single-longitudinal-mode it could be tuned continuously over 5 GHz without mode hopping. One of the most important benefits of a fiber geometry is the high confinement of the pump and laser fields over long distances, which produces high optical gains at low pump powers. This feature enables comparatively lossy elements, such as e´talons and diffraction gratings, to be introduced in the cavity without a significant increase in the threshold or a reduction in the output power of the laser. For example, O’Sullivan et al. [49] showed that a line-narrowed output could be obtained from a linear cavity Er-doped fiber laser by placing an e´talon in the cavity. The e´talon was formed between the high reflector that completed the cavity and the cleaved end of the doped fiber. The mismatch in reflection coefficients between these two reflectors meant that the additional spectral filtering introduced by the e´talon was not significant enough to induce single-longitudinalmode operation. An e´talon, however, is not the ideal structure for frequency control in a linear cavity, as reflections between the optical surfaces of the e´talon and the cavity reflectors can result in the formation of subcavities that can prevent single-longitudinal-mode operation. Takushima et al. [129,130] have shown that it is possible to use an e´talon to control the frequency of a fiber laser, as long as backreflections from the e´talon are prevented from circulating in the cavity. This was achieved using a complicated combination of Faraday rotators and polarizers (Fig. 18a). Spatial hole burning was eliminated by placing the active fiber between two 45° Faraday rotators. As a result, two counterpropagating beams with the same circular polarization were generated in the gain medium. Spurious reflections from the e´talon were eliminated by placing the e´talon between two Faraday isolators aligned to pass light transmitted by the e´talon but to reject light reflected by the e´talon (see Fig. 18b). Coarse wavelength control over 40 nm was possible using a simple band-pass filter. A resolution-limited linewidth of 1 MHz was recorded. Various ways of eliminating the standing-wave pattern responsible for spatial hole burning have already been discussed in this section. The standing-wave pattern is due to the interference of two counter propagating beams oscillating at the same frequency. If the two beams oscillate at different frequencies, then the spatial modulation is eliminated from the gain medium. This technique has been successfully applied to Nd-doped fiber lasers by Sabert and Ulrich [131–135] who placed an AO modulator at each end of a linear cavity. When light propagates through an AO modulator operating at a frequency


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(a)

(b)

Figure 18 (a) Cavity configuration including reflection-free e´talon; (b) the component layout of the reflection-free e´talon. (Courtesy of Y. Takushima.)

ω m , the interaction between the acoustic wave and the light wave results in an optical frequency shift of ω m . The two modulators used by Sabert and Ulrich imposed an equal, but opposite frequency shift on the counterpropagating fields in the cavity, which meant that the fields had a frequency difference of 2ω m and did not interfere. The laser frequency was defined by a pair of intracavity e´talons and the linewidth produced by their laser was determined to be 12 kHz. A novel technique was developed to tune the laser just described above. Each one of the two e´talons exhibits a Fabry–Pe´rot transmission response. The laser will oscillate when at the frequency of minimum loss, which generally coincides with a transmission maximum of the e´talon. If the frequency changes, the transmission through the e´talon is reduced, the intracavity loss experienced by that mode increases to a point at which a neighboring mode may begin to oscillate instead. If this occurs, the laser frequency will change randomly. This frequency change can be eliminated if the oscillating mode and e´talon track any frequency variations. To do this an error signal must be derived from the laser. In bulk laser systems such as Ti:sapphire lasers, the error signal is normally produced by modulating the optical path length of the laser which imposes both a phase and amplitude modulation on the output of the laser. The amplitude-modulated signal is sensed using a phase-sensitive detector and a control signal can be derived to allow the e´talon to follow the frequency changes. For long-cavity fiber lasers this is not an attractive approach. Sabert [133] developed an alternative technique, whereby a small fraction of the intracavity light is reinjected into the cavity after passing twice through an additional AO modulator, which detunes the oscillating frequency. The e´talon imposes a loss on the

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frequency-detuned component, and by comparing the intensity ratio between the frequency-detuned component and the actual oscillating frequency, an error signal was derived. This signal was used to ensure that oscillating mode was locked to a transmission maximum of the e´talon. The laser frequency could thus be tuned by varying the relative phase between the modulators at the end of the cavity. Any variation in the phase alters the effective optical path length of the cavity and thus defines the oscillating frequency. The latter could be tuned continuously over 110 GHz, a range limited only by the intracavity e´talons. The effects of the standing-wave pattern on the gain medium can also be minimized if there is a relative motion between the two waves [134]. For a fiber laser it is easier to move the standing-wave pattern relative to the gain medium; for example, by periodically modulating the cavity length using phase modulators. There is, however, one proviso, which is that the relative motion must be fast enough that the population inversion cannot follow the variations in the standing-wave pattern. This condition is satisfied if the modulation frequency is greater than the laser relaxation oscillation frequency. If a phase modulator is placed at each end of a standing-wave cavity, and if they are driven with equal amplitudes, but opposite phases, the cavity optical path length remains the same, whereas the standing wave is swept through the gain medium. For a sinusoidal phase modulation of amplitude Θ the time-averaged optical power distribution 〈P(z)〉 in the gain medium takes the form 〈P(z)〉 ⫽

1 [1 ⫹ J 0 (2Θ)sin(2nkz)] 2

(19)

where J 0 is the lowest order Bessel function, n is the refractive index of the fiber, and k is the free space propagation constant. It is evident from Eq. (19) that when J 0 (2Θ) is equal to zero (2Θ ⫽ 2.4, 5.52, 8.65, etc.), 〈P(z)〉 is constant (i.e., the optical power is uniformly distributed in the cavity). Sabert and Ulrich [135] exploited this principle by placing two fiber-stretching elasto-optic phase modulators at each end of a linear cavity Nd-doped fiber laser. By driving the modulators with opposite phases at 100 kHz, they observed single-mode operation with a stochastic linewidth of 5 kHz. There was, however, one drawback with this method: the laser output spectrum exhibited sidebands spaced by the modulation frequency. These sidebands were attributed to phase modulation amplitudes, imposed by the modulators, which were not exactly identical, so that the oscillating frequency was slightly phase-shifted. This problem was overcome by a subsequent cavity design improvement, whereby one of the modulators was replaced by a length of undoped fiber, which acted as a buffer, allowing expansion and contraction of the standing-wave pattern. Hence, a spatially uniform-intensity distribution was realized in the gain medium, enabling single-longitudinal-mode operation [135]. In this section, several narrow-linewidth linear-cavity fiber lasers have been described. One of the major problems associated with a linear-cavity laser is spatial hole burning, which can preclude single-frequency operation. Various methods to overcome this effect have been discussed, ranging from simple short two-mirror cavities to complex long cavities containing many optical components. However, the simplest method to eliminate spatial hole burning is to ensure that the laser operates as a unidirectional ring, such that the gain medium is interrogated by a traveling wave. There have been many studies of such traveling-wave ring fiber lasers, which are described in the next section.


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5.6 SINGLE-FREQUENCY TRAVELING-WAVE FIBER LASERS Elimination of spatial hole burning was demonstrated with modified Sagnac cavities [115], but this approach is not ideal-owing to the excess loss introduced by the cavity design. A more attractive cavity configuration is the unidirectional ring resonator. In a bulk ring laser, unidirectional operation is obtained by making the loss experienced in one direction greater than that of the opposite direction. Typically, a differential loss of ⬃5% is sufficient to ensure unidirectional operation. In a fiber laser, however, such a level of loss does not necessarily eliminate bidirectional operation, and a more effective method of forcing unidirectional operation is required. The simplest one is to prevent one of the counterpropagating signals from making a complete round trip in the cavity by inserting an optical isolator into the cavity. The development of integrated fiber-optic isolators with a low insertion loss, typically 1 dB, and a high optical isolation, typically greater than 35 dB, have been used to force unidirectional operation from a range of rare earth doped fiber lasers [9,136]. Because of their important applications in optical communications, single-frequency Er-doped fiber lasers operating at about 1550 nm have been extensively studied in the unidirectional ring configuration. In fact, the first report of a unidirectional single-frequency fiber laser used an Er-doped fiber [9]. The ring cavity contained a length of Erdoped fiber and an integrated optical isolator (see Fig. 19). The laser was pumped with a 980-nm Ti:sapphire laser through a 980/1550-nm dichroic fused fiber coupler. The cavity length was 4 m, which gave a longitudinal-mode spacing of ⬃50 MHz. Singlelongitudinal-mode operation was realized by controlling the polarization of the intracavity

Figure 19

Diagram of a unidirectional erbium-doped fiber ring laser. (Courtesy of D. N. Payne.)

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field. A resolution-limited linewidth of 60 kHz was then observed at 1555 mm. A similar cavity design was used by Ohishi and Kanamori [136] to produce narrow-linewidth light from a Pr-doped fluoride fiber ring laser. Because of the lack of fluoride fiber-based optical components, such as fused fiber couplers and isolators, they had to use silica fiber-based optical elements. Because fluoride and silica fibers cannot be spliced together, the silica fiber-based components had to be glued to the fluoride fiber. The mismatch in numerical aperture between the two fibers meant that the joint introduced a significant loss. This loss was minimized by introducing a short length of high numerical aperture fiber between the cavity components and the fluoride fiber. Once the ring was constructed the laser oscillated at 1299.4 nm with a resolution-limited linewidth of less than 28 kHz. One of the most attractive and useful features of rare earth doped amorphous fibers is their broad gain bandwidth, which offers the potential for broad tunable operation. To exploit this feature a tuning element must be incorporated in the cavity. A variety of integrated fiber-optic tuning elements have been developed, ranging from Fabry–Pe´rot filters [33], integrated interference filters [32] and continuous-fiber overlay filters [35]. Iwatsuki et al. [10] extended the cavity design outlined by Morkel et al. [9] by replacing the gain fiber with a polarization-maintaining (PM) fiber and introducing a tunable bandpass filter in the cavity. The PM fiber eliminated potential problems associated with competition between polarization modes. Single-frequency operation was observed over the 1549 to 1552 nm window, with a linewidth of 1.4 kHz and an output power of 1.3 mW. Schmuck et al. [137] studied a cavity design similar to that of Iwatsuki et al. [10], but their gain medium was a weakly birefringent Er-doped fiber. The output coupling of the laser was optimized using a tunable coupler, and the maximum output power was obtained for an output coupling of 90%, in accordance with a numerical analysis of the gain dynamics of the laser [138]. However, for this level of output coupling the ratio of the spectral power density to amplified spontaneous emission (ASE) noise floor was only 30 dB. Reducing the output coupling to 10% increased this ratio to 50 dB. This is because reducing the output coupling reduces the cavity loss and thus the round-trip gain, thereby lowering the ASE power. Furthermore, decreasing the output coupling resulted in narrowing of the laser line. For an output coupling of 10% the linewidth was 20 kHz. This observation contradicts the theory developed by Schalow–Townes, as discussed earlier, and was attributed to the following: the laser is sensitive to environmental changes, which induce random phase fluctuations that broaden the linewidth. The laser is most susceptible to these perturbations when the output coupling and, hence the loss, is high, so that by reducing the intracavity loss the effect of these perturbations is minimized. Although the work of Iwatsuki et al. [10] demonstrated tunable single-frequency operation, their laser was not tunable over the full-gain profile of the erbium ion. Maeda et al. [139] used a different design of filter to tune a unidirectional ring laser over some 45 nm (1523–1568 nm). The filter was a Fabry–Pe´rot e´talon made of a 10-µm–thick nematic liquid crystal layer placed between two high-reflecting dielectric-coated glass plates. Its transmission bandwidth was 0.4 nm. The liquid crystal layer is birefringent. Application of an AC voltage to the film changes the refractive index of one of the birefringent axes, which alters the optical path length. If the amplitude of the applied AC voltage is varied, the filter can be wavelength-tuned. In addition to the filter, the cavity contained a 2-m–long Er-doped fiber, an optical isolator, and a linear polarizer, to ensure that the polarization of the light entering the filter was aligned with the voltage-sensitive optical axis of the filter. Even though this laser was tunable, the wavelength did not tune continuously as the drive voltage was changed, but switched wavelengths at 1-nm intervals. This


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was attributed to the fact that the isolator was birefringent. The combination of the isolator and intracavity polarizer acted as a birefringent filter with transmission maxima separated by 1 nm. A self-heterodyne measurement revealed a linewidth under 100 kHz. Wysocki et al. [61] showed that it was possible to tune a standing-wave Er-doped fiber laser with an intracavity AO modulator. Smith et al. [11] extended this idea to a unidirectional ring configuration in which an integrated optic acoustically tunable filter was used as the wavelength selective element. The laser cavity was similar to that described by Maeda et al. [139] except that the liquid crystal filter was replaced by the acoustic filter. The latter had a transmission bandwidth of 1.5 nm and an insertion loss of 6 dB. When an rf signal was applied to it, the observed tuning factor was 8.8 nm/MHz. By varying the modulator drive frequency from 170.9 to 172 MHz, the laser wavelength was tuned from 1560 nm to 1548 nm. The linewidth was determined to be 10 kHz. The laser showed weak relaxation oscillations that peaked at a frequency of 30 kHz. As with the laser developed by Maeda et al. [139], continuous wavelength tuning was possible only after the additional birefringence induced by the optical isolator had been compensated. Tuning of air-space Fabry–Pe´rot fiber filters can also be accomplished simply by varying the separation between the fiber ends. These filters are attractive because they exhibit minimal polarization dependence and their finesse is determined primarily by the reflectivities of the dielectric coatings applied to the fiber ends. Schmuck et al. [140] incorporated a Fabry–Pe´rot fiber filter with a finesse of 60 and a free spectral range of 58 nm in a unidirectional Er-doped ring fiber laser, and they were able to tune the output from 1528 to 1572 nm. Narrow-linewidth emission (⬃9.5 kHz) was observed over this entire tuning range. This laser had a tendency to operate in a multimode fashion, which limits its usefulness. As described in Section 5.2, multimode operation can be inhibited by increasing the spectral selection in the cavity. It can be achieved by concatenating two Fabry–Pe´rot fiber filters with different free spectral ranges. This approach was applied to Er-doped fiber lasers [141,142]. Park et al. [141] configured a unidirectional ring fiber laser using two fiber Fabry–Pe´rot filters (Fig. 20a). The first filter was broadband: it had a free spectral range of 4 THz and a transmission bandwidth of 26.1 GHz; it was used for coarse electrical tuning of the laser. The second filter had a 100-GHz free spectral range and a bandwidth of 1.39 GHz. An optical isolator was placed between the two filters to prevent intere´talon effects. As shown in Figure 20b, the laser was tunable over 30 nm (1530–1560 nm). Its average output power of ⬃1 mW. Inclusion of the 100-GHz filter in the cavity completely suppressed the multimode operation that affected the laser developed by Schmuck et al. [140]. In addition, the laser frequency was observed to continuously change, in response to environmentally induced fluctuations in the cavity length. If this frequency change was such that the loss imposed by the spectral filtering on the oscillating mode was greater than that of a neighboring mode, then the laser would undergo a mode hop. The laser linewidth was measured using a recirculating, delayed, self-heterodyne interferometer to be 1.4 kHz with a frequency jitter of 2.4 kHz owing to thermal phase noise. The noise characteristics of the laser system were also quantified [16,17]: The stochastic noise imposed on the laser by spontaneous emission could be reduced to the detector shot-noise by optimizing both the output coupling of the laser and the sequence of the intracavity filters. The gain medium not only amplifies the intracavity field, but it also adds ASE to all the cavity modes. It is the mixing of the oscillating mode with these ASE modes that results in the excess intensity noise at the detector. If the amount of ASE power coupled to the cavity modes is reduced, the dominant source of noise will be the

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(a)

(b)

Figure 20

(a) Erbium-doped unidirectional ring resonator containing two fiber Fabry–Pe´rot filters with different free spectral ranges: FFP, fiber Fabry–Pe´rot; NB, narrowband; BB, broadband; PC, polarization controller; WDM, wavelength-division multiplexer; Er, erbium-doped fiber; (b) tuning range of the fiber laser. (Courtesy of K. Vahala.)

detector itself. The simplest way to reduce the number of modes containing ASE at the detector is to place the narrowband filter between the gain medium and the output coupler. Sanders et al. [17] measured the noise characteristics of their tandem Fabry–Pe´rot laser with either the broadband filter or the narrowband filter before the output coupler, as depicted in the two configurations of Figure 21a. As expected, there was a significant reduction in the excess intensity noise with the narrowband filter placed before the output


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coupler (see Fig. 21b). As was observed by Schmuck et al. [138], the ASE noise was further reduced by varying the output coupling of the laser. In fact, with a 10% output coupling on the laser, Sanders et al. [17] found that the intensity noise reached the shotnoise limit, as shown in Figure 21b. This feature makes the fiber laser an ideal source of light for high-resolution ultrasensitive spectroscopy. Although this laser was shot-noise limited, its overall frequency stability was limited by random longitudinal mode hops induced by environmental changes in the cavity length. As discussed in Section 5.2, this can be prevented if the oscillating mode experiences the same loss at all frequencies. Park et al. [143] used a variation of the Pound–Drever method [144] to satisfy this constraint. The laser frequency was stabilized to both a transmission maximum of one of the intracavity mode-selecting Fabry–Pe´rot fiber filters and to an external Fabry–Pe´rot fiber cavity. In the Pound–Drever scheme, a light field is locked to an optical reference source (e.g., a cavity), by phase modulating the field at a frequency ω. This results in the generation of optical sidebands. The phase-modulated field is then incident on the frequency reference, in this case a cavity, and the reflected signal is monitored using a phase-sensitive detection. As the optical frequency drifts in and out of resonance with the reference frequency, a dispersive error signal is generated by the phasesensitive detector, which is used to adjust either the reference frequency or the frequency of the light source, thereby keeping the two in resonance. In the case of Park et al. [143] the optical sidebands necessary for the locking process were generated using an intracavity integrated phase modulator (Fig. 22). The error signal derived from the phase-sensitive detector was used to control either the mode-selecting Fabry–Pe´rot or the temperature of a length of metal-coated fiber, so that the oscillating frequency was in resonance with a mode of the external cavity. Stable, mode hop-free operation was observed for periods in excess of several hours. A similar approach was adopted by Sabert [145], who stabilized an Nd-doped ring fiber laser containing two intracavity e´talons. In this system, however, the error signal was derived by modulating the optical path lengths of the e´talons. If a sinusoidal modulation at a frequency f dith is applied to the e´talon, then the center frequency f c (t) of the e´talon varies as f c (t) ⫽ ⬍ f c ⬎ ⫹ δf d sin(2πf dith t)

(20)

where ⬍ f c ⬎ is the center frequency of the e´talon in the absence of an applied dither signal, and δf d is the amplitude of the driving field. If the laser oscillates at frequency f 0 , which is resonant with ⬍ f c ⬎, the periodic modulation of the center frequency f c (t) introduces a time-varying loss in the cavity which, in turn, produces an intensity-modulated output. Phase-sensitive detection of this output generates an error signal that can be used to lock the oscillating frequency and the e´talon center frequency together. By dithering each e´talon, Sabert [145] obtained mode hop-free operation with a linewidth equal to or under 10 kHz. There is one drawback to this technique: the periodic detuning of the e´talon introduces not only an amplitude modulation, but also a phase delay, which results in a frequency-modulated laser output. If the peak-to-peak detuning of the e´talon, 2δf d , is small compared with the transmission bandwidth ∆ν e of the e´talon, the phase shift δF imposed on the cavity by the modulation can be approximated by δF ⫽

2δf d ∆ν e

(21)

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(a)

Figure 21 (a) The layout of a unidirectional ring cavity showing two arrangements of the spectral filters: FFP, fiber Fabry–Pe´rot; NB, narrowband; BB, broadband; PC, polarization controller; WDM, wavelength-division multiplexer; Pol, polarizer; (b) the noise characteristics of the laser for different output couplings and locations of the filters in the cavity. (Courtesy of K. Vahala.)

Sabert [145] showed that this modulation could be eliminated if the phase shifts imposed by the e´talons have equal magnitudes, but opposite signs, which is achieved in practice by carefully selecting the amplitudes of the drive signals applied to the e´talons. In fact, Sabert was able to demonstrate that if the two e´talons were driven in phase the laser output had a peak-to-peak frequency modulation of 1.6 MHz, whereas if the two dither voltages were balanced and in opposite phase this modulation was reduced to less than 30 kHz. The use of two Fabry–Pe´rot fiber filters to ensure single-frequency mode hop-free operation of an Er-doped fiber laser has been very successful, and it produced shot-noiselimited light with a narrow linewidth [17], but there are several penalties to pay with this approach. First, the Fabry–Pe´rot fiber filter exhibits an insertion loss typically in the range of 2–3 dB, and the isolator required between the two Fabry–Pe´rot filters not only adds


(b)

Figure 21

Continued

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Figure 22

Schematic of the experimental arrangement used to lock the oscillating frequency of a unidirectional ring fiber laser to an external reference e´talon: FFP, fiber Fabry–Pe´rot; NB, narrowband; BB, broadband; PC, polarization controller; WDM, wavelength-division multiplexer; Er, erbium-doped fiber; ISO, isolator; MOD, phase modulator; MCF, metal-clad fiber; MS, mode selecting filter. (Courtesy of K. Vahala.)

to the loss, but also to the cost. Furthermore, the fiber Fabry–Pe´rots are formed by breaking, coating, and realigning the fiber ends, which requires time and care in practice. The construction of the fiber laser would be simplified if the additional spectral filtering could be carried out without the light leaving the fiber. Indeed, this can be accomplished with suitable combinations of 2 ⫻ 2 and 3 ⫻ 3 fused fiber couplers [146–149]. One approach is to configure a dual-coupler fiber ring with two fused fiber couplers (see Fig. 3c). This ring has a frequency response similar to that of a Fabry–Pe´rot e´talon [150]. If a length of doped fiber is spliced to one of the input ports of one of the couplers and to one of the output ports of the other coupler, a dual-loop resonator is formed, as illustrated in Figure 23a. This resonator has the spectral characteristics shown in Figure 23b. From this figure it appears that the longitudinal-mode spacing of the cavity is modulated by the transmission response of the dual-coupler fiber ring. Zhang et al. [151] showed that a longitudinal mode of the cavity oscillates if the following phase condition is satisfied: βL ⫺ tan ⫺1

冢

冣

R sin βl ⫽ 2mπ l ⫹ R cos βl

(m ⫽ 1,2..)

(22a)


289

(a)

(b)

(c)

Figure 23

(a) Unidirectional fiber ring laser containing a dual coupler fiber ring for longitudinal mode control; (b) the computed frequency response of the combined resonators; (c) a homodyne measurement of the oscillating linewidth using a dual-coupler loop containing a 100-m length of fiber.

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where R ⫽ √k 1 k 2 (1 ⫺ δ 1) (1 ⫺ δ 2) exp(⫺αl )

(22b)

and β is the laser mode propagation constant, L the length of the main cavity, l the length of the subcavity, k i the intensity coupling ratio, δ i the excess intensity loss of the coupler, and α the intrinsic intensity loss of the fiber. This offers the possibility of longitudinal mode control. When the optical path length of the dual-coupler fiber ring is modulated, the cavity mode is taken out of resonance with the dual-coupler fiber ring mode. As a result, a time-varying loss is imposed on the laser, which results in an amplitude modulation of the output and the appearance of a modulated signal at port O of Figure 23a. If either one of these two modulated signals is monitored using a phase-sensitive detector, an error signal can be derived, which can then be used to prevent mode hopping. This approach was adopted by Zhang et al. [146] and Gloag et al. [147], who both used a dualcoupler fiber ring to stabilize Er-doped fiber lasers. In the case of Zhang et al. [146], the dual-coupler fiber ring was formed from two couplers with intensity coupling coefficients of 97% and 98%, respectively, and the ring had an optical path length of 10 cm. The resulting loop had a free spectral range of 2 GHz and a finesse of 100. Without the control signal applied to the laser cavity, the laser linewidth was 5 kHz but the laser had a tendency to mode hop every 30 s. Application of a 500-Hz sinusoidal voltage to the cavity resulted in mode hop-free operation, with a linewidth broadened to 80 kHz owing to the frequency modulation induced by the 500-Hz signal. This frequency modulation could be eliminated by modulating both the cavity optical path length and the dual-coupler fiber ring [152]. Under these conditions, the frequency shift δf imposed by the modulation of both optical path lengths is given by δf (sδl ⫹ δL ⫽⫺ f L ⫹ sl

(23a)

where R cos(βl ) ⫹ R 2 s⫽⫺ 1 ⫹ 2R cos(βl ) ⫹ R 2

(23b)

In these equations, δl and δL are the amplitude of the modulation signals applied to each cavity, while l and L are the path lengths of the dual-coupler fiber loop and of the cavity, respectively. Thus the frequency modulation can be eliminated if the drive signals applied to the two cavities have opposite phases and their amplitudes satisfy sδl ⫽ ⫺δL. In fact once the frequency modulation was compensated the linewidth was determined to be 5 kHz again. The dual-coupler fiber ring configured by Zhang et al. [146] used high-intensity coupling ratio couplers. Hence the finesse and throughput of the loop were sensitive to the excess loss in the loop. Gloag et al. [147] also used a dual-coupler fiber ring to prevent longitudinal-mode hopping in a single-frequency Er-doped fiber laser containing an overlay filter, but in this case the fiber loop was made from two fused fiber couplers with coupling coefficient of 50%. Although this reduced the finesse of the dual-coupler fiber ring, the system was less sensitive to excess loss within this ring. Mode hops were eliminated by modulating the optical path length of the filter but at a frequency of 8 kHz. The oscillating frequency was also stabilized, with a side-of-fringe technique [144], to a confo-


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cal e´talon with a free spectral range of 300 MHz and a finesse of 600. The resulting laser generated narrow-linewidth light with a resolution-limited linewidth of 68 kHz (see Fig. 23c) and an RMS frequency jitter of 25 kHz. A significant amount of this jitter was attributed to the side-of-fringe locking technique. Modulating the optical path length of the dual-coupler fiber ring results in an amplitude modulation of the laser output. When this modulated signal is coupled into the confocal e´talon, the error signal follows the modulation and converts the amplitude modulation into a frequency modulation. By using a simple balanced detection scheme [147], the RMS frequency jitter could be reduced to 5 kHz. Forming the dual-coupler fiber ring is a complex process that requires two additional couplers in the cavity and adds excess loss to the cavity. Also, a length of fiber is common to the cavity and the dual-coupler fiber ring. Any change in this length affects the frequency response of both the cavity and the dual-coupler fiber ring to different extents. An alternative approach to longitudinal-mode control [148,149] consisted in introducing a 3 ⫻ 3 fused fiber coupler in a unidirectional ring laser cavity (Fig. 24a). Two separate fiber loops were formed by splicing two of the output ports to their respective input ports. The main cavity contained the cavity elements, and the other loop formed the subcavity that provided the additional spectral filtering. The optical path length of the subcavity was much shorter than that of the main cavity. Numerical analysis of this composite resonator predicted that when the two cavities are in resonance, the signal coupled out of the monitor port of the 3 ⫻ 3 coupler is minimum (see Fig. 24b). A minimum arises when the fields coupled to the monitor port from the two cavities have equal amplitudes, but opposite phases. When the two cavities are off resonance, the field coupled to the monitor port increases, which provides a frequency-sensitive signal and allows the derivation of an error signal as previously described. With the laser frequency stabilized to a 300-MHz free-spectral-range confocal e´talon, a linewidth of 14 kHz was recorded [149]. The 3 ⫻ 3 fused fiber coupler approach is relatively simple to implement, but it suffers from the frequency-modulation problems that plagued the lasers developed by Sabert [145], Park et al. [143], and Zhang et al. [146]. This problem could have been overcome by applying a corrective cavity length modulation to the main cavity, but this is a complex approach, and it requires precise control of the amplitude of the drive signals. A more attractive method would be to derive the error signal in a passive manner, whereby a change in the intracavity flux provides the necessary information. It was possible to prevent mode hops in a unidirectional fiber laser by sensing changes in the polarization state of the light coupled from the cavity [153,154]. This technique was an extension of the polarization spectroscopy frequency-stabilization scheme [155]. The cavity configuration used in this work was similar to that shown in Figure 24a. The important elements in the cavity were first the overlay filter, which not only defined the laser wavelength but also the polarization state of the laser, and second the 3 ⫻ 3 fiber coupler, which was inserted in the cavity as described in the foregoing. The fiber forming the cavity is weakly birefringent. As a consequence, the light circulating in the cavity takes an arbitrary polarization state, but at any given point the polarization state must be repeated after one round trip through the cavity. When light couples from the main cavity to the subcavity, the amount of light that leaves the cavity at the monitor port is determined by the birefringence of the subcavity. If the laser frequency changes, not only the amount of light rejected from the cavity changes, but also its polarization state changes. Sensing these changes in polarization state with a polarization analyzer containing a quarter-wave plate and a linear polarizer allows the derivation of a dispersive type of error signal (Fig. 25). Implementing

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(a)

(b)

Figure 24 (a) Unidirectional ring laser containing a 3 ⫻ 3 fused fiber coupler in which the light propagates in a clockwise direction around the cavity: (I, isolator; F, filter; LS, length stabilizer; OC, output coupler; PC, polarization controller; PD, pump diode; WDM, wavelength-division multiplexer; EDF, erbium-doped fiber; (b) the computed output from the monitor port as a function of subcavity phase change for a 3 ⫻ 3 coupler with an inverse coupling length of π/3 (dotted curve), π/9 (solid curve), and 2π/9 (dashed curve).


293

Figure 25

Computed signals obtained from the monitor port (dashed curve) and dispersive error signal (solid curve) obtained from the polarization-stabilized fiber laser.

this approach enabled the authors to produce light with a linewidth of 14 kHz and a measured RMS frequency jitter, when the laser frequency was locked to a fringe of a 300–MHz free–spectral-range confocal e´talon, of 2 kHz. The subcavity approach using either the dual-coupler fiber ring or the 3 ⫻ 3 fiber coupler is a suitable method for longitudinal-mode control, although the subcavity adds complexity to the cavity. The all-fiber equivalent of a Fabry–Pe´rot fiber e´talons can be formed using fiber Bragg reflectors [156,157]. A pair of chirped Bragg reflectors, with reflection bandwidths of 10 nm, formed the e´talon. With the polarization–spectroscopylocking technique, mode hop-free, stable, and narrow-linewidth operation from the fiber laser was obtained [157]. The polarization spectroscopy-stabilization scheme [154] relies on sensing changes in the polarization state of the light circulating in the cavity. If the cavity is made from weakly birefringent fiber, unless special care is taken, the fiber laser can oscillate on two orthogonally polarized cavity modes, resulting in two discrete frequency components. This is normally avoided by including a polarization-sensitive device in the cavity. The intrinsic birefringence of a fiber laser cavity can be exploited to meet this goal [158]. A unidirectional ring was configured that did not contain a linear polarizer, so that the laser oscillated on two orthogonally polarized modes. The gain medium, an Er-doped fiber, was coiled onto a small-radius drum to induce an additional birefringence that can be utilized to generate circularly polarized fields in the cavity. The direction of rotation of the two circularly polarized fields is flipped using a half-wave plate, which fixes the frequency separation between the two orthogonally polarized modes, under ideal conditions, to exactly half the longitudinal-mode spacing of the cavity. By introducing frequency-selective elements into the cavity, these two polarization modes experience a different loss and only one of them oscillates. A linewidth of 5 kHz was observed with this technique.

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The unidirectional ring lasers described in the foregoing all contain an integrated optic isolator to ensure unidirectional light propagation in the cavity. Even though this is a very effective way of eliminating spatial hole burning, optical isolators do exhibit an insertion loss ranging from 0.5 to 2.0 dB, which lowers the laser output power. A bidirectional ring laser can be made to operate in a unidirectional fashion if the light from one direction is coupled into the other direction. The reinjected signal serves as an injected seed to the field circulating in the opposite direction, which results in a stronger oscillation in that direction. With suitable design of the ring laser, nonreciprocal operation is possible without the inclusion of an optical isolator [159]. In this study, an Er-doped fiber ring cavity was configured with two 3-dB fused fiber couplers. The output from one coupler was spliced to the input of the other coupler so that light propagating counterclockwise around the loop was injected into the clockwise direction. With this approach the ratio of clockwise to counterclockwise intensities was 150: 1. Although single-mode operation was observed, the laser showed a strong tendency to mode hop. The authors also showed that it was possible to achieve tunable single-frequency operation from a ring laser containing only one 3-dB coupler. The output signal from one port of the coupler was backreflected into the cavity of a diffraction grating operating in the Littrow regimen. By varying the angle of incidence on the grating the laser wavelength could be tuned from 1556 to 1562 nm. An alternative approach to realizing a unidirectional ring laser without an isolator was developed by Sabert and Ulrich [160], who used two AO modulators and an intracavity filter to introduce the nonreciprocal loss. The two AO modulators, separated by a distance La , are driven by a common source operating at a frequency F. One modulator imposes a frequency upshift, and the other one a frequency downshift, on the light circulating in the cavity. In the region between the two modulators, light propagating in one direction has an optical frequency f ⫹ F, and light propagating in the other direction a frequency f ⫺ F, where f is the laser frequency. Consequently, a phase delay ∆φ is introduced between the two circulating fields: ∆φ ⫽ 4πFT g

(25)

where Tg ⫽

Ng La c

(26)

and N g is the group-velocity refractive index. If the drive signal to one of the modulators is phase delayed by ∆φ, the initial phase delay can be compensated, allowing continuous tuning of the laser frequency. The tuning element inserted between the two modulators ensures unidirectional operation of the laser as follows: The center frequency f c of the filter is detuned from the laser frequency f, and because the counterpropagating fields passing through the filter have different frequencies, one direction experiences a greater loss. Thus, by varying the filter center frequency it is possible to switch the direction of oscillation. If this center frequency is tuned to the laser frequency f, both modes see the same loss and bidirectional operation occurs. Sabert and Ulrich used this technique to obtain a narrow-linewidth Nd-doped fiber ring laser. The two modulators were driven at 80 MHz. The frequency was defined by including two Fabry–Pe´rot filters in the cavity, one with a free spectral range of 41.5 GHz


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and a finesse of 35, the other with a free spectral range of 3 THz. Unidirectional operation was observed from the laser with a linewidth less than 10 kHz. The laser frequency was tuned over 300 MHz without mode hopping by applying the necessary phase correction to one of the modulators and tracking the change in frequency with the filters. When the center frequency of the filters was varied, the direction of oscillation was observed to change, with a switching time of 10 ms. During the direction switch, the laser would oscillate simultaneously in both directions, and by applying a suitable feedback to the cavity that maintained the power levels in each direction, stable dual-frequency operation was possible. The two counterpropagating fields were well correlated, with a measured rf beat note of 80 Hz. With the correct feedback applied to laser, dual-frequency operation could be maintained over a tuning range of 50 GHz, limited only by the design of one of the filters. A simpler cavity design was provided by Kiyan et al. [161], who showed that it was possible to achieve dual-frequency operation of a bidirectional Er-doped ring laser by including a Faraday rotator in the cavity, so that the counterpropagating fields excite different eigen-polarization states of the cavity. The frequency difference between the two fields was adjusted between 100 kHz and 26 MHz by varying the settings of intracavity polarization controllers. Again the two counterpropagating fields were well correlated, as shown by the recorded beat note of 100 Hz. In this section various methods to achieve stable single-frequency operation from rare earth doped ring fiber lasers have been reviewed, ranging from simple structures containing a single tuning element, to highly complex cavities containing combinations of 2 ⫻ 2 or 3 ⫻ 3 fused fiber couplers. These lasers generate narrow-linewidth light, and usually, they are widely tunable, opening up many avenues for further research. 5.7 MULTIPLE-WAVELENGTH OPERATION OF RARE EARTH DOPED FIBER LASERS Multiple-frequency operation of rare earth doped fiber lasers is expected to have diverse applications, ranging from distributed sensing networks to light sources for wavelength– division-multiplexed communications systems, as described in Section 5.8. In the previous section, dual-frequency operation of narrow-linewidth ring fiber lasers was outlined. In one of the lasers described, this was achieved by precise control of the spectral filtering in the cavity, and the two frequencies were separated by 20 MHz [161]. For a true multiple wavelength laser, simultaneous operation of many wavelengths with a wavelength spacing of several nanometers would be desirable. To satisfy this requirement, the effects of crosssaturation in a homogeneously broadened gain medium must be overcome, whereby one wavelength depletes the gain available for another wavelength. The wavelength range over which cross-saturation plays a significant role is determined by the homogeneous linewidth of the transition. For a rare earth doped fiber at room temperature, it is typically tens of nanometers. The homogeneous linewidth is influenced by temperature; cooling an Er-doped fiber to 77 K reduces the homogeneous linewidth to 0.5–1.0 nm [19]. One of the first demonstrations of multiple-wavelength operation in a fiber laser was made by Park et al. [162], who observed six discrete wavelengths from an Er-doped fiber laser configured in either a standing-wave or a traveling-wave geometry. Wavelength selection was achieved with a fiber-pigtailed, eight-channel grating, wavelength-division multiplexer. The channels were separated by 4.8 nm and had a pass-bandwidth of 0.8 nm. The linear cavity was formed by fusion splicing the wavelength-division multiplexer to

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the Er-doped fiber, then by fusion splicing fiber loop mirrors to the free ends of the gain fiber and the wavelength-division multiplexer. Although six different wavelengths were observed, a severe temporal modulation on a millisecond time scale was present, attributed to spatial hole burning. This problem was eliminated by using two wavelength-division multiplexers and forming a unidirectional ring laser. Again six independent wavelengths were observed, and the power fluctuations that affected the linear cavity were absent. A total output power of 1 mW was observed, and the average power associated with each wavelength was in the range of 50–150 µW. A similar approach was developed by Okamura and Iwatsuki [163]. In a unidirectional ring resonator they observed multiple wavelength operation, with each oscillating wavelength having a resolution-limited linewidth of 1 MHz. An alternative approach to obtain multiple wavelength operation from an Er-doped fiber laser was developed by Dawson et al. [164]. They used a unidirectional ring cavity containing a Mach–Zehnder interferometer made from two 3-dB fused-fiber couplers. Each arm of the Mach–Zehnder interferometer contained a fiber Fabry–Pe´rot filter. Dualwavelength operation was achieved by tuning the filters to the desired wavelength. The observed tuning range was 1525–1570 nm, with a resolution-limited linewidth of 1 MHz. Both oscillating wavelengths experienced the same gain. To prevent cross-saturation effects required balancing the net gain and loss experienced by each wavelength. This problem was overcome by placing an amplifier in each arm of the Mach–Zehnder interferometer so that each wavelength, accessed a different gain medium. Although this technique produced narrow-linewidth dual-wavelength operation, when the tuning elements had similar transmission wavelengths the laser would oscillate on a single wavelength, rather than on two wavelengths. This effect was attributed to an interplay between the Mach–Zehnder interferometer and the Fabry–Pe´rot filters. When the two transmission maxima overlap, the Mach–Zehnder imposes an additional spectral modulation on the cavity, which preferentially selects one frequency. If the filter transmission profiles are not coincident, the Mach–Zehnder does not come into play because the different wavelengths are not transmitted by each arm of the Mach–Zehnder. Yamashita and Hotate [165] used a reflection-free Fabry–Pe´rot e´talon [129] to obtain multiple-longitudinal-mode operation from a linear cavity Er-doped fiber laser. With the gain medium held at room temperature, the laser was observed to oscillate on three discrete wavelengths with 0.8-nm–wavelength separations, corresponding to the transmission maxima of the etalon. Subsequent cooling of the fiber to 77 K increased the number of oscillating wavelengths to 17. Spectral analysis showed that at each wavelength the laser oscillated on either two or three longitudinal modes of the cavity. The cavity designs outlined in the foregoing require wavelength-division multiplexers or several filters to achieve a narrow linewidth. A single filter with a comb-like transmission response would simplify the laser and would be ideal for multiple-wavelength operation. Such filters can be generated in a variety ways. One of the simplest approaches is to exploit the intrinsic birefringence of the optical fiber. A comb-like filter was produced [166] by introducing a length of PM fiber into a linear Nd-doped fiber laser cavity, (Fig. 26a). The PM fiber acts similar to a birefringent filter with transmission maxima separated by ∆λ ⫽

λ2 2| n s ⫺ n f |L hibi

(26)


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(b)

Figure 26

(a) Linear neodymium-doped fiber laser cavity containing a length of high-birefringence fiber as a filter; (b) the comb-like structure of the laser output, measured for two different lengths of PM fiber. (Courtesy of M. Tur.)

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where λ is the oscillating wavelength, n s,f the refractive index of the slow and fast birefringence axes of the PM fiber, respectively, and L hibi the PM fiber length. In the laser constructed by Ghera et al. [166] four different wavelengths (see Fig. 26b) were observed to oscillate simultaneously with a PM fiber length of 1.2 m, and eight different wavelengths with a length of 2 m. This technique was extended subsequently to an Er-doped fiber laser by Park and Wysocki [167], who configured a unidirectional ring containing a length of PM fiber, a polarization controller, and a linear polarizer. The doped fiber was placed in liquid nitrogen to minimize the effects of cross-saturation. When the polarization controllers were optimized, this combination of components acted as a Lyot filter, with transmission maxima separated by 1.1 nm. Twenty-four wavelengths were observed to oscillate, each one with a measured linewidth of 0.15 nm. The reason for so many wavelengths was attributed to polarization hole burning, which further reduced the effects of cross-saturation. To cool the doped fiber, the latter was wrapped on a tight mandrel, which induced a significant strain birefringence, such that different wavelengths propagated through the gain fiber in different polarization states. Each polarization state saturated the gain independently from other polarization states. The influence of polarization hole burning was verified by placing the fiber Lyot filter in a traveling-wave cavity built around an optical circulator. The gain medium was spliced to the common port of the circulator and terminated with a Faraday rotating mirror that reflected the light back through the gain fiber in an orthogonally polarized state, thereby eliminating polarization hole burning. As expected, this laser yielded fewer spectral peaks. The birefringence-based filters used by Ghera et al. [166] and Park and Wysocki [167] rely on the coupling of light between the fast and slow axes of the intracavity PM fiber to provide spectral filtering. The latter can also be achieved if a length of multiple transverse-mode fiber is introduced in the cavity of a single-transverse-mode fiber laser. If the cores of the single-mode and multimode fiber are misaligned slightly, the LP 11 mode family can be excited so that it propagates together with the LP 01 mode. Spatial beating between these modes produces the optical filter [168]. The wavelength spacing of the transmission maxima of this filter is determined by the differential propagation coefficient between the LP 01 and LP 11 modes and the length of the multimode fiber, whereas the filter modulation depth is governed by the lateral offset between the two fibers. It was possible to force multiple-wavelength operation in both Nd-doped and Er-doped fiber ring lasers by adding a short length of multimode fiber in their cavities [169]. In the Er-doped laser, four wavelengths were observed to oscillate, separated by 1.5 nm, whereas the Nd-doped fiber supported six wavelengths separated by 2.5 nm. The variation in the number of oscillating wavelengths was ascribed to the large inhomogeneity associated with the Nddoped fiber, which resulted in less gain competition between the wavelengths. The work of Poustie et al. [169] showed that spatial beating between LP 01 and LP 11 modes can produce a multiple wavelength filter. However, the effectiveness of this filter was limited, in the Er-doped fiber laser, by the homogeneous broadening of the gain medium. This effect can be minimized by cooling the gain fiber, thereby reducing the homogeneous linewidth of the transition. An alternative way of realizing an inhomogeneous gain distribution in the active fiber is to use a doped twin-core fiber. In a twin-core fiber light periodically couples between the two cores, with a beat length that is wavelengthdependent [170]. Doping both cores produces a gain medium with a large-scale spatial inhomogeneity. This can be used to decouple the gain experienced by different wavelengths, allowing the possibility of multiple-wavelength operation. This approach was


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demonstrated by Graydon et al. [171] whereby an 8-m, twin-core, Er-doped fiber was placed in a unidirectional ring cavity containing an optical circulator. The common port of the optical circulator contained a multiple wavelength fiber grating. At the input end of the twin-core fiber, only one core was spliced into the cavity, whereas at its output end both cores were spliced into the cavity. Simultaneous-wavelength operation was observed on three different lines centered around 1543.5 nm and spaced by ⬃0.5 nm. Because the ring was unidirectional, the output at each wavelength was expected to have a narrow linewidth. This was confirmed by a delayed self-heterodyne technique, which showed that the linewidth was ⬃10 kHz. Although the approaches outlined in the foregoing, which rely on spatial mode beating or coupling between the cores of a twin-core fiber, successfully produced multiplewavelength operation, they are rather complex and difficult to implement. A simpler method would be to create the multiple-wavelength filter directly in the fiber. The most obvious method is to use fiber Bragg reflector technology. One of the first demonstrations of dual-wavelength operation, [172] did, in fact used such a filter (Fig. 27). The laser comprised two separate gain fibers and cavities formed with Bragg reflectors with slightly overlapping reflectivities. The two cavities were thus weakly coupled, which made possible stable dual-frequency operation. The oscillating wavelengths were separated by 0.47 nm and their linewidths were ⬃45 kHz. When the two cavities were coupled, the oscillating linewidths narrowed to 16 kHz. This linewidth narrowing was attributed to the increase in cavity length brought about by the coupling of the two laser cavities. The relative frequency stability between the two wavelengths was 3 MHz. Li et al. [173] also used discrete fiber Bragg reflectors to achieve dual-wavelength operation in an Er-doped fiber laser. However, instead of a standing-wave linear cavity geometry they used a Sagnac loop geometry and placed a fiber Bragg reflector at each of the output ports of the loop. Dual-wavelength operation was observed at 1530.5 and 1532 nm. By stretching each grating the wavelengths could be tuned independently over 1.0 nm. As discussed in Section 5.5, distributed-feedback fiber lasers can oscillate on two orthogonally polarized modes, resulting in a dual-frequency output. The frequency spacing between the two modes is determined by the intrinsic birefringence of the doped fiber. The birefringence of a fiber can be greatly increased by deliberately deforming the core during the fiber pulling process. For example, if the core is elliptical the mode polarization

Figure 27

Schematic representation of a coupled-cavity Bragg-reflector laser for multiple wavelength operation. (Courtesy of J. R. Taylor.)

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becomes robust against external perturbations and a PM fiber is formed. This feature has been exploited by [174] to form a dual-frequency distributed-feedback laser. The laser was constructed in an elliptical core fiber. The excessive birefringence associated with this type of fiber increased the frequency spacing between the two orthogonally polarized modes to 40 GHz. The linewidth of the beat signal between these two modes was 900 Hz. By varying the temperature of the laser the beat frequency was observed to shift by ⫺9.1 MHz/°C. To increase the number of oscillating wavelengths, using either the coupled cavity approach [172] or the twin-grating approach [173], would require more gratings, which is an inefficient way to proceed. It is possible to make a continuous fiber Fabry–Pe´rot filter using fiber Bragg gratings [175]. To obtain a broad wavelength response, chirped Bragg reflectors were used as the resonator mirrors. A single chirped grating is a dispersive device. However, if two chirped gratings are used in series to form a resonator and the chirp is in the same direction, the net dispersion inside the resonator is zero and the transmission of the resonator resembles that of a Fabry–Pe´rot e´talon, but the phase response is modified by the single pass through the two chirped gratings. With two chirped gratings separated by 8 mm and with a reflectivity of 50% over a bandwidth of 150 nm, an allfiber Fabry–Pe´rot filter was formed with a free spectral range of 0.09 nm and a fringe width of 0.03 nm. A filter of this type would be ideal for multiple-wavelength operation of rare earth doped fiber lasers. Indeed, Chow et al. [176] used one in a unidirectional Er-doped fiber ring laser in which the gain medium was cooled to 77 K (Fig. 28a). The all-fiber Fabry–Pe´rot filter had a free spectral range of 0.65 nm and a finesse of 4, and it allowed the simultaneous operation of 11 wavelengths (see Fig. 28b). As discussed in Section 5.4, a sampled Bragg grating also has a Fabry–Pe´rot transmission, and Chow et al. [176] also used one to obtain multiple-wavelength operation. The sampled Bragg grating (see inset, Fig. 28a) had a free spectral range of 1.8 nm and a finesse of 15. Multiplewavelength operation occurred at five discrete wavelengths. For both of the lasers studied by Chow et al. the number of oscillating wavelengths was limited by a 6-nm transmission placed in the cavity to prevent the laser from oscillating on wavelengths that fell outside the reflection band of the Bragg gratings. The short-cavity standing-wave fiber lasers described in Section 5.5 exhibited singlefrequency operation because the large axial-mode spacing (∆ν ⬇ 10 GHz) and crosssaturation allowed only one mode to reach threshold. An example of the type of laser for which these features have been exploited to the fullest is the short-cavity fiber Fabry– Pe´rot laser [112]. Yamashita et al. [177] showed that by cooling the gain medium to liquid nitrogen temperatures, thereby minimizing cross-saturation, narrow-linewidth multiple wavelength operation was possible from this class of laser. In a 2-mm long Er :Yb-doped fiber Fabry–Pe´rot laser a maximum of 29 separate wavelengths were observed to oscillate simultaneously, with a wavelength spacing of 0.4 nm and output powers ranging from 2 to 10 µW. The measured linewidth was less than 100 kHz. The 0.4-nm wavelength spacing correlated with the measured 0.5 nm homogeneous linewidth of the Er:Yb-doped fiber. The multiple wavelength fiber lasers described in the foregoing rely on inhomogeneous broadening of the gain medium to enable many wavelengths to oscillate. An alternative method [178–180] consisted in a hybrid laser using both Brillouin gain and the gain provided by an Er-doped fiber. The Brillouin gain, seeded by a narrow-linewidth pump, acted as a narrowband filter and resulted in the discrete frequencies, whereas the Er-doped fiber amplified the Brillouin signal and enabled high-power extraction from the laser. Because the Er-doped fiber compensates for the losses in the laser, the need for critical


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Figure 28

(a) Pictorial representation of a laser cavity containing either an all-fiber Fabry–Pe´rot filter, or a sampled Bragg grating; (b) the wavelength output from the laser operated with the chirped grating Fabry–Pe´rot. (Courtesy of G. E. Town.)

coupling of the Brillouin pump to the resonator is obviated. The Brillouin signal is frequency shifted from the pump and counterpropagates relative to the pump. The magnitude of the frequency shift is determined by the acoustic velocity in the fiber [181]. In this laser, multiple-wavelength operation was realized by making each generated Brillouin signal the seed for the next Brillouin wavelength. This was accomplished by coupling a small amount of the intracavity circulating field into the opposite direction using the cavity (Fig. 29a). With both approaches narrow-linewidth multiple-wavelength operation was observed, with a frequency spacing of 10.3 GHz (see Fig. 29b). Although the Er-doped gain medium amplifies the Brillouin signals, it is not solely responsible for the gainclamping process. This is partly controlled by the Brillouin gain and, as different wave-

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(a)

(b)

Figure 29 (a) Hybrid erbium/Brillouin fiber laser cavity: SMOF, single-mode optical fiber; BEFL, Brillouin/erbium fiber laser; WDM, wavelength division multiplexer; EDF, erbium–doped fiber); (b) the laser output spectrum. (Courtesy of Cowle and Stepanov.)

lengths experience a different Brillouin gain, the effects of cross-saturation can be minimized without having to cool the fiber. 5.8 APPLICATIONS OF SINGLE-FREQUENCY FIBER LASERS The narrow linewidths and excellent frequency noise characteristics of single-frequency fiber lasers make them ideal for many applications. One key area for which the fiber geometry is attractive is remote sensing. The advent of fiber lasers based on Bragg reflectors has triggered a revolution in sensing applications, making possible, in particular, the ultrasensitive detection of strain and magnetic fields. Prior to fiber lasers based on Bragg reflectors, a Bragg reflector was normally probed using a broadband, low-power (⬍100 µW) light source. The narrowband reflection of the Bragg reflector meant that only a small percentage of the incident signal was reflected by the device, resulting in difficulties in extracting the optical signal from the background noise. The ability to incorporate


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Bragg gratings into fiber lasers, as described in Section 5.4, has allowed the development of high-power (⬎1-mW) sensitive optical sensors and alleviated these signal-to-noise problems. Several approaches have been investigated to develop fiber–laser-based strain sensors [2,182–188]. One of the earliest demonstrations, by Melle et al. [182], used a linear cavity, with one fiber end reflection coated to form a mirror and the other end spliced to a fiber Bragg reflector. When the Bragg grating is strained, its reflectivity characteristics are altered, which changes the wavelength of the fiber laser. By detecting this wavelength change a measure of the applied strain can be obtained. With this approach strains of 5.4 µstrain have been measured. As mentioned in Section 5.4, cavities for narrow-linewidth fiber lasers can be made with matched pairs of fiber Bragg reflectors. These lasers have been used to produce both single-point and multipoint sensors [183–185]. Instead of using the Bragg reflector to sense the environmental change, the actual laser cavity serves as the sensor. A change in the optical path length induces a change in the frequency [see Eq. (6.2)], so by monitoring the wavelength change the environmental perturbation can be monitored. The multipoint sensor consists of a series of fiber lasers made from Bragg reflectors peaking at different wavelengths. Ball et al. [183] compared the performance of two fiber–laser-based sensors, namely, a 30-mm single-longitudinal-mode laser and a 250-mm multilongitudinal-mode laser. As expected, the longer cavity sensor gave a higher frequency resolution. When the short-laser cavity was used as a strain sensor, a wavelength change of 1.2 nm/millistrain was recorded. The response of the systems to thermal changes was 0.01 nm/°C. Although the fiber laser sensors responded linearly to the applied perturbation, the resolution of each sensor was ultimately limited by longitudinal mode hops in the laser. An alternative approach to strain sensing [184] used a modified version of the cavity illustrated in Figure 15. The Er-doped fiber, an integrated optical isolator and a fiber Fabry–Pe´rot e´talon filter were included in the loop mirror section of the cavity, and the cavity was completed by a series of Bragg reflectors, each separated by a length of fiber. Each Bragg reflector had a different operating wavelength and a reflection bandwidth narrower than the Fabry–Pe´rot e´talon. The laser would oscillate only when a filter pass band was in resonance with a Bragg reflector, thereby forming a distributed sensor. This allowed one Bragg reflector to be interrogated at a time. A strain was then applied to the Bragg reflector of interest and the shift in oscillating wavelength was detected. With this approach a minimum strain of 25 µstrain was measured. Magnetic fields can be detected using an active fiber laser sensor [3]. A singlefrequency fiber laser was attached to a magnetostrictive element. This element exhibits a quadratic dependence to the applied field, and it can be used to detect either AC or DC magnetic fields. By applying a linear DC bias to the magnetostrictive element, AC magnetic fields as low as 0.9 pT/√Hz at an applied frequency of 30 kHz were observed. When used as a DC magnetometer, fields as low as 300 pT/√Hz were observed. The foregoing sensors rely on changes in laser wavelength to provide information on the perturbation applied to the active sensor. The polarization properties of fiber lasers can also be exploited to produce a sensor. Dual-frequency operation can be obtained in narrow-linewidth fiber lasers by exciting the orthogonal polarization axes of the weakly birefringent laser cavity. Because the refractive indices associated with polarization axes are different, the oscillating frequencies of the two modes are also different. Detection of these two frequencies result in a beat note at the detector. By applying to the cavity a perturbation that alters its birefringence, the beat frequency changes, and by monitoring this frequency change the applied perturbation can be quantified.

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Several variants of this system have been developed [186–188] using different doped fibers as the sensing fiber. In a broadband Nd-doped fiber laser a frequency change of 4.8 kHz/g of applied stress was observed [186]. This work has been extended to the 1.5-µm region using two different cavity configurations. The first sensor was constructed from two Er-doped PM fibers of equal lengths that were spliced together with their polarization axes at 90°. The effect of this rotation was to reduce the total birefringence of the cavity and, thereby, the beat frequency between polarization modes. Frequency shifts of 30 kHz/°C cm ⫺1 and 432 kHz/µm were observed for applied thermal and strain perturbations [187]. Aligning the polarization axes of the doped fibers at the splice is difficult. More recently, Kim et al. [188] developed a new form of polarimetric sensor that uses a non-PM doped fiber fusion spliced to a short length of PM fiber. The latter acts as the sensor. Shifts in frequency of 124 kHz/°C cm ⫺1 and 137 kHz/µm were measured when the laser experienced either a thermal or strain perturbation. Narrow-linewidth fiber lasers have also been used as light source for high-resolution spectroscopy. One example is the work of Fox et al. [189], who used a narrow-linewidth Er-doped fiber laser to probe the 5 P 3/2 → 4 D 5/2 transition in rubidium. This transition has a center wavelength of 1.529 µm, and it is of key importance as a potential optical wavelength standard in the 1.5-µm communication window. The need for a suitable standard close to 1.5 µm is driven by the use of narrowlinewidth lasers for wavelength-multiplexed communication systems. In general, the light sources used for wavelength-multiplexed communication systems have been distributedfeedback semiconductor lasers. However, Mizrahi et al. [82] have demonstrated that narrow-linewidth fiber lasers are a potentially suitable replacement. Using an amplified singlemode fiber laser they demonstrated that bit-error-rate transmission at the 10 ⫺15 level in a 5 Gbit/s data stream was possible. When comparing the performance of the fiber laser with that of a semiconductor laser, no appreciable difference between them was found.

5.9 CONCLUSIONS In this chapter I hope to have given the reader an indication of the extent to which singlefrequency rare earth doped fiber lasers have become an accepted form of laser. The diverse range of applications for which these lasers are being employed is a testament to their appeal. In fact, single-frequency fiber lasers are now commercially available from several companies. Although the instantaneous linewidth of a narrow-linewidth fiber laser is considerably narrower than that of a semiconductor laser (a value of 100 kHz is typical for commercial semiconductor lasers) [190], there are several practical reasons why fiber lasers may not replace semiconductor lasers as the source of narrow-linewidth radiation in the third communication window. To achieve a large tuning range (⬎50 nm) from a fiber laser requires significant engineering of the wavelength selective device and proper design of the cavity, as discussed in Sections 5.5 through 5.8. In contrast, such a tuning range can be obtained readily with an external-cavity semiconductor laser [190]. Furthermore, to ensure mode hop-free operation over the entire tuning range requires very complicated cavities, which do not afford themselves to simple compact packaging. With a semiconductor laser, however, mode hop-free operation is possible over the entire tuning range [190]. A more restrictive and, ultimately perhaps, the most serious limiting factor is the cost of the laser. External-cavity semiconductor lasers require minimal components, and they are relatively simple to design and construct. On the other hand, as has been seen


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throughout this chapter, to achieve unidirectional narrow-linewidth operation in a rare earth doped fiber laser requires a number of complex optical components, such as wavelength division multiplexers, integrated fiber filters, and optical isolators. Although narrow-linewidth fiber lasers may not replace semiconductor lasers for a range of applications that require ultranarrow linewidth, such as wavelength standards, the fiber laser may be the ultimate choice. Furthermore, the ability to amplify the output from the fiber laser while retaining a fiber geometry is an attractive feature that may open up the possibility of a range of novel frequency conversion schemes requiring high average powers. REFERENCES 1. E. Snitzer. Optical maser action of Nd 3⫹ in a barium crown glass. Phys. Rev. Let. 7:444, 1961. 2. A. D. Kersey, W. W. Morey. Multi-element Bragg-grating based fibre-laser strain sensor. Electron. Lett. 29:964, 1993. 3. K. Koo, A. Kersey, F. Bucholtz. Fiber Bragg grating laser magnetometer. Proceedings of the Conference on Lasers and Electro-Optics, Baltimore, MD, postdeadline paper PD41, 1995. 4. J. R. Taylor. Soliton fiber lasers. Proceedings of the Conference on Lasers and ElectroOptics, Baltimore, MD, paper CWM3, 1995. 5. See, for example, W. Koechner. In: Solid State Laser Engineering. Berlin: Springer Verlag, 1988, Chap. 2. 6. I. M. Jauncey, L. Reekie, J. E. Townsend, D. N. Payne, C. J. Rowe. Single–longitudinalmode operation of an Nd 3⫹-doped fibre laser. Electron Lett. 24:24, 1988. 7. G. A. Ball, W. W. Morey, W. H. Glenn. Standing-wave monomode erbium fiber laser. IEEE Photon. Technol. Lett. 3:613, 1991. 8. A. Asseh, H. Storoy, J. T. Kringlebotn, W. Margulis, B. Sahlgren, R. Stubbe, G. Edwall. 10 cm Yb 3⫹ DFB fibre laser with permanent phase-shifted grating. Electron. Lett. 31:969, 1995. 9. P. R. Morkel, G. J. Cowle, D. N. Payne. Traveling-wave erbium fibre ring laser with 60 kHz linewidth. Electron. Lett. 26:632, 1990. 10. K. Iwatsuki, H. Okamura, M. Saruwatari. Wavelength-tunable single-frequency and singlepolarization Er-doped fibre-ring laser with 1.4 kHz linewidth. Electron. Lett. 26:2033, 1990. 11. M. W. Maeda, J. S. Patel, D. A. Smith, C. L. Lin, M. A. Saifi, A. V. Lehman. An electronically tunable fiber laser with a liquid-crystal etalon filter as the wavelength-tuning element. IEEE Photon. Technol. Lett. 2:787, 1990. 12. See, for example, A. E. Siegman. In: Lasers , University Science Books, 1988;451–455. 13. See, for example, M. J. F. Digonnet, E Snitzer. Nd 3⫹ and Er3⫹-doped silica fiber lasers. In: M. J. F. Digonnet, ed. Rare Earth Doped Fiber Lasers and Amplifiers. Marcel Dekker, New York, 1993. 14. J. Ye, L. S. Ma, J. I. Hall. Ultrasensitive detections in atomic and molecular physics: demonstration in molecular overtone spectroscopy. J. Opt. Soc. Am. B 15:6, 1998. 15. See, for example, M. D. Levenson, S. S. Kano. In: Introduction to Nonlinear Laser Spectroscopy. Academic Press, London, 1987;67. 16. S. Sanders, J. W. Dawson, N. Park, K. J. Vahala. Measurements of the intensity noise of a broadly tunable, erbium-doped fiber ring laser, relative to the standard quantum limit. Appl. Phys. Lett. 60:2583, 1992. 17. S. Sanders, N. Park, J. W. Dawson, K. J. Vahala. Reduction of the intensity noise from an erbium-doped fiber laser to the standard quantum limit by intracavity spectral filtering. Appl. Phys. Lett. 61:1889, 1992. 18. See, for example, A. E. Siegman. In Lasers. University Science Books, 1988, Chap. 1. 19. J. L. Zyskind, E. Desurvire, J. W. Sulhoff, D. J. Giovanni. Determination of homogeneous

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165. S. Yamashita, K. Hotate. Multiwavelength erbium-doped fibre laser using intracavity etalon and cooled by liquid nitrogen. Electron. Lett. 32:1298, 1996. 166. U. Ghera, N. Friedman, M. Tur. A fiber laser with a comb-like spectrum. IEEE Photon. Technol. Lett. 5:1159, 1993. 167. N. Park, P. F. Wysocki. 24-Line multiwavelength operation of erbium-doped fiber-ring laser. IEEE Photon. Technol. Lett. 8:1459, 1996. 168. J. N. Blake, B. Y. Kim, H. J. Shaw. Fiber-optic modal coupler using periodic microbending. Opt. Lett. 11:177, 1986. 169. A. J. Poustie, N. Finlayson, P. Harper. Multiwavelength fiber laser using a spatial mode beating filter. Opt. Lett. 19:716, 1994. 170. A. W. Snyder, J. D. Love. In: Optical Waveguide Theory. Chapman & Hall, London, 1983, Chap. 29. 171. O. Graydon, W. H. Low, R. I. Laming, L. Dong. Triple-frequency operation of an Er-doped twincore fiber loop laser. IEEE Photon. Technol. Lett. 8:63, 1996. 172. S. V. Chernikov, J. R. Taylor, R. Kayshap. Coupled-cavity erbium fiber lasers incorporating fiber grating reflectors. Opt. Lett. 18:2023, 1993. 173. S. Li, H. Ding, K. T. Chan. Erbium-doped fibre lasers for dual wavelength operation. Electron. Lett. 33:52, 1997. 174. W. H. Loh, J. P. de Sandro, G. J. Cowle, B. N. Samson, A. D. Ellis. 40 GHz optical-millimetre wave generation with a dual polarisation distributed feedback fibre laser. Electron. Lett. 33: 594, 1997. 175. G. E. Town, K. Sugden, J. A. R. Williams, I. Bennion, S. B. Poole. Wide-band Fabry–Perotlike filters in optical-fiber. IEEE Photon. Technol. Lett. 7:78, 1995. 176. J. Chow, G. E. Town, B. Eggleston, M. Ibsen. K. Sugden, I. Bennion. Multiwavelength generation in an erbium-doped fiber laser using in-fiber comb filters. IEEE Photon. Technol. Lett. 8:60, 1996. 177. S. Yamashita, K. Hsu, W. H. Loh. Miniature erbium :ytterbium fibre Fabry-Perot multiwavelength lasers. IEEE J. Select. Top. Quant. Electron. 3:1058, 1997. 178. G. J. Cowle, D. Y. Stepanov. Hybrid Brillouin/erbium fiber laser. Opt. Lett. 21:1250, 1996. 179. G. J. Cowle, D. Y. Stepanov. Multiple wavelength generation with Brillouin/erbium fiber lasers. IEEE Photon. Technol. Lett. 8:1465, 1996. 180. D. Y. Stepanov, G. J. Cowle. Properties of Brillouin/erbium fiber lasers. IEEE J. Select. Top. Quant. Electron. 3:1049, 1997. 181. See, for example, G. P. Agrawal. In: Nonlinear Fiber Optics. Academic Press, New York, 1987, Chap. 9. 182. S. M. Melle, A. T. Alavie, S.E. Karr, T. Coroy, K. Liu, R. M. Measures. A Bragg gratingtuned fiber laser strain sensor system. IEEE Photon. Technol. Lett. 5:263, 1993. 183. G. A. Ball, W. W. Morey, P. K. Cheo. Singlepoint and multipoint fiber-laser sensors. IEEE Photon. Technol. Lett. 5:267, 1993. 184. A. Othonos, S. Melle, A. T. Alavie, S.E. Karr, R. M. Measures. Fiber Bragg grating laser sensor. Opt. Eng. 32:2841, 1993. 185. A. T. Alavie, S.E. Karr, A. Othonos, R. M. Measures. A multiplexed Bragg grating fiber laser sensor system. IEEE Photon. Technol. Lett. 5:1112, 1993. 186. H. K. Kim, S. K. Kim, H. G. Park, B. Y. Kim. Polarimetric fiber laser sensors. Opt. Lett. 18:317, 1993. 187. H. K. Kim, S. K. Kim, B. Y. Kim. Polarization control of polarimetric fiber-laser sensors. Opt. Lett. 18:1465, 1993. 188. H. K. Kim, S. K. Kim, B. Y. Kim. Polarimetric fiber laser sensors using Er-doped fiber. Opt. Quant. Electron. 27:281, 1995. 189. R. W. Fox, S. L. Gilbert, L. Hollberg, J. H. Marquardt, H. G. Robinson. Optical probing of cold trapped atoms. Opt. Lett. 18:1456, 1993. 190. See, for example, New Focus Catalog 9:24, 1989.

6 Broadband Fiber Sources MICHEL J. F. DIGONNET Stanford University, Stanford, California

6.1 INTRODUCTION Superfluorescent fiber sources (SFS) first appeared in 1987, shortly after the advent of low-loss rare earth doped silica fibers. Similar to a laser, an SFS relies on the amplification of stimulated emission, but it differs from a laser in that it does not utilize an optical resonator. Its output is simply the superfluorescence, or amplified spontaneous emission (ASE), generated by the optically pumped laser ions of the doped fiber. Because this ASE has not been spectrally filtered by a resonator, it covers a sizable fraction of the bandwidth of the laser transition, which is generally quite broad for rare earth ions in a glass host. Thus, unlike most lasers, an SFS emits a broadband signal, typically a few to a few tens of nanometers. It is this unique property that spells its key role in several important applications. In response to the demand from several industries, particularly for fiber-optic gyroscope (FOG) applications, extensive research has been carried out over the past decade to develop stable, high-power broadband sources based on rare earth doped fibers, preferably pumped with a laser diode (LD). A large number of source configurations, dopants, devices, and properties have been investigated, both experimentally and theoretically. This chapter reviews the field’s state of the art, in particular the physical principles of broadband fiber sources and the properties of the main sources developed to date, focusing on more widely studied 1.55-µm Er-doped SFSs. 6.2 APPLICATIONS AND SOURCE REQUIREMENTS The primary engine behind the effort to research and produce broadband sources has been the FOG. A broadband signal is needed in an FOG to reduce detrimental coherent noise 313

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effects, caused by both backscattering and polarization coupling, that takes place along the sensing coil fiber. When uncorrected, these effects cause a significant reduction in rotation sensitivity [1,2]. A broadband signal also dramatically reduces the gyroscope bias drift induced by the Kerr effect by power variations in the two signals counterpropagating in the FOG coil [3]. The bandwidth and power requirements of the broadband signal depend on the accuracy required from the gyroscope. The most stringent requirements arise in high-grade FOGs for aircraft inertial navigation: a bandwidth of 20 nm and a fibercoupled power of 10 mW are usually considered to be minimum requirements; broader bandwidths [4] are generally preferable. The choice wavelength for the FOG and several other applications is around 1.55 µm (Er-doped fibers), primarily to benefit from the lower loss of silica fibers at this wavelength. For aircraft navigation and space applications another benefit is the shorter recovery time of the fiber transmission at this wavelength after the fiber has been exposed to high-energy radiation. This requirement is not an issue for other applications, such as automobile navigation, and other wavelengths have been investigated, in particular around 1.06 µm in ytterbium-doped fibers. Another important requirement of the FOG is that the mean wavelength of the broadband signal must be stable. The gyroscope is an interferometric instrument in which rotation induces a phase change. The measured phase change and the rotation rate are related by a scale factor inversely proportional to the signal mean wavelength [5]. For mediumto high-accuracy gyroscopes (minimum detectable rotation rates of a few degrees per hour or lower), to be able to retrieve the absolute rotation rate from the phase accurately enough, the scale factor must be known accurately. The most desirable solution is a source with a mean wavelength that is very stable against all perturbations, in particular changes in temperature and pump power, wavelength, and polarization. The required stability is reasonably low for automobile navigation, but it is quite stringent for high-grade FOGs, typically less than 1 part per million (ppm) [5]. Very few technologies can provide a source with such unique properties. One possible candidate is the superluminescent laser diode (SLD), developed by the semiconductor laser industry in part to meet this specific market. However, in spite of significant improvements, commercial SLDs still suffer from a few shortcomings. Their sizable beam astigmatism limits the fiber-coupled power to a few milliwatts [6,7]. Their mean wavelength exhibits a high intrinsic dependence on temperature, typically 400 ppm/°C [8]. To achieve a scale factor stability of 1 ppm thus requires stabilizing the SLD temperature to 0.0025°C, a difficult engineering task that adds complexity and cost to the FOG. Another issue is the SLD’s high wavelength susceptibility to the signal returning from the gyroscope [7], a problem that is common, in varying degrees, to all broadband sources. Rare earth doped fibers showed quite early the promise of producing broadband sources with superior properties. After more than 10 years of research and development, this technology now offers compact, laser–diode-pumped Er-doped SFSs with a broad emission (typically 10–30 nm) [9–12], a high conversion efficiency (up to 56%) [9], a high output power (over 70 mW) [12], and an optionally polarized output [11]. Other rare earths, in particular Yb [13] and Nd [14], have also produced high-performance broadband fiber sources. Because all of the power that is produced is in the LP 01 mode of the singlemode doped fiber, essentially all of it can be coupled into a standard single-mode fiber. Finally, without compromising the foregoing characteristics, Er-doped SFSs have been developed with an overall mean wavelength stability under 1 ppm with reasonable control

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of the device temperature and current [10]. Several academic and industrial laboratories have demonstrated broadband SFSs with properties far exceeding those of SLDs. It is a gauge of the success of SFSs that for some years now they have been a key component in commercial FOGs. SFSs are also utilized in several instruments requiring a low temporal coherence signal, such as imaging devices for medical applications, in particular in ophthalmology [15], and optical time domain reflectometry for fiber characterization [16]. They are also receiving increasing attention in optical communications for dense WDM systems [17,18]. In this application, the broadband signal from an SFS is sliced into multiple channels, each of which is used as the input signal into the WDM communication link. 6.3 TYPES AND BASIC PRINCIPLES OF BROADBAND FIBER SOURCES Four general types of broadband fiber sources have been investigated: namely, resonant fiber lasers, superfluorescent fiber sources, wavelength-swept fiber lasers, and sources involving an SLD and an Er-doped fiber amplifier (EDFA). Their principles are briefly reviewed in this section. 6.3.1 Broadband Fiber Lasers Although most continuous-wave (cw) fiber lasers produce a narrow emission, under proper conditions they can be operated as a broadband source [19]. The laser transitions of triply ionized rare earths are broadened by both homogeneous and inhomogeneous processes (see Chap. 2). The spectral properties of a fiber laser are strongly influenced by which one of these two processes dominates. Homogeneous mechanisms broaden the linewidth of the transitions between Stark levels in the same manner for all ions. On the other hand inhomogeneous broadening leads to a change in the distribution of the Stark levels that differs from ion to ion depending on the ion’s physical site within the host. When a dopant is pumped near the center of one of its absorption bands, pump photons have a high probability of being absorbed by one of the several Stark transitions of every ion in the material. All ions have roughly equal probability of absorbing (i.e., the medium behaves quasihomogeneously). However, if the dopant is pumped in the tails of the band, the probability of absorption is greater for groups of ions that exhibit a stronger transition at that wavelength. Absorption is then site-specific. The medium behaves as if it were more strongly inhomogeneously broadened. This principle was studied in detail in Nd-doped fibers [20]. Based on this effect, a fiber laser can be made to produce a broadband emission, provided the fiber dopant is at least partly inhomogeneously broadened and pumped on the edge of an absorption band. This principle was demonstrated with an Nd-doped fiber laser [19], as described in Section 6.6.1. 6.3.2 Superfluorescent Fiber Sources An SFS is made of an optically end-pumped rare earth doped fiber. The inverted ions produce a spontaneous emission, some of which is captured by the fiber core in both the forward direction (cotraveling with the pump) and the backward direction (against the pump). The forward and backward spontaneous photons are amplified as they travel along

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the fiber and produce amplified spontaneous emission (ASE), or superfluorescence, at the forward and backward output port, respectively. Several SFS configurations are possible [21], each with its own characteristics, benefits, and disadvantages. The first one is the forward SFS (Fig. 1a). This device produces both a forward and a backward output, but only the former is used; namely, the output from the end opposite the pump input. This is a single-pass device: the ASE travels only once through the fiber. In general, for the output power to be sizable the fiber must be pumped hard to exhibit a high gain. Consequently, if reflections into the fiber are allowed to occur from both ends, in particular Fresnel reflections at the fiber ends, this device will become a laser and emit an undesirably narrow spectrum. To avoid this effect the fiber

Figure 1 Diagram of four basic configurations of superfluorescent fiber source: (a) forward configuration; (b) backward configuration; (c) double-pass configuration; and (d) fiber amplifier source (FAS).


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ends are usually polished at an angle (typically 7 degrees or greater). If need be, reflections from the pump optics can also be reduced by placing an optical isolator on the pump input arm. Another single-pass configuration is the backward SFS (see Fig. 1b) [22]. The signal that is used is now the backward ASE, which comes out at the pump input end. The pump is filtered out from the output by a wavelength division multiplexing (WDM) fiber coupler that couples minimally at the pump wavelength (ideally 0%), but strongly over the bandwidth of the ASE (ideally 100%) (or vice versa). One advantage of the backward SFS is that its sensitivity to feedback is lower (especially if the fiber is very long, as required for high efficiency) than that of a forward SFS. However, it is often used with an isolator placed at the output to reduce the sensitivity of its mean wavelength to changes in feedback levels. For a four-level laser, such as the 1060-nm 4 F 3/2 → 4 I 11/2 transition of Nd 3⫹, if the fiber propagation loss is negligible compared with the gain (as is generally true), the forward and backward output powers are essentially equal, and both configurations exhibit the same conversion efficiency [23]. However, for a three-level laser transition (e.g., the 1550-nm 4 I 13/2 → 4I 15/2 transition of Er 3⫹), the forward signal generally carries a lower power, as discussed further on. The backward SFS is thus more efficient. However, it requires a longer fiber, because its efficiency is maximized for a longer fiber than the forward SFS. A third configuration is the double-pass SFS (see Fig. 1c). A high reflector at the ASE wavelength is added (e.g., at the pump input port), to propagate the backward ASE through the fiber a second time. This configuration produces only a forward output. Alternatively, the reflector can be placed at the other end of the doped fiber to produce a backward output only. The primary advantage of the double-pass configurations is that the signal photons travel through the fiber twice and experience a higher gain than in a single-pass SFS (by as much as a factor of 2). Thus, the threshold of a double-pass SFS is concomitantly lower, and its pump power requirement is reduced. Also, the length of fiber that maximizes its efficiency is shorter than for a forward SFS. The main disadvantage of the double-pass SFS is that the high reflector exacerbates the spectrum susceptibility to external feedback from the system to which light is coupled, which means that a higherextinction isolator is required. In the double-pass backward SFS it is also generally required to reduce reflection from the pump optics by placing an isolator between the pump source and the WDM coupler. The fourth and last SFS configuration is the fiber amplifier source (FAS; see Fig. 1d) [22]. It was originally designed for the FOG. It is a backward SFS without an isolator, so that the signal returning from the FOG can travel through the doped fiber and be amplified before reaching the detector. The FAS acts as both a source and an amplifier. Thus, it increases the detected signal power, which reduces electronic noise in the detection and simplifies electronic processing [22]. This configuration offers the same potential benefits for applications other than the FOG. The round-trip gain of a medium- to high-power SFS is typically 40–60 dB. Even minor reflections occurring simultaneously at both ends will turn the SFS into a laser [24]. Experimental studies of an SFS showed that, for output powers greater than 20 mW, this is avoided by keeping the product of reflectivities R 1 and R 2 at each end under 1.2 10 ⫺6 [25,26]. If, by design, one of the reflectivities is high (e.g., in a double-pass SFS or if the SFS is connected to a low-loss FOG), the other reflectivity must be kept extremely low, which usually requires a very good optical isolator. The backward SFS and the FAS,

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which do not receive reflections from one of the fiber ends, are less susceptible to this problem. 6.3.3 Other Types of Broadband Fiber Sources The two other types of broadband fiber sources have received much less attention. The first one is the SLD–EDFA tandem source, in which the broadband output of an SLD is amplified by an EDFA [27]. Its main benefit is that, because the EDFA is seeded by an external signal, it has a lower threshold than a single-pass SFS, which is seeded by spontaneous photons. An SLD–EDFA tandem source with an output signal of 20 mW and a bandwidth of 21 nm was demonstrated using 60 mW of pump power [27]. Further studies of this interesting source are warranted, in particular of its thermal stability (as the seed source is strongly temperature-sensitive). The last type of broadband fiber source is the wavelength-swept fiber laser (WSFL). It is a fiber laser with an acousto-optic (AO) modulator incorporated in the cavity [28,29]. For a given acoustic frequency and a given alignment of the two cavity reflectors, the Bragg condition is satisfied only at a specific wavelength, and the laser oscillates at this lower-loss wavelength. When the acoustic frequency is changed, the laser wavelength also changes. If the acoustic frequency is scanned slowly enough to allow buildup of the laser field in the resonator at each acoustic frequency before moving on to the next one, the wavelength is swept continuously across the gain curve. This produces emission that is broad over a long time scale compared with the inverse of the sweeping rate. The WSFL works equally well with homogeneously and inhomogeneously broadened transitions. Also, because the photons are recirculated, its threshold can be lower than that of an SFS. Because the laser frequency is continuously shifted at each round-trip through the resonator, this source may also be less sensitive to feedback than other sources. This principle was demonstrated with an Er-doped fiber and a bulk AO modulator [28,29]. An all-fiber version could be constructed using existing all-fiber components. 6.4 THEORETICAL MODEL OF THE OUTPUT POWER AND SPECTRUM OF SFSs Several theoretical models have been developed to describe the output power and spectrum of SFSs [12,21,23,25,30–32]. A wide variety of situations have been modeled, including three-level and four-level systems, forward, backward, double-pass, and FAS configurations, bidirectional pumping, and polarization effects. The reader is referred to these references for further detail. In all cases, the basic growth of the ASE waves that underlies the model is described by the same mathematical expressions, which are presented in this section. 6.4.1 Three-Level Systems We consider a unidirectionally pumped, doped fiber, with the pump launched at z ⫽ 0 and propagating in the ⫹z direction. The pump induces along the fiber a gain per unit length (or gain factor) that depends on z. Spontaneous photons generated in the fiber are amplified in both the forward (⫹z) and backward (⫺z) directions and give rise to two ASE waves, one in each direction. These waves deplete the excited-state population of the rare earth ions which, in turn, affects both the pump absorption and the gain factor. This physical system is described by coupled equations involving the pump power, the

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ground-state and excited-state populations of the ions, and the forward and backward ASE powers. To illustrate this complex interaction, consider first the case of a three-level transition, as applicable to the widely studied 4 I 13/2 → 4 I 15/2 transition of Er 3⫹. Each frequency component in the (wide) ASE spectrum exhibits its own absorption and emission cross section, and thus its own saturation behavior. To model the spectral behavior of an SFS, the spectrum is sliced into n adjacent segments centered at frequency ν i and with a narrow width δν i . We label P ⫾s (z,ν i ) the ASE power at position z and in the frequency range (ν i ,ν i ⫹ δν i) in the forward and backward directions, respectively, and P p (z) the pump power at z. The evolution of these quantities along z are determined by the following coupled first-order differential equations [21]: dP ⫾s (z,ν i ) ⫽ ⫾γ s (z,ν i) P s⫾ (z,ν i) ⫾ γ se (z,ν i ) 2hν i δν i dz

(1)

dP p (z) ⫽ ⫺γ p (z) P p (z) dz

(2)

where γ s (z,ν i) and γ se (z,ν i ) are the signal gain coefficients at position z and frequency ν i , and γ p (z) is the pump absorption coefficient at z. A second equation for the pump power, similar to Eq. (2), must be added when the fiber is pumped bidirectionally. The gain and absorption parameters are related to the population density of the excited state N 2 (z) and of the ground state N 1 (z) by γ s (z,ν i) ⫽ σ e (ν i )N 2 (z) ⫺ σ a (ν i )N 1 (z)

(3)

γ se (z,ν i ) ⫽ σ e (ν i)N 2 (z)

(4)

γ p (z) ⫽ σ a (ν p)N 1 (z) ⫺ σ e (ν p)N 2 (z)

(5)

where σ a (ν i ) and σ e (ν i) denote the absorption and emission cross-sections at ν i , respectively. The second term in Eq. (5) was included to account for possible pump emission, as applies, for example, when pumping Er 3⫹ ions at 1480 nm. The population densities N 1 (z) and N 2 (z) are obtained by solving the laser rate equations at steady-state. Assuming homogeneous broadening, these solutions are [21] N 1 (z) ⫽ N 0

冤

P p (z) 1⫹ ⫹ I pe,sat A p

n

冱 i⫽1

冥冫冤

P s (z,νi) I se,sat (ν i ) A s

P p (z) 1⫹ ⫹ I p,sat A p

n

冱I i⫽1

冥

P s (z,ν i) s,sat (ν i ) A s

(6)

where N 0 is the total ion density and P s (z,ν i) is the total (forward ⫹ backward) ASE power at position z and frequency ν i , P s (z,ν i) ⫽ P ⫹s (z,ν i ) ⫹ P ⫺s (z,ν i ). The population density N 2 (z) is obtained from Eq. (6) and the electron conservation condition N 1 (z) ⫹ N 2 (z) ⫽ N 0 . The quantities A p and A s are the effective areas of the pump and signal modes, respectively. They are introduced here as an approximation to account for the effect of the radial distributions of the pump, signal, and dopant on the population densities. They involve spatial overlap integrals between the pump and/or signal modes and the dopant spatial distribution across the core region [21]. For a fiber doped uniformly across its core and low gain, A p and A s can be approximated by relatively simple expressions [33] or replaced by the core area as a rougher estimate. More rigorous and accurate approaches should involve radial integration of the differential equations.

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The saturation intensities appearing in Eq. (6) are [21] I p,sat ⫽

hν p [σ a (ν p) ⫹ σ e (ν p)]τ 2

(7a)

I pe,sat ⫽

hν p σ e (ν p) τ 2

(7b)

I s,sat ⫽

hν i [σ a (ν i ) ⫹ σ e (ν i)] τ 2

(7c)

I se,sat ⫽

hν i σ e (ν i) τ 2

(7d)

where hν p and hν s are the pump and signal photon energies, respectively, and τ 2 is the excited-state lifetime. These equations assume no excited-state absorption (ESA) at either the pump or the signal wavelengths. The effects of ESA can easily be incorporated in this formalism by adding the relevant absorption term to the gain coefficient [see Eq. (3)] and/or to the pump absorption coefficient [see Eq. (5)] [21]. These equations also assume no ion clustering. In the presence of clusters, which tend to form at higher ion concentrations, a percentage of the ions act as unsaturable, nonradiative absorbers. They absorb pump photons, then return to the ground state rapidly without emitting a signal photon (i.e., they waste the pump power). The effects of clusters can be accounted for by adding an absorption term to the signal gain [see Eq. (3)] and pump absorption [see Eq. (5)] coefficients [21]. A mathematical description of these effects is presented (Chap. 11 and [12,34,35]). For a given fiber with known parameters and a given pump wavelength, the saturation intensities [see Eqs. (7)] are known and the effective areas A s and A p can be calculated. The remaining 2n ⫹ 1 unknowns are the pump power distribution P p (z) and the ASE power distributions P s⫾ (z,ν i). They are obtained by solving 2n ⫹ 1 coupled equations, namely 2n signal equations [see Eqs. (1)] and one pump equation [see Eq. (2)], subject to 2n ⫹ 1 boundary conditions. The latter specify the signal and pump power coupled into each fiber end, if any, which depends on the source configuration. In the most common case of unidirectional pumping discussed here, pump is coupled only at z ⫽ 0 and the pump boundary condition is P p (0) ⫽ P 0p. For a single-pass SFS with no optical feedback at either fiber end, the signal boundary conditions are P ⫺s (l,ν i ) ⫽ 0 and P s⫹ (0,ν i) ⫽ 0 for i ⫽ 1 to n, where l is the fiber length. If some feedback is present, the latter conditions are changed accordingly. For example, in a forward SFS (see Fig. 1a) if a fraction ε of the forward signal output power is recoupled into the fiber, the boundary conditions at z ⫽ l become P ⫺s (l,ν i) ⫽ εP ⫹s (l,ν i ) for i ⫽ 1 to n. For a forward double-pass SFS, the backward signal power is fully reinjected into the SFS (see Fig. 1c); the boundary conditions at z ⫽ 0 are P ⫹s (0,ν i )⫽ P ⫺s (0,ν i) for i ⫽ 1 to n. The very same equations and similar boundary conditions are used to model the gain and noise figure of fiber amplifiers (see Chaps. 10 and 11). Modeling the output power and spectrum of an SFS involves solving all 2n ⫹ 1 coupled differential equations. If the values of the pump, forward signal, and backward signal powers were known at z ⫽ 0, this equation system would be easy to solve numerically by propagating the pump and signal powers from z ⫽ 0 to z ⫽ l. However, this is not possible because the backward signal powers P s⫺ (z,ν i) are not known at z ⫽ 0. They


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are known at z ⫽ l only. This difficulty complicates root finding considerably, as the problem must now be solved iteratively using clever algorithms. 6.4.2 Four-Level Systems For superfluorescent sources based on four-level systems [23,25] the equations for the pump and the ASE powers are similar to the foregoing equations. They differ only in the form of the population densities N 1 (z) and N 2 (z), and in the fact that there is no signal ground-state absorption (GSA). Also, if the fiber scattering loss at the signal is small, as is generally true, the gain experienced by the forward and backward ASE waves are essentially identical, and the forward and backward output powers are also almost identical; that is, P ⫹s (l,ν i) ⬇ P ⫺s (0,ν i). This condition can be conveniently used as a criterion of convergence when solving the 2n ⫹ 1 coupled differential equations, which speeds up convergence dramatically. Convenient approximate expressions for the forward and backward output powers of a four-level SFS can also be obtained by describing their evolution in terms of the single-pass gain of the fiber (instead of in terms of the pump power) [23]. The dependence of the gain on pump power is then removed from the model. Following this approach, ⫾ the forward and backward ASE output power P out can be shown to be P ⫾out ⫽ P 0 [G 0 ⫺ 1] ξ 1

(8)

where G 0 is the single-pass gain at linecenter and ξ 1 is a dimensionless parameter [23] that depends on the gain spectral lineshape and G 0. As G 0 increases, ξ 1 decreases from a maximum value close to 1 (depending on the lineshape) to 0. This dependence is weak compared with the (G 0 ⫺ 1) dependence: for a Lorentzian lineshape, ξ 1 ⫽ 0.88 for G 0 ⫽ 10 (10 dB) and ξ 1 ⫽ 0.57 for G 0 ⫽ 100 (20 dB). The factor P 0 in Eq. (8) is the spontaneous power corresponding to one photon per mode: P 0 ⫽ 2hν s ∆ν s

(9)

where ∆ν s is the full width at half maximum (FWHM) of the small-signal gain spectrum. This result yields useful information concerning the conversion efficiency of an SFS. Equation (8) states that for a four-level SFS, the output power grows slightly sublinearly with G 0. Because P 0 is in the microwatt range, high gains are required to produce sizable output powers. For example, for the 4 F 3/2 → 4 I 11/2 transition of Nd 3⫹ in a silica fiber, hν s ⫽ 1.88 10 ⫺19 J, ∆ν s ⬇ 8.0 10 12 Hz (30 nm), and P 0 ⬇ 3.0 µW. For a 30-dB gain at linecenter and a gaussian lineshape, ξ 1 ⬇ 0.32 [23] and Eq. (8) predicts an output power ⫾ P out ⬇ 0.96 mW in each direction. As the pump power is increased, G 0 increases exponentially, and so does the ASE power. However, as the ASE power increases it saturates the gain. These two opposite effects are such that at high pump powers the output power grows linearly with absorbed pump power [23,25], just as in a fiber laser. For the 1.06-µm transition of Nd 3⫹, the gain increases slowly with pump power (by typically under 1 dB/mW) so that an Nd-doped SFS exhibits a more gradual threshold than a fiber laser [23,25]. Convenient closed-form expressions have been derived for the threshold of an SFS, and for the slope of its output power versus absorbed pump power curve, or conversion efficiency. They predict that, with sufficient pump power, large conversion efficiencies are possible. For a four-level transition with a unity quantum efficiency, in the limit of high pump power this conversion efficiency takes the form [23]:

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s⫽ε

hν s hν p

(10)

where ε ⫽ 1/2 for a single-pass SFS and ε ⫽ 1 for a double-pass SFS. In a double-pass SFS, the high-pump conversion efficiency approaches the ratio hν s /hνp . Essentially every absorbed pump photon is transformed into an output photon. The reason for this high conversion is that the gain is so large that the signal intensity triggers the relaxation of the excited electrons as fast as they are excited by the pump. For comparison, for a well-designed fiber laser with a unity quantum efficiency the conversion efficiency is also given by Eq. (10) with ε ⫽ 1 [36]. The main difference is that in a fiber laser the signal intensity in the fiber is increased by the optical resonator, so that the threshold, and consequently the overall pump power requirement, can be lower than in a double-pass SFS. In a single-pass SFS [ε ⫽ 1/2; see Eq. (10)], the conversion efficiency is half that of a double-pass SFS. This result is expected, since essentially equal signal powers are generated in two directions. For a four-level transition the efficiency cannot exceed about 50%. 6.4.3 Application to Er-Doped SFS The kind of predictions that can be made with this model are illustrated in Figure 2 for a single-pass Er-doped SFS with no feedback at either end. The pump power, forward and backward signal powers, and the gain per unit length are plotted along the fiber length. (The parameters of the fiber modeled here, listed in Ref. 21, are irrelevant for this discussion.) The forward ASE power grows from the pump input end and the backward ASE

Figure 2 Simulated pump power and signal power (in a 5-nm bandwidth at about 1529 nm) in both directions along a single-pass Er-doped SFS: computed for a 2.4-m length of the fiber of Ref. [21] pumped at 976 nm with 100 mW of launched power.


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power from the pump output end. The sum of these two signals (not represented for clarity) obviously exhibits a local minimum at some intermediate location (⬃0.6 m, in this example). At this point the gain is less depleted and thus maximum (see Fig. 2). This point of maximum gain is generally not located in the middle of the fiber, but is closer to the pump input end, because the far end of the fiber is not as strongly inverted. The rate of decay of the pump power is lower in the vicinity of the high-gain region (see Fig. 2) because fewer ions are in the ground state to absorb the pump. The backward signal power grows monotonically, whereas the forward power first grows, then decreases (see Fig. 2). This is because at the far end of the fiber fewer ions are inverted, and forward signal photons traveling through this region are absorbed. The maximum in the forward power occurs where the fiber gain goes through zero. On the other hand backward-traveling ASE starts being generated near this zero-gain point and, consequently, its growth is monotonic. Thus, in a single-pass SFS, the forward output power is lower than the backward output power. The effect of fiber length is illustrated in Figure 3 for three configurations. For very short fibers, the gain is nearly uniform along the fiber, and the forward and backward powers behave the same way. As the length is increased, the forward signal power increases, then decreases, eventually dropping to very close to zero because the gain is negative at the far end of the fiber. The double-pass backward SFS also exhibits a maximum: as the fiber is lengthened, absorption at its far end reduces the round-trip gain and thus the total output power. Consequently, for both the forward and double-pass SFS there is an optimum length that maximizes the output power. The curves shift to longer lengths with a 1475-nm pump because of pump emission and weaker pump absorption. In comparison, in the backward SFS the signal power increases monotonically with increasing fiber length (see Fig. 3). The output power is maximum for an infinite length [31] (in practice, long enough for ⬃200 dB of small-signal pump absorption). The back-

Figure 3

Simulated output power dependence on fiber length for three configurations of an Erdoped SFS pumped either at 976 nm or 1475 nm: computed for the fiber of Ref. [21] and a launched pump power of 100 mW.

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Figure 4 Dependence of the output power of a single-pass Er-doped SFS on launched pump power for the forward and backward direction: computed for the fiber of Ref. [21].

ward efficiency can then approach the quantum limit, which is ⬃64% with a 976-nm pump [31]. The reason is the following: In a very long three-level SFS, at the far end of the fiber the gain is negative, and forward-traveling photons are strongly absorbed. Thus, they excite electrons into the metastable level, which eventually relax and emit signal photons. A fraction of these photons are captured in the backward direction, where they are amplified by the fiber and add to the backward signal. Rayleigh backscattering is also a significant source of back-reflected ASE photons [14]. Because of the large gain, these small back-reflected signals contribute to a sizable increase in backward efficiency. Figure 4 shows the dependence of the output power on launched pump power for the same fiber with a length of 2.4 m. For both the forward and backward SFS, the output power grows linearly above some threshold, as in a fiber laser [36]. The knee in the curve at threshold is relatively sharp. This is because for the 1.55-µm transition of Er 3⫹ the gain grows very rapidly with increasing absorbed pump power, typically by a few to over 10 dB/mW, so that the device evolves rapidly from the unsaturated to the saturated regime. 6.5 Er-DOPED FIBER SOURCES (⬃1.55 ␮m) Most of the work on SFS has been done with the well-characterized 1.55-µm transition of Er 3⫹-doped fibers. This research has strongly benefited from extensive parallel studies of these fibers as amplifiers and lasers. Their high gain per unit pump power is ideal for producing low-threshold, efficient SFSs. These sources are typically pumped at 980 nm or 1480 nm where pump excited-state absorption (ESA) is negligible in silica-based fibers. 6.5.1 Output Power Table 1 summarizes the performance of representative Er-doped SFSs [9–12,16,37–39]. The highest conversion efficiency for a single-pass SFS (54%) was reported by Falquier

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Table 1 Summary of the Output Characteristics of Various Er-Doped SFS SFS type Forward Forward Forward Forward Backward Backward Backward Backward Double pass Double pass Double pass

Pump source

Threshold

Output power

976 nm Ti :S 1.48 µm LD 1.48 µm LD 1.053 µm Nd :YLF 978 nm Ti :S 976 nm Ti :S 1.48 µm LD 1.47 µm LD 1.48 µm LD 980 nm Dye 1.48 µm LD

25 mW (l) ⬃45 mW (na) 4.5 mW (l) (na) 12.5 mW (na) 25 mW (l) 4 mW (l) 7 mW (a) ⬃14 mW (l) (na) ⬃3 mW (l)

26 mW @ 212 mW (l) 3.8 mW @ 77 mW (na) 7 mW @ 32 mW (l) 1.03 W @ 4.5 W (na) 33 mW @ 124 mW (na) 73 mW @ 220 mW (l) 12.5 mW @ 32 mW (l) 13 mW @ 31 mW (a) 14 mW @ 49 mW (l) 2 mW @ 33 mW (l) 17 mW @ 32 mW (l)

Slope efficiency ∆λ (nm) Ref. ⬃14% ⬃17% 25% ⬎23% 30% 38% 45% 54% 44% ⬍6 % 56%

8 2 18 4 ⬃32 22 18 20 14 2 21

12 37 9 39 10 12 9 11 16 38 9

(a), absorbed pump power; (l), launched pump power; (na), not available.

et al. with a laser-diode-pumped backward SFS emitting 13 mW for 31 mW of launched pump power at 1.47 µm [11]. Similar characteristics were reported by Fevrier et al. [9] and Takada et al. [16]. The output power curve of a forward, a backward, and two doublepass SFSs are reproduced from Ref. 9 in Figure 5. As predicted, above threshold the output power grows almost linearly with pump power. These sources have the lowest threshold (less than 5 mW) of any reported SFSs. The forward SFS has a lower output power, and the double-pass SFSs have the highest output powers. This trend is also reflected in Table 1. For the Er-doped double-pass SFS, the current record is held by the 25-m device of Figure 5, which emitted nearly 17 mW with just 33 mW of launched

Figure 5

Measured output power versus absorbed pump power for various Er-doped SFSs pumped with a 1.48-µm laser diode. (From Ref. 9.)

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pump power [9]. The highest output power to date was reported in an Er/Yb co-doped fiber SFS that used a forward ASE source as a seed, which was amplified by a preamplifier and an amplifier, both made of Er/Yb co-doped fiber [39]. Pumped by a 4.5-W Nd:YLF laser at 1053 nm, it produced just over 1 W of output power, although its bandwidth was only 4 nm. 6.5.2 Emission Spectra Typical emission spectra are shown in Figure 6 for a backward and a forward SFS pumped at 976 nm at two different powers. The spectrum of an SFS is shaped by both the emission and absorption cross-section spectra of Er 3⫹. It typically exhibits two peaks, around 1529 and 1558 nm [40]. The forward and backward spectra are generally different. Their shape is a complex function of pump power and wavelength, fiber length, and source configuration [12]. If the fiber is relatively short and highly pumped, the gain is positive throughout the fiber, and the forward and backward sources produce spectra closely related to the emission cross-section spectrum (i.e., with a more pronounced peak around 1530 nm). If the fiber is long, the forward output is filtered by the absorbing far end of the fiber, and because absorption is stronger near 1530 nm, the forward spectrum has a more prominent peak near 1560 nm than the backward spectrum. This trend is clearly apparent in Figure 6. In a double-pass SFS, the output consists mostly of the photons that have traveled twice through the fiber, thus twice through the absorbing region, and the 1560-nm peak is even more prominent. Linewidths approaching or exceeding 20 nm have been reported for all three configurations (see Table 1). The spectrum depends on the core glass composition, which accounts for at least some of the variations in reported linewidths. Other representative spectra can be found elsewhere [30,40].

Figure 6 Measured superfluorescence spectra for a single-pass Er-doped SFS pumped at 976 nm: (a) backward, (b) forward. (From Ref. 21.)

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6.6 BROADBAND FIBER SOURCES AROUND 1 ␮m Three different dopants have been studied to produce emission in the 1-µm range, namely, neodymium (1.06 µm), ytterbium (0.976 and 1.04 µm), and praseodymium (1.049 µm). 6.6.1 Broadband Nd-Doped Fiber Lasers (1.06 ␮m) The first broadband fiber source to be demonstrated was an Nd-doped fiber laser LDpumped at about 820 nm (see first two entries in Table 2) [19] based on the principle presented in Section 6.3.1. It was made from 2–10 m of fiber doped with Nd 3⫹ and P 2 O 5, with a miniature high reflector and a 95% output coupler bonded to the polished fiber ends. As is typical for a fiber laser, the threshold was very low (1 mW absorbed). The output power was 2.5 mW for only 6.5 mW of launched pump. The conversion efficiency measured with a dye laser pump was 59%, which is one of the highest reported values for a fiber laser and approaches the theoretical limit [36] of λ p /λ s ⬇ 77%. With proper selection of the pump wavelength (λ p ⬎ 815 nm) the source linewidth was very broad and increased rapidly with pump power to an asymptotic FWHM value of 19 nm [19]. 6.6.2 Nd-Doped SFSs (1.06 ␮m) Neodymium-doped silica-based fibers have been used to demonstrate both single-pass and double-pass SFSs operating on the 4 F 3/2 → 4 I 11/2 transition (see Table 2, last six entries). Because of its relatively low gain per unit pump power, a single-pass Nd-doped SFS requires a comparatively high pump power to achieve a significant output power (e.g., third entry in Table 2). However, the same fiber used in the double-pass configuration (seventh entry in Table 2) gave excellent results, as illustrated in Figure 7a [23]. This source emitted 13 mW with 75 mW of absorbed pump power. The differential conversion efficiency (slope of the output curve) at this point was 75%, which is close to the theoretical limit of 78% predicted by Eq. (10). At low pump power, the linewidth of an SFS is close to the gain linewidth. For this transition in a silica-based host, it is in the range of 20–40 nm, depending on the host composition (see Chap. 2). As the pump power is increased, photons emitted near linecenter experience a higher gain than photons emitted near the edges of the spectrum, and

Table 2 Summary of the Output Characteristics of Broadband Nd-Doped Fiber Sources Around 1060 nm Type

Pump source

Fiber laser Fiber laser SFS (single-pass) SFS (single-pass) SFS (double-pass) SFS (double-pass) SFS (double-pass) SFS (double-pass)

LD Dye Dye LD LD LD Dye LD

Threshold

Output power

1 mW (a) 1.3 mW (a) ⬎65 mW (a) Not measured ⬃12 mW (l) ⬃50 mW (l) 35 mW (a) (na)

2.5 mW @ 6.5 mW (l) 18 mW @ 34 mW (a) 0.2 mW @ 65 mW (a) 3 mW @ 100 mW (l) 5.2 mW @ 45 mW (l) 80 mW @ 270 mW (l) 13 mW @ 75 mW (a) 320 mW @ ⬃1.75 W (l)

Pump wavelengths are in the range of 800–830 nm. (l), launched pump power; (a), absorbed pump power; (na), not available.

Slope efficiency ∆λ (nm) Ref. 50% 59% 1.2% ⬃3% 24% 41% 75% na

19 19 33 12 5 5 17 4.6

19 19 23 22 41 25 23 14

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Figure 7 Measured output power of several double-pass Nd-doped SFSs: (a) forward configuration using a standard fiber; (b) backward configuration using a double-clad fiber pumped with a high-power diode array and a 100% reflector; and (c) forward configuration using a different doubleclad fiber, the same pump, and a 2% reflector. (From: a, Ref. 23; b,c, Ref. 25.)

the linewidth decreases. For the double-pass SFS of Figure 7a, the linewidth dropped from 33 nm at low power to an asymptotic value of 17 nm at outputs of 5 mW and greater. [23]. The lineshape of Nd-doped SFSs can be adjusted by modifying the pump wavelength [20], for the same physical reason as the pump wavelength dependence of Nd-doped fiber lasers invoked in Section 6.3.1. At all powers the emission spectrum was free of longitudinal mode structure. Another study of a double-pass SFS utilized a phosphate fiber heavily doped with neodymium (1 wt%) [41]. This source emitted around 1053 nm, and it had a lower threshold and a good conversion efficiency (see fifth entry of Table 2), although its linewidth was unexpectedly narrow (5 nm). Several independent studies concur that both Nd-doped fiber lasers and SFSs are significantly more thermally stable than SLDs [8,42,43]. For example, to stabilize the mean wavelength of an LD-pumped Nd-doped SFS to ⬃1 ppm requires control of the temperature to 0.1°C and the pump power to 0.05 mW [43], which is relatively straightforward. An even lower requirement is anticipated from phosphate-based fibers [8], although their intrinsic temperature stability needs to be assessed. A clever solution to increase the output power of an Nd-doped SFS is the doubleclad Nd-doped fiber. This design was first developed by Snitzer and co-workers to effectively transfer the high power output of a low-spatial-coherence LD array to a doped core [44]. As described in Chapter 3, a double-clad fiber comprises a standard single-mode doped core, which carries the signal, surrounded by an undoped inner cladding, itself surrounded by an outer cladding with a lower refractive index, so that the inner cladding is a waveguide. The pump light from the LD array is coupled in the inner cladding, and


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because it travels partly through the core it is absorbed by the Nd ions. Because the inner cladding has a large area and NA, and its shape is matched to that of the pump beam, pump coupling is efficient [44]. The spatial overlap between the pump and the dopant distributions being lower than in a standard fiber, a longer fiber is required to absorb a given pump power. However, since the fiber propagation loss is negligible, this length increase has no adverse effect on the source performance. Other merits and designs of double-clad fibers are discussed at length in Chapter 3. Diode–array-pumped Nd-doped SFSs with high output powers have been reported with two types of double-clad fibers [14,25,26,44,45]. Figure 7b shows the output power versus pump power measured in a 10-m fiber pumped with a 1-W 806-nm LD array (see sixth entry in Table 2) [25]. As much as 80 mW was observed, or an overall conversion efficiency of 31%. The bandwidth was relatively small, around 5 nm at output powers of 40 mW or greater. The reduced slope efficiency compared with Figure 7a may be partly due to the fact that the latter is plotted versus absorbed pump power, whereas Figure 7b may have been plotted versus launched pump power. Another possible reason is loss of pump power in the multimode inner cladding. With a different double-clad fiber and a 2% (instead of 100%) reflector, the output power was about 50% lower (see Fig. 7c) [25]. Such a device still qualifies as a double-pass source because even with such a weak reflector most of its output originates from the amplified 2% reflection. Lower outputs were reported with a true single-pass double-clad SFS [22,24]. In one particular source, a 20m fiber pumped with a 500-mW LD array produced 3 mW and a bandwidth of 12 nm (fourth entry of Table 2) [22]. Although its output power is much lower than for a doublepass SFS, this source exhibits a larger bandwidth and a greater immunity to optical feedback. Double-clad Nd-doped fibers were also used in a source-amplifier tandem application, in which a primary superfluorescent fiber source of moderate power was used to seed a double-clad fiber amplifier pumped with a high-power diode array [14]. This configuration was designed to prevent lasing from Rayleigh backscattering in the source fiber. By pumping the seed source with a 500-mW LD array and the amplifier fiber with a 3-W array, a maximum superfluorescence output power of 320 mW with a bandwidth of 4.6 nm was observed (see Table 2, last entry). Although the bandwidth is relatively limited, this is the highest reported output power for an Nd-doped SFS. 6.6.3 Yb-Doped SFSs (0.974 and 1.04 ␮m) Ytterbium-doped fibers have produced superfluorescent emission around 0.974 or 1.04 µm using transitions between different Stark levels of the 2 F 5/2 (metastable) and 2 F 7/2 (ground) manifolds [46]. The 0.976-µm transition terminates on the lowest energy level of the ground state (three-level system). The 1.04-µm transition terminates on a higher, nearly unpopulated Stark level (essentially a four-level system). Because the shorter-wavelength transition has a larger emission cross section, in a short fiber it experiences a larger gain and a greater emission. On the other hand, in a long fiber the far end of the fiber is not fully inverted, GSA is large at 974 nm but negligible at 1040 nm, and 1040 nm is favored. As a consequence, nearly pure 974-nm emission was observed in short fibers, and pure 1040-nm emission in long fibers [46]. These two Yb-doped SFSs used double-pass configurations pumped at 850–900 nm with a cw dye laser [46] (see first two entries in Table 3). The fiber length was 0.5 m for

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Table 3 Summary of the Output Characteristics of Broadband Fiber Sources Using Yb 3⫹, Pr 3⫹, and Tm 3⫹ SFS type Yb-silica (DP) Yb-silica (DP) Yb-silica (SP) Yb-silica (DP) Yb-silica (DP) Pr-silica (SP) Pr-silica (DP) Pr-ZBLAN (SP) Tm-ZBLAN (SP)

λs (nm) 974 1040 1055 1060 1075 1049 1049 1306 1820

Pump source Dye (900 nm) Dye (850 nm) LD (975 nm) Ti: Al 2 O 3 (1010 nm) 3 LDs (980 nm) Dye (592 nm) Dye (592 nm) Ti: Al 2 O 3 (1017 nm) Col. cent. (1640 nm)

Threshold (a)

15 mW 22 mW (a) (na) (na) (na) ⬃80 mW (a) ⬃48 mW (a) 100 mW (l) 1.5 mW (l)

∆λ (nm) Ref.

Output power (a)

10 mW @ 35 mW 27 mW @ 70 mW (a) 485 mW @ ⬃1.3 W (l) 62 mW @ 366 W (i) 30 mW 32 mW @ 190 mW (a) 60 mW @ 190 mW (a) ⬃0.2 mW @ 540 mW (l) 2.3 mW @ 16.3 mW (l)

2 19 41 62 75 20 20 27 na

46 46 13 48 47 49 49 50 51

(l), launched pump power; (a), absorbed pump power; (SP), single-pass; (DP), double-pass; (na), not available.

optimum output power at 974 nm (at 30 mW of launched pump power), and 5 m for 1040 nm. The thresholds were reasonably low and the output power in the 10–30-mW range. These devices would provide interesting alternative sources to 1.06-µm Nd-doped SFSs. More recently, a high-power Yb-doped SFS was reported based on a double-clad fiber [13]. It used a 7.2-m fiber pumped with a 2-W broad-stripe LD via a novel Vgroove technique specifically designed to couple light into a double-clad fiber, with a 65% coupling efficiency. In the forward configuration, this source produced an output power of 180 mW around 1055 nm. In the backward configuration, it emitted 485 mW, which is the highest value reported for a Yb-doped SFS. At this power the spectrum was flat (⫾0.25 dB) and had a FWHM bandwidth of 41 nm. An important issue in broadband sources is spectral narrowing at higher output power. As a result of the wavelength dependence of the gain, high-gain wavelengths grow more rapidly than low-gain wavelengths and thus tend to rob the gain, producing a narrower SFS spectra at high pump power. This undesirable effect can be eliminated by utilizing a filter that introduces loss preferentially in the wavelength regions of high gain, which has been successfully implemented with two approaches, both in double-pass configurations [47,48]. In the first approach, a length of unpumped Yb-doped fiber placed between two lengths of independently pumped Yb-doped fiber served as a passive filter [47]. This LD-pumped SFS produced a flat output spectrum with a record FWHM linewidth of 75 nm at an output power of 30 mW, although no efficiency figure was reported. In the second approach, the forward output of a pumped Yb-doped fiber was first sent through a filter, which consisted of a pair of bulk-optic gratings followed by a spatial filter. It was then reflected, sent through the filter a second time, and coupled back into the Yb-doped fiber in the backward direction, where it was amplified. With a suitable fiber length (15 m) and 366 mW of incident pump power at 1010 nm from a Ti:sapphire laser, this SFS emitted 62 mW with a spectrum centered on 1060 nm and a 62-nm FWHM bandwidth. With fine adjustments of the spatial filter, the spectrum could be adjusted to have a peak-to-peak flatness as low as 0.5 dB [48]. Further amplification was also demonstrated with a built-in Nd-doped fiber amplifier pumped by an 815-nm laser diode. With a 30-mW launched pump power, the SFS output power was boosted to 108 mW and the FWHM bandwidth to 65 nm [48].


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6.6.4 Pr-Doped SFSs (1.049 ␮m) Superfluorescence emission has been observed at 1.049 µm using the 1 D 2 → 3 F 3,4 transition of Pr 3⫹ [49]. The fiber was pumped with a dye laser at 592 nm. Table 3 summarizes the characteristics reported for a single-pass and a double-pass SFS (sixth and seventh entries). The thresholds were relatively high (50–80 mW), but the slope efficiencies were fairly high, about 25% and 40%, respectively. 6.7 SFSs AROUND 1.3 ␮m The development of broadband sources around 1.3 µm has been impeded by the lack of rare earths exhibiting a high-gain transition close to this wavelength. Only one SFS in this wavelength range was reported, based on a Pr-doped fluorozirconate (ZBLAN) fiber (see eighth entry in Table 3) [50]. ASE from the 1 G 4 → 3 H 5 transition was observed at 1.306 µm by exciting the metastable manifold 1 G 4 directly with a 1.017-µm Ti:sapphire laser. In a single-pass SFS, it produced a broad emission (at least 27 nm) but the output was only 166 µW for a launched pump power of 540 mW. This low conversion efficiency was attributed to the small quantum efficiency of the 1 G 4 level (around 3%), which is largely nonradiatively coupled to the ground state [50]. It should be pointed out that for several applications the exact wavelength of the SFS around 1.3 µm is not critical. Consequently, several of the dopants with transitions around 1.3 µm that have failed to produce satisfactory lasers in the second communication window may actually perform adequately as SFSs. 6.8 SFSs AROUND 1.8 ␮m A superfluorescent fiber source around 1.82 µm was demonstrated in a Tm-doped fluorozirconate fiber (see last entry in Table 3) [51]. The reason for this choice of host is that the lifetime of the excited state 3 H 4 of Tm 3⫹ in fluorozirconate glass is considerably longer than in silica, by a factor of typically about 30, which leads to sources with much lower thresholds. In this SFS, Tm 3⫹ was used as a quasi–three-level system: it was pumped at 1.64 µm to excite the Tm 3⫹ ions from the ground state 3 H 6 into high-energy sublevels of the 3 H 4 manifold, and stimulated emission took place from the lower levels of this manifold back to the 3 H 6 level [51]. In the forward configuration, this SFS exhibited a launched power threshold of 1.5 mW and a maximum output power of 2.3 mW for a launched pump power of 16.3 mW (slope efficiency of ⬃15%). The pump source was a color center laser, although laser diode pumping is also possible: the same fiber pumped with a 1.64µm laser diode produced high-efficiency 1.82-µm lasers. The bandwidth of this SFS was not mentioned [51], although the wide stimulated emission spectrum of the Tm-doped fiber around 1.8 µm suggests that it may have been substantial.

6.9 POLARIZED Er-DOPED SFSs The emission and absorption properties of Er 3⫹ (and other rare earth ions) in a glass host are slightly anisotropic [52], which results in a slight polarization-dependent gain (PDG), typically a fraction of a decibel [53]. Thus in an SFS the two eigenpolarizations exhibit almost identical gains and the output is essentially unpolarized. Although this property

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Figure 8 Experimental polarized Er-doped SFS in the backward configuration. (From Ref. 11.) has some benefits, for some applications a polarized broadband output is preferable. This is true in particular for the FOG, in which half of the output of an unpolarized SFS is lost at the input polarizer [5]. This loss is eliminated with a linearly polarized SFS. A polarized SFS was first demonstrated in a backward double-pass SFS by placing a polarizer between the fiber and the high reflector [16]. It produced 14 mW of polarized output with a 14-nm bandwidth for 48 mW of pump power (see eighth entry of Table 1). Subsequent theoretical work showed that the output of an SFS can be polarized with little reduction in power by placing the polarizer at an optimum position along the fiber [32]. This is illustrated in Figure 8, which shows an experimental polarized backward SFS [11]. The pump polarization was aligned to the polarizer with a polarization controller to pump both segments of the Er-doped fiber. Alternatively, one could use a polarization-maintaining doped fiber. As the backward ASE travels (from right to left) toward the polarizer, its two polarization components experience essentially the same gain and carry nominally equal power. Past the polarizer, the polarization that has been attenuated grows from noise, while the other one grows from a stronger signal. Thus, in this segment, the total ASE power is reduced, the gain is higher, and the power in the desired polarization grows to a higher value, by some factor k, than without the polarizer. The same argument applies to the forward ASE. Energy conservation stipulates that k does not exceed 2. If the polarizer is placed at the pump input end, the SFS output is as strongly polarized as the polarizer’s extinction ratio (ER), but half its power is wasted. Placing the polarizer at the other end clearly has no effect. Thus, there is an optimum intermediate position for which the output is significantly polarized and yet carries substantially the same power as without a polarizer. This argument was confirmed theoretically using the model of Section 6.4.1 [11,54]. It showed that in a backward SFS, if the first segment has an optimum length and the second fiber segment is long enough the favored polarization carries nearly twice as much power as it does without a polarizer (i.e., k ⬇ 2). The optimum polarizer position is near the middle of the inverted region [11]. This optimum is broad, which relaxes fabrication tolerances, and a modest polarizer ER (20 dB) is sufficient. However, the polarizer loss needs to be low (less than ⬃0.5 dB) as such loss affects both the pump and signal and strongly negates the benefit of reduced gain saturation [11]. A backward polarized SFS was demonstrated using a low-loss polarizing fiber (see Fig. 8) [11,55]. With the polarizer optimally positioned, the polarized output power was 13 mW and the ER nearly 18 dB for 31 mW of absorbed pump power (see seventh entry in Table 1). This is 76% more power than without the polarizer (k ⫽ 1.76), or a reduction


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in pump power by a factor of 1.63, which is significant given the high cost of pump LDs. A similar performance was observed with a forward polarized SFS [55]. 6.10 NOISE CHARACTERISTICS OF SFSs The noise of an SFS has been studied by several authors [4,56,57]. The signal-to-noise ratio (SNR) of the signal received by a detector illuminated with an unpolarized thermal source such as an SFS is given by [56] SNR ⫽

⬍ Is ⬎ B 2eB ⫹ ⬍ I s ⬎ ∆ν

(11)

where ⬍ I s ⬎ is the mean photocurrent, e is the electron charge, B the detection bandwidth, and ∆ν the source optical linewidth. The first term in the denominator is shot noise (2eB ⬍ I s ⬎). The second term is excess noise, which is characteristic of all thermal sources and due to beating between the Fourier components of the broad optical signal [56]. If the source is broad enough [∆ν ⬎⬎ ⬍ I s ⬎/(2e)], the SNR is shot-noise limited. In the opposite limit, the SNR is beat-noise limited and equal to ∆ν/B. It is then proportional to the source bandwidth and independent of the detector current (i.e., it does not improve with power, unlike a shot–noise-limited source). The SNR depends only on the linewidth of the source and the detector current. These properties are applicable to all thermal sources, in particular SLDs. This behavior is illustrated in Figure 9, which shows the SNR measured for four types of broadband sources, namely a white light source, two SLDs (0.82 and 1.28 µm), and an Nd-doped double-pass SFS (1.06 µm) [57]. For the while light source, the spectrum is so broad that up to the highest detector current the SNR is shot-noise limited. The SNR behavior is quite different for the three other sources. It is almost shot-noise limited at

Figure 9 Measured signal-to-noise ratio of various broadband sources. The theoretical curves were computed from Eq. (11). (From Ref. 57.)

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low currents and slowly becomes beat-noise limited as the current increases. The SNR for the Nd-doped SFS behaves in much the same way as that of the SLDs. In the highcurrent limit, the SNR is independent of the detected power and in the range of 128– 131 dB. The experimental data points are in good agreement with the theoretical curves, calculated from Eq. (11) [57]. 6.11 MEAN WAVELENGTH STABILITY The broadband sources used in high-accuracy FOGs must exhibit a very stable mean wavelength. The mean wavelength ⬍ λ s ⬎ entering in the FOG scale factor is [58] ⬍ λs ⬎ ⫽

∫ spectrum λP(λ)dλ ∫ spectrum P(λ)dλ

(12)

where P(λ) is the normalized power density at wavelength λ s . The mean wavelength is primarily affected by five parameters, namely, the temperature T of the fiber, the pump power P p , the pump wavelength λ p , the pump state of polarization SOP p , and the feedback power F returning from the FOG. This dependence can be expressed as: ∆ ⬍ λs ⬎ ⫽

∂ ⬍ λs ⬎ ∂ ⬍ λs ⬎ ∂ ⬍ λs ⬎ ∆T ⫹ ∆P p ⫹ ∆λ p ∂T ∂P p ∂ λp ∂ ⬍ λs ⬎ ∂ ⬍ λs ⬎ ⫹ ∆SOP p ⫹ ∆F ∂SOP p ∂F

(13)

The first term in Eq. (13), ∂ ⬍ λ s ⬎/∂T, is the intrinsic thermal coefficient. It arises from the temperature dependence of the rare earth’s absorption and emission cross-section spectra. As the temperature changes, these spectra change, as do the SFS output spectrum and mean wavelength. The temperature dependence of the cross-sections vary significantly from fiber to fiber [59]. The term ∂ ⬍ λ s ⬎/∂T also depends on pump wavelength and pump power [60], as well as fiber length [10]. These dependencies are partly responsible for the wide range of experimental values reported for ∂ ⬍ λ s ⬎/∂T. For Nd-doped SFSs this range is about ⫺10 ppm/°C [43] to ⫺15 ppm/°C [8]. For Er-doped SFSs, values of ⫺3 to 8 ppm/°C [60], 3 ppm/°C [10], and 10 ppm/°C [38] have been reported. The second contribution in Eq. (13), ∂ ⬍ λ s ⬎/∂P p , arises from the dependence of the ASE spectrum on pump power through gain saturation. The main parameters that affect the pump power itself are the LD temperature and drive current. Measurements have shown that ∂ ⬍ λ s ⬎/∂P p depends on pump power and pump wavelength, and that it can be canceled to first order by proper selection of the pump power [60]. It also depends on fiber length, and the latter can be selected to cancel ∂ ⬍ λ s ⬎/∂P p [61]. This property widens the range of pump power that minimizes ∂ ⬍ λ s ⬎/∂P p , and it adds flexibility to the source design. This contribution can be made very small (less than 0.5 ppm) with standard control of the LD current (0.1 mA) and temperature (0.1°C) [61]. The third term, ∂ ⬍ λ s ⬎/∂λ p , reflects the dependence of the ASE spectrum on pump wavelength. The latter is affected by the LD temperature and current. When the pump wavelength varies, the pump power absorbed by the dopant changes, which affects the population inversion along the fiber and thus the ASE mean wavelength. This term can be minimized by selecting λ p at a maximum of absorption, which cancels first-order


335

variations in pump absorption [60]. This effect was confirmed experimentally in Er-doped SFS pumped at 980 nm [10,60]. The fourth term arises from the dependence of the mean wavelength on pump polarization. Because the pump is generally polarized, as discussed above, the gain produced by the doped fiber depends slightly on polarization. As a result, the SFS output is slightly polarized. It means that if the SFS output is sent through a polarizer, the mean wavelength of the transmitted signal will depend on the polarizer orientation. In other words, the two output eigenpolarizations exhibit different mean wavelengths. This effect can be sizable. In a particular backward Er-doped SFS, as the pump polarization was varied over all possible states, the mean wavelength varied by 110 ppm [62]. As the SFS temperature or the stresses within the SFS change, the distribution of the pump polarization along the doped fiber changes. Thus, the distribution of power between the two eigenpolarizations changes, and the overall mean wavelength varies. This effect was successfully reduced in a backward Er-doped SFS by depolarizing the pump with a Lyot fiber depolarizer placed between the pump source and the WDM coupler [62]. A second depolarizer was also placed at the output port to offset the slight polarizing effect of the WDM coupler. The sensitivity to pump polarization was thus reduced to less than 3 ppm. Another solution is to utilize a polarization-maintaining doped fiber. The last term in Eq. (13) accounts for the effect of the feedback power returning from the gyro (or any system to which the source is coupled), which affects the gain and thus the mean wavelength. The feedback power itself depends on the rotation rate (unless the gyroscope is operated in a closed-loop mode) and temperature. Simulations show that this contribution is fairly large, for example, around 20 ppm/dB for a backward SFS with ⫺40 dB of feedback [12]. It means that closed-loop operation or an isolator is mandatory to keep the mean wavelength stable against feedback variations. Assuming a temperature coefficient for the FOG feedback ∂F/∂T ⫽ 0.1 dB/°C, the gyroscope’s temperature must be controlled to ⬃0.5°C to achieve a 1-ppm stability. The general conclusion is that each one of these five contributions can be minimized by controlling one source parameter and, fortunately, a different parameter for each of them. The intrinsic term is largely controlled by the fiber spectroscopy, the second term by the fiber length, the third term by the pump wavelength, the fourth term by either depolarizing the pump or controlling the pump polarization along the doped fiber, and the last term by controlling the level of feedback. The magnitudes of these terms are expected to vary from fiber to fiber, which makes it difficult to draw general quantitative conclusions applicable to all fibers. However, independent studies involving different fibers have shown that an overall mean wavelength stability in the ppm range is achievable with reasonable control of the temperature and drive current of the source [10,63]. The control requirements can be further relaxed because the various contributions in Eq. (13) can have opposite signs, depending on operating conditions, and can thus partly or fully cancel each other [60]. For example, modeling showed that in a particular FAS, by selecting the right pump wavelength (976 nm) and pump power (60 mW) the pump power term was 0 ppm/mW and the intrinsic term was ⫹6 ppm/°C. By fine-tuning the pump wavelength around 976 nm, the pump-wavelength term could be adjusted to be ⫺6 ppm/°C without affecting these values (i.e., to first order it canceled the intrinsic term) [60]. Further improvement in source stability has been achieved by filtering [64]. The main physical origin of some of the foregoing contributions is the difference in gain between the 1530-nm peak and the 1550-nm shoulder of the Er-doped fiber. The mean wave-

336

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length of the source [see (Eq. (12)] can be pictured as the center of gravity of the spectrum. This center of gravity changes if the wavelength of the peak and/or the shoulder changes. Because the spectrum is not flat, the center of gravity will also change if both the peak and shoulder are infinitely stable in wavelength, but if their relative gain changes. This effect explains, for example, the change in mean wavelength due to changes in the feedback level. One possible method to reduce this general effect is to incorporate in the source a filter that eliminates either the peak or the shoulder of the gain spectrum [64]. This improvement was implemented in a double-pass SFS by replacing the broadband reflector (see Fig. 1c) by a wavelength-dependent fiber Bragg reflector that reflects only the shoulder area (approximately 1550–1560 nm) [64]. The merit of this approach over placing an external filter at the output (which reduces the output power) is that because some of the reflected signal has been removed, more gain is available to the narrower reflected signal compared with the same source with a broadband reflector. As a result, the output signal power is almost the same as with a broadband reflector. The mean wavelength of this filtered source varied by less than 10 ppm peak to peak over the ⫺40 to ⫹80°C temperature range. Two other contributions have not been budgeted in Eq. (13), because they cannot be expressed simply in terms of a partial derivative. The first one is the effect of the relative polarization of the pump and the feedback. As this quantity changes, primarily through temperature variations, because of PDG the powers in the two eigenpolarizations change. Since these two polarizations have slightly different spectra, the mean wavelength varies. Simulations show that for a backward SFS this effect depends weakly on pump power, pump wavelength, and feedback level. The mean wavelength change is 100–200 ppm when the pump and feedback polarizations, assumed linear, are changed from parallel to orthogonal, in broad agreement with experimental tests in an FOG [63]. This sensitivity was reduced to less than 10 ppm by placing a polarization scrambler between the gyroscope loop and the source. One last contribution is the pump mode. If the fiber carries multiple pump modes, each mode overlaps differently with the dopant profile and, therefore, yields a different gain and ASE spectrum. If power is exchanged between these modes along the doped fiber, the SFS mean wavelength changes. In an Er-doped SFS, this effect is nonexistent with a 1480-nm pump, where the fiber carries a single mode. However, it can be present with 980-nm pumping. Numerical simulations of a backward SFS showed a high mean wavelength sensitivity to mode coupling, around 1400 ppm when the pump power is fully exchanged from the LP 01 to LP 11 mode [21]. It is thus essential to use a fiber that supports a single pump mode. For a double-pass SFS the sensitivity is considerably lower [21], although a single-mode pump may still be needed to accomplish a stability in the part per million range. The mean wavelength stability of other broadband sources has been studied, in particular the broadband Nd-doped fiber laser [42], Nd-doped SFSs [8,43], and the Er-doped FAS [63]. Compared with the backward SFS, the FAS has a mean wavelength that is less sensitive to variations in pump wavelength, feedback power, and feedback polarization, but more sensitive to variations in pump power and temperature. For the particular fiber studied, the FAS exhibited a superior overall wavelength stability of 4 ppm with reasonable control of the source parameters [63]. 6.12 CONCLUSIONS Several types of broadband fiber sources utilizing transitions in Er 3⫹, Nd 3⫹, Yb 3⫹, Pr 3⫹, and Tm 3⫹ have been demonstrated in a variety of configurations, including fiber lasers,


337

superfluorescent sources, and wavelength-swept fiber lasers. Er-doped superfluorescent sources have emerged as the most versatile sources, and they are now the most advanced devices. They are capable of producing a high-power (hundreds of milliwatts) signal around 1.55 µm, with a large bandwidth (10–30 nm). Their efficiency is very high, typically in excess of 50%, so that they are routinely pumped with a low-power (under 40 mW) laser diode and they are very compact. They can also be configured to produce a strongly polarized output with minimal output power sacrifice. For fiber-optic gyroscope applications, the fiber parameters can be selected to produce a highly stable mean wavelength, of the order of 1 ppm, by applying reasonable control to a few of the source and FOG parameters. These exceptional properties make superfluorescent fiber sources the light source of choice for the fiber-optic gyroscope and a number of other commercial applications, including in medicine. Other than the evaluation of alternative dopants to produce broadband light at other wavelengths, current activities are focusing on the development of broadband sources with higher power, with flat spectra tailored to communication applications, and with a greater mean wavelength stability. REFERENCES 1. C. C. Cutler, S. A. Newton, H. J. Shaw. Limitation of rotation sensing by scattering. Opt. Lett. 5:488–490 (1980). 2. K. Bohm, P. Marten, K. Petermann, E. Weidel, R. Ulrich. Low-drift fibre gyro using a superluminescent diode. Electron. Lett. 17:352–353 (1981). 3. R. A. Bergh, B. Culshaw, C. C. Cutler, H. C. Lefevre, H. J. Shaw. Source statistics and the Kerr effect in fibre-optic gyroscopes. Opt. Lett. 7:563–565 (1982). 4. K. Iwatsuki. Excess noise reduction in fiber gyroscope using broader spectrum Er-doped superfluorescent fiber laser. IEEE Photon. Technol. Lett. 3:281–283 (1991). 5. R. A. Bergh, H. C. Lefevre, H. J. Shaw. An overview of the fiber-optic gyroscope. J. Lightwave Technol. 2:99–107 (1984). 6. C. S. Wang, J. S. Chen, R. Fu, V. S. Sunderam, R. Varma, J. Zarrabi, C. Lin, C. J. Hwang. High power long life superluminescent diode. In: Fiber Gyros: 10th Anniversary Conference. Proc SPIE 719:203–207 (1986). 7. R. P. Moeller, et al. Open-loop output and scale factor stability in a fiber optic gyroscope. J. Lightwave Technol. 7:262–269 (1989). 8. P. R. Morkel, E. M. Taylor, J. E. Townsend, D. N. Payne, Wavelength stability of Nd 3⫹-doped fibre fluorescent sources. Electron. Lett. 26:873–875 (1990). 9. H. Fevrier, J. F. Marcerou, P. Bousselet, J. Auge, M. Jurczyszyn. High power, compact 1.48 µm diode-pumped broadband superfluorescent fibre source at 1.55 µm. Electron. Lett. 27: 261–263 (1991). 10. D. C. Hall, W. K. Burns, R. P. Moeller. High-stability Er 3⫹-doped superfluorescent fiber sources. IEEE J. Lightwave Technol. 13:1452–1460 (1995). 11. D. G. Falquier, J. L. Wagener, M. J. F. Digonnet, H. J. Shaw. Polarized superfluorescent fiber source. Opt. Lett. 22:160–162 (1997). 12. P. F. Wysocki. Broadband erbium-doped fiber sources for the fiber-optic gyroscope. PhD dissertation, Applied Physics Department, Stanford University, Stanford, 1992. 13. L. Goldberg, J. P. Koplow, R. P. Moeller, D. A. V. Kliner. High-power superfluorescent source with a side-pumped Yb-doped double-cladding fiber. Opt. Lett. 23:1037–1039 (1998). 14. J. D. Minelly, P. R. Morkel, K. P. Jedrzejewski, E. R. Taylor, J. Wang, D. N. Payne. Nd 3⫹doped singlemode fiber superfluorescent source with 320 mW output power. Electron. Lett. 29:1613–1614 (1993). 15. E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C. A. Puliafito, J. G. Fujimoto. In vivo retinal imaging by optical coherence tomography. Opt. Lett. 18:1864– 1866 (1993).

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60. P. F. Wysocki, M. J. F. Digonnet, B. Y. Kim. Wavelength stability of a high-output, broadband, Er-Doped superfluorescent fiber source pumped near 980 nm. Opt. Lett. 16:961–963 (1991). 61. D. C. Hall, W. K. Burns. Wavelength stability optimisation in Er 3⫹-doped superfluorescent fibre sources. Electron. Lett. 30:653–654 (1994). 62. D. G. Falquier, M. J. F. Digonnet, G. S. Kino, H. J. Shaw. Polarization Dependence of the Mean Wavelength of Er-Doped Superfluorescent Fiber Sources. SPIE Proc. Doped Fiber Devices II. 3542:26–29 (1998). 63. J. L. Wagener, M. J. F. Digonnet, H. J. Shaw. A high-stability fiber amplifier source for the fiber optic gyroscope. J. Lightwave Technol. 15:1689–1694 (1997). 64. T. Gaiffe, P. Simonpie´tri, J. Morisse, N. Cerre, E. Taufflieb, H. C. Lefe`vre. Wavelength stabilization of an erbium-doped-fiber source with a fiber Bragg grating for high-accuracy FOG. In: Fiber Optic Gyros: 20th Anniversary Conference. Proc. SPIE 2837:375–380 (1996).

7 Q-Switched Fiber Lasers MICHEL MORIN, ROBERT LAROSE, and FRANC ¸ OIS BRUNET Institut National d’Optique, Sainte-Foy, Que´bec, Canada

7.1 INTRODUCTION Thanks to waveguiding, the high gains required for efficient pulsed operation of fiber amplifiers and lasers can be easily achieved with low-power laser diode pumps. The gain medium is then used as an energy storage device to either amplify or generate short pulses. This chapter discusses the generation and amplification of pulses on a nanosecond time scale by rare earth doped fiber devices. Recent increases in laser diode power and improvements in source design have led to a steady rise of the pulse energy and peak power of fiber lasers to the 500 µJ and multikilowatt level, respectively. Such short and intense pulses are anticipated to find applications in nonlinear optics, distributed sensing, optical time domain reflectometry, range finding and LIDAR systems. Section 7.2 presents a theoretical description of pulsed amplification and oscillation in doped single-mode fibers. It provides a basic understanding of the mechanisms at play in amplifiers and Q-switched lasers and provides several mathematical tools to analyze them. Both three- and four-level devices are discussed. Section 7.3 reviews the different methods that can be used to Q-switch a fiber laser. It also provides an up-to-date tabulation of performances achieved by pulsed fiber lasers operating in the nanosecond range. Finally, Section 7.4 discusses factors that limit the performance of such sources. 7.2 THEORY OF OPERATION The objectives of the present section are twofold: (1) to provide a basic understanding of the mechanisms involved in the amplification of short pulses with a fiber amplifier and in the generation of short pulses with a Q-switched fiber laser; (2) to provide theoretical models to analyze these devices. The discussion focuses essentially on energy and time 341

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and does not consider the spectral performance of pulsed devices. It is rather general in scope and relies on the use of normalized variables to reduce the number of parameters involved in the analysis. Both three-level dopants with a long-lived upper laser level (e.g., erbium; Er 3⫹) and four-level dopants with a short-lived upper laser level (e.g., neodymium; Nd 3⫹) are discussed. The analysis relies mostly on a rate equation formalism applicable to uniform intensity beams, which has been applied with great success to the study of bulk amplifiers and lasers. This formalism presents the advantage of providing a wide range of analytical results and a good understanding of pulsed amplifiers and oscillators. It is shown how and under what circumstances this formalism can be applied to the study of guided amplification and oscillation, thereby avoiding the complex and time-consuming numerical analyses required to model rigorously a pulsed single-mode fiber device. Amplifiers are discussed first. Relevant questions relating to pumping (excitation efficiency, gain recovery, and energy storage) and energy extraction (pulse distortion, and extraction efficiency) are examined. The understanding gained from this study is then applied to Q-switched lasers, which can be viewed as self-seeded amplifiers. Analytical expressions are provided, which can be used to determine all relevant characteristics (energy, duration, and peak power) of pulses generated by a Q-switched fiber laser. Both single-shot and repetitive operations are discussed, the second one being by far the most advantageous with continuous-wave (CW)-pumped fiber amplifiers and Q-switched lasers. 7.2.1 Rate Equation Formalism Basic Assumptions The laser rate equations can be used to describe the behavior of pulsed amplifiers and oscillators provided the temporal dynamics involved are slow compared with the reciprocal of the laser transition linewidth, a condition that is well met in the present instance. Contrary to the situation encountered in mode-locked lasers, in Q-switched lasers the optical pulses are not short enough to be affected by dispersion. Nonlinear effects are ignored in this description: the limitations they impose on achievable performances are addressed in Section 7.4.2. Pulse shaping is thus assumed to be essentially determined by time-varying saturation effects in the gain medium. The following theoretical developments bear some resemblance to those presented [1] for CW sources, and some effort has been made to use the same notation. Three-Level Laser Material A three-level laser transition is modeled according to the energy level diagram presented in Figure 1, which is applicable to the important case of an Er-doped fiber pumped at 980 nm. Ions in the ground state are excited to a pump band by absorption of a pump photon of energy hv p , where h is Planck’s constant and v p the pump frequency. Relaxation to the upper laser level takes place very rapidly by multiphonon interaction. This mechanism being usually much faster than typical pumping rates, it can be considered instantaneous, so that the total ion population is divided between levels 1 and 2 only. Decay from the upper laser level to the ground state by emission of a spontaneous photon of energy hv s , where v s is the signal optical frequency, occurs with a time constant τ 2 . The rates of stimulated transitions between the laser levels, W e and W a , are determined by the laser field intensity and the emission (σ e) and absorption (σ a) cross sections. Excited-state absorption of the pump and of the laser field are left out of this model, because they play

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Figure 1 Simplified energy-level diagram of a three-level laser with possible excited-state absorption at the pump wavelength. Excited-state absorption of the pump and of the laser field are left out of the present model, because they play no part in current practical systems (From Ref. 1.)

no part in current practical Er-doped lasers operating close to 1.55 µm. The evolution of the laser level populations is thus described by the following rate equations:

冤

冥

∂N 2 (z,t) 1 ⫽ [R 13 (z,t) ⫹ W a (z,t)]N 1 (z,t) ⫺ W e (z,t) ⫹ N 2 (z,t) ∂t τ2

(1a)

N 1 (z,t) ⫹ N 2 (z,t) ⫽ N 0

(1b)

and

where N j (z,t) is the population density in level j at position z along the fiber and at time t, and N 0 is the total ion concentration. The transition rates are equal to R 13 (z,t) ⫽

σ p (I ⫹p (z,t) ⫹ I ⫺p (z,t)) hv p

(2a)

W a (z,t) ⫽

σ a (I ⫹s (z,t) ⫹ I ⫺s (z,t)) , hv s

(2b)

W e (z,t) ⫽

σ e (I ⫹s (z,t) ⫹ I ⫺s (z,t)) , hv s

(2c)

where σ p is the ground-state absorption cross section of the pump, and I p⫹ (I ⫹s ) and I ⫺p (I s⫺) represent the intensity of the pump (signal) mode propagating in the positive and negative z direction, respectively. Equations (1) and (2) describe the temporal evolution of the population inversion at a position z along the fiber. The model must be completed by equations describing the evolution of the pump and signal intensities, which can be derived by considering the energy balance at each point along the fiber [2]. These equations can be written as

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冤1c ∂t∂ ⫾ ∂∂z冥 I (z,t) ⫽ ⫺σ I (z,t)N (z,t) ⫾ p

⫾ p p

(3)

1

for the pump intensities, and

冤1c ∂t∂ ⫾ ∂∂z冥 I (z,t) ⫽ σ I (z,t)[N (z,t) ⫺ γ N (z,t)] ⫹ ∆ΩN4πτ(z,t)hv ⫾ s

⫾ e s

2

2

s

1

s

(4)

2

for the signal intensities, where γ s ⫽ σ a /σ e . The first term on the right hand side of Eq. (4) represents the contribution of stimulated transitions to the laser field. The second term originates from spontaneous emission, ∆Ω/4π representing the fraction of spontaneous photons that are guided in each direction by the optical fiber. Four-Level Laser Material The energy diagram of a four-level laser transition is illustrated in Figure 2. Relaxation from the pump band to the upper laser level is still assumed to be fast enough to impede any significant population buildup in the pump band. In an ideal four-level laser material, the lower laser level also remains empty because of fast relaxation to the ground state. This assumption must be exercised with care in Q-switched lasers producing pulses with a duration comparable with the relaxation time of the lower laser level. A significant population may then occur in the lower laser level, which reduces the available population inversion [3]. In Nd-doped glass, the relaxation time of the lower laser level is shorter than 1 ns and is deemed negligible [4]. The populations of levels 1 and 2 thus evolve according to

冤

冥

1 ∂N 2 (z,t) ⫽ R 13 (z,t)N 1 (z,t) ⫺ W e (z,t) ⫹ N 2 (z,t) ∂t τ2

(5)

and Eq. (1b). The evolution of the pump intensities is still described by Eq. (3), whereas the evolution of the signal intensities is now described by

冤1c ∂t∂ ⫾ ∂∂z冥I (z,t) ⫽ σ I (z,t)N (z,t) ⫹ ∆ΩN4πτ(z,t)hv . ⫾ s

⫾ e s

2

s

2

2

Figure 2 Simplified energy level diagram of a four-level laser (From Ref. 1.)

(6)

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Normalized Formulation For convenience, the previous equations are recast as follows: ∂m 2 ⫽ [i ⫹p ⫹ i ⫺p ]m 1 ⫺ m 2 ⫺ [i s⫹ ⫹ i ⫺s ][m 2 ⫺ γ s m 1] ∂ t′

(7a)

m1 ⫹ m2 ⫽ 1

(7b)

冤cτL ∂t′∂ ⫾ ∂∂z′冥 i

⫾ p

⫽ ⫺α p Li p⫾ m 1

(7c)

2

and

冤cτL ∂t′∂ ⫾ ∂z′∂ 冥i

⫾ s

2

⫽ g max Li s⫾ [m 2 ⫺ γ s m 1] ⫹

∆Ω g max Lm 2 4π

(7d)

where t′ ⫽ t/τ 2 is the time variable normalized to the lifetime of the upper laser level, z′ ⫽ z/L is the longitudinal position normalized to the fiber length L, i ⫾p,s ⫽ I ⫾p,s /I sat p,s are the intensities normalized to the relevant saturation intensity (i.e., the pump saturation intensat sity I sat p ⫽ hv p /σ p τ 2 or the signal saturation intensity I s ⫽ hv s /σ e τ 2). Moreover, m j ⫽ N j /N 0 is the local fractional population in level j, α p ⫽ σ p N 0 is the unsaturated pump absorption coefficient and g max ⫽ σ e N 0 is the maximum achievable gain coefficient (i.e., gain per unit length) in a fully inverted gain medium. This set of equations can be used to model both three-level and four-level gain media, the constant γ s vanishing in the second case. Equations (7) allow for bidirectional pumping and signal propagation. Populations and field intensities are assumed to vary longitudinally and temporally. These coupled partial differential equations must be solved with boundary conditions appropriate for the system under study. Usually, a numerical solution is required. However, simplifications are often used to make these equations more amenable to analysis and to gain better insight into the behavior of pulsed amplifiers and oscillators. It is customary to distinguish between excitation of the gain medium and energy extraction, as these operations are quite different in character. In a first step, a population inversion builds up within the pumped gain medium. The situation is then dominated by ground-state absorption of the pump mode and spontaneous emission. Following this, the stored energy is extracted by a short pulse, on a time scale so short that pumping and spontaneous emission are negligible: the situation is then dominated by the signal and stimulated emission. These steps can be analyzed independently by retaining in the foregoing equations only the terms relevant to each regimen, as shown in the following sections. Waveguiding Effects Except for the angular capture factor ∆Ω, Eqs. (7) leave out the transverse aspects of the situation. As discussed [1], transverse modeling is usually carried out through the evaluation of spatial overlap integrals between the intensity profiles of the pump and signal modes and the rare earth ion concentration profile. This approach amounts to modeling the rare earth ion-doping as an imaginary perturbation of the index of refraction of the fiber. This results in an imaginary perturbation of the propagation constant of the fiber modes, which are thus either amplified or attenuated as they propagate along the fiber. However, the modes preserve their transverse profile. According to the variation theorem for dielectric waveguides, the attenuation coefficient or the gain coefficient of the modes

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can be evaluated through an overlap integral between the modal fields of the unperturbed guide and the transverse profile of the refractive index perturbation [5,6]; that is ∆β v ⫽ 2ωε 0

∫ n(r)∆n(r)E v (r) ⋅ E*v (r)d 2 r ∫ [E v (r) ⫻ H*v (r) ⫹ E*v (r) ⫻ H v (r)] ⋅ zˆd 2 r

(8)

where r represents the position in a plane perpendicular to the fiber axis, zˆ is a unit vector along the fiber axis, ω is the angular frequency of oscillation, ε 0 is the dielectric constant of vacuum, n is the index of refraction and ∆n its perturbation, and E v and H v are the electric and magnetic fields of mode v, respectively. The modal fields are assumed to propagate as exp(⫺jβ v z). In a weakly guiding fiber, the index of refraction is nearly constant and can be taken out of the integral in the numerator of Eq. (8). Likewise, the modes are very nearly transverse electromagnetic (TEM) waves with negligible longitudinal field components. Eq. (8) then becomes: ∆β v ⬇

2π ∫ ∆n(r)I v (r)d 2 r λ ∫ I v (r)d 2 r

(9)

where I v represents the intensity of mode v. A local gain coefficient g(r) can be represented by an imaginary perturbation to the index of refraction; that is, ∆n(r) ⫽ j

λ g(r) 4π

(10)

As a result, the mode is amplified as a whole, with an effective power gain coefficient g v ⫽ j(∆β*v ⫺ ∆β v) ⬇

∫ g(r)I v (r)d 2 r ∫ I v (r)d 2 r

(11)

Absorption can be treated in a similar fashion. According to this perturbation theory, the power P ⫾s carried by a signal mode thus varies over a small-distance increment ∆z as P ⫾s (z ⫾ ∆z,t ⫹ ∆z/v s) ⫽ P ⫾s (z,t) exp(g s (z,t)∆z),

(12a)

where g s (z,t) ⫽

冮 σ [N (r,z,t) ⫺ γ N (r,z,t)]s (r)d r e

2

s

1

0

2

(12b)

is the power gain coefficient of the signal mode and v s is its group velocity, nearly equal to the speed of light within the single-mode fiber material. The function s 0 (r) appearing in Eq. (12b) is the normalized intensity profile that relates the local intensity I s⫾ (r,z,t) of the signal mode to its power P ⫾s (z,t) [1]; that is, I ⫾s (r, z, t) ⫽ P s⫾ (z, t)s 0 (r)

(13)

Retaining only the first-order terms in ∆z, Eq. (12a) is consistent with the following partial differential equation: 1 ∂P ⫾s (z,t) ∂P s⫾ (z,t) ⫾ ⫽ g s (z,t)P ⫾s (z,t) vs ∂t ∂z

(14)

which is the time-varying equivalent of Eq. (4b) in Ref. [1]. Such an equation can be derived for the pump powers P ⫾p (z,t) as well:

347


1 ∂P ⫾p (z,t) ∂P ⫾p (z,t) ⫾ ⫽ g p (z,t)P ⫾p (z,t) vp ∂t ∂z

(15a)

where

冮

g p (z,t) ⫽ ⫺ σ p N 1 (r,z,t)p n (r)d 2 r

(15b)

is a negative gain coefficient and v p is the group velocity. The function p n (r) is the normalized intensity profile of the pump, which relates the local intensity of the pump I ⫾p (r,z,t) to its power [1]: I ⫾p (r,z,t) ⫽ P ⫾p (z,t)p n (r) ⫽ P ⫾p (z,t)r n (r) cos 2 (nφ)

(16)

where (r,φ) are transverse cylindrical coordinates attached to the axis of the fiber. Equation (16) allows for a pump mode of azimuthal order n. Equation (15) is the ‘‘guided’’ equivalent of Eq. (3). Likewise, the similarity between Eq. (14) and Eq. (4) or Eq. (6) is clear, except for the lack of a spontaneous emission term. Until now, the strength of the spontaneous emission contribution to the signal intensity has been assumed to depend on the capture angle of the fiber. This geometrical view needs to be modified, especially in a single-mode fiber. A coupling factor must be evaluated that takes into account the transverse distribution of the population inversion as well as the field distribution of the mode under consideration. This so-called spontaneous emission factor represents the fraction of spontaneous photons that contribute to the buildup of the mode power [7]. Given that the index-guided modes of the unperturbed waveguide are power orthogonal, spontaneous emission is found to contribute one photon per unit bandwidth in each mode [8]. To include spontaneous emission, Eq. (14) must be modified to 1 ∂P ⫾s (z,t) ∂P ⫾s (z,t) ⫾ ⫽ g s (z,t)P s⫾ (z,t) ⫹ g e (z,t)P 0 vs ∂t ∂z

(17a)

where g e (z,t) ⫽ σ e

冮 N (r,z,t)s (r)d r 2

0

2

(17b)

and P 0 ⫽ 2hv s ∆v is an equivalent noise input power that depends on the bandwidth ∆v of the signal. A more rigorous description of the amplified spontaneous emission can be developed when necessary, which takes into account the spectral variation of the emission and absorption cross sections. A set of equations similar to Eqs. (17) must then be solved, each describing the evolution of the spontaneous emission power within a narrow spectral domain [9,10]. An alternative approach to model the whole spectrum of spontaneous emission is to adjust the value of bandwidth ∆v, which then represents an equivalent spontaneous emission bandwidth [10]. Amplification of the mode as a whole by a localized gain distribution must involve some radial flow of energy [6]. For example, if rare earth ions are present only in the fiber core, some energy must flow outward to amplify the wings of the modes extending within the cladding. Under most circumstances, the energy flow remains predominantly along the fiber axis. Local saturation of the gain g(r) (or of the absorption) can then be assumed to result from the intensity of the modes of the unperturbed fiber. This is actually

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a necessary condition for the variation Eq. (8) to be valid: the perturbation must be small enough not to affect significantly the modal field profiles. This will be true if |∆n | ⫽

gλ (NA) 2 ⬍⬍ δn ⫽ 4π 2n

(18)

where δn is the real change in refractive index that provides guiding within the unperturbed fiber. Equation (18) is very well met in practice. (One should consider also the change in the real part of the refractive index resulting from the presence of the rare earth ions: the overall conclusion remains the same.) The validity of this formalism was verified by careful measurements in an Er-doped fiber amplifier [11]. Accordingly, Eqs. (1) and (5) can still be used to describe the evolution of the local population inversion, but where the local intensities are now the mode intensities as given in Eqs. (13) and (16). The population evolution equation thus becomes: ∂N 2 (r,z,t) [P ⫹p (z,t) ⫹ P ⫺p (z,t)] p n (r)N 1 (r,z,t) ⫽ ∂t τ 2 I sat p [P ⫹s (z,t) ⫹ P ⫺s (z,t)] s 0 (r)[N 2 (r,z,t) τ 2 I sat s N (r,z,t) ⫺ γ s N 1 (r,z,t)] ⫺ 2 τ2 ⫺

(19)

The local population evolution described by Eq. (19) is consistent with the global amplification or attenuation of the signal and pump modes described in the foregoing. Energy is extracted locally and redistributed over the entire mode cross section by the waveguiding action of the optical fiber. (The foregoing propagation equations for the pump and signal powers can be derived by treating the intensity amplification [or attenuation] locally at each point of the mode profile and integrating over the entire transverse cross section to obtain a global gain [or attenuation] coefficient. A purely local approach to model amplification is justifiable in the context of propagation over an infinitesimal distance. However, using it to describe amplification over macroscopic lengths amounts to neglecting the waveguiding action of the fiber [12].) As long as amplification occurs over distances that are much longer than the characteristic waveguiding distance (β ⫺1 v ), which is another way of stating the condition of validity of the perturbation approach, it will manifest itself as a global amplification of the mode. The mode profile remains otherwise unchanged. Equations (15), (17), and (19) are coupled and must be solved in order to provide a complete and rigorous description of pulsed fiber lasers and amplifiers, which is a very demanding numerical task. Their complexity results from the coupling between the local energy extraction and the global amplification of the mode. Guiding effects have been discussed at length for CW oscillation [1]. In general, numerical evaluations are required because of the saturation of the transverse gain profile, even though approximate solutions can be derived. The situation is even more complicated in the present instance, because overlap integrals now depend on time as well as position along the fiber. To our knowledge, no rigorous numerical analysis of pulsed fiber devices that includes transverse effects has yet been published. To simplify the discussion and focus on aspects specific to the pulsed operation of fiber amplifiers and oscillators, in the following transverse effects will be addressed mostly qualitatively.

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7.2.2 Gain Medium Excitation Pumping Dynamics The analysis of pumping is greatly simplified by assuming that no signal field is present. Under these conditions, and assuming unidirectional pumping, as is applicable to many systems, Eqs. (7) reduce to ∂m 1 ⫽ 1 ⫺ [1 ⫹ i p]m 1 ∂t′

(20a)

and

冤cτL ∂t′∂ ⫹ ∂z′∂ 冥i ⫽ ⫺α Li m p

p

p

1

(20b)

2

The change of variables z′l ⬅ z′

and

t′l ⬅ t′ ⫺ z′L/cτ 2

(21)

simplifies this set of equations to [2] ∂m 1 ⫽ 1 ⫺ [1 ⫹ i p]m 1 ∂t′l

(22a)

∂i p ⫽ ⫺α p Li p m 1 ∂z′l

(22b)

and

The variable z′l still represents the normalized position along the fiber, whereas the variable t′l now represents the normalized time within the pump pulse local referential. If we assume, for example, that the pump pulse enters the fiber at z′ ⫽ 0 and at time t′ ⫽ 0, t′l ⫽ 0 corresponds to the time of arrival of the pump pulse at each position along the fiber. Integration of Eq. (22b) along the fiber length is straightforward and leads to in ˆ 1 (t′l )] i out p (t′l ) ⫽ i p (t′l ) exp[⫺α p Lm

(23)

where ˆ j (t′l ) ⫽ m

冮

1

m j (z′l ,t′l )dz′l

(24)

0

and where i pin (t′l ) ⫽ i p (0,t′l ) and i out p (t′l ) ⫽ i p (1,t′l ) are the input and output pulse intensity, respectively. Equation (23) states that the intensity of a temporal slice of a pump pulse leaving the optical fiber is equal to the intensity of the same slice as it entered the optical ˆ 1 (t′l ) reprefiber multiplied by the integrated attenuation that it experienced. The quantity m sents the ground-state population integrated over the fiber length that has been encountered by the pump pulse slice. Insertion of Eq. (22b) into Eq. (22a) and subsequent integration along the fiber length leads to ˆ 1 (t′l ) 1 out ∂m ˆ 1 (t′l ) ⫹ [i p (t′l ) ⫺ i inp (t′l )] ⫽1⫺m ∂t′l αp L

(25)

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By using Eq. (23), this result can be rewritten in terms of the upper laser level population as i in (t′) ˆ 2 (t′l ) ∂m ˆ 2 (t′l ) ⫹ p l {1 ⫺ exp[α p L(m ˆ 2 (t′l ) ⫺ 1)]} ⫽ ⫺m ∂t′l αp L

(26)

The first term on the right-hand side of this equation represents depletion by spontaneous emission, whereas the second term represents the contribution of saturable pumping to the upper laser level. Equation (26) can easily be solved numerically to obtain the inteˆ 2 (t′l ) as a function of the input pulse intensity. Contingrated upper laser level population m uous pumping is used in most fiber lasers and amplifiers, in which case i pin (t′l ) ⫽ i pin is a constant. The pump dynamics then depends solely on two parameters: the normalized pump intensity i inp, and the unsaturated absorption α p L. In the following, continuous pumping is assumed. Approximate analytical solutions of Eq. (26) that have some practical value are readily available. As long as depletion of the ground-state population remains weak ˆ 2 dependence of the exponential on the right-hand side of the equation ˆ 2 ⬍⬍ 1), the m (m can be neglected, which leads to the following solution: ˆ 2 (t′l ) ⬇ m ˆ 2 (0) exp(⫺t′l ) ⫹ m

i inp [1 ⫺ exp(⫺α p L)][1 ⫺ exp(⫺t′l )] αp L

(27)

A different approximate solution can be obtained by neglecting the spontaneous emission term on the right-hand side of the equation, which leads to ˆ 2 (t′l ) ⬇ 1 ⫹ m

i pin t′l 1 ˆ 2 (0) ⫺ 1)]} ⫺ ln{exp[i inp t′l ] ⫺ 1 ⫹ exp[⫺α p L(m αpL αp L

(28)

The upper laser level population then depends only on the integrated input energy i inp t′l . This approximation is applicable when the pumping rate is much larger than the spontaneous decay rate. Figure 3 presents the evolution of the population of the upper laser level in fibers pumped hard enough that bleaching of the absorption transition occurs, such as in typical Er-doped fibers pumped with tens of milliwatts at 980 nm. The upper laser level population increases rapidly until saturation sets in. It eventually settles down to an equilibrium value when the spontaneous decay rate equals the saturated absorption rate. As shown in Figure 3, saturation is reached faster with stronger pumping and slower with increased pump absorption. As a result, the time required to reach the equilibrium population inversion can be sizably shorter than the upper laser level lifetime in strongly pumped fibers. For example, the pump saturation time in typical Er-doped fiber amplifiers is 100 µs – 1 ms, whereas the upper laser lifetime is 10 ms [13–15]. At equilibrium, the population verifies the following equation: ˆ 2 ⫽ (m ˆ 2) eq ⫽ m

i pin ˆ 2) eq ⫺ 1)]} {1 ⫺ exp[α p L((m αp L

(29)

In a strongly pumped fiber where i pin ⬎⬎ α p L, the rare earth ion population is nearly completely inverted and ˆ 2) eq ⬇ (m

i inp i ⫹1 in p

(30)


351

Temporal variation of the upper laser level population when (a) α p L ⫽ 2, i inp ⫽ 15; (b) α p L ⫽ 2, i inp ⫽ 50; (c) α p L ⫽ 5, i inp ⫽ 50. Strong saturation of the pump absorption occurs, as evidenced by the sizable population buildup at equilibrium. The dashed curves were obtained with approximate Eq. (28).

Figure 3

The maximum achievable inversion then depends on only the pump intensity. Under these conditions, increasing the fiber length or its absorption coefficient will result in a proporˆ 2) eq N 0 L. tional increase in the stored energy at equilibrium, which is proportional to (m This is because the longer fiber absorbs a larger fraction of the pump power. The dashed curves in Figure 3 are approximate solutions calculated with Eq. (28): Their fit to the exact solution is seen to be good only in strongly pumped fibers. They predict a full inversion at equilibrium because they neglect spontaneous emission. In contrast, Figure 4 illustrates the behavior of a fiber in which pumping is insufficient to completely bleach the absorption transition (i pin ⬍ α p L), as is true for Nd 3⫹ pumped at close to 800 nm. The pump saturation time is mostly determined by the upper laser level lifetime. Intensifying the pump speeds up the pumping process and increases the equilibrium inversion. At low pump intensities, as in cases (a) and (c), the upper laser level population remains moderate. Such a regimen is practical only in a four-level laser material for which optical gain is positive, even for small population inversions. As shown by the dashed curves in Figure 4, the approximate solution given by Eq. (27) provides an accurate representation of this situation. It predicts the upper laser level population at equilibrium to be equal to ˆ 2) eq ⬇ (m

i pin [1 ⫺ exp(⫺α p L)] αp L

(31)

According to Eq. (31), lengthening the fiber has little effect on the stored energy at equilibrium. This is because under the condition of validity of this equation, most of the pump power is already absorbed by the fiber. Excitation Efficiency Two mechanisms reduce the excitation efficiency: (1) bleaching of the absorption transition, which impedes transfer of energy from the pump field to the gain medium; and (2)

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Figure 4 Temporal variation of the upper laser level population when (a) α p L ⫽ 5, i inp ⫽ 2; (b) α p L ⫽ 5, i inp ⫽ 4; (c) α p L ⫽ 10, i inp ⫽ 2. The dashed curves were obtained with approximate Eq. (27). In case (c), the exact and approximate curves are indistinguishable.

spontaneous emission, which depletes the stored energy. These mechanisms come into play when the pump pulse duration becomes comparable with the inversion build up time discussed in the foregoing. They can be avoided by properly tailoring the pump pulse duration. This strategy is used in Q-switched bulk lasers operated at a low-repetition rate, in which the pump pulse duration is typically limited to one lifetime of the upper laser level. Continuous pumping, as used in most fiber devices, is incompatible with an efficient low-repetition–rate operation. Fiber lasers and amplifiers are most efficient when operated with a pulse-to-pulse interval comparable with, or smaller than, the population inversion buildup time. A dimensionless power excitation efficiency η exc can be defined as η exc ⫽

hv s ∂Nˆ 2 I inp ∂t

(32a)

where I inp is the intensity of the pump launched in the fiber and Nˆ 2 (t) ⫽

冮

L

N 2(z,t)dz

(32b)

0

is the population of the upper laser level integrated along the length of the fiber. Thus defined, the power excitation efficiency represents the ratio between the rate of increase of the energy made available to the signal field and the pump power. It not only reflects the proportion of pump photons that actually excite a rare earth ion to the upper laser level, but also the rate at which excited ions are lost through spontaneous decay. It vanishes at equilibrium, when the pump compensates for only spontaneously decaying ions. The power excitation efficiency can be rewritten in terms of normalized variables as η exc ⫽

ˆ2 v s α p L ∂m v p i inp ∂t′l

(33)

353


Equation (26) allows writing η exc in terms of the upper laser level population as η exc ⫽

冤

冥

α L vs ˆ 2 ⫺ 1)] ⫺ pin m ˆ2 1 ⫺ exp[α p L(m vp ip

(34)

The excitation efficiency is maximum when all ions occupy the ground state. It is then equal to (v s /v p) [1 ⫺ exp(⫺α p L)] (i.e., the product of the Stokes ratio times the fraction of the pump that is absorbed by the uninverted gain medium). Figure 5 illustrates the reduction in power excitation efficiency resulting from the absorption bleaching that occurs when the pump intensity far exceeds the saturation intensity, a situation that can be encountered, for example, in Er-doped fibers. The excitation efficiency is then mostly improved by increasing the unsaturated absorption of the fiber, so that absorption of the pump remains sizable even when a large fraction of the rare earth ion population occupies the upper laser level. On the other hand, Figure 6 applies to fibers in which the stored energy is limited by spontaneous emission from a short-lived upper laser level, as in Nddoped fibers. The linear decrease in efficiency observed in this case is described by η exc ⬇

冤

冥

αp L vs ˆ2 1 ⫺ exp[⫺α p L] ⫺ in m vp ip

(35a)

The condition of validity of this linear approximation is found to be ˆ 2 ⬍⬍ 1 ⫺ ln(i inp)/(α p L) m

(35b)

ˆ 2. The excitation efficiency in such by taking the derivative of Eq. (34) with respect to m fibers is improved by increasing the pump intensity (i.e., by increasing the pumping rate relative to the relaxation rate of the upper laser level). The quasilinear behavior of the curves in Figure 6 is an indication that saturation of the absorption is negligible in these systems. The excitation efficiency in fiber (c) of Figure 6 is seen to decrease to the same ˆ 2 that is nearly twice as small. Because level as in fiber (a) at a normalized population m

Figure 5

Power excitation efficiency as a function of the upper laser level population when (a) α p L ⫽ 2, i inp ⫽ 15; (b) α p L ⫽ 2, i inp ⫽ 50; (c) α p L ⫽ 5, i inp ⫽ 50. The efficiency is normalized to the Stokes ratio v s /v p .

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Figure 6 Power excitation efficiency as a function of the upper laser level population when (a) α p L ⫽ 5, i inp ⫽ 2; (b) α p L ⫽ 5, i pin ⫽ 4; (c) α p L ⫽ 10, i inp ⫽ 2. The efficiency is normalized to the Stokes ratio v s /v p .

fiber (c) contains twice as many ions, the excitation efficiency in fibers (a) and (c) thus depends on mostly the absolute number of ions in the upper laser level. This is to be expected when pumping is counteracted mainly by relaxation from the upper laser level. In all cases, operation at lower inversion levels favors a high excitation efficiency. Devices relying on a three-level gain medium are disadvantaged from this point of view, for they operate at fairly high inversion levels. The power excitation efficiency is useful in illustrating the influence of the population inversion on the rate of increase of the stored energy. However, it cannot be used to characterize the overall pumping efficiency in a practical device because it varies as the energy level populations evolve under the action of the pump. To this end, a more useful parameter is the energy excitation efficiency, defined as ˆ2 η (t′)dt′ v α L∆m ηˆ exc ⫽ exc l l ⫽ s pin ∆t′l v p i p ∆t′l

(36)

where ∆t′l is the time interval over which pumping takes place. It represents the ratio of the stored energy increase over the energy launched into the fiber during pumping. In a repetitive regimen of operation, each signal pulse being amplified (or generated through oscillation) will usually not completely deplete the energy stored in the gain medium. The excitation efficiency will depend on the residual energy remaining in the gain medium after each signal pulse, and will thus be determined in part by the amplification (or oscillation) conditions, as discussed further on. Amplified Spontaneous Emission A small fraction of the stored energy lost to spontaneous emission is guided by the fiber and is amplified. Given the high gains achievable in fiber devices, this amplified spontaneous emission (ASE) can reach sizable intensities and deplete even further the upper laser level population. This is especially troublesome in pulsed operation when the gain medium is used for energy storage. Whenever ASE becomes sizable, the stored energy and the gain

355


Figure 7

Measured peak power of the pulses produced by a Q-switched Er-doped fiber laser. Saturation of the peak power results from depletion of the stored energy by ASE. (From Ref. 16.)

are clamped to levels lower than those predicted by the previous analysis. This depletion mechanism manifests itself in Figure 7, in which the measured peak power of pulses obtained from a Q-switched Er-doped fiber laser is seen to saturate as the absorbed power becomes too large [16]. Proper modeling of this self-saturation mechanism requires the simultaneous solution of all four Eqs. (7a)–(7d). This relatively complex task must be carried out numerically [9]. In a four-level device, the gain at which the ASE must be taken into account can be assessed as follows. During pumping, only ASE contributes to the signal field. Its evolution is then driven by the evolution of the laser level populations. Even in a very strongly pumped fiber, this evolution is quite slow compared with the time of flight of light along the fiber. The signal field can then be safely assumed to react instantaneously to any laser level population fluctuation and, at all times, reach its equilibrium value corresponding to the existing populations. The time derivative can thus be dropped and Eq. (7d) rewritten as ⫾

冤

冥

∂i ⫾s ∆Ω ⫽ g max Lm 2 i s⫾ ⫹ ∂z′ 4π

(37)

It can be easily shown from this equation that the product (i ⫹s ⫹ ∆Ω/4π)(i s⫺ ⫹ ∆Ω/4π) is a constant along the fiber [1]. Taking into account the relevant boundary conditions [i.e., i s⫹ (0,t′) ⫽ i s⫺ (1,t′) ⫽ 0], it is thus found that i ⫹s (1,t′) ⫽ i ⫺s (0,t′): a four-level device emits the same ASE power at both ends [1]. Equation (37) can be readily integrated in z′ and leads to i ⫹s (z′,t′) ⫹ i ⫺s (z′,t′) ⫽

冦冤 m (ξ,t′)dξ冥 ⫹ exp 冤g L 冮 m (ξ,t′)dξ冥 ⫺ 2冧

∆Ω exp g max L 4π

冮

z′

2

0

1

max

2

z′

(38)

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Morin et al.

The ASE intensity at either end of the fiber is equal to i s⫺ (0,t′) ⫽ i s⫹ (1,t′) ⫽

∆Ω {G ⫺ 1} 4π

(39a)

where ˆ 2 (t′)] G(t′) ⫽ exp[g max Lm

(39b)

is the single-pass gain. By taking the derivative of Eq. (38), the total ASE intensity (forward plus backward) is found to reach an extremum at the position z′1 /2 along the fiber where the gain seen from either end of the fiber is equal, at which point i s⫹ (z′1 /2,t′) ⫹ i s⫺ (z′1 /2,t′) ⫽

∆Ω 1/2 {G ⫺ 1} 2π

(40)

Whenever G ⬎ 0 dB, this is smaller than the ASE intensity at either end of the fiber: the ASE intensity is thus minimum at z′1 /2 and maximum at the fiber ends. According to Eq. (39a), the ASE intensity becomes comparable with the signal saturation intensity when G ⬇ 1⫹ 4π/∆Ω, at which point it is likely to reduce the energy stored in the fiber. Assuming that the capture angle ∆Ω is equal to the geometrical capture angle of the fiber, that is, ∆Ω ⫽ π

冢冣 NA nc

2

(41)

where nc is the fiber core refractive index, the ASE is expected to be significant when the gain becomes comparable with G ⬇ 1 ⫹ 4(n c /NA) 2, which translates into a 23-dB gain in a typical fiber (n c ⫽ 1.46, NA ⫽ 0.2). The ASE behaves somewhat differently in a three-level device. As shown previously [1,9], the ASE power is usually larger at the fiber end into which the pump is launched. The analysis is more complicated and cannot be carried out in terms of the integrated gain as in the foregoing. Through numerical solutions of the rate equations, the ASE is predicted to become significant at gain levels (⬃20 dB) comparable with those given earlier (see, e.g., Sec. 5.5 in Ref. [9]). The gain should be kept smaller than this value to avoid depletion of the upper laser level population by ASE. This limitation is rather restrictive, as many pulsed systems operate at gain levels somewhat higher than this. The curves in Figure 3 were obtained using parameters representative of practical Er-doped fiber devices. Using the cross sections given in Table 1, and assuming that γ s ⫽ 1, the maximum gain predicted by curves (a), (b), and (c) is found to be 32, 36, and 89 dB, respectively. Gain depletion by ASE is thus expected to take place in all three cases (it actually makes it impossible to achieve an 89-dB gain in practice). Likewise, the parameters used to plot the curves in Figure 4 are representative of practical Nd-doped devices. In this case, using the cross sections given in Table 2, the maximum gain predicted by curves (a), (b), and (c) is 19, 33, and 20 dB, respectively. Gain depletion by ASE should thus be limited in cases (a) and (c) but sizable in case (b). The foregoing analytical tools can help in understanding the pumping of pulsed fiber devices, but they ignore ASE and these examples make it clear that they should be used with care. Some measures can be implemented to reduce the ASE problem. It has been proposed, for example, to dope the fiber with a saturable absorber to avoid the growth of the

357


Table 1 Parameters of the Er-Doped Silica Fiber Used in the Model [1] Parameter Core radius, a Numerical aperture, NA Signal wavelength, λ s Fractional signal core energy (LP 01), η s Emission cross section, σ e Absorption/emission, γ s Pump wavelength, λ p Pump absorption cross section, σ p Lifetime, τ 2 Dopant concentration, N 0

Value 2.5 µm 0.20 1.55 µm 0.748 7.5 ⫻ 10 ⫺21 cm 2 1 0.980 µm 1.75 ⫻ 10 ⫺21 cm 2 12 ⫻ 10 ⫺3 5.1 ⫻ 10 ⫹18 cm ⫺3

initially weak ASE signal [17]. Isolators can be inserted into forward-pumped devices to reduce the backward ASE, which is the most troublesome in three-level devices [10]. Likewise, narrow spectral elements can be distributed along the fiber to limit the fraction of spontaneous photons that can develop into a significant ASE signal [10]. This amounts to reducing the input noise power generated by spontaneous emission. Storage Capacity In a CW oscillator, continuous pumping replenishes the population inversion to sustain the laser field. Ions are recycled and can contribute many photons to the output field. When a short pulse is amplified or generated in a Q-switched oscillator, energy extraction generally takes place during a time interval that is too short to allow reexcitation of ions. Each ion then contributes at most one photon per output pulse. The storage capacity of the gain medium thus imposes an ultimate limit on the possible output energy per pulse.

Table 2 Nd-Doped Silica Fiber Parameters Used in the Model [1] Parameter Core radius, a Numerical aperture, NA Signal wavelength, λ s Emission cross section, σ e Fractional signal core energy (LP 01), η s Absorption/emission, γ s Pump wavelength, λ p Pump absorption cross section, σ p Fractional pump core energy (LP 01), η p Overlap factor (LP 01 /LP 01), F n Lifetime, τ 2 Dopant concentration, N 0 Fiber length, l

Value 2.0 µm 0.20 1.060 µm 1.0 ⫻ 10 ⫺20 cm 2 0.817 0 0.810 µm 4.3 ⫻ 10 ⫺21 cm 2 0.901 0.931 400 ⫻ 10 ⫺6 9.0 ⫻ 10 ⫹19 cm ⫺3 0.10 meter

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Morin et al.

The maximum energy that can be stored per unit length of fiber at full inversion is given by E max sto ⫽ N 0 A c hv s

(42)

where A c is the area of the fiber core, assumed to be uniformly doped. The concentration N 0 is limited to avoid ion–ion interactions that result in quenching [9]. In highconcentration Er-doped fibers (N 0 ⬇ 4 ⫻ 10 19 /cm 3) and Nd-doped fibers (N 0 ⬇ 10 20 /cm 3) with a typical core area of 15 µm 2, the storage capacity is limited to about 80 µJ/m and 280 µJ/m, respectively. Lengthening the doped fiber is not a preferred approach in Qswitched oscillators, where the pulse duration scales with the cavity length. Moreover, lengthening the fiber means a higher gain, which compounds the problem of self-saturation by ASE. The preferred approach to improve energy storage while minimizing the ASE problem is to increase the transverse area of the doped region [12]. For example, a large core area fiber (A c ⫽ 167 µm 2) with a storage capacity of 680 µJ/m was used successfully as the gain medium in a Q-switched fiber laser [18]. Single-mode operation at the signal wavelength was achieved by reducing the numerical aperture of the fiber to 0.08. The ensuing increased sensitivity to bend loss was not a problem in the short fiber (63 cm) used for Q-switching. Pulses with an energy of 50 µJ resulted from the improved energy storage capacity of the fiber. The core area is limited by the requirement of single-mode propagation at the signal wavelength. This limitation can be overcome by doping the cladding of the fiber. According to Eq. (12b), storing the energy in areas where the signal field is weak results in a lower gain, which alleviates the ASE gain depletion problem. This approach was implemented in a Yb-doped fiber amplifier, in which the gain medium was shaped as a ring surrounding a single-mode core [19]. Up to 69 µJ of energy were extracted from the amplifier, whereas the small-signal gain was limited to a reasonable value of 20 dB. A different approach has been to use a slightly multimode Er-doped fiber, in which oscillation of the fundamental mode was ensured by a more favorable overlap with the lasing ions [20,21]. The low-NA fiber core was surrounded by a raised-index ring that increased the fundamental mode field area to 910 µm2 while reducing the bending loss to an acceptable level. To favor oscillation of the fundamental mode, only the inner core of the fiber was doped with erbium. Fundamental transverse mode Q-switched pulses with over 500 µJ of energy were produced with this fiber. Ultimately, further storage capacity can be gained by increasing sizably the fiber core area, thus dropping the single-mode propagation requirement for the signal. In doing so, however, one loses a most attractive feature of fiber sources, namely the production of a near–diffraction-limited beam. Waveguiding Effects It is straightforward to transform Eqs. (15) into

冤v Lτ

p 2

冥

∂ ∂ ⫾ P ⫾p ⫽ ⫺α p,eff LP ⫾p m 1,p , ∂t′ ∂z′

(43a)

where α p,eff ⫽ σ p

冮 N (r)p (r)d r 0

n

2

(43b)

359


and m j,p (z′,t′) ⫽

∫ N j (r, z′,t′)p n (r)d 2 r ∫ N 0 (r)p n (r)d 2 r

(43c)

Comparison with Eq. (7c) indicates that a guided pump mode propagates similarly to a uniform-intensity beam. The populations, however, are affected by the spatial overlap integral between the pump intensity and the population distribution profiles. Pump absorption thus depends on the spatial overlap between the pump mode and the rare earth concentration, with ions in the cladding contributing less to the absorption than ions in the core. Likewise, simple algebraic manipulations can be used to transform Eq. (19) into ∂m 2,p (P ⫹p ⫹ P p⫺)/A p,eff ⫽ m 1,p ⫺ m 2,p ∂t′ I sat p

(44a)

where the pump effective area is: A p,eff (z′,t′) ⫽

∫ N 1 (r, z′,t′)p n (r)d 2 r ∫ N 1 (r, z′,t′)p 2n (r)d 2 r

(44b)

and where the term relating to the signal field has been dropped. This last result is equivalent to Eq. (7a) applied to pumping. The apparent intensity of the pump mode, considered as a uniform-intensity mode, is obtained by dividing its power by the pump effective area A p,eff . Noting that the definition of the fractional population [see Eq. (43c)] is consistent with Eq. (7b), the equivalence between guided pump mode and uniform pump distribution is seemingly complete. The guided case is actually much more complicated, because of the space–time dependence of the pump mode effective area A p,eff , which is explicit in Eq. (44b). To take this dependence into account, it is necessary to keep track of the transverse distribution of the ground-state population N 1 at all times and positions along the fiber. This can be achieved only through a full-scale numerical analysis in time and space. A major simplification results from the low-saturation approximation, whereby the pump mode effective area of Eq. (44b) is approximated by A p,eff ⬇

∫ N 0 (r)p n (r)d 2 r ∫ N 0 (r)p 2n (r)d 2 r

(45)

The effective pump mode area is then a constant, and the foregoing equations used to model pumping with a uniform-intensity distribution can be applied directly to guided pumping with the following substitutions: N0 →

冮 N (r)p (r)d r 0

n

2

I p (z, t) → P p (z, t)/A p,eff

(46)

This approximation eliminates the need to know the actual transverse distributions of the laser level populations, because the populations involved in the calculations are defined globally by Eq. (43c). It obviously applies at the beginning of pumping in a previously unexcited fiber. As the ground-state population becomes depleted, at a rate that depends on the local pump intensity, the effective pump mode area varies in time at each point along the fiber. The largest changes relative to the initial unsaturated value given by Eq.

360

Morin et al.

Figure 8

Evolution of the normalized pump power distribution p(z) along an Er-doped fiber pumped with the LP 01 mode. (From Ref. 1.)

(45) are expected to occur when the pump is kept on long enough for the level populations to reach equilibrium, as in CW operation. The approximation involved in Eq. (45) was discussed [1] within this context, and it was quite accurate even when low absorption saturation clearly cannot be invoked. [Equation (45) is actually a generalization of Eq. (73) given in Ref. [1], which permits for an arbitrary transverse distribution N 0 (r) of rare earth ions in the fiber.] For example, the CW pump absorption in Er-doped fibers is shown in Figure 8 to be fairly well predicted by this approximation, even when ground-state depletion is strong. This observation can be explained as follows. The effective pump area A p,eff is a form factor that depends on the transverse distribution profile, rather than on the absolute value of the ground-state population. The results in Figure 8 indicate that this form factor depends weakly on the level of saturation in the fiber. The possibility of this occurrence can be evoked simply by considering a fiber in which the rare earth ion concentration N 0 (r) is limited to a thin radial region over which the pump mode radial function r n , defined in Eq. (16), is nearly constant. The effective pump area in such a fiber does not depend on the saturation level of the pump transition. It is closely approximated by h n ⬍ r n ⬎ ⫺1, where h n is a constant that depends on the pump mode azimuthal order, whereas ⬍ r n ⬎ represents the average value of r n over the region of interest. The conditions of validity of the approximation involved in Eq. (45) in a fiber can be assessed as follows. According to Eq. (19), the ground-state population density at equilibrium in the absence of ASE is [N 1 (r,z′)] eq ⫽

N 0 (r) 1 ⫹ [P p (z′)] eq p n (r)/I sat p

(47a)

361


where [P p (z′)] eq ⫽ P ⫹p (z′,t′ → ∞) ⫹ P p⫺ (z′,t′ → ∞)

(47b)

is the pump power at equilibrium at position z′. In the limit of an infinite pump power, this becomes [N 1 (r,z′)] eq ⫽

N 0 (r)I sat p [P p (z′)] eq p n (r)

Pp → ∞

(48)

and Eq. (44b) reduces to A p,eff ⫽

∫ N 0 (r)d 2 r ∫ N 0 (r)p n (r)d 2 r

Pp → ∞

(49)

A comparison of Eqs. (45) and (49) provides a quick check of the validity of the former. If both expressions give similar results, the unsaturated approximation is clearly applicable to the fiber under consideration. If not, one may insert Eq. (47a) in Eq. (44b) to verify the validity of the approximation of Eq. (45) as a function of pump power. Analytical expressions are readily available when the ion concentration is constant between two radii; that is,

N 0 (r) ⫽

冦0

N 0 if r 1 ⱕ r ⱕ r 2

(50a)

elsewhere

and the pump mode profile is gaussian; that is, p n (r) ⫽ p 0 (r) ⫽

冤冢冣冥

2 r exp ⫺2 2 πω p ωp

2

(50b)

Equation (44b) then becomes

(A p,eff) eq

冮 ⫽ 冮

r2

r1 r2

r1

p 0 (r)/(1 ⫹ [P p] eq p 0 (r)/I sat p ) rdr (51) p 20 (r)/(1 ⫹ [P p] eq p 0 (r)/I sat p ) rdr

The integrals can be carried out analytically and yield: (A p,eff ) eq ⫽

ln[(1 ⫹ i p1 )/(1 ⫹ i p2)] 1 ⫻ p 0 (r 1) 1 ⫺ (i p2 /i p1) ⫺ (1/i p1) ln[(1 ⫹ i p1 )/(1 ⫹ i p2)]

(52a)

where i pj ⫽

(P p) eq p 0 (r j) I sat p

(52b)

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Morin et al.

Figure 9 Effect of absorption saturation on the pump mode effective area, evaluated according to Eqs. (52). The rare earth ion concentration is assumed constant between radii r 1 and r 2 . The pump mode profile is gaussian. The pump mode effective area has been multiplied by the pump mode function p 0 evaluated at r 1 and is plotted as a function of the normalized pump intensity at r 1 , as defined in Eq. (52b).

is the normalized pump intensity at r ⫽ rj. The pump mode effective area is plotted in Figure 9 as a function of the normalized pump intensity i p1 for different ratios i p2 /i p1 . The limiting values of the effective area are given by (A p,eff) eq ⫽

2 p 0 (r 1) ⫹ p 0 (r 2)

when

i p1 → 0

(53)

in the unsaturated case, and (A p,eff) eq ⫽

ln(p 0 (r 1)/p 0 (r 2)) p 0 (r 1) ⫺ p 0 (r 2)

when

i p1 → ∞

(54)

in the case of an infinitely strong pump. The pump effective area is seen to increase with intensity. This happens because of preferential depletion of the ground-state population at those radii at which the pump mode is the most intense. This, in turn, spoils the spatial overlap between available ground-state ions and the pump mode, and thus decreases the effectiveness of energy transfer from the pump to the ions. Within the present model, this effect is represented by an increase of the pump effective area which, for a given pump power, translates into a reduction of the effective pump intensity. According to Figure 9, the pump intensity i p1 must be quite high for this effect to be significant. It illustrates the robustness of the approximation of Eq. (45), especially in fibers where the pump intensity does not vary significantly over the radial area containing rare earth ions. 7.2.3 Pulse Amplification Pulse Distortion Amplification can be used to increase the energy of individual pulses significantly. For this process to be efficient, the incoming pulse must extract a sizable fraction of the energy

363


stored in the gain medium. The ensuing gain depletion necessarily translates into a significant pulse distortion, because the trailing portion of the pulse benefits from a reduced gain. The situation can be modeled with Eqs. (7) adapted to this amplification step: ∂m 2 ⫽ ⫺i s [m 2 ⫺ γ s m 1] ∂t′

(55a)

and

冤cτL ∂t′∂ ⫹ ∂z′∂ 冥 i ⫽ g s

max

Li s [m 2 ⫺ γ s m 1]

(55b)

2

Single-pass amplification has been assumed. Equations (55) apply to an input pulse propagating toward the positive z-axis (although the following analysis will make it clear that the direction of propagation is irrelevant). The input pulse and its transit time through the amplifying medium are assumed short enough that pumping and spontaneous emission can be neglected. Accordingly, only stimulated emission terms have been retained in the equations. By using the same change of variables as before, Eqs. (55) can be transformed into

and

∂∆m ⫽ ⫺(1 ⫹ γ s)i s ∆m ∂t ′l

(56a)

∂i s ⫽ g max Li s∆m ∂z′l

(56b)

where ∆m ⫽ m 2 ⫺ γ s m 1 represents the normalized population inversion. These equations can be solved analytically, as detailed in Ref. [2]. The intensity of the output pulse is given by in i out s (t′l ) ⫽ G(t′l )i s (t′l )

(57a)

where ˆ (t′l )] G(t′l ) ⫽ exp[g max L∆m

(57b)

is the overall gain experienced by the pulse at time t′l and ˆ (t′l ) ⫽ ∆m

冮

1

∆m(z′l , t′l )dz′l

(57c)

0

is the normalized population inversion integrated along the fiber, whereas ′ i ins (t′l ) ⫽ i s (0,t′l ) and i out s (1,t′l ) i i (1,t l ) represent the input and output signal pulse intensity, respectively. The intensity of the output pulse slice at time t′l is thus equal to the intensity of the input pulse slice at the same local time multiplied by the overall gain experienced by this slice as it propagated along the fiber. The gain is found to vary according to [2] G(t′l ) ⫽

Gi G i ⫺ (G i ⫺ 1)exp[⫺(1 ⫹ γ s)u ins (t′l )]

(58a)

364

Morin et al.

where G i ⫽ G(0) is the initial gain when the pulse enters the fiber and u ins (t′l ) ⫽

冮

t l′

i ins (ξ)dξ

(58b)

0

is the normalized fluence of the input pulse up to time t′l . This last result can be recast in a more familiar form as G(t l) ⫽

Gi G i ⫺ (G i ⫺ 1) exp[⫺U ins (t l)/U sat s ]

(59a)

where t l ⫽ τ 2 t′l represents time (nonnormalized) in the pulse local referential, U sin (t l) ⫽

冮

tl

I ins (ξ)dξ

(59b)

0

is the integrated fluence (J/cm 2) of the input pulse up to time t l and U sat s ⫽

τ 2 I sat s 1 ⫹ γs

(59c)

is the saturation fluence (J/cm2) of the gain medium. Equation (59a) relates the available gain remaining in the gain medium at a given time to the pulse fluence that has been injected into it up to this time. The output pulse shape is obtained by multiplying the input pulse shape with this time-varying gain, as indicated in Eq. (57a). When the input fluence is small compared with the saturation fluence, Eq. (59a) can be approximated by G(t l) ⬇

Gi . 1 ⫹ [G i ⫺ 1]U ins (t l)/U sat s

(60)

Pulse distortion is small as long as (G i ⫺ 1)U sin (t l)/U sat s ⬍⬍ 1 (i.e., whenever the fluence of the amplified pulse remains small compared with the saturation fluence). Pulse distortion calculations have been performed for a variety of input pulse shapes [22]. Figure 10 shows the shape of the output pulse when a step pulse of constant intensity I ins is injected into the gain medium, in which case I out Gi s (t l) ⫽ G(t l) ⫽ I ins G i ⫺ (G i ⫺ 1) exp[⫺I ins t l /U sat s ]

(61)

The early portion of the output pulse is described approximately by I out Gi s (t l) ⬇ in Is 1 ⫹ t l /τ G

(62a)

where τG ⫽

U sat s (G i ⫺ 1)I ins

(62b)

The dashed curves in Figure 10 were obtained using the approximate form of Eq. (62). The accuracy clearly improves as the initial gain is increased. According to Eq. (62a), τ G represents the time by which the gain has decreased to 50% of its initial value. It becomes shorter as either the input intensity or the gain is increased. All things being equal, this time constant is twice as small in a three-level medium (γ s ⫽ 1) because each stimulated


365

Output pulse shape resulting from the injection of a step pulse at time t l ⫽ 0 in a fiber with an initial gain G i ⫽ 10, 20, and 30 dB. The dashed lines were obtained with the approximation of Eq. (62).

Figure 10

emission event reduces the population inversion by two. Square input pulses will suffer little distortion as long as their duration is much smaller than this time constant. (This condition is the same as that stated earlier in terms of the fluence of the amplified pulse.) Otherwise, the output pulse will be strongly distorted, its front part being much more intense than its trailing edge. According to parameters given in Table 1 of Ref. 1, the saturation fluence in Er-doped fibers is about 8.6 J/cm2. Given a typical mode area of 50 µm 2, Eq. (62) states that a square input pulse with an energy as low as 43 nJ will come out of an Er-doped fiber, with a moderate 20-dB gain, with a trailing edge half as intense as its leading edge. A similar calculation for an Nd-doped fiber, using parameters given in Table 2 of Ref. 1 leads to a 95-nJ pulse energy. This analysis makes it clear that the output pulse shape depends solely on the overall gain integrated along the fiber. The longitudinal distribution of the population inversion is of no importance, nor is the direction of propagation of the pulse. Extraction Efficiency According to Eq. (59a), a very energetic pulse launched into an amplifying fiber can deplete its gain all the way down to 0 dB. In principle, it is thus possible to extract all the energy stored in a four-level gain medium, but not in a three-level medium, because in the latter the gain drops to 0 dB before complete depopulation of the upper laser level. The extraction efficiency for three- and four-level gain media is evaluated as follows. The output pulse fluence is given by U sout (t end) ⫽

冮

t end

I out s (t l)dt l

(63)

0

where t end is a time long enough for the integration interval to cover the entire output pulse. By using Eqs. (57a) and (59a) and noting that I sin (t l) ⫽ dU ins (t l)/dt l , this integral can be transformed into

366

Morin et al.

U sout (t end) ⫽ G i

冮

U in s (t end )

0

dU sin G i ⫺ (G i ⫺ 1)exp[⫺U ins /U sat s ]

(64)

which is readily integrated as in sat U sout (t end) ⫽ U ins (t end) ⫹ U sat s ln{G i ⫺ (G i ⫺ 1) exp[⫺U s (t end)/U s ]}

(65)

A fluence gain can be defined as GU ⫽

U sat U sout (t end) s ⫽ 1 ⫹ ln{G i ⫺ (G i ⫺ 1)exp[⫺U sin (t end)/U sat s ]} U ins (t end) U sin (t end)

(66)

It represents the ratio between the output and input pulse total fluence. It is plotted in Figure 11 as a function of the input pulse fluence for G i ⫽ 10, 20, and 30 dB. These curves apply to both three- and four-level amplifiers. The fluence gain decreases rapidly as a function of the input pulse fluence, even more so in amplifiers with a large initial gain. It eventually drops to 0 dB when the input pulse energy is very large compared with the energy stored in the gain medium. The extraction efficiency η ext is defined as η ext ⫽

U sout (t end) ⫺ U ins (t end) U sto s

(67)

2 where U sto s is the stored energy per unit transverse area (J/cm ). It represents the fraction of the stored energy that is extracted by the amplified pulse. The stored energy per unit area is given by

ˆ 2 (0)N 0 Lhv s U sto s ⫽ m

(68)

ˆ 2 (0) represents the fraction of rare earth ions that occupy the upper laser level, where m as defined in Eq. (24). By using Eq. (57b), it can be related to the unsaturated gain by

Figure 11

Influence of the input pulse fluence on the energy gain provided by a three-level or a four-level amplifier with an initial gain G i ⫽ 10, 20, and 30 dB. The dashed curves represent the achievable gain when the amplifiers are used in a double-pass configuration. The maximum gain then reaches 20, 40, and 60 dB, respectively (even though the ordinate axis ends at 30 dB).

Q-Switched Fiber Lasers sat U sto s ⫽ U s [ln(G i) ⫹ γ s g max L]

367

(69)

The extraction efficiency can thus be rewritten as η ext ⫽

ln{G i ⫺ (G i ⫺ 1)exp[⫺U ins (t end)/U sat s ]} ln[G i] ⫹ γ s g max L

(70)

This can be shown to be equivalent to η ext ⫽ ζ

ln{G i ⫺ (G i ⫺ 1)exp[⫺U sin (t end)/U sat s ]} ln[G i]

(71a)

where ζ⫽

ˆ 2 (0) ⫺ m ˆ trans m 2 ˆ 2 (0) m

(71b)

is the maximum achievable extraction efficiency and ˆ trans ⫽ m 2

γs γs ⫹ 1

(71c)

is the upper laser level population required to make the fiber transparent (G i ⫽ 0 dB). Only the fraction of upper laser level population that supersedes this minimum population is thus available for extraction. This is consistent with the observation that the residual gain at the end of the amplification process is at least equal to 0 dB. In a four-level amplifier, ζ ⫽ 1, and all the stored energy can be extracted. In a three-level gain medium, the most favorable situation is a full inversion, in which case the maximum achievable extraction efficiency reaches (1 ⫹ γ s) ⫺1. Figure 12 presents the extraction efficiency in an amplifier as a function of the normalized input pulse fluence. The efficiency has been normalized to the maximum

Figure 12

Influence of the input pulse fluence on the extraction efficiency (normalized to the maximum achievable extraction efficiency ζ) in amplifiers with an initial gain G i ⫽ 10 dB, 20 dB, and 30 dB. The dashed curves represent the efficiency achieved when the amplifiers are used in a double-pass configuration.

368

Morin et al.

achievable extraction efficiency ζ, defined by Eq. (71). The curves thus apply to both three-level and four-level lasers. Efficient extraction of energy requires a pulse fluence comparable with the saturation fluence of the laser transition. A higher initial gain favors extraction because the pulse fluence then builds up rapidly to a sizable level within the fiber. Previous results apply to single-pass amplification. The extracted energy depends only on the input pulse fluence and on the overall gain integrated along the fiber. The input pulse shape has no bearing whatsoever on the extraction. Consequently, each pass of a double-pass amplification process can be analyzed with the previous equations. The input fluence to the second pass corresponds to the output fluence of the first pass, given by Eq. (65), whereas the gain applicable to the second pass corresponds to the depleted gain remaining after the first pass, evaluated with Eq. (59a) with t l ⫽ t end . The output fluence of the double-pass amplification is thus found to be equal to

冦

U sout (t end) ⫽ U ins (t end) ⫹ U sat s ln G i ⫺

(G i ⫺ 1) exp[⫺2U sin (t end)/U sat s ] in G i ⫺ (G i ⫺ 1) exp[⫺U s (t end)/U sat s ]

冧

(72)

The dashed curves in Figures 11 and 12 represent the fluence gain and the extraction efficiency achieved in a double-pass amplifier, which is clearly advantageous, especially for the amplification of low-fluence input pulses. Repetitive Amplification Usually, CW-pumped fiber amplifiers are used to amplify trains of pulses. The output energy per pulse then depends on the input energy per pulse and on the pulse repetition rate f. This situation can be analyzed by assuming that amplification takes place instantaneously, which is a reasonable assumption when the duty factor of the pulse train is low. Let us consider that an nth pulse enters the amplifier when G ⫽ (G i) n. The remaining gain (G f ) n after its passage through the amplifier, calculated with Eq. (59a), is (G f ) n ⫽

(G i) n (G i) n ⫺ ((G i) n ⫺ 1) exp[⫺U ins /U sat s ]

(73)

where U ins now represents the total fluence of the input pulse. Following this pulse, the upper laser level is replenished by the pump until the arrival of the next input pulse (i.e., during a time equal to the period of the pulse train). The upper laser level population varies during this pumping interval according to Eq. (26), which can be translated into an evolution equation for the amplifier gain with the help of Eq. (57b). This equation must be solved to obtain the gain (G i) n⫹1 available for the next input pulse. Steady-state operation of the amplifier is reached when (G i) n⫹1 ⫽ (G i) n . The approximate expressions of Eqs. (27) and (28) can be used to avoid solving the population evolution equation numerically. The net result is an implicit equation for the initial gain G i . For example, in a four-level amplifier operated at a moderate population inversion, Eq. (27) can be rewritten in the present context as ln[(G i) n⫹1] ⬇ exp(⫺1/fτ 2) ln[(G f ) n] σ ⫹ e i pin [1 ⫺ exp(⫺α p L)] [1 ⫺ exp(⫺1/fτ 2)] σp

(74)


369

and, with the use of Eq. (73), the steady-state gain G i verifies the following equation ln[G i] ⫹

ln[G i ⫺ (G i ⫺ 1) exp(⫺U ins /U sat σ s )] ⬇ e i inp [1 ⫺ exp(⫺α p L)] exp(1/fτ 2) ⫺ 1 σp

(75)

which can be easily solved numerically. When the repetition rate is increased, less time is allowed to build up the population inversion between pulses. If the energy per pulse is kept constant, a higher repetition rate results in the amplifier operating at a lower average inversion level. This translates into an improved excitation efficiency, but also a lower gain and a reduced extraction efficiency. The gain eventually drops to 0 dB when the average input power becomes very large compared with the pump power. The following figures illustrate a less trivial situation; namely, the amplification of periodic signals with a constant average intensity I ins , in which case the fluence per pulse is reduced in proportion to the signal period (U sin ⫽ I ins /f ). The effect of the signal repetition frequency on the output of Er-doped amplifiers amplifying such signals is illustrated in Figure 13, obtained with a numerical solution of Eq. 26. The unsaturated absorption of the fiber and the pumping levels correspond to those of curves (a) and (b) in Figure 3, whereas I ins ⫽ 0.01 I sat s . The gain (in fluence per pulse or in average intensity) increases steadily at low-repetition frequencies. It eventually reaches a steady-state value when the pulse train period becomes shorter than the time taken by the amplifier’s absorption to become saturated (see Fig. 3). The amplifier then operates as if it were subjected to a continuous input beam of intensity I ins . As shown in Figure 13, this regimen optimizes power extraction. On the other hand, the output pulse fluence decreases steadily as the frequency is increased, slowly at first, then at an accelerated rate once the gain has reached its steady-state value.

Figure 13

Influence of the repetition frequency on the output of an Er-doped amplifier submitted to a constant average input normalized intensity i ins ⫽ 0.01. The repetition frequency is normalized to the inverse of the laser-level lifetime. The pump intensities are (a) i inp ⫽ 15 and (b) i inp ⫽ 50, and the amplifier unsaturated absorption is α p L ⫽ 2. Other relevant parameters are σ e /σ p ⫽ 4.29 and γ s ⫽ 1. Solid curves represent the effective gain (i.e., the ratio of the average output and input intensities (or pulse fluences)). Dashed curves represent the output pulse fluence normalized to the saturation fluence.

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Figure 14

Influence of the repetition frequency on the initial gain G i (available as an incoming pulse enters the amplifier), the final gain G f (remaining after amplification of a pulse) and the fluence gain G U for each pulse. The parameters are those of curve (a) in Figure 13 (three-level laser).

Repetitive amplification is further illustrated in Figures 14 and 15. At low repetition rates, the pumping interval between signal pulses is long enough for the upper laser level ˆ 2) eq , to which corresponds a maximum achievable gain to reach its equilibrium value (m G i (see Fig. 14). The amplifier maintains this maximum initial gain G i as long as the signal period is longer than its absorption saturation time. Under these conditions, the excitation efficiency ηˆ exc defined in Eq. (36) is very low (see Fig. 15) because most of the pump power is unabsorbed by the amplifier. On the other hand, the extraction efficiency η ext is

Figure 15

Influence of the repetition frequency on the excitation efficiency (solid curve), as defined in Eq. (36), and on the extraction efficiency (dashed curve) of each individual pulse, as defined in Eq. (71). The pump and signal wavelengths are assumed to be 0.980 µm and 1.55 µm, respectively. Other parameters are those of curve (a) in Figure 13. The ripples at high frequencies on the excitation efficiency curve are numerical artifacts.

371


quite good because the input pulses are energetic and the initial gain is high. The initially slow decrease in output pulse fluence observed at low frequencies results from the input pulse fluence decrease with frequency, which comes along with a concomitant loss of extraction efficiency, as evidenced by the increase in final gain G f (see Fig. 14). The fluence gain G U increases because the extracted energy becomes relatively more important in comparison with that of the input pulses, even though the extraction efficiency decreases. As the repetition rate is increased further, pumping can no longer replenish the upper laser level population to its equilibrium value, and the initial gain G i decreases. This operation at a lower population inversion improves the excitation efficiency, but the lower gain G i further reduces the extraction efficiency. The initial and final gains eventually converge, at which point the amplifier runs as if amplifying a continuous signal with an intensity I ins. The Nd-doped amplifiers discussed in Figure 4 behave in a similar fashion. As a result of their weaker pump (normalized to the saturation intensity), which translates into slower pumping dynamics (in terms of the upper laser level lifetime), they reach their steady-state regimen at lower normalized repetition frequencies fτ 2 . The extraction efficiency shown in Figure 15 represents the fraction of stored energy that is extracted by a single pulse. It is useful in characterizing the pulsed amplification that takes place in the amplifier. However, it should not be confused with the power extraction efficiency of the pulse train, which is proportional to (G U ⫺ 1) and increases with the repetition rate. The power extraction efficiency is higher under the steady-state regimen because fewer pump photons are wasted to maintain the population inversion while waiting for the next input pulse. Amplified Spontaneous Emission Amplified spontaneous emission reduces the gain achievable during the pumping phase. It also contributes an output signal between amplified pulses, which is a source of noise. Noise in fiber amplifiers is discussed in Chapter 10. Waveguiding Effects Waveguiding effects during amplification can be discussed in the same way as those occurring during pumping. Starting from Eqs. (14) and (12b), the propagation equation for the signal field is rewritten as

冤vLτ ∂t′∂ ⫾ ∂z′∂ 冥P

⫾ s

⫽ g max,eff LP s⫾ [m 2,s ⫺ γ s m 1,s] ,

(76a)

s 2

where g max,eff ⫽ σ e ∫ N 0 (r)s 0 (r)d 2 r

(76b)

and m j,s (z′,t′) ⫽

∫ N j (r,z′,t′)s 0 (r)d 2 r ∫ N 0 (r)s 0 (r)d 2 r

(76c)

The populations involved in the propagation equation are now determined by the overlap integral between the signal mode intensity profile and the population distributions. The signal gain depends on the spatial overlap between the signal mode and the rare earth ion concentration. Likewise, retaining only the stimulated emission term, Eq. (19) is transformed into

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(P ⫹s ⫹ P s⫺)/A s,eff ∂m 2,s ⫽⫺ [m 2,s ⫺ γ s m 1,s ] ∂t′ I sat s

(77a)

where A s,eff (z′,t′) ⫽

∫ ∆N(r,z′,t′)s 0 (r)d 2 r ∫ ∆N (r,z′,t′)s 20 (r)d 2 r

(77b)

and ∆N(r,z′,t′) ⫽ N 2 (r,z′,t′) ⫺ γ s N 1 (r,z′,t′)

(77c)

The apparent intensity of the signal mode, when modeled as a uniform-intensity profile, is now obtained by dividing the signal power by the signal mode effective area A s,eff . As previously, the seemingly complete equivalence between the guided and unguided cases is offset by the space–time dependence of A s,eff . To simplify the calculations, this varying parameter must be replaced by a suitable constant. Some particular conditions may facilitate the choice of a proper value for A s,eff . For example, when the rare earth ions are concentrated in a radial region over which the signal mode intensity profile is nearly constant, A s,eff is closely approximated by ⬍ s 0 ⬎ ⫺1, ⬍ s 0 ⬎ being the average value of s0 over the region of interest. In less trivial situations, a major simplification is obtained by neglecting the effect of the population inversion depletion by the signal field and approximating Eq. (77b) as A s,eff (z′) ⬇

∫ ∆N(r,z′,0)s 0 (r)d 2 r ∫ ∆N (r,z′,0)s 20 (r)d 2 r

(78)

where ∆N(r, z′, 0) is the undepleted population inversion created by the pump before the presence of a signal field. This approximation eliminates the time dependence of the signal mode effective area. When CW pump conditions have been established before oscillation or amplification, the initial inversion can be obtained from Eq. (47) and is equal to

冦

∆N(r,z′,0) ⫽ N 0 (r) 1 ⫺

冧

1 ⫹ γs 1 ⫹ [P p (z′)] eq p n (r)/I sat p

(79)

In four-level lasers (γ s ⫽ 0) operating at moderate population inversions, Eq. (79) can be approximated by ∆N(r,z′,0) ⬇ N 0 (r)[P p (z′)] eq p n (r)/I sat p

(80)

Equation (78) then reduces to A s,eff ⬇

∫ N 0 (r)p n (r)s 0 (r)d 2 r ∫ N 0 (r)p n (r)s 20 (r)d 2 r

(81)

Under these conditions, to first order the signal mode effective area does not depend on the pump power, but only on the ion distribution and the modal properties of the fiber. Likewise, in three-level lasers where a very strong pump nearly completely depletes the ground state, Eq. (78) becomes A s,eff ⬇

∫ N 0 (r)s 0 (r)d 2 r ∫ N 0 (r)s 20 (r)d 2 r

(82)


373

Intermediate situations can be analyzed with Eqs. (78) and (79), which can be used to evaluate the signal mode effective area as a function of the pump power along the fiber and determine an appropriate average constant value for the signal mode undepleted effective area. In a fiber with an ion concentration that is constant between two radii [see Eq. (50)], and when the pump and signal wavelengths are close enough that s 0 (r) ⬇ p 0 (r), the integrals can be solved analytically. It is thus found that (A s,eff ) eq ⫽

1 p 0 (r 1)

(83) 1 ⫺ (i p2 /i p1) ⫺ ((1 ⫹ γ s)/i p1)ln[1 ⫹ i p1 )/(1 ⫹ i p2)] ⫻ (1/2)(1 ⫺ i 2p2 /i 2p1) ⫺ ((1 ⫹ γ s)/i p1){1 ⫺ (i p2 /i p1) ⫺ (1/i p1)ln[(1 ⫹ i p1 )/(1 ⫹ i p2)]}

where i pj is the normalized pump intensity at r ⫽ r j as defined in Eq. (52b). Figure 16 presents the dependence of the signal effective mode area on pump intensity, calculated from Eq. (83) for a four-level laser material (γ s ⫽ 0). The undepleted effective area increases with pump intensity, a behavior similar to that of the pump mode effective area (see Fig. 9). This increase indicates that a stronger pump creates a population inversion that overlaps less efficiently with the signal mode. Note that the relative variations of (A s,eff) eq are rather moderate, especially when the rare earth ions are concentrated in a radial region over which the intensity of the signal mode varies only a little. The modeling of the population evolution with Eq. (77a), in which A s,eff is assumed to be a constant, thus appears well adapted to four-level transitions. The situation is somewhat different in three-level transitions, as depicted in Figure 17. In this case, the undepleted signal mode effective area remains fairly constant over a wide range of pump intensity, but drops sharply to zero when the pump becomes weak enough. This behavior can be explained as follows. According to Eq. (12b), the numerator appearing in the definition [see Eq. (77b)] of A s,eff is proportional to the local signal mode gain coefficient. For a four-level transition, this gain coefficient drops to zero only when the population inversion ∆N does so itself. As a result, the denominator in Eq. (77b) also

Figure 16

Effect of the normalized pump intensity, defined in Eq. (52b), on the signal mode undepleted effective area for a four-level transition (γ s ⫽ 0), evaluated according to Eq. (83). The fiber is characterized by Eqs. (50) and the condition s 0 (r) ⬇ p 0 (r).

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Figure 17

Effect of the normalized pump intensity, defined in Eq. (52b), on the signal mode undepleted effective area in a three-level transition (γ s ⫽ 1), evaluated according to Eq. (83). The fiber is characterized by Eqs. (50) and the condition s 0 (r) ⬇ p 0 (r).

vanishes in such a way that A s,eff remains finite, as exemplified by Eq. (81). For a threelevel transition, the gain coefficient can drop to zero when the local population inversion ∆N is positive at some radii and negative at others, in a such a way that the integral in Eq. (12b) vanishes. This in no way ensures that the denominator in Eq. (77b) vanishes at the same time; hence, the possibility of the signal mode effective area dropping to zero or even becoming negative at low pump powers. Equation (77a), in which A s,eff is assumed to be a constant, is thus not appropriate to model the evolution of the population inversion in a three-level fiber for which the signal gain coefficient is close to zero. However, threelevel fibers are usually pumped strongly to avoid reabsorption of the signal field. If the pump power remains sizeable over the entire fiber length, the representation of A s,eff by a single number is justified, especially when the rare earth ions are concentrated in a thin radial region, as shown in Figure 17. Moreover, the foregoing discussion on amplification makes it clear that sections of a three-level fiber in which the signal gain coefficient approaches zero do not contribute significantly to the amplification of a signal pulse, nor to the generation of a signal field in an oscillator. Inaccuracies in modeling such sections are thus less significant. The validity of Eq. (78) can be examined as follows. Equation (19) is first rewritten as ∂∆N(r,z,t) (1 ⫹ γ s) [P s⫹ (z,t) ⫹ P ⫺s (z,t)] s 0 (r)∆N(r,z,t) ⫽⫺ ∂t τ 2 I sat s

(84)

where the pump and decay terms have been discarded. This equation is readily integrated along the length to yield

冤

∆N(r,z,t) ⫽ ∆N(r,z,0) exp ⫺

冥

E s (z,t)s 0 (r) U sat s

(85a)


375

where the saturation fluence U sat s is defined in Eq. (59c), and

冮 [P t

E s (z,t) ⫽

⫹ s

0

(z,ξ) ⫹ P ⫺s (z,ξ)]dξ

(85b)

is the signal mode energy that has passed through position z along the fiber up to time t. This last result can be inserted in Eq. (77b), which becomes A s,eff (z′,t′) ⫽

2 ∫ ∆N(r,z′,0)exp[⫺E s (z′,t′)s 0 (r)/U sat s ]s 0 (r)d r 2 2 ∫ ∆N(r,z′,0)exp[⫺E s (z′,t′)s 0 (r)/U sat s ]s 0 (r)d r

(86)

where the coordinates (z,t) have been changed to their normalized counterparts (z′,t′). This equation can be used to determine the effect of the signal energy on the signal mode effective area. According to the foregoing discussion, large variations of A s,eff may be expected in a three-level fiber amplifying a signal pulse that is energetic enough to strongly deplete the initial population inversion and bring the signal gain coefficient close to zero. On the other hand, as its signal gain coefficient decreases, a fiber section loses its relevance relative to the amplification process. Inaccuracies in modeling the evolution of its population inversion are thus less important at this point and should affect mostly the later portion of the amplification process. The populations m j,s appearing in Eqs. (76a) and (77a) differ from those involved in the equations describing pumping and defined by Eq. (43c). Transformation rules are required in order to use the populations predicted by the analysis of the pumping step as initial conditions for the analysis of the amplification step, and vice versa. According to their respective definitions, these populations are related by m j,s (z′,t′) ∫ N 0 (r)p n (r)d 2 r ∫ N j (r,z′,t′)s 0 (r)d 2 r ⫽ m j,p (z′,t′) ∫ N 0 (r)s 0 (r)d 2 r ∫ N j (r,z′,t′)p n (r)d 2 r

(87)

The first integral ratio can be readily obtained from the geometry of the doped fiber. The second ratio depends on the population distribution at the beginning of either the pumping step or the amplification step. When the pump and signal wavelengths do not differ markedly from each other, the ratio in Eq. (87) is close to unity. This is the case also when the rare earth ions are concentrated in a radial region over which the pump and signal intensity profiles vary only a little. 7.2.4 Q-Switched Oscillation General Principles Q-switching of a laser oscillator cavity is a powerful method for producing short and intense pulses. A loss modulator initially impedes the buildup of the laser field in the cavity, while the gain medium is being pumped to possibly high gain values. Once sufficient energy has been stored in the gain medium, the loss modulator is switched to its high-transmission state to allow oscillation. The laser field builds up from spontaneous emission at a rate that depends at first on the gain and the cavity losses. Once it reaches a fluence level comparable with the saturation fluence of the gain medium, the field extracts energy very efficiently from the gain medium and rises very rapidly to a high-intensity level. When the depleted gain becomes insufficient to compensate for the cavity losses, the laser field decreases at a rate determined mostly by the cavity length and losses. This

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technique typically produces pulses with a width equal to the duration of a few roundtrips in the cavity. Different techniques have been used to Q-switch a fiber laser, which are discussed in Section 7.3. Q-switching can be achieved actively through the action of an electrically controlled loss modulator. It can also be carried out passively. For example, a saturable absorber placed in the cavity acts as a loss modulator, with an intensity-dependent transmission controlled by the laser field itself. Active Q-switching has been used preferentially with fiber lasers. Ideally, in its low-transmission state the loss modulator should introduce a loss as high as possible, to maintain the laser below threshold while gain is built-up to high values. On the other hand, it should be as transparent as possible in its high-transmission state, to minimize the loss it adds to the laser field. Finally, the switching time of the loss modulator should be short enough to accommodate the rapidly expanding laser field. A slow-opening modulator is a source of loss and can also result in multiple pulsing [2,23]. According to this summary description, Q-switching involves two distinct phases: a pumping phase that takes place while the cavity quality factor is spoiled by the modulator loss, followed by a rapid extraction of energy from the gain medium once the modulator has been switched to its high-transmission state. The pumping phase essentially determines the initial conditions prevailing at the time the modulator is switched to its high-transmission state, and it can be analyzed with the tools developed in Section 7.2.2. In typical Q-switched lasers, the extraction of energy takes places so quickly that spontaneous emission and pumping can be neglected. It can thus be analyzed with the equations derived in Section 7.2.3, except for two differences. In a standing-wave cavity, the laser field propagates in both directions along the fiber and both signals i ⫾s must be considered in the analysis. (Ring cavities can be designed in which the signal propagates only in one direction.) The boundary conditions must also reflect the geometry of the laser resonator. For example, a standing-wave resonator can be analyzed with the following set of equations: ∂∆m ⫽ ⫺(1 ⫹ γ s)[i ⫹s ⫹ i ⫺s ] ∆m ∂t′

(88a)

冤cτL ∂t′∂ ⫹ ∂z′∂ 冥i

⫹ s

⫽ g max Li s⫹ ∆m

(88b)

冤cτL ∂t′∂ ⫺ ∂z′∂ 冥i

⫺ s

⫽ g max Li s⫺ ∆m

(88c)

2

and

2

with the boundary conditions: i s⫹ (0,t′) ⫽ R(t′)i ⫺s (0,t′)

and

i ⫹s (1,t′) ⫽ i ⫺s (1,t′)

(88d)

whereas the initial conditions i ⫾s (z′,0) and ∆m(z′,0) are determined by the analysis of the pumping phase. In the present case, the amplifying medium is assumed to occupy the entire cavity length. A perfect reflector completes the cavity at z′ ⫽ 1 and the combination of a reflector and a modulator produces an effective time-varying reflectivity R(t′) at z′ ⫽ 0. Such a set of equations must be solved numerically to take into account longitudinal variations in the population inversion and in the signal intensities [24].

377


Point Model To avoid having to solve numerically partial differential equations such as those given in the foregoing, the analysis of Q-switching is most often carried out by considering the rate equations for the laser cavity as a whole, which can be derived as follows. Integration of Eqs. (88a–88c) along z′ leads to ˆ ∂∆m ⫽ ⫺(1 ⫹ γ s) ∂t′

冮

L ∂ıˆs ⫽ g max L cτ 2 ∂t′

i s ∆mdz′ ⫺ (1 ⫺ R)i s⫺ (0, t′)

1

i s ∆mdz′

(89a)

0

and

冮

0

1

(89b)

where i s ⫽ i ⫹s ⫹ i ⫺s represents the total signal intensity and ˆı s (t′) ⫽

冮

1

i s (z′,t′)dz′

(89c)

0

The second term on the right-hand side of Eq. (89b) results from the boundary conditions given by Eq. (88d). The total intensity i s is then assumed to be constant along the cavity, in which case i s ⫽ ˆı s , so that ˆ ∂∆m ˆ ⫽ ⫺(1 ⫹ γ s)ıˆs ∆m ∂t′

(90a)

1⫺R L ∂ıˆs ˆ ⫺ ˆı s ⫽ g max Lıˆs ∆m cτ 2 ∂t′ 1⫹R

(90b)

and

By reverting to nonnormalized variables and functions, and noting that I s ⫽ cn p h v s , where n p is the volume density of signal photons, these equations can be transformed into

冢冣

cσ e ∂∆Nˆ nˆ p ∆Nˆ ⫽ ⫺ (1 ⫹ γ s) ∂t L

(91a)

and

冢冣

∂nˆ p cσ e ⫽ nˆ p ∆Nˆ ⫺ nˆ p /τ c ∂t L

(91b)

where τc ⫽

冢

冣

1⫹R L 1⫺R c

(91c)

is the photon lifetime in the cavity, ∆Nˆ is the population inversion integrated along the cavity, and nˆ p is the signal photon number integrated along the cavity. The photon lifetime depends on the losses and the round-trip time in the cavity. The opening of the switch is often assumed instantaneous, in which case the photon lifetime is a constant.

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Equations (91) are the familiar rate equations that describe the evolution of the total inversion and photon population in the cavity. Their validity relies on the assumption of a uniform laser field intensity along the resonator. For this condition to be met, the laser field should not vary too quickly relative to the cavity round-trip time. Moreover, the reflectivity of the output coupler should be high enough. This requirement can be made visible by considering the longitudinal distribution of intensity in a CW oscillator. In a standing-wave resonator, as defined by the boundary conditions of Eq. (88d), the total intensity is minimum at the back mirror. The ratio of intensities at the back mirror and at the output coupler is given by 2 √R I s (z ⫽ L) ⫽ I s (z ⫽ 0) 1⫹R

(92)

and is plotted in Figure 18. The intensity remains fairly uniform in resonators with a reflectivity larger than 50%, but clearly not in low-reflectivity resonators. This limitation can be illustrated in another way; namely, by considering the solution to Eq. (91b) in the absence of gain, in which case the photon count decreases exponentially as exp(⫺t/τ c). This exponential decrease must result from passive and coupling losses, so that exp(⫺2L/cτ c) ⫽ R exp(⫺δ) ⫽ R eff ,

(93)

where δ is the round-trip passive loss. A cavity lifetime τc ⫽

2L 2L ⫽ c[δ ⫹ ln(1/R)] c ln(1/R eff )

(94)

is thus expected which, in a lossless cavity, as assumed in the foregoing, corresponds to Eq. (91c) only when the reflectivity R approaches unity. Notwithstanding their apparent limitations, Eqs. (91) have been applied with great success to model Q-switched lasers, by allowing identification of the parameters that determine their performance. They form the basis of what is sometimes called the point model. The solution of these equations is

Figure 18

Ratio of the CW intensities at the back mirror and at the output coupler in a lossless standing-wave resonator as a function of the output coupler reflectivity.

379


discussed in detail in several papers and textbooks [2,3,25,26] and is not reproduced here. Only salient features of the solution are discussed. A first question to consider is the speed at which the Q-switched laser pulse develops, which determines the required switching time for the loss modulator. In bulk lasers, the field builds up initially from a very weak spontaneous emission signal that is amplified without significantly depleting the stored energy. In this early stage of its development, the field increases exponentially, with a time constant proportional to τ inc ⫽ τ c /(r in ⫺ 1) [2]. The initial inversion ratio r in is defined as ∆Nˆ i (95) r in ⫽ ∆Nˆ th where ∆Nˆ i is the population inversion just before switching and ∆Nˆ th is the population inversion required to reach threshold. There is some arbitrariness in assessing the time required for the laser field to reach a ‘‘sizable’’ level. In typical bulk lasers, a reasonable evaluation for this buildup time is 20 times τ inc . This view may not apply to a fiber laser, where the ASE signal can be significant and speed up the buildup time. Buildup times of many tens of nanoseconds have been reported in Q-switched fiber lasers at low repetition rates, but they were measured with a relatively slow loss modulator, which could have slowed down the pulse development [16,27]. Numerical evaluations taking into account the finite opening time of the loss modulator indicate that switching times of 10 ns or less are required in typical fiber lasers to avoid switching-related losses [28,29]. The extraction efficiency η ext of the stored energy by the Q-switched pulse depends solely on the inversion ratio and is determined implicitly by the following equation [2]: r in ⫽

1 η ext /ζ

ln

冤1 ⫺ 1η /ζ冥 ,

(96)

ext

where ζ is the maximum achievable extraction efficiency defined in Eq. (71). As shown in Figure 19, the extraction efficiency increases monotonically with the inversion ratio.

Figure 19

Extraction efficiency in a Q-switched fiber laser as a function of the initial inversion ratio. The efficiency is normalized to the maximum achievable extraction efficiency ζ defined in Eq. (71).

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This behavior can be understood by considering the Q-switched laser as a self-seeded regenerative amplifier, in which the amplifier itself provides the signal to be amplified. As the inversion ratio increases, so does the overall gain experienced by the photons, either because the single-pass gain is increased or because the photons are allowed to make more passes through it. According to Figure 19, over 90% of the energy available for extraction is taken up by the Q-switched pulse at an inversion ratio as small as 3. From this point of view, there is not much sense in trying to operate a Q-switched laser at much higher inversion levels. Moreover, only part of the extracted energy is delivered as a useful output, because some of it is dissipated by internal cavity losses. Contrary to what might be suggested by Figure 19, increasing the output coupler reflectivity to raise the inversion ratio r in does not necessarily translate into more energetic output pulses, for a larger fraction of the extracted energy is then dissipated within the cavity. As in CW oscillators, there is a range of reflectivity over which the output pulse energy is maximized. The peak power per unit area that is extracted from the gain medium verifies the following equation [2]: I peak ext ⫽

∆Nˆ th hv s [r in ⫺ 1 ⫺ ln(r in)] (1 ⫹ γ s)τ c

(97)

The peak power is inversely proportional to the cavity photon lifetime. The parameters in front of the bracketed expression characterize the cavity and do not depend on pumping. The influence of pumping is determined solely by the bracketed term, which is plotted in Figure 20. This curve compares well with the experimental measurements presented in Figure 21. These results were obtained with a moderately pumped Nd-doped fiber laser, in which the inversion ratio is expected to be approximately proportional to the pump power. Such an agreement is not expected with measurements taken in lasers where pump saturation or strong ASE is involved. According to Eq. (57b), the initial single-pass gain G i is equal to G i ⫽ exp[σ e ∆Nˆ i]

(98a)

Figure 20 Theoretical dependence of the peak power per unit area extracted from a Q-switched fiber laser as a function of the inversion ratio.

381


Figure 21

Peak power and duration of pulses produced by a Q-switched Nd-doped fiber laser, as functions of the launched pump power. (From Ref. 28.)

whereas the oscillation threshold condition can be expressed as R eff exp[2σ e ∆Nˆ th ] ⫽ 1

(98b)

Taking into account Eqs. (94), (98), and (59c), Eq. (97) can be rewritten as I peak ext ⫽

冤

冦

U sat ln(G 2i ) ln(G 2i ) s ln 2 (R ⫺1 ⫺ 1 ⫺ ln eff ) ⫺1 4L/c ln(R ⫺1 ln(R eff ) eff )

冧冥

(99)

The peak power per unit area is proportional to the saturation fluence of the gain medium divided by the round-trip time of the cavity. All things being equal, shorter cavities produce more powerful pulses. This expression can be used to investigate the influence of the effective reflectivity R eff of the cavity on the peak power for different initial gains G i , as shown in Figure 22. There is an optimum effective reflectivity that maximizes the output peak power. When the reflectivity is low, the inversion ratio is too small for efficient

Figure 22 Influence of the effective reflectivity R eff on the peak power per unit area extracted from a Q-switched fiber laser.

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extraction. When it is large, photons remain trapped for a long time within the cavity and seep out only slowly (i.e., the peak power is lower). The curves presented in Figure 22 take into account all of the extracted power, part of which may be dissipated as intracavity losses. When intracavity losses are present, the useful extracted power will thus go down even faster as a function of reflectivity. The shape of the curves of Figure 22 is representative of experimental measurements obtained with an Nd-doped fiber laser, as illustrated in Figure 23. The Q-switched pulse width is obtained by dividing the pulse energy by its maximum power [2]; that is, τs ⬇

r in η ext /ζ ⫻ τc r in ⫺ 1 ⫺ ln r in

(100)

The pulse width scales similar to the photon cavity lifetime and is thus proportional to the cavity length. The pulse width normalized to the photon cavity lifetime is plotted in Figure 24 as a function of the inversion ratio. The pulse width decreases rapidly at small inversion ratios, but it changes only slowly as the inversion ratio increases. This behavior is displayed, for example, in the measured pulse width of the Q-switched Nd-doped fiber laser of Figure 21, and it has been observed in other fiber lasers as well [27–30]. The effect of the output coupler reflectivity on the pulse width is also illustrated in Figure 23 for a Q-switched Nd-doped fiber laser. Lowering the output coupler reflectivity reduces the inversion ratio, but also the photon lifetime in the cavity, which have opposite effects on the expected pulse width. As a result, there is an optimum reflectivity that produces the shortest pulses. For a given pump power, there is also an optimum fiber length that produces the most powerful pulses. This is illustrated in Figure 25 for a Q-switched Nddoped fiber laser. The gain of the laser depends on the fiber length, but so does the photon lifetime in the cavity; hence, the observed behavior of the output pulse peak power and duration. Repetitive Operation The performance of a Q-switched laser as a function of the repetition rate is very similar to that of an amplifier subjected to a constant average intensity load (see Sec. 7.2.3). Figure 26 presents experimental data obtained from a Q-switched Er-doped fiber laser as

Figure 23

Influence of the output coupler reflectivity on the peak power and on the duration of the pulses produced by a Nd-doped Q-switched fiber laser. (From Ref. 28.)


383

Figure 24

Influence of the inversion ratio on the Q-switched pulse width normalized by the photon lifetime in the cavity.

a function of the Q-switching repetition rate [16]. At low repetition rates, the pump has enough time between pulses to completely replenish the population inversion to its steadystate level. The characteristics of each individual output pulse remain the same as long as this is so. (This is slightly different from the repetitive amplification discussed earlier, in which a slow decrease of the individual pulse energy at low repetition rates resulted from a decrease of the input pulse energy. In the Q-switched laser, the ‘‘input pulse’’ energy is spontaneous emission provided by the excited gain medium, which remains constant as long as the repetition rate is low enough.) When the repetition rate increases, the available gain decreases, which results in a reduced inversion ratio and less energetic, less powerful, and longer pulses. The average power of the Q-switched pulses is seen to increase rapidly at low-repetition rates, then to saturate when the laser moves into a ‘‘steady-state’’ regimen (see Fig. 26a). As shown in Figure 13, stronger pumping replenishes the population inversion faster and allows the laser to maintain its low repetition rate

Figure 25

Influence of the fiber length on the width and peak power of Q-switched pulses produced by an Nd-doped fiber laser operated at a constant launched power. (From Ref. 28.)

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Figure 26 Effect of the repetition rate on the performance of a Q-switched Er-doped fiber laser. (From Ref. 16.)

behavior up to higher pulse frequencies. This frequency behavior has also been reported in other references as well [28,29,31]. Waveguiding Effects The analysis of a Q-switched oscillator just presented above assumes that both the signal intensity and the gain are transversally uniform. These conditions clearly do not correspond to the physical reality of a fiber laser. However, as discussed previously, the rate equations describing the amplification of a guided mode by a transversally confined population inversion can, in principle, be solved approximately by considering instead their one-dimensional counterparts applicable to uniform beams. To this end, the space–time varying overlap integrals, defined in Eqs. (44b) and (77b), must be replaced by constant values. That the population distributions are likely to vary significantly in Q-switched lasers may raise some questions about this procedure. However, it is well justified when the rare earth ions are concentrated in a radial region over which the pump and signal mode intensity profiles do not vary too much. The examples given in the foregoing also suggest that this approach should apply well to four-level lasers that operate at moderate


385

inversion levels. In three-level lasers, the proposed uniform beam approach is likely to fail to accurately model the tail of a Q-switched pulse that extracts enough energy to bring the gain of the fiber close to zero. In a Q-switched fiber laser, an important parameter is clearly the initial gain experienced by the signal mode when the modulator is switched to its high-transmission state (i.e., the effective inversion ratio applicable to the guided mode). The signal gain depends on the overlap integral between the signal mode intensity profile and the ion concentration profile, as given in Eq. (76b), which can be readily evaluated. It also depends on the effective population inversion experienced by the signal mode, as determined from the population inversion profile resulting from pumping [see Eq. (43c)] and its transformation by Eq. (87). An educated guess may be required to assess the initial inversion ratio. Waveguiding effects in Q-switched fiber lasers have been discussed [32]. The Q-switching of Nd-doped fibers was considered, and the upper laser population profile was assumed to reflect the profile of the pump mode in the uniformly doped fiber core. Longitudinal Effects The point model relies on the assumption that the total intensity does not vary along the cavity. The validity of this model has been evaluated numerically [33]. The point model overestimates the pulse peak power and underestimates its rise time in high-gain lasers operating with strong output coupling and losses. Further numerical calculations indicated that the switching time as well as ASE can strongly influence the output pulse shape in Q-switched fiber lasers [24]. Strongly modulated pulses can be produced, the exact pulse shape depends largely on the actual cavity geometry. For example, Figure 27 presents the computed pulse shape in a ring cavity [24]. The highly structured output pulse clearly appears to result from the regenerative amplification of an initial ASE pulse. Development

Figure 27 Ref. 24.)

Computed output pulse shape in a long ring laser with a fast-opening switch. (From

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of the laser field resulting from the regenerative amplification of ASE was demonstrated in a long cavity Q-switched with a fast multiple-quantum–well modulator [34]. 7.3 Q-SWITCHING METHODS A variety of methods are available to Q-switch a fiber laser. Most of them are adaptations of those used to Q-switch bulk lasers. They are briefly reviewed in this section. Further details can be found in textbooks [2,25]. For the sake of completeness, the generation of high-peak–power pulses through amplification is also discussed. An up-to-date survey of pulsed fiber sources is also presented. 7.3.1 Bulk Active Q-Switching Mechanical Q-switching One of the simplest and oldest methods for Q-switching a laser is to modulate the roundtrip loss of the laser cavity with a mechanical device. This modulation can be achieved either by tilting or rotating one of the laser mirrors, or by inserting a mechanical chopper in the cavity [35,36]. Mechanical Q-switching is often associated with an undesirably long rise time, a rather poor pulse quality, and a severe pulse-to-pulse jitter. Electro-optic Q-Switching A better way to actively Q-switch a laser is through electro-optic modulation (EOM). It involves the use of an electro-optic crystal, to which an external electric field is applied to modulate its birefringence, in combination with one or more polarizing elements. The applied electrical signal allows control of the state of polarization of the laser field, whereas the polarizing elements translate any change in this state of polarization into a loss modulation. Because of its speed, repeatability, and large hold off ratio, this is the preferred device to Q-switch high-gain, high-energy bulk lasers. However, it is also rather expensive and bulky, and it requires a fast-rising high-voltage pulse source. For these reasons, electrooptic Q-switching has seldom been used so far in fiber lasers. Acousto-optic Q-switching Another way to control electrically the loss in a laser cavity is by diffracting the optical beam with an acousto-optic modulator (AOM) driven by a radio-frequency generator [28,37]. This method has been used to Q-switch many fiber lasers because it requires only low voltages. Also, it introduces only a small optical loss in the laser cavity, and it can be used at high repetition rates. 7.3.2 Bulk Passive Q-switching Another way of achieving Q-switched operation is to insert a saturable absorber in the laser cavity [38–40]. The high loss introduced by the unsaturated absorber prevents laser oscillation and allows the buildup of a sizable gain. When threshold is reached through pumping, the laser field begins to grow and, eventually, saturates the absorber, which thus becomes partially transmitting and opens up the cavity. Saturation of the absorber should preferably occur at low laser power to avoid excessive losses. The main advantage of passive Q-switching is its simplicity: the laser field itself switches the cavity into its highQ state and no external circuitry is required. On the other hand, the laser behavior then


387

critically depends on the saturation properties of the gain medium and the saturable absorber, which may vary or deteriorate over time. Passive Q-switching is thus prone to shotto-shot amplitude fluctuations and timing jitter. The achievable repetition rate depends on the recovery time of both the gain media and the absorber. When the absorber has a recovery time short enough to respond nearly instantaneously to intensity variations of the laser field, it may favor the preferential growth of an initial spike within the weak laser field. The laser is then mode-locked and produces a train of ultrashort pulses separated by one cavity round-trip time. Passive Q-switching and mode-locking have been thoroughly discussed [2]. 7.3.3 Integrated Optic Q-Switching The foregoing methods require that light be allowed to exit from the optical fiber so that it can be coupled to bulk optical components. This feature increases the susceptibility of the laser to environmental disturbances. The use of an integrated optic switch to modulate the loss of a laser cavity while maintaining the guided character of the light can alleviate this problem. Integrated optic switches also usually require a lower drive voltage than their bulk counterparts. The main disadvantage of these devices is their high insertion loss resulting from the mismatch between their mode and the fiber mode, and Fresnel reflection losses at the fiber–switch interface. They also often suffer from sizable propagation losses. As an example of the performance of this type of device, we refer the reader to Ref. [41], which describes Q-switching of an Nd-doped fiber laser using a LiNbO 3 integrated optic directional coupler. 7.3.4 All-Fiber Q-Switching To fully take advantage of waveguiding (small-volume, low-environmental susceptibility) and avoid losses associated with integrated optics devices, the Q-switching of a fiber laser should ideally take place in the fiber itself. Some novel in-fiber modulation schemes can be integrated to a fiber laser cavity, thereby eliminating bulk components and free-space propagation. For example, a fiber laser can be Q-switched by detuning a fiber Bragg grating [42] or by using a side-polished coupler to modulate the cavity loss [27]. Moreover, samarium-doped fibers appear to be a candidate for passive Q-switching [43]. However, in spite of their great potential, for the time being these all-fiber modulation techniques offer rather limited repetition rates and long rise times. 7.3.5 Pulse Amplification High-peak–power pulses can also be produced by amplifying a seed source (a low-power Q-switched laser or a semiconductor laser) in a high-power booster [44–48]. Several amplification stages can be cascaded, and interlaced with spectral filters or time gates to avoid gain saturation by ASE. This method offers a high flexibility because the repetition rate, the pulse width, and occasionally the wavelength can be adjusted independently. However, the appreciable length of fiber in the amplifier chain makes it more susceptible to detrimental nonlinear effects. Techniques are then needed to circumvent the energy loss owing to unwanted wavelength conversion. With subpicosecond pulses, chirped-pulse amplification (CPA) is often used to eliminate nonlinear effects. This technique uses a stretcher to spread the pulse and reduce its intensity before amplification. A compressor restores the pulse width after amplification, thereby producing a high-peak–power pulse

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[49–51]. Use of a large mode area or multimode fibers can also reduce nonlinear effects [46,48,51]. 7.3.6 Survey of Pulsed Fiber Sources Table 3 presents a survey of pulsed fiber sources. It includes Q-switched oscillators as well as master-oscillator–power-amplifier (MOPA) systems. Fiber lasers and amplifiers are identified by their rare earth dopant. When applicable, the number of amplifying stages is indicated. Numbers with the approximation symbol (⬃) indicates figures that are not specifically provided in the reference but that have been estimated from other parameters. A few examples of chirped-pulse amplification are also listed, even though the pulses they produced are much shorter than those obtainable by Q-switching. 7.4 LIMITATIONS 7.4.1 Optical Damage Threshold Excessive optical intensities can lead to dielectric breakdown and destruction of the optical fiber material itself. The bulk optical damage threshold for silica is about 50 GW/cm 2 at 1064 nm for a single pulse focused to a 5-µm diameter [61]. Assuming an effective mode area of 50 µm 2, the maximum peak power that can be guided in a typical fiber is about 25 kW, which corresponds to an energy of 250 µJ for a 10-ns pulse. Defects in the fiber material can lower the damage threshold. The resistance of the ends of a fiber to a high optical intensity depends on their surface finish and cleanliness. The peak power handling of a fiber can be pushed farther by using fibers with a large mode field area, or even multimode fibers when a diffraction-limited beam is not required [20,40,44,47,51]. 7.4.2 Nonlinear Effects Silica is by no means a material that is strongly nonlinear. However, the guided propagation of a well-confined mode over long distances in a low-loss optical fiber can give rise to sizable nonlinear effects, even at low powers. These effects can be detrimental and usually occur well before optical damage becomes an issue. A thorough discussion of nonlinear effects in optical fibers has been presented [62]. Self-Phase Modulation Self-phase modulation (SPM) results from the intensity dependence of the refractive index of the fiber, which is described by the following equation: n˜ ⫽ n ⫹ n 2 I

(101)

where n is the linear index of refraction, n 2 is the nonlinear index coefficient, and I is the intensity in the fiber. The nonlinear index coefficient in silica fibers is in the range of 2.2 ⫻ 10 ⫺20 to 3.4 ⫻ 10 ⫺20 m 2 /W [62]. When a pulse propagates over a distance L in a fiber, it undergoes a nonlinear phase shift φ NL ⫽

2πn 2 L I λ

(102)

that varies in time with the pulse intensity envelope. The time variation of the nonlinear phase shift translates into a change in the instantaneous frequency of the pulse. This mech-

53 59 56 16 30 31 18 20 58 60 35 38 39 27 42 52 54 57 19 45 55 40 47 48 46 44 49 50 51

Ref.

Nd Pr 3⫹ Nd 3⫹ Er 3⫹ Er 3⫹ Er 3⫹ Er 3⫹ Er 3⫹ Er 3⫹ –Yb 3⫹ Tm 3⫹ Er 3⫹ –ZBLAN Nd 3⫹ Er 3⫹ Er 3⫹ Er 3⫹ Yb 3⫹ Yb 3⫹ DFB laser diode Nd :YLF DFB laser diode Nd 3⫹ Er 3⫹ Laser diode Er 3⫹ Laser diode DFB laser diode DBR laser diode Mode-locked Er 3⫹ Mode-locked Er 3⫹

3⫹

Oscillator — — — — — — — — — — — — — — — — —

Amplifier

Er 3⫹ Yb 3⫹ Er 3⫹ Yb 3⫹ Er 3⫹ 3 ⫻ Er 3⫹ Er 3⫹ 3 ⫻ Er 3⫹ –Yb 3⫹ 3 ⫻ Er 3⫹ 2 ⫻ Er 3⫹ 2 ⫻ Er 3⫹ 4 ⫻ Er 3⫹ –Yb 3⫹

Table 3 Pulsed Fiber Sources

1.046–1.083 1.05 1.06 1.53 1.53 1.55 1.5 1.56 1.535 1.92 2.7 1.06 1.5 1.55 1.552–1.556 1 1.08–2.2 1.55 1.047 1.535 1.06 1.53 1.534 1.53 1.545 1.535 1.55 1.5 1.5

Wavelength (µm) 2.2 ⬃0.75 ⬃2 ⬃2 ⬃4 6 50 500 ⬃0.9 ⬃0.5 ⬃2.3 0.8 ⬃0.05 ⬎5 ⬃5nJ 1600 ⬃50 1.1 69 ⬃1 ⬃50 112 118 40 ⬃125 340 2.5 26 100

Energy per pulse (µJ) 1.1 0.03 ⬎0.7 0.23 0.34 0.29 ⬎4 — 0.058 0.004 0.0023 .009 ⬃22 mW 0.4 2.1 mW — 10 1.8 — 0.18 — ⬎1 100 5 25 111 — — 30 MW

Peak power (kW) 1.0 10 ⬍1 1 0.4 0.7 0.5 0.2 0.5 4 1 10 — 0.1 1 ⬃3 1 — 0.1 2 30 — 1 10 10 0.4 555 1 0.8

Repetition rate (kHz)

EOM Q-switching AOM Q-switching AOM Q-switching AOM Q-switching Ring oscillator/AOM Q-switching AOM Q-switching Large mode area oscillator/AOM Q-switching Multimode fiber/AOM Q-switching AOM Q-switching AOM Q-switching AOM Q-switching Passive Q-switched mode-locking Passive Q-switching All-fiber modulator All-fiber modulator (Bragg gratings) Multimode fiber Super continuum generation Gated loop amplifier Gated pulse amplification — Double-clad amplifier Passive Q-switching/large mode area fibers Large mode area fiber Multimode amplifier Multimode amplifier Multimode amplifier CPA CPA CPA/multimode amplifier

Remarks

Q-Switched Fiber Lasers 389

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anism results in a spectral broadening of the pulse. It can also enhance the temporal broadening of the pulse in a fiber where the group-velocity dispersion (GVD) is normal, or it can decrease it when GVD is anomalous. (The coexistence of SPM and anomalous GVD is responsible for the existence of solitons.) In Q-switched fiber lasers, pulses are too long and fibers are too short for GVD to play a significant role, and SPM manifests itself only through a spectral broadening. The analysis of SPM-induced spectral broadening in the absence of GVD is straightforward, as detailed in Ref. 62. In the case of an unchirped gaussian input pulse, the RMS spectral broadening is given by (∆v) RMS 4 2 φ max , ⫽1⫹ (∆v) 0 3 √3

(103a)

where (Dv) 0 is the initial pulse bandwidth, φ max ⫽

2πn 2 L P 0 λ A eff

(103b)

is the maximum nonlinear phase shift, P 0 is the peak power of the pulse, A eff is the effective mode area, and absorption of the pulse over the fiber length L has been assumed negligible. In a typical fiber at 1.55 µm (A eff ⬇ 50 µm 2), the nonlinear phase shift reaches φ max ⬇ 2 and the pulse bandwidth is roughly quadrupled (see Eq. 103a) even in a fiber as short as 1 m and for a peak power as low as 1 kW. Sizable spectral broadening is thus expected to occur in Q-switched fiber lasers and in fibers carrying the output of such lasers. This may be detrimental in applications requiring a high spectral purity, such as nonlinear conversion in crystals with a narrow spectral acceptance. Inelastic Interactions Contrary to SPM, inelastic nonlinear effects involve an energy transfer between the signal mode and the dielectric medium. Stimulated Brillouin scattering (SBS) refers to the interaction of an optical pulse with acoustic phonons, whereas stimulated Raman scattering (SRS) involves optical phonons. Both phenomena are characterized by a threshold above which they become significant. Stimulated Brillouin scattering (SBS) results from electrostriction in the fiber material, which creates an acoustic shock wave that copropagates with the optical mode along the fiber. This acoustic wave acts similar to a grating, reflecting part of the incident light in the backward direction. Beyond some threshold power, the transmitted power saturates and any additional injected power is backscattered. Because the grating is moving at the speed of sound in glass (i.e., 5.96 km/s in silica), the optical frequency of the backscattered wave is downshifted by about 11 GHz. SBS can be modeled as a parametric interaction between the incident optical wave, the backscattered wave, and the acoustic wave. If depletion of the incident wave is neglected, and if the pulse has a narrow linewidth, the threshold power can be expressed by the following approximate expression [62]: g B P CR

L eff ⬇ 21 A eff

(104)

where g B is the Brillouin gain factor and P CR is the critical power at which the Brillouin threshold occurs. The effective fiber length L eff is given by


L eff ⫽

1 [1 ⫺ exp(⫺α p L)] αp

391

(105)

where α p is the attenuation coefficient of the fiber at the signal wavelength. The effective length nearly equals L when the fiber is short or when absorption is negligible (α p L ⬍⬍ 1). In a typical doped fiber (g B ⫽ 5 ⫻ 10 ⫺11 m/W, A eff ⫽ 50 µm 2), the product P CR L eff is roughly equal to P CR L eff ⬇ 21 W ⋅ m

(106)

A 21-W signal can thus propagate only over 1 m of fiber before reaching the Brillouin threshold. This simplified analysis is valid for pulses with a narrow linewidth, specifically for pulses longer than about 100 ns. As the pulse width becomes comparable with, or smaller than, the phonon lifetime of 1 ns, the scattering is less stimulated, and it even disappears for picosecond pulses. The Brillouin gain bandwidth is about 10–100 MHz. This rather narrow gain spectrum comes from the high-damping coefficient of the acoustic wave in the fiber. Because the linewidths of Q-switched fiber lasers are typically two to three orders of magnitude larger than this, SBS effects are rarely detrimental in actual devices. Besides, simple techniques can be used in practice to increase the Brillouin threshold. For example, cable television (CATV) requires high-quality, high-spectral–purity, high-power laser sources. The average power of such a transmission system is well above the Brillouin threshold but a phase modulation is added to the signal pulses, which artificially broadens the laser linewidth and renders SBS negligible for all practical purposes. Stimulated Raman scattering (SRS) arises from a transition between two vibrational states in the fiber material. This transition is induced by an incoming optical wave and involves optical phonons. Unlike SBS, both forward and backward Raman scattering are possible. However, the backscattering threshold is higher than the forward threshold, and typically only forward SRS is observed in optical fibers. Because optical phonons are much more energetic than acoustical phonons, SRS produces a larger downshift of the optical frequency than SBS. In silica, this downshift is about 13 THz, and the useful Raman gain bandwidth is several terahertz. Using an approach similar to that for SBS, one can find an approximate expression for the SRS threshold: g R P CR

L eff ⬇ 16 A eff

(107)

where g R is the Raman gain and L eff is defined in Eq. (105). By using g R ⫽ 3.2 ⫻ 10 ⫺13 m/W for silica and A eff ⫽ 50 µm 2, one obtains a value of the P CR L eff product for SRS: P CR L eff ⬇ 2500 W ⋅ m

(108)

A 2.5-kW pulse guided in a 1-m fiber is thus expected to produce significant Raman scattering. In a Q-switched fiber laser, Raman scattering limits the output power that can be achieved at the lasing wavelength. The output power in excess of this limit is diverted to longer wavelengths. In long fiber lasers, and particularly double-clad fiber lasers, multiple pulses at different wavelengths can appear because of GVD, the signal and scattered Raman waves then experiencing different group velocities. This effect can be a serious source of concern for applications such as OTDR and LIDAR.

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8 Mode-Locked Fiber Lasers MARTIN E. FERMANN and MARTIN HOFER IMRA America, Ann Arbor, Michigan

8.1 INTRODUCTION Mode-locked fiber lasers are capable of producing pulses with widths from close to 30 fs to 1 ns at repetition rates, ranging from less than 1 MHz to 100 GHz. This versatility, as well as the compact size of optical fibers, is quite unique in laser technology, and thus open up fiber lasers to a large range of applications. Indeed, mode-locked fiber lasers have been established as a premier source of short optical pulses, ranking equally with semiconductor and solid-state lasers. As mode-locked fiber laser technology matured and these lasers became commercially available, they have been used in many different fields, such as laser radar, all-optical scanning delay lines, nonlinear frequency conversion, injection-seeding, two-photon microscopes, THz generation, and optical telecommunications, just to mention the most widely publicized areas. This chapter is intended to give an overview of the technologies related to modelocked fiber lasers. Owing to the depth of the field, only the basic operation characteristics in a variety of applications can be described. To adapt this chapter to the interests of a more general audience, some of the practical issues in the construction of mode-locked fiber lasers are also discussed. Detailed reviews of the early work on mode-locked fiber lasers can be found in Refs. 1 and 2. 8.2 MODE-LOCKED FIBER LASERS IN THE FIELD OF ULTRAFAST LASER TECHNOLOGY Broadly speaking, four types of ultrafast fiber laser systems can be distinguished: actively and passively mode-locked single-mode fiber oscillators, mode-locked multimode fiber oscillators, and femtosecond fiber amplifiers. When trying to determine the place of mode395

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locked fiber lasers in ultrafast technology in general we need to look at their basic operation characteristics as well as their complexity and adaptability to currently pursued applications. For example, single-mode gigahertz actively mode-locked fiber lasers typically produce very high quality pulses with ⬃ 1-ps width and ⬃ 1-pJ pulse energies, which are ideal for a number of advanced communication systems [3]. As an alternative to fiber lasers in this operation regimen, semiconductor lasers have been developed that offer significant advantages in terms of reduced complexity and cost [4]. Indeed highly integrated active–passive mode-locked semiconductor laser systems can also operate at gigahertz repetition rates and can produce widely tunable pulses, with pulse widths ranging from 17 ps to 180 fs [5]. Typical pulse energies are more like 30 fJ, however, and are more than an order of magnitude lower compared with fiber lasers in this operation regimen. Moreover, the quality of pulses generated with fiber lasers is also expected to be higher compared with semiconductor lasers, particularly in the femtosecond regimen. However, in ultrahigh-bit-rate applications, semiconductor lasers seem like an attractive alternative to fiber lasers, particularly owing to the size advantage of semiconductor lasers. Compared with actively mode-locked, single-mode fiber lasers, passively modelocked single-mode fiber lasers operate with a relatively low component count and produce much higher pulse energies. In fact, 3-nJ, 100-fs pulses have been obtained from erbium (Er)-doped single-mode fiber lasers [6]; these pulse energies are only about one order of magnitude lower than the energy outputs of bulk femtosecond lasers [7]. On the other hand single-mode fiber lasers can have very low timing jitter compared with bulk lasers [8] and also the capability for a high degree of integration. Thus, in applications sensitive to timing jitter and laser size with reduced power requirements, fiber lasers can hold an advantage over bulk femtosecond lasers. The power limits of single-mode fiber lasers can be greatly expanded with passively mode-locked multimode fiber lasers [9]. Passively mode-locked multimode fiber lasers are compatible with cladding-pumping with high-power diodes and can produce pulse energies up to 20 nJ or maybe even higher. These pulse energies are comparable with the performance of typical bulk-optic solid-state lasers. Moreover, multimode fiber lasers can potentially minimize constraints from thermal management, complicated alignment, and packaging procedures that have thwarted the integration of solid-state lasers for decades. As an alternative to fiber lasers, passively mode-locked integrated optics waveguide lasers have also appeared [10], which may potentially allow the construction of even more compact, high-power laser systems. Because such lasers can be very short, they can potentially allow the construction of completely integrated high-power femtosecond laser systems operating at gigahertz repetition rates. Femtosecond fiber oscillator–amplifier systems [11] can produce pulse energies up to ⬃ 1 µJ, which is about one to two orders of magnitude higher than possible with conventional solid-state lasers. Because very compact designs are possible with such systems, fiber lasers may also have the edge in this operation regimen. Even more impressively, ultrafast fiber lasers have been constructed that potentially allow the production of pulses with energies of 1 mJ or higher [12]. Owing to the relatively low gain (⬃20 dB) of saturated fiber power amplifiers several amplification stages are required which, in turn, call for several acousto-optic gates to suppress amplified spontaneous emission. However, highly integrated designs can be implemented, providing great opportunities for ultra–high-power fiber laser systems for the future.

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As an alternative to femtosecond fiber amplifier systems producing pulse energies in the millijoule range, parametric chirped-pulse amplification [13] (PCPA) looks most promising. With PCPA a gain of up to 90 dB can be obtained in a single-pass. Although just as for ultra–high-power fiber amplifiers, bulk-optic pulse compression stages are required. 8.3 CONSTRUCTION GUIDELINES FOR MODE-LOCKED FIBER LASERS 8.3.1 Laser Transitions Optical fibers offer laser transitions ranging nearly continuously from 380 nm to 3.9 µm [14,15]. Of these, however, only a few have been mode-locked. For example pulses of the order of 100 fs have been obtained from neodymium (Nd) [8,16], ytterbium (Yb) [17], erbium (Er) [6,18], Er/Yb [19], praseodymium (Pr) [20], and thulium (Tm) [21]-doped silica and fluoride fiber lasers. Er-doped fiber lasers have been most extensively studied owing to their compatibility with telecommunication systems at 1.55 µm and ultrafast optical systems operating at about 800 nm, which can be accessed through frequencydoubling of Er-doped fiber lasers. For ease of handling, silicate Er-doped fibers are preferred, and of these, Er-doped aluminosilicate fibers exhibit the largest bandwidth, although their bandwidth is still smaller than that of Er-doped fluoride fibers [22]. An undesirable feature when manufacturing Er-doped fiber lasers emitting at 1.55 µm is that the acting transition 4 I 13/2 → 4 I 15/2 is three-level, which leads to a cavity-loss–dependent emission wavelength and bandwidth. We can calculate the emission wavelength of an Er-doped fiber laser in the presence of a wavelength-dependent cavity loss l(λ) from the minimum average erbium inversion I inv that is required for a round-trip gain of zero as [23] σ e (λ)I inv ⫺ σ a (λ)(1 ⫺ I inv )sN 0 L ⫽ l(λ)

(1)

where σ e (λ) and σ a (λ) are the stimulated emission and the absorption cross section of the laser transition, respectively, and N 0 is the erbium ion concentration. L is the active fiber length, and s is equal to either 1 or 2, depending on whether a ring or a Fabry–Perot cavity is considered. By subtracting the right side of Eq. (1) from the left-side, the gainbandwidth of the Er-doped fiber oscillator can be obtained. To account for a length-dependent erbium inversion, I inv is averaged over the active fiber length as I inv ⫽ ∫L I inv (z)dz. In this expression I inv ⫽ N 2 /N 0 is the fractional occupation of the upper laser level with an excited erbium ion concentration of N 2 . Assuming a typical Er-doped aluminosilicate fiber, using this approach we obtain the gain spectra shown in Figure 1 for various assumed average amounts of inversion. For small amounts of inversion the 3-dB gain bandwidth is typically near 40 nm. Note that when the inversion exceeds ⬃ 0.8, the peak gain-wavelength moves to 1.530 µm, with a correspondingly much smaller bandwidth, at which pulses shorter than about 500 fs may not be sustained. 8.3.2 Pump Sources From a practical point of view fiber lasers that can be pumped with low-cost pump sources are of the greatest interest. Secondary CW solid-state (or fiber) lasers can also be used

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Figure 1 Gain/absorption spectra of a typical partially inverted erbium-doped aluminosilicate amplifier. The value of average inversion varies from 1.0 (top curve) to 0.0 (bottom curve) in steps of 0.2.

for fiber laser pumping, as demonstrated for Pr, Tm [20,21], and Er/Yb-doped [24] fiber lasers pumped with Ti:sapphire and Nd :YAG lasers. However, diode laser-pumped fiber lasers are even more attractive because of their greater compactness, higher overall efficiency, and lower cost. Current choices include master-oscillator power amplifier diode lasers (MOPAs), single-mode (SM) laser diodes, and wavelength and polarization multiplexed single-mode laser diodes. Multiplexed single-mode laser diodes and MOPAs can be pigtailed to deliver about 500 mW in an SM fiber at wavelengths ranging from 700 to 1480 nm, which is more than sufficient to pump even the least efficient fiber oscillator designs. On the other hand, limits on allowable electrical pump power level and size may sometimes dictate the choice of SM pump diodes. Fiber pigtailed SM diode optical power levels of up to 220 mW can indeed be obtained at wavelengths of 780, 800, 915, 980, 1020, and 1480 nm, which are ideally compatible with Tm, Nd, Yb, Er, Pr, and Er-doped fiber lasers, respectively. Further near-term improvements in diode laser technology can also be expected, which will lead to even higher-power single-mode laser diodes. Perhaps the ultimate in simplicity is to pump fiber lasers with diode lasers with low spatial coherence, such as broad-stripe diode lasers or diode laser arrays. Low-coherence pump sources can be effectively coupled into optical fibers by using double-clad fiber laser designs [25,26]. A double-clad SM fiber core is doped with an active ion as in a standard SM doped fiber design. But the fiber cladding is surrounded with a low-index material producing a multimode cladding fiber guide. In turn, the multimode cladding allows the guiding of low-coherence pump light. An example of the refractive index profile of a double-clad Er-doped fiber [27] is shown in Figure 2. Compared with a single-clad fiber, the effective absorption of the pump light is approximately reduced by the ratio of the core area/cladding area A co /A cl . The pump light may nevertheless be fully absorbed by increasing the fiber length appropriately, which can be done with negligible penalty for a four-level laser, but requires high-brightness diodes for three-level lasers or co-doping with ions with large absorption cross section, as for Er/Yb co-doped systems. Because the


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Figure 2 Refractive index profile of a double-clad erbium-doped fiber. (From Ref. 27.) diameter of the inner cladding of such fibers can be as large as 1 mm, clearly much higher diode power levels can be utilized compared with SM fiber lasers. As single-mode mode-locked fiber oscillators typically require optical pump power levels of less than 500 mW, at present the use of single-mode double-clad fibers is not an absolute necessity, although a reduction in component count can be obtained by employing side-pumped, mode-locked fiber lasers [28]. On the other hand, mode-locked multimode fiber lasers [9] greatly benefit from cladding-pumping and, in fact, claddingpumping is almost a requirement for high-power operation of multimode oscillators and high-power fiber amplifiers. To date, cladding-pumped, single-mode mode-locked fiber oscillators have been demonstrated with Er/Yb-doped fiber [19,28] and Nd-doped fibers [29], whereas cladding-pumped multimode fiber oscillators have been demonstrated only in Er/Yb-doped fibers. In principle, very simple cavity designs can be implemented by way of claddingpumping as shown in Figure 3. In contrast to the use of wavelength-division multiplexing (WDM) couplers for coupling the pump light into the laser cavity, side-pumping of a lowcoherence diode laser to the active fiber is implemented.

Figure 3

Experimental setup for a side-pumped, double-clad, passively mode-locked Er/Ybdoped fiber laser. (From Ref. 28.)

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8.3.3 Dispersion and Soliton Propagation in Fibers In the design of mode-locked fiber lasers the dispersion of the fiber cavity is always an important parameter. Dispersion becomes particularly critical in the design of passively mode-locked lasers, for which dispersion needs to be minimized to generate the shortest possible pulses. Dispersion arises from the wavelength-dependence of the refractive index and the dispersion parameter β 2 at a frequency ω 0 is obtained by expanding the modepropagation constant β in a Taylor series about the center frequency β(ω) ⫽ β 0 ⫹ β 1 (ω ⫺ ω 0 ) ⫹

1 β 2 (ω ⫺ ω 0 ) 2 ⫹ . . . 2

(2)

Here 1/β 1 ⫽ v g is the group velocity at the frequency ω 0 . Owing to the presence of dispersion, optical pulses broaden along the fiber length. The amount of dispersive broadening scales with the dispersive length z d ⫽ T 20 /|β 2 |, where T 0 ⫽ ∆τ/1.665, and ∆τ is the full width at half-maximum (FWHM) pulse width for gaussian-shaped pulses. For gaussian pulses propagating one dispersive length, the pulse width increases by a factor of √2. The dispersively broadened pulses acquire a frequency chirp (i.e., a phase modulation across the pulse width). The phase modulation Φ(t) corresponds to a frequency variation via δω(t) ⫽ ⫺∂Φ(t)/∂t. The frequency variation is linear in time and given by δω(t) ⫽

2sign (β 2 )(z/z d ) T 1 ⫹ (z/z d ) 2 T 20

(3)

where z is the propagation length and T is the time delay measured from the center of the pulse. Thus, in positive dispersion fiber (sign(β 2 ) ⬎ 0), low frequencies travel to the leading edge (T ⬍ 0) of the pulse and high frequencies travel to the trailing edge (T ⬎ 0) of the pulse (i.e., the chirp is conventionally considered to be positive). The situation is reversed in negative-dispersion fiber. In single-mode Er-doped fibers operating at 1.55 µm it is possible to control the fiber dispersion by making use of the fiber waveguiding properties. To illustrate this point, we show in Figure 4 the dispersion of typical telecommunication and Er-doped singlemode fiber amplifiers. By changing the numerical aperture (NA) and the core size of the

Figure 4 Typical dispersion as a function of wavelength for a variety of fibers.


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Er-doped fiber, the fiber dispersion coefficient β 2 at 1.55 µm can be easily varied between ⫺20 ps 2 /km and greater than 50 ps 2 /km. Although most Er-doped fiber amplifiers operate with large numerical apertures and small core sizes to minimize the pump-power requirements, high-power Er-doped femtosecond lasers in fact require large core sizes to minimize the light intensity inside the fiber core and are typically matched to standard 1.3µm telecommunication fiber. In a typical telecommunication fiber operating at 1.55 µm we have a dispersion of ⫺20 ps 2 /km and, thus, the dispersive length for a gaussian-shaped pulse with a half-width of 1 ps is 18 m. In multimode Er-doped fibers, the influence of the waveguiding properties on dispersion are essentially negligible and the dispersion is governed by the dispersion of the fiber material. For a typical silica multimode fiber laser, operating at a wavelength of 1.55 µm, the dispersion is thus ⫺20 ps 2 /km. Early work on ultrafast fiber lasers utilized positive-dispersion Nd-doped fiber operating at 1.06 µm; therefore, complex bulk diffraction gratings [16] or prism pairs [17,30] had to be used inside the laser to minimize the amount of dispersion inside the cavity. Diffraction gratings or prisms can be used for compensating the fiber dispersion, as the sign of the dispersion introduced by these components can be selected freely by appropriate optical arrangements. Inside a laser cavity, however, only the introduction of negative-dispersion bulk-optic elements is practical owing to the higher complexity of setups that produce positive dispersion. Nowadays further degrees of freedom in the dispersion design can be obtained by using chirped-fiber gratings [31] inside the cavity [32,33]. In a chirped-fiber grating the grating period varies along the grating length. The resulting dispersion of a typical chirpedfiber grating with length L g , center wavelength λ 0 , and bandwidth δλ can be written as [34] β2 ⫽

n L g λ 20 π c 2 δλ

(4)

where n is the refractive index and c is the velocity of light in vacuum. Using chirpedfiber gratings essentially any value of dispersion can be obtained at any wavelength within the transparency range of silica glass. Another important parameter in an optical fiber is the amount of self-phase modulation induced by the nonlinear dependence of the refractive index n ⫽ n 0 ⫹ n 2 I inside the fiber on the intensity I of the light. n 2 ⫽ 3.2 ⫻ 10⫺20 m 2 /W in standard telecommunication fiber [35]. Self-phase modulation scales with the nonlinear length z nl ⫽ 1/(γP0 ), where P0 is the peak power of the pulse, γ ⫽ 2πn 2 /(λA), and A is approximately the core area in single-mode fibers. The time-dependent nonlinear phase shift for a pulse with a temporal profile s(t) due to the nonlinear refractive index of a fiber of length L is given by Φ nl ⫽ γP0 s(t)L ⫽ s(t)L/z nl

(5)

The nonlinear phase shift leads to spectral broadening and the formation of a nonlinear frequency chirp, where additional low frequencies are formed at the front edge of the pulse and additional high frequencies are formed at its trailing edge. In the vicinity of the pulse center, however, the frequency chirp is approximately linear and positive. In the negative-dispersion regimen a fiber supports solitons pulses [36] characterized by a sech 2 intensity profile s(t) ⫽ sech 2 (t/τ) and a FWHM pulse width given by ∆τ ⫽ 1.763τ :τ is also referred to as the soliton pulse width. Solitons remain unchanged in a fiber in the presence of both self-phase modulation and dispersion, as the positive chirp

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induced by the pulses through self-phase modulation is exactly compensated by the negative chirp arising from negative dispersion. Thus soliton lasers can typically tolerate larger amounts of self-phase modulation compared with lasers operating with overall positive dispersion. Soliton pulses are characterized by a balance of the dispersive and nonlinear lengths (i.e., z d ⫽ z nl ), from which we obtain the soliton power [35] Ps ⫽

|β 2 | 3.11|β 2 | ⫽ γτ 2 γ∆τ 2

(6)

In turn, the energy of a soliton can be calculated as Es ⫽

3.53 |β 2 | γ∆τ

(7)

It is also instructive to introduce the soliton period z s ⫽ (π/2)z d , which is the oscillation period of a higher-order soliton in the fiber. The wave vector of the soliton is given by k s ⫽ 2π/8z s , which is independent of frequency. Thus, in one soliton period a soliton accumulates a nonlinear phase delay of π/4. 8.3.4 Fiber Polarization Although a large variety of cavity configurations exist for mode-locked single-mode fiber oscillators, the basic operation principles of all of them are quite similar. Perhaps the first parameter to control in single-mode fiber oscillators is the polarization state of the laser signal. Single-mode fiber lasers, in general, are not isotropic and support two polarization eigenmodes. Note that in a multimode fiber, where only the fundamental mode is excited, the polarization degeneracy of the fundamental mode also needs to be considered. However, the control of the polarization state of the fundamental mode in a multimode fiber follows essentially the same procedures as in single-mode fibers. Unless a fiber is twisted extensively, it is typically sufficient to attribute a linear birefringence to the laser fiber. The strength of the birefringence is conveniently described by the polarization mode beat length L B (i.e., the length at which the polarization state is reproduced). L B is given by LB ⫽

2π δβ

(8)

where δβ is the difference in the propagation constants of the two polarization eigenmodes. A detailed account of polarization properties of single-mode mode-locked fiber lasers can be found in Ref. 37. For optimal stability of mode-locked fiber lasers, generally a single polarization state should be selected in the cavity. If both polarization eigenmodes are allowed to modelock simultaneously (which is possible in a fiber cavity without polarization-sensitive loss), unless the round-trip phase delay of the two polarization states is close to a multiple of 2π, the polarization eigenmodes will beat with each other, leading to a time-dependent polarization output state and undesirably noisy operation of the laser [38]. Examples of single-polarization, single-mode fiber cavity designs are shown in Figure 5. In this figure we stylized an arbitrary mode-locking mechanism as a box in the cavity. In Figure 5a, a nearly isotropic (low-birefringence) fiber is used in conjunction with a polarizer and a fiber-loop polarization controller to ensure single-polarization opera-


403

Figure 5 Single-polarization fiber cavities: from top to bottom: (a) standard Fabry–Perot cavity with polarization controllers; (b) single-polarization ring cavity using highly birefringent fiber to eliminate polarization drifts; (c) environmentally stable, polarization insensitive cavity comprising two Faraday rotators and no polarization controllers.

tion and a low loss for that polarization state. In Figure 5b, we show a cavity consisting of only polarization-maintaining fiber arranged in a ring to eliminate polarization drifts. Finally, in Figure 5c a cavity is shown with two 45-degree Faraday rotators in conjunction with a nearly isotropic fiber. The Faraday rotators are used to compensate the round-trip linear phase and group delay of the two polarization eigenmodes of the fiber to zero [39]. Note that the cavity in Figure 5a has the disadvantage that the transmission loss through the polarizer dependends on fiber perturbations, which is not desirable when packaging the laser. On the other hand the cavity in Figure 5b must use polarization-maintaining components throughout, such as polarization-maintaining couplers, which greatly inflates the cost of such devices. In the cavity of Figure 5c, the need for polarizationmaintaining fiber is eliminated, but the Faraday rotators also add additional cost, and they are not too conducive to miniaturizing the cavity. In addition, compact Faraday rotators operating at wavelengths shorter than 1.3 µm are not readily available. 8.4 ACTIVELY MODE-LOCKED SINGLE-MODE FIBER LASERS 8.4.1 Basic Operation Principles Most of the principles of active or passive mode-locking apply equally well to singlemode and multimode fibers. For simplicity, however, we initially restrict the discussion to single-mode fiber lasers; mode-locked multimode fiber lasers are described in detail in Section 8.8.

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Active mode-locking of single-mode fiber lasers is most attractive for high-bit-rate communication systems, because active mode-locking produces pulses in synchronism to a well-defined radio-frequency clock signal. The clock signal can be obtained directly from the circuitry of an optical communication network, or it can be generated by clockrecovery from an existing data stream. Synchronized modulators subsequent to the signal source can then be used for information encryption. A classic explanation of the principles of active mode-locking in Ref. 40 can be found. Here, we just reproduce a brief summary of the most important features. In general amplitude modulation (AM) and frequency modulation (FM) mode-locking are distinguished. In AM mode-locking the cavity loss is periodically modulated with a modulation frequency exactly matched to the cavity round-trip time. A pulse can then build up synchronously with the exerted modulation, where the pulse will be centered in the middle of the modulation function and is successively shortened in each round-trip. Eventually, pulse shortening is limited by the finite gain bandwidth of the optical laser medium and a steady-state pulse, with a width very much smaller than the modulation window, is obtained. An illustration of the process is given in Figure 6. In the frequency domain it is assumed that the modulator produces sidebands to each of the oscillating axial modes at the axial mode-spacing, which tends to lock the modes of the laser in phase. The width of the generated pulses is then approximately given by T/N, where T is the cavity round-trip time and N is the number of axial cavity modes mode-locked by the modulator. In FM mode-locking the phase, rather than the cavity, is modulated at the cavity round-trip time, which also leads to pulses very much shorter than the modulation period, which can be understood from the similarity of the explanation of AM and FM mode-locking in the frequency domain. Although active mode-locking is most interesting at gigahertz repetition rates, the first work in this area dealt with actively mode-locked lasers operating at megahertz repetition rates. At megahertz repetition rates, AM-mode-locked lasers were constructed using bulk acousto-optic modulators [41–43], and FM mode-locked lasers were constructed using bulk LiNbO 3 phase modulators [44]. In Nd-doped fibers, bandwidth-limited pulses with widths ranging from 8 to 20 ps have been so generated. In an interesting experiment all-fiber integrated phase modulators were also used for FM mode-locking. By setting up

Figure 6

Conceptual drawing of an amplitude modulation function and the corresponding pulse location in an AM–mode-locked laser.

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a standing acoustic wave in the fiber, the fiber refractive index is altered periodically by electrostriction and picosecond pulses at repetition rates as high as 417 MHz were so generated [45]. For applications in telecommunications, integrated LiNbO 3 amplitude or phase modulators can be used to produce AM or FM mode-locked pulses at repetition rates of tens of gigahertz, with highly integrated cavity designs [46,47]. A typical arrangement for an integrated actively mode-locked fiber laser is shown in Figure 7. The active fiber length in such devices can be as long as several kilometers. Polarization drifts can be eliminated as discussed in Section 8.3.4. Mode competition between counterpropagating waves and different polarizations is avoided by the use of a polarizing isolator. Typically, a phaselocked loop is used to lock the repetition rate of the fiber laser to an external clock, where the cavity length is continuously adjusted with a fiber stretcher (see also Sec. 8.7). Actively mode-locked fiber lasers can be described by the mode-locking theory for homogeneously broadened gain media [40,48]. Typically, the time-varying modulation exerted by the modulator may be cast into the form M(t) ⫽ exp[⫺(δ a ⫺ iδ p )ω 2m t 2 /2]

(9)

where ω m ⫽ 2πf m and f m is the optical modulation frequency. δ a and δ p are the amplitude and phase modulation indices, respectively. δ p is simply the exerted peak phase retardation in the cavity. For pure FM mode-locking, the predicted output is a train of chirped gaussian-shaped pulses with a FWHM pulse width of

冢冣冢冣

2g ∆τ ⫽ 0.45 δp

1/4

1 f m ∆f a

1/2

(10)

where ∆f a is the 3-dB bandwidth of the gain medium, and g is the saturated intensity gain in the cavity. The time–bandwidth product in this case is ∆τ∆f ⫽ 0.63, where ∆f is the FWHM spectral bandwidth of the pulses. The time–bandwidth product for bandwidthlimited gaussian pulses is ∆τ∆f ⫽ 0.44 and, therefore, the chirp produced by FM modelocking is relatively small. To describe the case of pure AM mode-locking, δ p has to be

Figure 7 Experimental setup for an actively mode-locked fiber laser.

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replaced by δ a in Eq. (10). The resulting pulses also have a gaussian shape and are bandwidth-limited. Equation (10) is valid both for fundamental and higher-harmonic modelocking, when more than one pulse oscillates in the cavity. Typical modulation indices for standard electro-optic and acousto-optic modulators are of the order of 1. 8.4.2 Active–Passive Mode-Locking Because of the long interaction length of the signal with the gain medium in single-mode fibers, the pulses are susceptible to distortions arising from self-phase modulation. When the phase-modulation arising from self-phase modulation becomes significant, the pulse– forming process is typically referred to as active–passive mode-locking. From Eq. (5) we can derive that near the pulse center the phase modulation induced by self-phase modulation follows a quadratic function. In turn, this allows us to define a self-induced complex modulation index according to Eq. (9). For a sech 2 pulse the self-induced–modulation index is then calculated as [2] δ sm ⫽

2Φ nl , ω 2m τ 2

(11)

where Φ nl ⫽ γP0 L is the peak nonlinear phase delay in the round-trip fiber length L. For example, assuming a nonlinear phase delay Φ nl ⫽ π/30, a modulation frequency of 300 MHz and a FWHM pulse width of 15 ps, we obtain δ sm ⬇ 600. Thus, even a very small self-phase–modulation-induced phase delay produces a modulation index much higher than possible with the best optical modulators. As the chirp induced by self-phase modulation is not uniform, an excessive amount of nonlinearity in the cavity leads to pulse breakup and unstable pulse formation. However, in a mode-locked fiber laser cavity with overall positive dispersion, self-phase modulation can lead to pulse-shortening by up to a factor of 2 compared with Eq. (10) before instabilities set in [49], as demonstrated in early work in fiber lasers [43,44]. For negative dispersion, self-phase modulation in the cavity can be compensated by dispersion, and soliton pulses can be generated. The corresponding pulses have a sech 2 shape with a FWHM pulse width given by Eq. (6). In general the soliton pulses are accompanied by a weak continuum that arises from the perturbations of the soliton in the cavity. For the pulses to be stable, the loss of the continuum should be higher than the loss of the soliton. From this condition, it can be shown [50] that soliton pulses, with a width decreased by a factor R below the value given by standard linear active mode-locking theory, can be sustained in the cavity, where R is given by

冢

β2 L R ⱕ 1.37 g/(2πδfa ) 2

冣

1/4

(12)

For the pulses to remain stable, the amount of self-phase modulation in the cavity should be limited to a fraction of π to reduce the amount of continuum generation. Typically, pulse widths of the order of 1 ps can be obtained at repetition rates up to 20 GHz [3,51,52]. An example of an actively mode-locked erbium fiber laser cavity in the presence of soliton shaping is shown in Figure 8 [3]. A cavity design with one Faraday rotator is used to compensate for polarization drifts (the operation principle is similar to Fig. 5c). The measured pulse width as a function of average power is given in Figure 9. The pulse width decreases as a function of circulating pulse energy, as expected from Eq. (7). The


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Figure 8 Sketch of an active–passive, mode-locked soliton laser: The Er/Yb-doped fiber amplifier (Yb:Er FA) has a saturated output power of 200 mW. The propagation length consists mainly of dispersion-shifted fiber and is 90 m in length. (From Ref. 3.)

laser was harmonically mode-locked at a repetition rate of 10 GHz with nearly 10,000 pulses oscillating simultaneously in the cavity. Pulses with widths of 1.3 ps were generated. However, simply modulating the laser at a harmonic of the fundamental cavity frequency does not ensure pulse stability. In fact, owing to the long relaxation times of typical trivalent rare earths, individual pulses of the harmonically mode-locked pulse train cannot saturate the gain of the laser and the fiber laser saturates only relative to the average laser

Figure 9 Output pulse duration as a function of average power of the output pulses in the modelocked fiber laser from Figure 8. The dotted curve is a phenomenological fit to the data. (From Ref. 3.)

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power. Thus, there is no mechanism to ensure that the pulses inside the pulse train have equal energy. Hence, harmonically mode-locked pulses can suffer from considerable pulse-to-pulse instabilities, which show up in the RF spectrum of the laser as sidebands at multiples of the fundamental cavity frequency [51]. In the experimental setup shown in Figure 8, a large degree of sideband suppression was achieved by implementing nonlinear polarization evolution (see Secs. 8.5.1 and 8.5.2) as an optical limiting mechanism [53]. When operated as an all-optical limiter, nonlinear polarization evolution in the cavity is set to produce a minimal cavity loss at a certain pulse power; hence, an increase or a decrease in pulse power increases the cavity loss. The peak power of the pulses in the cavity is thus fixed and the pulse energies, equalized accordingly as the pulse widths, are relatively insensitive to power fluctuations. As an alternative all-optical limiting mechanism a narrowband intracavity filter was also demonstrated [52]. A filter has the advantage that it is compatible with an all-polarization–maintaining cavity. 8.5 PASSIVE MODE-LOCKING OF SINGLE-MODE FIBER LASERS For the generation of the shortest possible pulses from a relatively simple system, passively mode-locked fiber oscillators are still the lasers of choice. Since the early work in 1991 [16,30,54,55], essentially only three passive mode-locking techniques have been developed to a degree of maturity that allows their use in advanced applications. We can distinguish (1) passive mode-locking with an all-optical switch based on the Kerr nonlinearity of the optical fiber (or Kerr-type passive mode-locking [16,30,54]; (2) passive mode-locking with an external saturable absorber (or carrier-type passive mode-locking [55]); and (3) a combination of (1) and (2) [19,37]. 8.5.1 Fiber-Based All-Optical Switches The key element of Kerr-type mode-locked fiber lasers is an all-optical switch that allows for an intracavity loss that decreases as a function of intensity. All-optical switches come in a number of varieties and were initially developed for advanced ultrahigh bit rate communication systems, for which they are now widely used. The constraints of fiber laser cavity designs somewhat restricts the use of all-optical switches, and at present essentially only nonlinear loop mirrors [16,54] and polarization switches [18,30] are used in passive mode-locking of single-mode fiber lasers. In multimode fiber lasers only polarization switches are a viable option for facilitating mode-locked operation. As an example the nonlinear amplifying loop mirror (NALM) [56], which was the first all-optical switch used in passive mode-locking of fiber lasers, is shown in Figure 10. A pulse entering at port 1 of the four-port coupler, is split equally into ports 3 and 4. Ports 3 and 4 are connected by a fiber loop and an amplifier located asymmetrically inside the loop. The pulses from port 3 are propagating clockwise (cw) around the loop, whereas the pulses from port 4 are propagating counterclockwise (ccw) around the loop. The cw-propagating pulses are amplified in the beginning of their propagation path through the loop, whereas the ccw-propagating pulses are amplified at the end of their propagation path. In the linear regimen and assuming the polarization state is preserved inside the fiber loop, the NALM is essentially equivalent to a Sagnac interferometer, with an output amplified by the intraloop amplifier section. In this case, the cw and ccw pulses accumulate


Figure 10

409

Principle of operation of the nonlinear amplifying loop mirror operated in reflection.

the same linear phase delay across the loop and are recombined at the coupler and reflected back from port 1. Hence, here the NALM is completely reciprocal and will act as an amplifying mirror. The NALM becomes nonreciprocal when the polarization state is perturbed somewhere inside the loop. In particular, when the polarization state is rotated by 90 degrees somewhere in the loop, an arbitrary phase delay between the cw and ccw propagation direction can be implemented by an appropriate amount of birefringence in the loop. As a result the linear reflectivity can also be arbitrarily varied and the reflected pulse can be adjusted to fully emerge from port 2. Typically the linear phase delay between the cw and ccw propagation directions is adjusted by suitable polarization controllers. In the presence of self-phase modulation, the reflectivity of the NALM changes as a function of intensity, because the cw-propagating pulses are amplified first and see a larger nonlinear phase delay than the ccw-propagating pulses. The reflectivity of the NALM changes sinusoidally with intensity R ⫽ cos 2

冤21 冢Φ ⫹ γ 冢g ⫺ 1冣L 2I 冥 0

(13)

where Φ 0 is the linear phase delay in the NALM, I is the intensity of the light entering in port 1, and L is the loop length of the NALM, and we have neglected the length of the amplifier. Depending on the linear phase delay inside the NALM, either an increase or a decrease of the reflectivity with an increase of the intensity can be obtained. In Figure 10, the NALM is operated in reflection, which means that the reflectivity of the NALM is adjusted to increase with an increase in intensity. Rather than imbalancing the nonlinear phase delay in a nonlinear Sagnac fiber interferometer by locating an amplifier asymmetrically inside the loop, an uneven power splitting in the coupler can also be used. This nonlinear optical loop mirror (NOLM) [57] has the advantage that no additional amplifier is required to obtain a switching action. Another similar device uses fibers with different amounts of dispersion inside the loop [58,59] to imbalance the nonlinear phase delay in the Sagnac loop.

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One of the disadvantages of the NALM is that it has a relatively high component count, which is why it has been replaced by mode-locked fiber laser cavity configurations relying on nonlinear polarization evolution. The principle of nonlinear polarization evolution [30] as used in a Fabry–Perot cavity is explained in Figure 11. For simplicity only one high reflector is shown. The output coupling mirror is located just in front of the polarizer and is omitted. Here the nonlinear interferometer consists simply of the two polarization eigenmodes of the fiber, which are excited by the linearly polarized light coming from the polarizer. After one round-trip through the fiber, the two eigenmodes accumulate a differential linear phase delay and finally interfere again at the intracavity polarizer. Assuming the two eigenmodes are polarized along the x- and y-axes with intensity levels of I x and I y , the total phase delays Φ x and Φ y along the axes are obtained by adding the linear phase delays β x 2L and β y 2L, the self-phase and the cross-phase modulation terms [30]

冦

Φ x ⫽ β x ⫹ γI x ⫹ γ

冦

冢冣冧冢冣冧

2 I y 2L 3 (14)

2 Φ y ⫽ β y ⫹ γI y ⫹ γ I x 2L 3 where L is the fiber length. Note that the magnitude of the cross-phase modulation term is two-thirds the magnitude of the self-phase–modulation term.

Figure 11 Nonlinear polarization evolution in a weakly birefringent fiber: at high power the polarization state at the polarizer rotates into the axis of the polarizer. (From Ref. 30.)


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A nonlinear switching action is obtained by exciting the two polarization eigenmodes with different intensities (i.e., by rotating the polarizer such that the angle between the two polarization axes of the fiber is not equal to 45 degrees). Note that in Figure 11, we have assumed that the fiber is linearly birefringent resulting in two linearly polarized eigenmodes. This approximation is valid only if the polarization beat length of the fiber is at least about 10 cm at 1.55 µm [37]. If the beat length is longer, coupling between the eigenmodes due to fiber bends can no longer be ignored. However, for a round-trip linear phase delay between the eigenmodes larger than about 3π, a representation of the nonlinear-switching process in terms of linearly polarized eigenmodes is still reasonably accurate [30]. This makes sense, particularly for a Fabry–Perot laser, the polarization eigenmodes of which are always linearly polarized at the cavity end mirrors independently of the linear polarization evolution inside the cavity [60]. For even smaller linear-phase delays a representation of linear and nonlinear polarization evolution in terms of circularly polarized eigenmodes is preferred [30,37]. 8.5.2 Passive Mode-Locking Using Kerr-Type Optical-Switching Processes The cavity design of an Nd-doped fiber laser mode-locked with a NALM operated in reflection [16] is shown in Figure 12. Here a Faraday rotator is employed to compensate for the 90-degree polarization rotation inside the NALM, which was implemented to achieve a fully adjustable linear phase delay between the cw- and ccw-propagating pulses. The system did not produce pulses from noise and thus an acousto-optic modulator was used to initiate passive mode-locking. The cavity employed Nd-doped fiber with a peak gain wavelength at about 1.06 µm, at which the dispersion of the fiber is positive and, therefore, a bulk grating pair [35] was incorporated for dispersion compensation. With optimum dispersion compensation, 100-fs pulses with a pulse energy of 400 pJ were generated. Note that in contrast to bulk mode-locked lasers, the pulses in this system are subject to large dispersive perturbations (i.e., inside the cavity they are stretched and recompressed by close to a factor of 10). Both the terms additive pulse compression mode-locking [16] as well as ‘‘stretched-pulse operation’’ [6,18] were used for this phenomenon. As shown in the work by Haus et al. [61], because the dispersive perturbations are linear the stability of the stretched pulse laser is not adversely affected. In a stretched-pulse laser, short pulses occur only along a small fraction of the intracavity fiber, whereas, for example, in a soliton laser, the dispersive perturbations are kept small, which results in the oscillation of pulses

Figure 12

Passively mode-locked Nd-doped fiber laser using a nonlinear amplifying loop mirror in reflection: The laser delivered pulses with a width of 100 fs. (From Ref. 16.)

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with a constant pulse width and a high peak power along the whole length of the intracavity fiber. Because the amount of self-phase modulation sustainable in stretched-pulse and soliton lasers is about the same, stretched-pulse lasers can sustain higher pulse energies [62]. Erbium-doped fiber lasers passively mode-locked with a NALM were first demonstrated by Duling [54]. Because this type of cavity resembles a figure eight, it is commonly referred to as the figure-8 laser (F8L). F8Ls were the first all-fiber passively mode-locked fiber lasers. An example of an experimental set-up for a F8L is shown in Figure 13. Here the NALM is operated in transmission. Operation of the NALM in transmission has the advantage that no Faraday rotator is required to compensate for the polarization rotation inside the NALM. Rather, the linear polarization evolution in the loop outside the NALM can be used to rotate the polarization appropriately. To ensure unidirectional propagation in the loop outside the NALM an isolator is also required. Initially, the F8Ls lasers were operated as soliton lasers, for which the nonlinear intracavity phase delay is of the order of π [54], which in the NALM also corresponds to the switching power. From the NALM-switching power and the expression for the soliton pulse width, the FWHM width ∆τ of the pulses generated in the F8L is calculated as [54] ∆τ 2 ⫽ 0.49|β 2 |L(g ⫺ 1)

(15)

where L is the length of the fiber in the NALM loop and g is the gain of the NALM. In Figure 14, we show a spectrum of a typical F8L. Characteristic to the F8L as well as all soliton lasers in general are the spectral resonances (so-called Kelly side bands [63]) which occur because the soliton and the weak continuum arising from soliton perturbations couple coherently inside the cavity. For energy to couple between the soliton and the continuum wave, their phase delay per round-trip needs to be a multiple of 2π, from which the separation ∆Ω n of the sidebands from the central frequency can be calculated as [63]

Figure 13

Typical setup for an all-fiber, self-starting figure-8 laser made with Er-doped fiber. (From Refs. 54 and 64.)

413


Figure 14

Spectra of pulses obtained with different cavities of figure-8 lasers: the data listed next to each curve are the pulse durations and the total cavity dispersion. (From Ref. 64.)

1 ∆Ω n ⫽ ⫾ τ

√

⫺1 ⫹

8nz s L

(16)

where τ and z s are the soliton pulse width and period, respectively. From a measurement of the pulse width and the frequency spacing of the sidebands the dispersion of the cavity can be calculated. The minimal pulse width ∆τ min obtainable from the F8L and (other soliton lasers) is determined by the amount of intracavity dispersion. It was shown [64,65] that ∆τ min is given by ∆τ min ⱖ 0.75 √β 2 L,

(17)

where β 2 L is the total dispersion in the cavity. A good agreement of Eq. (17) with the measured pulse width was observed for pulse widths down to 100 fs. In Er-doped fiber lasers, pulses shorter than 100 fs are in general affected by the limited bandwidth of Er as well as higher-order dispersion. Fiber lasers based on nonlinear polarization evolution have allowed the generation of the shortest pulses from fiber lasers to date, namely 34 fs [37]. The autocorrelation of 37-fs pulses obtained from an Nd-doped fiber laser based on this principle is shown in Figure 15. These short pulses were made possible by implementing additive pulse compression mode-locking [16], where positive-dispersion fiber, and a bulk prism pair producing negative dispersion, were used to stretch and recompress the pulses dispersively in time inside the cavity. In a typical fiber, the fiber birefringence is temperature- and pressure-dependent, which leads to a time-varying linear and nonlinear phase delay between the eigenmodes of the fiber. However, when using nonlinear polarization evolution for passive modelocking, environmentally stable, cavity designs can be easily constructed, in which temperature and pressure drifts are eliminated. An example of an environmentally stable laser [39] is shown in Figure 16. Here, the Faraday rotator mirror rotates the back-reflected light by 90 degrees. Thus, the linear phase delay between the two polarization eigenmodes is compensated to zero after one round-trip. The second Faraday rotator is used to compen-

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Figure 15

Autocorrelation of the shortest pulses generated from fiber laser oscillators to date. The pulse width is 37 fs, assuming a sech2-shape. (From Ref. 37.)

sate for the polarization rotation of the Faraday rotator mirror. The linear phase delay between the polarization eigenmodes as well as the power distribution between them is then controlled by the intracavity quarter and half wave-plates. As shown in Figure 16 a saturable absorber is typically also used to initiate the mode-locking process. However, the final pulse formation can be dominantly governed by nonlinear polarization evolution in the cavity. Environmentally stable cavities have also been used in cladding-pumped oscillators [19] and in cladding-pumped multimode oscillators [9], providing the workhorse oscillator for a large number of applications, owing to their excellent long-term stability. 8.5.3 Self-Starting Single-Mode Fiber Ring Cavities The principle application of nonlinear polarization evolution is in self-starting Kerr-type mode-locked single-mode fiber ring cavities (i.e., in cavities where the mode-locking process starts from random noise fluctuations). In contrast to single-mode Fabry–Perot cavities, single-mode ring-cavities can be self-starting [66], as they are less sensitive to cavity

Figure 16

Experimental setup for an environmentally stable erbium-doped fiber laser: the waveplates are used to control both the linear and nonlinear polarization evolution in the fiber cavity. (From Ref. 39.)


415

reflections. The random noise fluctuations present in lasers before mode-locking arise from the presence of several axial modes in the cavity, which have randomly fluctuating amplitudes and phases and, therefore, produce long seed pulses with a certain lifetime. Cavity reflections lead to an uneven cavity mode-spacing inside the cavity, which reduces the lifetime of initial mode-beat fluctuations inside the cavity. A physical explanation for this phenomenon was given by Brabec et al. [67]. As the mode spacing is given by the ratio of the phase velocity of light over the round-trip cavity length, an uneven modespacing can be described as an uneven phase velocity for the axial cavity modes. An uneven phase velocity thus leads to a rapid temporal decay of the initial mode-beat fluctuations in the cavity. A condition for the self-starting of lasers can be derived by requiring that the lifetime of the mode-beat fluctuations is longer than the critical buildup time, so that the initial mode-beat fluctuations can develop into mode-locked pulses [67,68]. In the presence of spurious intracavity reflections, mode-beat fluctuations have no time to develop into modelocked pulses. The ‘‘quality’’ of a cavity relative to spurious cavity reflections can be evaluated by measuring the width ∆ν 3dB of the first beat note of the oscillating cavity modes in the free-running laser [67,68], which is related to the lifetime τ c of the mode-beat fluctuations by τ c ⫽ 1/∆ν 3dB . In typical cavities with low levels of intracavity reflections, ∆ν 3dB has a width of 1 kHz [68]. The self-starting theory for passively mode-locked lasers in the presence of beat-note broadening was extended to also include the effect of saturable absorbers in the cavity [69]. A unidirectional ring cavity is less sensitive than a Fabry–Perot cavity to spurious reflections because two reflectors inside a ring are required to produce coherent coupling of the reflected light to the circulating intracavity light. As a Fabry–Perot cavity is bidirectional, any one reflection can couple coherently to the intracavity light and lead to a frequency shift of the axial intracavity modes by mode pulling. An example of a stretched-pulse version [6,18,62] of an Er-doped fiber ring laser is shown in Figure 17. In this particular example, stretched-pulse operation is obtained by using lengths of positive- and negative-dispersion fiber in the cavity. The cavity is unidirectional and an all-fiber design is obtained by using a WDM coupler for pump light coupling as well as a 90/10-fiber coupler for output coupling. A single polarization is selected by the intracavity polarizing isolator and the polarization controllers on each side of the isolator are used to optimize linear and nonlinear polarization evolution for optimum mode-locked operation. 8.5.4 Semiconductor Saturable Absorber Mode-Locking Just as fiber-optic Kerr switches, semiconductor saturable absorbers can produce a transmission or a reflectivity, which increases with pulse intensity. Thus, they have been used as passive mode-locking elements for fiber lasers, since early on [55]. Saturable absorber mode-locking is the preferred method for generating pulses from fiber lasers with widths between 300 fs to a few picoseconds due to the simplicity of the cavity design. Saturable absorber mode-locking is compatible with all-polarization–maintaining cavity designs and saturable absorber mode-locking can produce stable pulses with negligible values of selfphase modulation in the cavity. Moreover, saturable absorbers are essential for the operation of self-starting passively mode-locked multimode fiber lasers and, therefore, offer the greatest prospect for industrial applications of the future.

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Figure 17

Experimental setup for a stretched pulse Er-doped fiber ring laser: the dispersion of the positive and negative dispersion fibers is balanced to produce a zero-dispersion cavity. (From Ref. 18.)

The saturation characteristics of the saturable absorber are determined by the carrier lifetime (1 ps–30 ns) and a time constant of about 300 fs arising from exciton screening [70] and carrier thermalization [71]. For pulses shorter than these time constants and for a cavity round-trip time very much longer than the relaxation times of the saturable absorber the absorption saturates as a function of pulse energy in the form α⫽∑

αi ⫹ α ns 1 ⫹ E p /E si

(18)

where α i is the saturable absorption due to an absorption mechanism, E p is the pulse energy density and E si ⫽ hν/σ si is the saturation energy density of the saturation mechanism with absorption cross-section σ si , hν is the photon energy, and α ns is the nonbleachable absorption. For passive mode-locking of Er-doped fiber lasers, bulk InGaAsP saturable absorbers [72] as well as saturable Bragg reflectors based on InGaAs/InP multiple quantum wells [73,74] have been successfully used. At 1.06 µm, InGaAs/GaAs multiple-quantum well saturable absorbers have been employed [75]. An example of a saturable Bragg reflector used for passive mode-locking of an Er-fiber laser [74] is shown in Figure 18, and an example of a multiple-quantum well saturable absorber [75] as used for an Nd-doped fiber laser is shown in Figure 19. Because of the broad bandedge of bulk saturable absorbers, compared with the narrow exciton absorption resonances of multiple quantum wells, bulk absorbers are the easiest to implement. In passively mode-locked fiber lasers, bulk absorbers are operated either at the band-edge or in the tail of the absorption band. Typical values for the saturation energy density of bulk InGaAsP at band edge owing to long-lived carriers are of the order of 100 µJ/cm 2. For the two fast mechanisms, saturation energy densities smaller by a factor of 3 are typically assumed. These values are inversely proportional to the linear absorption and increase linearly with the ratio of the absorption at the band edge to the absorption at the band tail.


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Figure 18

Experimental setup of an integrated Er/Yb-doped fiber laser: a saturable Bragg reflector (SBR) is used for passive mode-locking. SMF, single-mode fiber; SMF/DSF/DCF, single-mode, dispersion-shifted or dispersion-compensating fiber. (From Ref. 73.)

One attraction of saturable-absorber, mode-locked fiber lasers is that they allow completely integrated cavity designs. Femtosecond pulse generation from integrated cavity designs has indeed been demonstrated in Nd- [38], Er- [73], and Tm-doped [76] fiber lasers. These lasers simply consist of a length of amplifier fiber, a reflector or a fiber Bragg grating, and a saturable absorber. An example of an integrated Er fiber laser [74] is also shown in Figure 18. The output can be extracted directly by incorporating a coupler into the cavity or by butt-coupling an external wavelength-division-multiplexing coupler to the passive cavity mirror. A detailed theoretical description of pulse formation in integrated

Figure 19

Design of a GaAs saturable absorber mirror for passive mode-locking of Nd and Ybdoped fiber lasers. (From Ref. 75.)

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passively mode-locked fiber lasers was recently developed [74]. Stable operation with both positive and negative cavity dispersion was observed. In the positive-dispersion regimen, highly chirped pulses with rectangular spectra can oscillate, whereas in the negativedispersion regimen solitons are generated. Because the relaxation times of semiconductor saturable absorbers are very much longer than the response time of nonlinear fiber Kerr switches (⬃10 fs), the pulses are substantially longer than expected from the gain bandwidth of the amplifier. Most importantly, owing to the lack of polarization control in the cavity, both polarization eigenmodes mode-lock simultaneously and beat inside the cavity, which leads to a time-varying polarization output [38]. Polarization beating is only suppressed, and the two eigenmodes lock together in time when the linear phase delay between the eigenmodes is close to a multiple of 2 π. A limitation of saturable absorber mode-locked lasers is that they tend to be susceptible to a Q-switching instability. This is true particularly for gain-media with long upper state life-times such as Er-fiber lasers. Moreover, it is observed that generally Er-fiber lasers start passive mode-locking from a Q-switching instability, rather than from noise [77]. Since the peak power of the pulses during Q-switching can be significantly higher than in cw mode-locking, the intracavity elements and, in particular, the saturable absorber can easily be subjected to optical damage. Fabry–Perot fiber lasers also typically have a larger level of stray intracavity reflections compared with bulk solid-state lasers (especially when considering multimode fiber lasers); therefore, saturable absorbers with large nonlinearities are generally required to provide for reliable self-starting operation. On the other hand, it is this large nonlinearity that is causing the Q-switching instability. However, Q-switching instabilities can be suppressed by the incorporation of twophoton absorbers into the cavity, providing for saturable absorber mode-locked Er-fiber lasers that are uniquely robust against optical damage. Two-photon absorption at 1.55 µm can be conveniently obtained in InP, which is the favored substrate material for saturable absorbers operating at 1.55 µm. A combined two-photon absorber–saturable absorber structure can thus be obtained conveniently by using standard InGaAsP saturable absorbers grown on InP. A high-reflecting film can then be applied to the backside of the InGaAsP, whereas an antireflection coating on the InP minimizes bandwidth modulations from the Fabry–Perot resonances of the relatively thick substrate [77]. 8.5.5 High-Power Picosecond Single-Mode Fiber Lasers Using Fiber Gratings The maximum sustainable pulse energy in a passively mode-locked soliton single-mode (or multimode) fiber soliton laser can be raised by greatly increasing the cavity dispersion by the incorporation of a chirped fiber grating into the cavity (Fig. 20) [32]. In the presence of the grating the dispersion of a cavity of length L incorporating just a few meters of fiber is completely governed by the dispersion D 2 of the grating. The pulse energy then scales with √|D 2|/L, whereas the pulse width scales with √|D 2|. With this technique, pulses with widths of 4 ps and energies up to 10 nJ have been obtained directly from singlemode fiber oscillators [78]. Alternatively, narrow-bandwidth gratings have also been used in conjunction with saturable-absorber mode-locking to produce high-energy 1-ns pulses [79]. With chirped fiber Bragg gratings, high-power fiber lasers can be built in the whole transparency range of silica glass [32,33].


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Figure 20

Experimental setup for an erbium-doped fiber laser containing a chirped fiber grating to produce a high-power picosecond pulse source. (From Ref. 32.)

8.5.6 Passive Harmonic Mode-Locking of Single-Mode Fiber Lasers Whereas the output of passively mode-locked fiber lasers is a train of phase-locked pulses at the fundamental cavity round-trip time, passive harmonically mode-locked fiber lasers produce additional pulses located in between the train of phase-locked pulses. An example of the pulse train generated with passive mode-locking and passive harmonic mode-locking is shown in Figure 21. Passive harmonically mode-locked pulses are typically not

Figure 21

(Top) Conceptual drawing of pulse locations in a passively mode-locked laser operating at the fundamental cavity frequency and a passive harmonically mode-locked fiber laser operating at four times the fundamental cavity frequency. (Bottom) Number of pulses inside the cavity of a passive harmonically mode-locked fiber laser as a function of applied current to the pump laser. (From Ref. 81.)

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phase-locked and jitter around their average positions. At repetition rates of 2.5 GHz, pulse jitter as small ⫾ 15 ps has been measured in a cavity design similar to Figure 18 [80]. Passive harmonically mode-locked lasers are very useful in scaling-up the repetition rates of femtosecond fiber lasers, while still preserving a very simple cavity setup. Although the timing jitter of passive harmonically mode-locked fiber lasers is relatively high, making their use in nonlinear optical devices problematic, quite a few applications, such as some telecommunication systems (see Secs. 8.10.1 and 8.10.2), can tolerate this amount of timing jitter. Moreover, passive harmonically mode-locked lasers sometimes allow an adjustment of the repetition rate by simply changing the pump power level to the fiber cavity [80,81]. An example of a measurement of the number of pulses N as a function of pump current in a cladding-pumped fiber laser cavity [81] is also shown in Figure 21. In passive harmonic mode-locking, interactions between the intracavity pulses distribute all pulses approximately evenly across the cavity, producing an adjustable repetition rate Nf0 in steps of multiples N of the fundamental cavity frequency f0 . Passive harmonic mode-locking is generally observed in soliton fiber lasers with overall negative group velocity dispersion [82]. A number of different processes have been suggested that lead to the self-stabilization of the pulse trains in passive harmonically mode-locked fiber lasers. To generate repetition rates in the gigahertz regimen with any degree of stability generally requires saturable absorber mode-locking. Phase effects in the saturable absorber [81,83,84] as well as the recovery dynamics in the saturated gain medium [80] have been suggested to generate a repulsive force between the pulses that leads to harmonic mode-locking. In addition repulsive and attractive forces between pulses can also arise from an interaction of the soliton pulses with the small oscillating continuum in the cavity [84]. At subgigahertz repetition rates acoustic resonances of the fiber tend to further stabilize the harmonically mode-locked pulse train and lead to particularly small values of timing jitter [84–86]. 8.5.7 Generation of Noise Bursts In addition to active and passive mode-locking producing broadband femtosecond and picosecond pulses, optical fiber lasers can also be used for the generation of broadband partially mode-locked noise bursts with widths from 100 ps to tens nanoseconds. Although the temporal profile of such pulses is very noisy, the overall pulse energies can still have a high degree of stability, which is why they may be considered in some applications. For example, as such sources have a short temporal coherence length, they could be used in optical coherence tomography. Noise bursts were observed early on in the development of passively mode-locked fiber lasers [87,88], and their origin was recently explained by Horowitz et al. [89]. The fiber cavity design, as used for the generation of noise bursts by Horowitz et al. is reproduced in Figure 22. Here dispersion-compensating fiber was added to produce an overall positive-dispersion cavity for enhanced stability. Two polarizers and four polarization controllers were also added to the cavity. The cavity was made unidirectional by the isolator. The insertion of a fiber with a significant amount of birefringence between the two polarizers was useful for the reproducible production of noise bursts. The two polarizers in conjunction with the birefringent fiber thus produce a narrowband filter, with a linear transmission characteristic similar to a birefringent tuning plate.


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Figure 22 Schematic setup of an erbium-doped fiber laser source of noise bursts. (From Ref. 89.) However, because the fiber used here was comparatively long, the transmission characteristic of the fiber filter is nonlinear. When the group-velocity walk-off between the two polarization modes of the birefringent fiber is comparable with the pulse width, the nonlinear response of the fiber filter can be described as a nonlinear derivator [90] (i.e., the fiber filter optimally transmits the part of an impinging pulse with the highest temporal variation in intensity). For example, in a gaussian-shaped pulse only the deeply sloped sides of the pulse are transmitted. On the other hand, the center of the pulse is rejected as the derivative of the pulse intensity over time is zero at this point and the pulse is effectively split into two pulses. Owing to this pulse-splitting effect, derivators cannot support the generation of ultrashort pulses. Furthermore, because the transmission of long pulses in the derivator is small, and the cavity loss is reduced by the transmission of noise bursts, such cavities indeed favor the generation of noise bursts as the only stable operation point. Recently, 1-ns pulses with energies as high as 10 nJ were generated directly from such simple cavities [91]. 8.6 OTHER MODE-LOCKED SINGLE-MODE FIBER PULSE SOURCES For completeness, a few other pulse sources that have been demonstrated over the last few years are also summarized here. Optical FM mode-locking has been demonstrated using either an external data stream [92] or a stream of short, pump pulses [93]. Here, instead of an electro-optic modulator, cross-phase modulation from the external pulses is used to modulate the phase of the fiber laser cavity. Just as in active mode-locking the repetition rate of the pulses is determined by the frequency of the modulator, or the frequency of the external data stream in this case. Interestingly, gray solitons (i.e., repetitive pulses with an intensity minimum in an optical background wave with a constant amplitude) have also been generated by optically induced mode-locking [94]. A phase-insensitive passive additive pulse mode-locked (APM) laser using a coupled fiber laser cavity with three fiber gratings was also constructed [95]. Whereas NALMs constitute a nonlinear interferometeric optical switch, for which the length of the interferometer arms is automatically balanced by the Sagnac configuration, in principle other

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types of interferometers (such as Mach–Zehnder or Michelson configurations) can also be used to construct a nonlinear switch. In such interferometers the exact balancing of the length of the interferometer arms is typically a problem, but fiber gratings allow the construction of nonlinear interferometers, in which the interferometer phase for optimum mode-locking is automatically set by passive selection of the oscillating wavelength [95]. Another method for the generation of short optical pulses is the use of slidingfrequency soliton fiber lasers. In sliding-frequency lasers a continuous frequency shifter and a wavelength filter are incorporated into the cavity [96,97]. By continuously frequency-shifting the oscillating wave inside the cavity, the formation of axial modes is suppressed, and in conjunction with the wavelength filter, a loss mechanism for continuous oscillation is introduced. However, owing to the ability of soliton pulses to follow smallfrequency perturbations, the lower loss of soliton pulses can lead to the formation of a soliton pulse train. Soliton pulses at repetition rates of several gigahertz have been so generated. All-fiber versions have also been constructed by the incorporation of all-fiber frequency modulators [98]. 8.7 TIMING STABILIZATION OF SINGLE-MODE FIBER LASERS Most applications of mode-locked lasers require not only the presence of pulses of a certain short width, but also very often the timing of the pulses is just as critical. In an ideal case the position of the mode-locked pulses in the time domain would always be known to within a fraction of an optical half-cycle, which corresponds to a time of 2.5 fs at 1.55 µm. In fact, because the pulse train of lasers mode-locked at the fundamental cavity roundtrip time consists of a number of phase-locked axial modes, such a timing accuracy exists between successive pulses in the pulse train. However, owing to a variety of physical effects, the pulses are subject to timing jitter, and the pulse arrival times after many roundtrips inside the cavity will be subject to statistical deviations. However, one of the advantages of fiber lasers over bulk [8] and semiconductor lasers is that they provide pulse sources with the lowest timing jitter presently available. 8.7.1 Physical Origins of Timing Jitter The timing of the pulses in mode-locked fiber lasers is affected by cavity-length fluctuations, ASE, pump laser fluctuations, and acoustic interactions in the fiber. With present diode-laser technology, the effect of pump power fluctuations can generally be neglected. Equally, acousto-optic interaction are very weak and play a role only in passive harmonically mode-locked fiber lasers (see Sec. 8.5.6). Cavity length fluctuations arise mainly from temperature-induced refractive index fluctuations inside the optical fiber. With the temperature dependence of the refractive index of silica ∂n/∂T ⫽ 1.1 ⫻ 10⫺5, a temperature change of just 1°C produces an optical path length change of 11 µm in 1 m of fiber. Theories analyzing the jitter of mode-locked fiber lasers caused by ASE noise have been developed both for soliton [99] and stretched-pulse fiber lasers [100]. For a passively mode-locked soliton laser the expected timing jitter 〈∆t〉 in a time window T caused by ASE was evaluated as [99] 〈∆t〉 2 ⫽ 3D 2

θ 4 2 1 T Ωg τ g N ph TR

(19)


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where D is the cavity dispersion, θ is the noise enhancement factor resulting from imperfect inversion in a three-level system, g is the intracavity gain, Ω g is the gain bandwidth in circular frequency, N ph is the number of photons per pulse, and TR is the cavity roundtrip time. N ph is given by N ph ⫽ E /hν, where E is the pulse energy. The RMS timing jitter can be obtained by taking the square-root of Eq. (19). A related expression can also be obtained for stretched pulse lasers [100]. As expected for a random-walk process, Eq. (19) predicts an RMS timing jitter proportional to T1/2. Note, however, that direct measurements of the evolution of timing jitter have shown an increase in timing jitter proportional to T [101], which indicates that other noise sources in addition to ASE determined the jitter of the mode-locked fiber laser [101]. The timing jitter caused by ASE in erbium-doped fiber lasers was evaluated as a few 100 fs and less than 100 fs in a time interval of 100 ms for soliton [99] and stretchedpulse lasers [100], respectively. 8.7.2 Measurement of Timing Jitter Several methods to measure the timing jitter of mode-locked lasers have been developed. Traditionally, the jitter is inferred from the ratio frequency (RF) power spectrum of the mode-locked pulse train by using the method of von der Linde [102]. This method has the disadvantage that random stochastic noise is assumed and cross-correlations between the amplitude and phase noise are neglected [100]. Mode-locked fiber lasers can in fact be subject to nonrandom noise sources, such as acoustic resonances [82,84–86], which can lead to errors in the interpretation of the RF data. Another traditional method is to measure the cross-correlation between two phaselocked lasers, where one laser is used as the timing reference (master) for the secondary (slave) laser [103]. Cross-correlations measure the practically relevant drifts of the whole laser system, including the PLL electronics (see next section). A disadvantage of crosscorrelation techniques is that the noise is typically dominated by the PLL loop and very little information about the intrinsic quality of the laser system can be inferred. Recently, a new cross-correlation method [101] combining the advantages of the two foregoing measurement techniques was described. In this, a small fixed cavity length mismatch is introduced between two, otherwise identical, free-running mode-locked lasers, so that the pulses from the two lasers continuously scan through each other at a small difference in frequency. A Fabry–Perot etalon is placed after the output of one of the lasers. The pulses are then reflected back and forth within the Fabry–Perot etalon, producing a series of time-delayed pulses with decreasing intensity, which can be used as time calibration points. The jitter of the second laser relative to the first laser is mapped as a nonuniform separation of the cross-correlation peaks in the time domain. An example of an experimental setup is shown in Figure 23 [101]. Here the pulses are derived from a master and a slave laser, in which the fixed cavity length mismatch is introduced by the shown piezoelectric transducer in the slave laser. The Fabry–Perot etalon is placed in the path of the slave laser, producing the series of time calibration points. Because of the frequency offset between the two lasers, cross-correlation signals, as shown on the bottom left side of Figure 23 are obtained, for which the cross-correlations are measured by frequency-doubling the signals in periodically poled LiNbO 3 (PPLN), and detecting them with a photomultiplier (PMT). By using the cross-correlation from the first (most intense) pulse from the Fabry–Perot elaton as the trigger point, the cross-correlations from the subsequent pulses are arriving at different positions in time. As an example, the

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Figure 23

Measurement of laser jitter in the time domain: (top) experimental setup; (bottom left) cross-correlation peaks generated by Fabry–Perot (FP) etalon; (bottom right) close up of successive cross-correlations of the first and fifth peak. (From Ref. 101.)

time position of the fifth pulse from the Fabry–Perot etalon compared with the position of the first pulse measured for a number of scans is plotted in more detail on the bottom right-hand side of Figure 23. The higher jitter of the position of the fifth pulse is clearly visible. From the jitter of the pulses the jitter of the difference frequency between the two lasers can be inferred. This method is useful, particularly for the measurement of highfrequency noise, which is most strongly affected by the fundamental physical parameters of the laser. 8.7.3 Methods for Timing Stabilization of Mode-Locked Lasers To ensure the stability of actively mode-locked pulses, and to lock the repetition rate of passively mode-locked lasers to an external clock, phase-locked loops (PLLs) are generally used. PLLs can be implemented in various fashions. For example, the cavity length can be controlled by mounting a cavity mirror onto a moving piezoelectric transducer. Feedback bandwidths up to about 1 kHz, limited by the response time of the piezoelectric transducer


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can so be achieved [8]. Integrated cavity length adjusters can also be constructed by coiling the intracavity fiber onto a piezoelectric drum with an electronically controlled fiber diameter [3]. A third techniques does not require any piezoelectric transducers and relies on acousto-optically deflecting a beam on different parts of a diffraction grating. In this method, the deflection angle from the acousto-optic modulator is controlled by varying the modulation frequency. Although the cavity length adjustment goes along with a wavelength change, much higher feedback bandwidths compared with piezoelectric transducers can be obtained. Feedback bandwidths up to 10 kHz have indeed been implemented, limited by the response time of the drive electronics for the acousto-optic modulator [104]. The foregoing three techniques can be used both for actively and passively modelocked fiber lasers. For actively mode-locked lasers passive cavity length-adjustment techniques can also be employed. For example, in an AM-mode-locked fiber laser cavity with a relatively large amount of positive group velocity dispersion, small cavity length drifts can be self-adjusting. In this the large amount of cavity dispersion is sufficient to compensate for cavity length drifts by a change in wavelength [105]. To eliminate the use of cavity-length-controlling elements, the regenerative modelocking technique can be used in active mode-locking [106,107]. In regenerative modelocking, the RF beat note (see Sec. 8.5.3) of the initially free-running laser is detected. The signal is then passed through a narrow bandpass RF amplifier and fed back to an intracavity modulator. Provided the phase-setting of the feedback loop is correct, the mode-locking process starts from noise and the correct mode-locking frequency is continuously regeneratively generated from the laser signal itself, eliminating the need for cavitylength control. However, the repetition rate of the laser is now drifting in unison with the cavity length, which is a problem when the operation of the laser at a fixed clock frequency is required. Regenerative mode-locking can also be used to start the mode-locking process in passively mode-locked lasers. To minimize cavity length drifts between two fiber lasers, it is also useful to coil both fiber lasers onto a single drum and to ensure that they are subjected to the same environmental conditions (i.e., to environmentally couple the two lasers). A system of two environmentally coupled fiber lasers operating at 5 MHz has been electronically stabilized with relative timing jitters as low as 5 ps over a time period of 10 min [103], corresponding to a phase error of only 30 arcs. These phase errors are in general limited by long-term drifts in the PLL circuits, which are temperature-dependent and have a limited phase accuracy. Note that all the techniques for timing stabilization are equally applicable to multimode fiber lasers, which are discussed in the next section.

8.8 MODE-LOCKED MULTIMODE FIBER LASERS 8.8.1 Fundamental Mode Propagation in Multimode Fibers Whereas the material covered so far has dealt with only mode-locked fiber oscillators based on single-mode rare earth doped fibers [108], the improvements in rare earth doped fiber quality achieved during the last decade or so have also allowed the consideration of multimode rare earth doped fibers as serious contenders for practical fiber lasers, with great potential for the generation of high-peak power signal. Multimode fibers can be applied in ultrafast optic applications as long as modal speckle is suppressible. Modal speckle occurs from the interference of the modes at the

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end of the fiber, which leads to a very unstable mode-field distribution dependent on the phase difference between the various modes. However, because of group-velocity walkoff between the modes, modal interference can be suppressed by exciting multimode fibers using light with a short temporal coherence length, such as the broadband ASE source (see Chap. 8) or ultrashort pulses. Assuming a pulse with a half width of ∆τ, modal speckle is thus suppressed when (L∆n/c) ⬎ ∆τ, where L is the fiber length and ∆n is the difference in effective refractive index between next-neighbor modes; for large V-values the index difference between the fundamental and the next-order mode can be approximated by ∆n ⬇ λ 2 /2.2nd 2, where n is the core refractive index and d is the core diameter of the multimode fiber. For a 300-fs pulse in a 1-m length of fiber, we thus need an index difference ∆n ⬎ 9 ⫻ 10 ⫺5, and a fiber with a core diameter d smaller than 90 µm to suppress modal speckle at 1.5 µm. Moreover, highly circular and concentric multimode fibers are required to enable precision splicing of the multimode fiber to a single-mode fiber filter to ensure the excitation of the fundamental mode in the multimode fiber [9]. Whereas bulk optics requires aberration compensation, with many degrees of freedom of optical alignment, to launch the fundamental mode in a multimode fiber, fused fiber splices can readily achieve an excitation efficiency of 95% for the fundamental mode in the multimode fiber [9] with just two degrees of freedom (x, y) for the fiber alignment. For large V-values the fundamental mode in a multimode fiber has an effective mode-field diameter ω equal to the core diameter d; the effective intensity half width of the fundamental mode is thus d/√2. Owing to the large size of the fundamental mode in a multimode fiber, the peak power and energy storage limitations of multimode fibers can be significantly less stringent than those of single-mode fibers. Because of the higher peak powers, higher average powers are also possible; hence, multimode fibers greatly benefit from cladding-pumping, which provides a convenient means of supplying high pump powers to these system. However, the stability of the fundamental mode inside a multimode fiber also requires a minimization of microbending-induced mode-coupling, which leads to a reduction in mode quality along the length of the multimode fiber. The quality of single-mode propagation can be checked by splicing a multimode fiber in between two single-mode fiber filters and by measuring the insertion loss of the device as a function of the length z of the multimode fiber. Neglecting splice losses caused by insufficient mode-matching at the fiber splices, the obtainable launching efficiency into the second SM fiber is given by [109]

冢

η(z) ⫽ 1 ⫹

⫺1

冣

16d Dz λ2

(20)

where D is the mode-coupling coefficient [110] and λ is the operation wavelength. The launching efficiency is related to the M 2 value that is typically used to characterize the quality of near–diffraction-limited optical beams [40] as 1/η ⬇ √M 2 . It can be shown that the mode-coupling coefficient in typical fibers is proportional to d 8 /b 6 λ 4, where b is the outside diameter of the fiber [109]. Thus mode-coupling is reduced by using fibers with large outside-cladding diameters. For a fiber with a cladding diameter of 250 µm and a core diameter of 50 µm, single-mode propagation can be preserved over lengths greater than 20 m. Mode-coupling in such fibers is also relatively


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insensitive to bending, allowing for bend diameters as small as 7 cm without a deterioration in mode quality in several meters of fiber [109]. 8.8.2 Mode-Locking of Multimode Fiber Lasers A typical experimental setup for a passively mode-locked multimode fiber laser is shown in Figure 24. In this particular example the fiber was doped with Er/Yb to permit claddingpumping with a broad-area diode laser, which was injected into the double-clad fiber through the beam splitter shown. The multimode fiber here had a core diameter of 16 µm and a numerical aperture of NA ⫽ 0.20. A saturable absorber in conjunction with a twophoton absorber [77] was used to induce passive mode-locking. The excitation of the fundamental mode in the multimode fiber is ensured with the intracavity single-mode fiber pigtail, spliced onto the multimode fiber, where an excitation efficiency of 95% is readily obtainable. Due to the limited excitation efficiency for the fundamental mode, about f ⫽ 5% of the signal is launched into higher-order modes at the fiber splice, where to first order, only the next-order, the LP11 mode, is excited. Hence, after a double pass through the oscillator, the higher-order modes contain time-delayed satellite pulses with a peak intensity up to f ⫽ 5% compared with the main pulse. However, at the output of the laser, the peak level of the satellite pulses is proportional to f 2, for the splice filters out the satellite pulses propagating in higher-order modes. Thus, the level of satellite pulse excitation in the output of the multimode fiber laser is reduced to 0.25% for the present case. The quadratic dependence of satellite pulse excitation on splice loss is clearly essential to obtain high-quality diffraction-limited pulses from mode-locked multimode fiber lasers. In the present oscillator, femtosecond pulses with an average power up to 300 mW were obtainable at a repetition rate of 67 MHz. The peak power of the pulses was higher than 6 kW. These performance data were obtained by operating the laser purely in the soliton regimen. Clearly, even higher powers can be expected by using larger-core fibers. Alternatively, by incorporating positive dispersion fiber into the cavity, chirped picosecond pulses, with an energy content up to 18 nJ, could be obtained using the same multimode fiber as in the foregoing. These pulses could then be frequency-doubled and compressed to a pulse width of 700 fs in chirped periodically poled LiNbO 3 (see Sec. 8.10.4), where a doubling efficiency as high as 25% was achievable [111].

Figure 24 Ref. 9.)

Passively mode-locked, cladding-pumped multimode Er/Yb soliton fiber laser. (From

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8.9 AMPLIFICATION AND COMPRESSION OF FIBER LASER PULSES In many applications the output powers or the pulse widths generated by fiber oscillators are not sufficient, and additional amplification or pulse compression stages need to be incorporated after the oscillator. Pulse compression schemes may be distinguished as operating with positive, zero, or negative dispersion fiber as has been reviewed [112]. Pulse compressors operating with low-pulse energies at high-repetition rates (GHz) are of interest mainly to broad-bandwidth telecommunication schemes, whereas here we are primarily interested in pulse compression schemes for megahertz-type repetition rate lasers that can compete directly with the performance of bulk femtosecond solid-state lasers. Most interesting are combined fiber amplifier–compressors and all-fiber chirpedpulse amplification systems relying on fiber gratings. 8.9.1 Fiber Amplifier–Compressors Simultaneous amplification and pulse compression can be obtained by permitting higherorder soliton generation and Raman soliton formation in single- and multimode optical fibers. Soliton compressors rely on negative-dispersion fiber and, therefore, are compatible with amplification in erbium-doped fiber amplifiers. Although soliton compressors are highly nonlinear, high-quality output pulses can be obtained in conjunction with an EDFA [113]. An example of a Raman–soliton amplifier–compressor [114] is shown in Figure 25. Here the output was efficiently frequency-doubled in PPLN (see Sec. 8.9.4). To obtain the highest-quality output pulses, codirectional pumping of the Er amplifier is preferred. In codirectional pumping, the peak gain wavelength of the erbium-doped fiber shifts toward the red part of the spectrum along the fiber length. Because of the soliton selffrequency shift [115], the Raman soliton also experiences a red shift along its propagation length, the Raman soliton is preferentially amplified. Typically, compression factors of about five times are obtained without the need for any phase control after the end of the compressor fiber [114]. This is in contrast with fiber compressors based on positive-dispersion fiber, for which gratings are needed to compensate for the chirp accumulated in the nonlinear fiber and to obtain pulse compression [35].

Figure 25 Cladding-pumped multimode Er/Yb-doped fiber compressor–amplifier and periodically poled LiNbO 3 (PPLN) frequency doubler. (From Ref. 114.)


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In single-mode fibers, pulses with widths of 100 fs and pulse energies of 2 nJ have been generated [113] in a setup similar to Figure 25. In the example in Figure 25, 100fs pulses with pulse energies up to 4.4 nJ were generated at a repetition rate of 52 MHz in a 2.3-m length of multimode Er/Yb fiber with a core diameter of 16 µm. Co-doping with Yb permitted cladding pumping with a 5-W pigtailed diode array operating at 980 nm, which produced an average output power of 230 mW at 1.62 µm. Frequency-doubling in PPLN produced a 100-fs pulse source, with an average power of 120 mW at 810 nm, which is highly competitive with sources with comparable performance levels based on diode-pumped bulk Ti:sapphire lasers [7]. Raman soliton formation is also compatible with even more multimoded fibers, and Raman solitons with pulse energies up to 10 nJ at a wavelength of 1.58 µm have been generated in 50-µm core diameter dopant-free fibers [116], in which the output was still diffraction-limited. 8.9.2 Chirped-Pulse Amplification Using Fiber Gratings In addition to increasing the fiber cross section, self-phase modulation in amplifiers can be further reduced by implementing chirped-pulse amplification. Chirped-pulse amplification was developed in 1985 [117] and also has recently been adapted to optical fibers [11,118]. A chirped fiber grating is used to stretch the pulses dispersively in time before amplification. After amplification, the pulses are recompressed with a fiber grating of opposite chirp. The compressed pulses thus only ‘‘see’’ a nonlinearity from propagating through a few centimeters of the fiber grating. An example of an experimental all-fiber chirped-pulse amplification system [11] is shown in Figure 26. Here a cladding-pumped oscillator, based on Er/Yb-doped fiber, generates 200-fs pulses with an average power of 5 mW. The top polarization beam splitter (PBS) is used to direct the oscillator pulses to the chirped fiber grating for pulse stretching. Note that the fiber grating has a reflectivity of greater than 90%, and this is why only one

Figure 26

Experimental setup for chirped-pulse amplification system using a chirped fiber grating. (From Ref. 11.)

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grating can be used for both pulse stretching and compression. After reflection from the fiber grating, the polarization of the pulses is rotated by 90 degrees and the same PBS is then used to direct the stretched pulses to the Er-doped preamplifier, which amplifies the pulses to an average power of about 30 mW. Another pair of PBSs are then used to direct the pulses to the cladding-pumped Er/Yb power amplifier, to recompress the pulses in the fiber grating and for output extraction. The polarization is appropriately controlled with the half- (λ/2) and quarter- (λ/4) wave-plates and the Faraday rotators as shown. To minimize optical leakage between the forward and backward propagation path through the fiber grating, the polarization between the two propagation directions is rotated by 90 degrees and also appropriately isolated with the PBSs and the polarization controllers. The power amplifier is used in a double-pass configuration and is pumped with 10 W from a broad-area pump diode operating at 980 nm through the dichroic mirror. After amplification, a power level of 1.0 W is obtained. After recompression, this system produced 300-fs pulses with an average power of 600 mW and a pulse energy of 30 nJ. In this system a 10-cm–long grating, with a bandwidth of 18 nm, was employed. The fiber grating stretched the pulses out to a width of 1 ns. Note that the use of only one grating is advantageous because in reverse propagation the phase modulation from the chirped fiber grating is the complex conjugate of the phase modulation from forward propagation [118]. Thus any small unavoidable deviation from chirp linearity in the fiber grating is completely compensated. 8.10 APPLICATIONS To illustrate the wide distribution of mode-locked fiber laser technology we will discuss in this section some of the most interesting applications that have been developed over the last few years. These applications take advantage of different aspects of mode-locked pulses. For example, in all-optical signal regeneration the mode-locking process itself is used to create an all-optical clock recovery circuit. In wavelength division multiplexing it is mainly the large spectral bandwidth generated by the compact fiber lasers that is important. The low phase noise properties of fiber lasers are used to advantage in alloptical scanning delay lines. The ultrafast feature of femtosecond fiber lasers is of primary interest in frequency-doubling and other wavelength conversion systems, where highpower ultrafast pulses are required to enable secondary nonlinear optical processes with high conversion efficiencies. 8.10.1 Optical Clock Recovery and Signal Regeneration Optical clock recovery circuits and all-optical signal regenerators are some of the key components for high-speed time-division multiplexed telecommunication systems. The transmission rate of these systems can exceed 100 Gbit/s and is thus outside the range of conventional electronic systems. Fiber lasers and nonlinear fiber devices, on the other hand, allow signal processing at terahertz bandwidths and were thus considered for clock recovery and signal regeneration applications early on [119]. The experimental setup for an all-optical signal regenerator, based on a mode-locked fiber laser is shown in Figure 27. The regenerator consists of a clock-recovery stage as well as a modulator stage. The system operated at a frequency of 1 GHz, but in principle, could be upgraded to a date rate of 100 GHz or higher. The data stream was derived from


Figure 27

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Experimental configuration of an all-optical regenerator. (From Ref. 119.)

a gain-switched laser producing 20-ps pulses, amplified to an average power of 1 mW, a pulse energy of 1 pJ, and operating at a wavelength of 1.54 µm. The clock recovery stage is based on an optically FM mode-locked erbium fiber laser [92] operating at 1.56 µm and driven by the incoming data stream (see Sec. 8.6). The length of the mode-locked fiber laser was 8.8 km. The mode-locking process relies only on the presence of the base-band frequency of the data stream, which is present even when the data stream dominantly contains randomly distributed zeroes. Similarly the presence of substantial amounts of jitter on the data stream does not affect the baseband, and thus a mode-locked pulse train can be recovered. Because the mode-locked pulse train contains all 1s, it can be used as the recovered clock signal. In the experiments [119] described, a jitter reduction from 6.5 ps from the data stream to 2.8 ps on the modelocked pulse train was reported. The regenerated signal is produced in the modulator stage by modulating the recovered clock by the original incoming data stream in the NOLM (see Sec. 8.5.1). The length of the NOLM was 6.5 km. Here the paths of the signal pulses and the clock pulses have to be adjusted such that they overlap in time in one arm of the NOLM. Note that the NOLM here can consist of a Sagnac interferometer with a 50/50 coupler. The nonlinear phase delay of the clock signals in the NOLM is imbalanced by the data stream, which copropagates with the clock signal in the cw direction and affects the phase of the clock by cross-phase modulation [35]. Clearly, the temporal overlap between the data stream and the clock in the ccw propagation direction is negligible, and no nonlinear phase delay is imparted on the clock in this direction. To make the operation of the NOLM insensitive to small values of pulse jitter [120], group-velocity walk-off between the signal at 1.54 µm and the clock at 1.56 µm inside the loop is used, which produces a switching window of about 40 ps in this case. To obtain the modulated clock (or the regenerated signal) as shown in Figure 27, the NOLM has to be operated in transmission (i.e., the linear phase delay in the NOLM is adjusted to be zero when no data are present). A problem with the

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foregoing designs are the long fiber lengths required to enable the operation of such devices with real data streams. Note that more compact all-optical signal regenerators can also be constructed based on semiconductor devices [121], which are based on similar operation principles. 8.10.2 Application of Mode-Locked Lasers in Wavelength-Division Multiplexing Whereas optical clock recovery circuits are mainly of interest in high-bit-rate time-division multiplexed communication systems, the broad-spectral–output fiber lasers can also be used in broadband wavelength-division multiplexing (WDM). In this a high-repetition rate (GHz), actively mode-locked erbium-doped fiber laser can be pulse compressed such that the spectral output exceeds the gain bandwidth of erbium amplifiers [122,123]. A multifrequency signal source can then be sliced from the output spectrum into narrower channels (1 nm or less), with a variety of optical filters such as fiber gratings. The advantage of this technique is that only one laser is required as a source, instead of a large number of single-frequency semiconductor lasers that would all have to be carefully selected and temperature controlled in conventional WDM systems. A further interesting twist to applications of mode-locked fiber lasers in WDM systems was recently suggested by Nuss and co-workers [124], for which a passively modelocked femtosecond erbium-doped fiber laser is used as a signal source at repetition rates of 50–150 MHz. An example of an experimental setup is shown in Figure 28. Here a passively modelocked fiber laser generates 100-fs pulses at a repetition rate of 31 MHz. The femtosecond pulses are stretched out to a length of 15 ns in 15 km of conventional telecom fiber. Owing to the dispersion of the telecom fiber, the stretched pulses are approximately linearly chirped (i.e., the wavelength of the pulses increases linearly with time over the duration of the stretched pulses). Information for different wavelength channels is now impressed directly on the stretched pulses in the time domain by the high-bandwidth modulator that is synchronized to a fixed multiple (N ⫽ 80 in this case) of the repetition rate of the fiber laser. Thus each subsequent data bit modulates a subsequent WDM channel, for which

Figure 28 Ref. 124.)

Schematic diagram of femtosecond chirped-pulse multifrequency fiber source. (From


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the channel spacing is determined by the chirp of the stretched pulses and the modulation frequency of the modulator. The modulated WDM channels are then demultiplexed by an appropriate conventional WDM splitter. The benefit of this technique is that simple integrated passively mode-locked oscillators can be used [73], which are highly competitive in terms of complexity with arrays of well-controlled semiconductor lasers. Equally, the use of a single modulator in this system is potentially another significant simplification compared with conventional approaches to WDM. 8.10.3 All-Optical Scanning Delay Lines The low-phase–noise properties of passively mode-locked erbium-doped fiber lasers can be used for high-precision, all-optical scanning delay lines [125]. Indeed, a large fraction of ultrafast optical applications, such as pump–probe experiments, terahertz imaging [126], or optical sampling [127], require two optical pulses with a continuously varying time delay. Conventionally, these two pulses are produced by bulk-optic scanning delay lines, for which scanning is achieved with a moving mirror mounted, for example, on a shaker [128] or on a galvanometer [129]. Bulk-optic scanning delay lines are of limited interest in industrial applications, owing to the presence of moving parts with limited longterm reliability. In addition, bulk delay lines with delays exceeding 10 cm are impractical with this approach because of the difficulty of moving a mirror over such long distances while keeping it aligned. In all-optical scanning, the two pulses are derived from two separate passively modelocked lasers, which are electronically phase-locked with a PLL (see Sec. 8.7.3) in a master–slave configuration. An example of an experimental setup is shown in Figure 29 [125]. The master and the slave laser produce two pulses with a fixed-time separation (i.e., a probe and a pump pulse, respectively), for which the time delay between the two pulses can be adjusted with an internal phase-offset inside the PLL. The maximum possible time separation between the two pulses is given by the cavity round-trip time of the two lasers. Because the PLL contains low-pass filters and amplifiers, the cavity length of the slave laser can be modulated at a high frequency without affecting the PLL. As a result of the cavity length modulation, the time delay between the pump and probe pulses is also continuously varying, as required for a scanning delay line. An application of the all-optical scanning delay line in a pump–probe experiment is also shown in Figure 29. The two pulses are combined with the polarizer, and the pump pulse is used to excite the electronic carriers in an InGaAsP saturable absorber (see Sec. 8.5.4). Owing to the time-dependent recovery of the carriers, the transmission of the probe pulses through the absorber is dependent on the time delay between the two pulses. The transmitted pump and probe signals are separated by a second polarization beam splitter, and the probe signal is detected and displayed on an oscilloscope. To trigger the oscilloscope and to relate the probe signal to the correct time delay between the pump and probe pulses the cross-correlator is used. By inserting a Fabry– Perot etalon into the path of the pump pulses, a train of equally spaced reference pulses, with a decaying intensity, is produced (see Sec. 8.7.2). The cross-correlator generates a signal whenever the probe pulse coincides in time with any of the pump pulses from the etalon. Hence, a train of time-calibration signal peaks on the oscilloscope appears. The separation of the calibration peaks can be related to the physical time delay between the pump and probe pulses as ∆t ⫽ 2nl/c, where n and l are the refractive index and the

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Figure 29

Experimental setup for an all-optical scanning delay line based on two phase-locked scanning passively mode-locked erbium-doped fiber lasers used in a pump–probe experiment. (From Ref. 125.)

length of the Fabry–Perot etalon, respectively. Clearly the function of the calibration peaks is to map the oscilloscope time to the correct physical time delay between the pump and probe pulses. The time-varying physical time delay between the pump and the probe pulses is related to the time integral of the cavity mismatch ∆L: TD (t) ⫽

1 L

冮 ∆L(t′)dt′ t

(21)

0

where L is the cavity length. It is also useful to describe the rate of change of the physical time delay per unit time as the scan velocity given by Vscan (t) ⫽

∆L(t) c L

(22)

For a mode-locked laser that is operating at a repetition rate of 100 MHz, scan velocities as high as 300 m/s are readily achievable. This compares with mechanical scan velocities of only about 1 m/s. To obtain the maximum-scanning accuracy, it is useful to couple the two lasers thermally by winding them onto the same drum and to use just one pump laser [103]. The spatial resolution of the scanning delay line is primarily limited by the jitter of the two lasers. For a scan range of 1.5 m, a spatial resolution of 15 µm has been obtained.

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8.10.4 Frequency-Doubling and Parametric Wavelength Conversion Although fiber lasers can produce picosecond and femtosecond pulses at a variety of wavelengths, as yet, only erbium fiber lasers operating at 1.55 µm have been turned into commercial products. The reasons are quite obvious; erbium-doped fiber lasers are particularly efficient and operate at a wavelength range for which both negative- and positive-dispersion fibers are readily available, permitting a maximum of integration and flexibility in fiber laser cavity designs. Equally, because 1.55-µm EDFAs are of primary interest in fiber-optic telecommunication, the cavity components required for the construction of mode-locked Er-doped fiber lasers are already available at a relatively small cost. It is thus often more advantageous to rely on the proved erbium-doped fiber laser technology, and to use nonlinear frequency conversion techniques to access different wavelength regions, than to construct fiber lasers operating directly at the targeted wavelengths. For example, most of the current ultrafast optical applications require pulse sources operating close to 800 nm, and pulses at this wavelength can be obtained simply by frequency-doubling of erbium fiber lasers. With the recent advent of periodically poled LiNbO 3 (PPLN), a highly efficient frequency-doubling crystal has become a reality [130]. The superior performance of PPLN becomes clear when comparing the calculated doubling efficiency for a variety of doubling crystals for 100-fs pulses, as reproduced in Table 1 [131]. With a doubling efficiency of 95%/nJ efficient pulse sources operating at 800 nm can indeed be generated by simply frequency-doubling erbium-doped fiber oscillators [131]. Compact pulse sources, producing 100-fs pulses with average power levels of 120 mW at 810 nm, have been obtained by frequency-doubling the output from a multimode Er/Yb-doped amplifier–compressor using a core diameter of 16µm [114]. An example of a typical experimental arrangement was shown in Figure 25. Clearly, much higher-power levels can be expected by using larger-core multimode amplifier fibers. In contrast with conventional frequency-doubling crystals, for which the phasematching characteristics are fixed and set by nature, in PPLN, one can freely design the phase-matching condition to vary along the crystal length by varying the poling period. By using PPLN with a chirped poling period, pulse compression of chirped pulses and frequency doubling can be simultaneously obtained [132]. Thus, compact in-line chirped pulse amplification systems can be constructed [133], as reproduced in Figure 30. Table 1

Nonlinear Coefficients and Estimated Frequency-Doubling Efficiencies for 100-fs, 1.55-µm Pulses Calculated for a Variety of Second-Order Nonlinear Crystals Material

Phasematching

PPLN PPLT LBO KTP BBO LilO 3

Noncritical Noncritical Noncritical Critical Critical Critical

a

FOM (pm 2 /V 2 )

Efficiency (%/nJ)

710 320 42 20 340 12

95 43 6 1.5 6a 0.6 a

100-fs pulse assumed, spatial walk-off included.

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Figure 30

In-line chirped-pulse amplification system using chirped PPLN for simultaneous pulse recompression and frequency doubling. (From Ref. 133.)

A length of fiber is used for pulse stretching to reduce the nonlinearity in the multimode Er/Yb-doped fiber amplifier. The pulses are recompressed and frequency-doubled in the chirped PPLN crystal. Pumped with 10 W, at a wavelength of 980 nm, this system produced 25-nJ pulses, with an average power of 1 W at 1560 nm. After frequencydoubling, 300-fs pulses with an energy of 7.5 nJ and an average power of 300 mW, were generated at 780 nm. The generated power at 780 nm as a function of fundamental power at 1560 nm is shown in Figure 31. In addition to frequency-doubling, optical parametric generation in PPLN was also implemented to produce broadly wavelength-tunable pulse sources based on erbium fiber lasers [134]. An experimental setup [135] of a fiber–laser-pumped optical parametric generator (OPG) is shown in Figure 32.

Figure 31

Second-harmonic power at 780 nm versus fundamental power at 1560 nm obtained for an in-line chirped-pulse amplification system based on Figure 30.


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Figure 32

Experimental setup for an ultracompact, tunable optical parametric generator laser source based on Er-doped fiber oscillators and amplifiers: AOM, acousto-optic modulator. (From Ref. 135.)

The system comprises a hybrid chirped-pulse amplification system based on a singlechirped fiber grating (see Sec. 8.9.2) and a chirped PPLN crystal. The oscillator operates at a repetition rate of 20 MHz and produces 200-fs pulses, with an average power of 5 mW. The pulses from the oscillator are passing through a polarization beam splitter and are stretched to a width of about 1 ns in the chirped fiber grating. Two waveplates inserted between the fiber grating and the polarization beam splitter control the polarization state in the fiber grating. The stretched pulses are directed to two stages of EDFAs, where an acousto-optic gate is implemented to reduce the repetition rate of the pulses to 71 kHz and to minimize ASE in the second-stage EDFA. The amplified and stretched pulses are recompressed in the same chirped fiber grating and are then directed through another set of two waveplates and a second polarization beam splitter to the chirped quasi-phasematched compressor crystal based on chirped PPLN. By insertion of appropriate lengths of dispersive fiber, the amount of pulse stretching and compression from the chirped fiber grating is unbalanced (i.e., the pulse width still remains at a few picoseconds after compression in the chirped fiber grating. Because this reduces the maximum peak power in the chirped fiber grating, the pulse energy handling capability of the grating is increased. As a final compression stage, the bulk chirped PPLN crystal is employed, as it can handle larger peak powers than a chirped fiber grating. At the output of the chirped PPLN, 300-nJ pulses with a pulse width of 600 fs were obtained. These pulse energies were sufficient for the demonstration of optical parametric generation in a second unchirped PPLN crystal with a conversion efficiency of up to 40%. The OPG output could be continuously tuned from 1.0 to 3.4 µm by varying the temperature of the PPLN crystal, as well as by using PPLN crystals with different poling periods.

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By replacing the second-stage EDFA with a large-core, slightly multimode EDFA (see Sec. 8.8.1) in Figure 32, a high-power, fiber-based OPG source operating at the fundamental repetition rate of 5 MHz of a long-fiber oscillator was also recently demonstrated [136], eliminating the need for an acousto-optic optical gate in Figure 32. The use of a multimode EDFA allows the amplification of pulses to high-peak powers; therefore, the fiber-grating pulse stretching and recompression stages in Figure 32 could also be omitted, which resulted in an ultracompact wavelength-tunable laser source. Clearly, the combination of ultrafast fiber laser and PPLN technology produces devices that greatly exceed the capabilities of conventional bulk wavelength-tunable lasers. Indeed, the unique potential of fiber lasers for integration should allow a revolutionary reduction in the complexity of many different ultrafast laser systems that are currently still based on bulk lasers. 8.11 CONCLUSIONS Clearly, mode-locked fiber lasers have enormous capabilities and greatly influence a variety of different research fields. In Table 2, we provide a summary of the performance data of several selected systems, based on mode-locked Er-doped fiber lasers that were previously discussed in this chapter. All the fiber lasers listed here provide bandwidthlimited pulses, apart from the noise burst source (entry 8) and the fiber-based OPG (entry 14). The data given in Table 2 are meant to be only a guideline for the interested reader. In general, Table 2 cannot be used to evaluate the technological impact factor of any particular system, as that depends on a variety of additional parameters, such as pump sources employed, complexity of the setup, as well as long-term stability. However, because the Er-doped fiber laser systems are based mainly on optical components that have been proved in optical telecommunications, proper engineering of the devices should always lead to excellent long-term reliability. The distinction between actively mode-locked (system 1) and active–passive fiber laser systems (system 2), operating at gigahertz repetition rates, is somewhat arbitary, for any actively mode-locked Er-doped fiber laser can be subjected to appreciable amounts of self-phase modulation by simply turning up the pump power. At repetition rates of tens of gigahertz these sources compete with diode lasers [5] and also fiber systems based on soliton pulse compression [137]. The passively mode-locked fiber laser systems (systems 3–7) have essentially no simple alternative in laser technology. Typically, such systems operate at repetition rates between 1 and 200 MHz; a range far wider than achievable with passively mode-locked bulk laser systems. The highest average powers from fiber oscillators can clearly be obtained by employing multimode fibers (system 4). Moreover, such oscillators also permit efficient cladding pumping. Integrated passive harmonically mode-locked Er-doped lasers (systems 6 and 7) permit significant cost reduction compared with other fiber oscillators and allow the generation of pulses at the technologically important frequency of 2.5 GHz. The main attractive feature of noise burst sources (system 8) is their short optical coherence length, which may eventually allow their use in some imaging applications. Also a further increase of the obtainable pulse energies to higher than 10 nJ can be expected. Mode-locked multimode fibers (entry 4) and the high-power fiber oscillator– amplifier laser systems (systems 9–14) (preferably also based on multimode fibers) can compete directly with conventional bulk lasers. Systems 9 and 10 are based on multimode Er/Yb-doped fiber amplifier compressors. Efficient frequency-doubling is obtained with

Pulse energy (nJ) 1 ⫻ 10⫺4 1 ⫻ 10⫺3 0.57 4.5 2.7 1.25 ⫻ 10⫺3 6 ⫻ 10⫺4 0.6 4.4 2.3 33 1 ⫻ 105 100 20

Rep. Rate (MHz) 4 ⫻ 104 1 ⫻ 104 88 67 31.8 200 2.6 ⫻ 103 16 52 52 18 5 ⫻ 10⫺3 5 5

The corresponding references are given in the system column.

Actively ML [47] Active–passive ML [3] Soliton [131] MM soliton [9] Stretched-pulse [6] Integrated soliton [74] Passive harmonic [80] Noise burst [89] EDFA compressor [114] Doubled compressor [114] All-fiber CPA [11] Fiber-bulk CPA [12] PPLN CPA [133,135] OPG [135]

1 2 3 4 5 6 7 8 9 10 11 12 13 14

a

System 0.09 0.77 2.5 ⫻ 10 3 ⬎6 ⫻ 10 3 2.7 ⫻ 10 4 3.0 1.4 15 4.4 ⫻ 10 4 2.3 ⫻ 10 4 1 ⫻ 10 5 1 ⫻ 10 8 3.3 ⫻ 10 5 6.7 ⫻ 10 4

Pulse power (W)

Typical Performance Data of a Variety of Devices Based on Mode-Locked Fiber Lasers a

No.

Table 2

1.1 1.3 0.23 0.36 0.1 0.41 0.415 1 ⫻ 10 4 0.1 0.1 0.31 1 0.3 0.3

Pulse width (ps) 4.3 10 50 300 85 0.25 1.6 10 230 120 600 500 500 100

Mean power (mW)

1.55 1.56 1.55 1.54 1.55 1.55 1.55 1.56 1.62 0.81 1.55 1.55 0.78 1–3

Wavelength (µm)

Mode-Locked Fiber Lasers 439

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PPLN. System 11 is the all-fiber, chirped-pulse amplification system. System 12 is an ultrahigh power chirped-pulse amplification system using bulk gratings. Systems 13 and 14 comprise a chirped-pulse amplification setup based on chirped PPLN for simultaneous frequency doubling and pulse compression. System 14 is an OPG based on such a highpower frequency-doubled Er-doped fiber laser. Particularly when it comes to wavelengthtuning, fiber lasers in conjunction with PPLN offer very compact and simple solutions. Mode-locked fiber lasers have come a long way since the first demonstration experiments [1,2,41] in the mid 1980s. Actively mode-locked fiber lasers similar to systems 1 and 2 and passively mode-locked fiber lasers similar to systems 3 and 5 are now commercially available and are being readily used in test and measurement systems. Even relatively complex fiber laser systems do not require much space, as apparent from some of the commercial developments. At IMRA America a commercial frequency-doubled highpower femtosecond fiber laser delivering more than 30 mW of average power at 780 nm, was developed, in which the optical head fits into a package size of 193 ⫻ 109 ⫻ 82 mm [138]. A photograph of the the fiber laser produced by IMRA America is reproduced in Figure 33. Apart from commercialization, the most important development over the last couple of years has been on the psychological side of potential users. Mode-locked fiber laser systems have clearly reached a sufficient level of simplicity that, unlike bulk lasers, that the laser is mode-locked is no longer considered exotic. In fact, owing to the simplicity of mode-locked fiber systems, one should ask whether a mode-locked laser could not perform better than a cw laser in many potential applications. The use of multimode modelocked fiber lasers in conjunction with multimode fiber amplifiers [9,114] is a good example of such an application. Also, in the context of fiber lasers, mode-locking is a very effective method to obtain low-noise, high-power signal sources. The alternative, a singlefrequency fiber laser, often does not provide any advantages over mode-locking.

Figure 33 Photograph of a commercially available frequency-doubled femtosecond Er-doped fiber oscillator–amplifier system. (Courtesy IMRA America Inc.)


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In terms of their applications, mode-locked fiber lasers offer a nearly unlimited range, and the potential for future research is enormous. Although the influence of modelocked fiber lasers in the telecommunications market is still limited, alternative uses have been developed that take full advantage of the benefits fiber technology offers. Being able to confine the light in an optical fiber over long distances renders nonlinear processes efficient and thus practical. Moreover, light confinement is compatible with very simple and efficient pumping schemes, such as cladding pumping, as well as the demonstration of both ultrahigh and ultralow repetition rate pulse sources. High-power cladding-pumped femtosecond multimode fiber lasers and amplifiers can compete effectively with conventional solid-state lasers and allow a previously unimaginable degree of integration for even highly sophisticated laser systems. Just as basic mode-locked fiber lasers have established their rightful place in ultrafast optics over the last couple of years, it can be expected that highly advanced fiber laser systems such as all–optical-scanning delay lines [125], high-power frequency-doubled erbium-doped fiber lasers [133], or erbium-doped fiber-based optical parametric generators [134] are at the threshold of making a large impression in laser technology. Although nonlinear frequency conversion techniques still appear exotic in many applications, the use of fiber lasers should permit these devices to become commonplace in the future. ACKNOWLEDGMENTS The authors would like to acknowledge T. F. Carruthers, B. C. Collings, M. L. Dennis, M. Horowitz, J. K. Lucek, M. C. Nuss, and K. Tamura for providing them with original material. The authors are also indebted to G. Sucha, A. Galvanauskas, and D. Harter for many stimulating discussions. M. Hofer would like to acknowledge support from the Austrian Academy of Sciences under project Apart 326. REFERENCES 1. Duling, I. N. III. In: Compact Sources of Ultra-Short Pulses. Cambridge Studies in Modern Optics, Cambridge University Press, Cambridge, 1995. 2. Fermann, M. E. Ultra-short pulse sources based on single-mode rare earth doped fibers. Appl. Phys. B58(3):197–209 (1994). 3. Carruthers, T., Duling I. N. III. 10 GHz, 1.3 ps erbium fiber laser employing soliton pulse shortening. Opt. Lett. 21:1927–1929 (1996). 4. Helkey R., Bowers, J. Mode-locked semiconductor lasers. In Semiconductor Lasers, Past, Present and Future. G. P. Agrawal, ed. AIP Series in Theoretical and Applied Optics, Woodbury, NY, 1995. 5. Ludwig, R., Ehrhardt, A. Turn-key-ready wavelength-, repetition rate- and pulsewidth-tunable femtosecond hybrid modelocked semiconductor laser. Electron. Lett. 31:1165–1167 (1995). 6. Nelson, L. E., Fleischer, S. B., Lens, G., Ippen, E. P. Efficient frequency-doubling of a femtosecond fiber laser. Opt. Lett. 21:1759–1761 (1996). 7. Lamb, K., Spence, D. E., Hong, J., Yelland, C., Sibbett, W. All-solid-state self-mode-locked Ti :sapphire laser. Opt. Lett. 19:1864–1866 (1994). 8. Haberl, F., Ober, M. H., Hofer, M., Fermann, M. E., Wintner, E., Schmidt, A. J. Low-noise operation modes of a passively mode-locked fiber laser. IEEE Photon. Technol. Lett. 3:1071– 1073 (1991). 9. M. E. Fermann, M. Hofer, R. S. Windeler. Multimode fiber soliton laser. Trends in Opt. Photon. 1. (1999; in press).

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9 Rare Earth Doped InfraredTransmitting Glass Fibers J. S. SANGHERA, L. B. SHAW, and I. D. AGGARWAL Naval Research Laboratory, Washington, D.C.

9.1 INTRODUCTION Rare earth doped silica glass fibers have received a great deal of attention for many practical applications, including fiber laser devices and amplifiers. Heavy-metal fluoride (HMF) and chalcogenide glass fibers doped with rare earth ions have also been investigated because they possess lower phonon energies than silica and, consequently, reduced multiphonon quenching. This property has led to more efficient fluorescence in the infrared (IR) as well as emission wavelengths that are not possible in silica-doped fibers. The present chapter describes the properties of HMF and chalcogenide glasses and of fibers containing rare earth ions, with emphasis on laser and amplification properties in the IR. The laser properties of HMF glass fibers in the visible and ultraviolet (UV) spectra are described separately in Chapter 4. We begin by describing the historical development of HMF and chalcogenide glasses, their different chemical compositions and special optical properties. The glassprocessing techniques are briefly described, for they are somewhat different from those for melting oxide glasses described in Chapter 1. From a practical viewpoint, HMF and chalcogenide glass fibers are of primary interest, and their fabrication techniques are also described. The elements that compose the rare earth series, their special optical properties and the reasons for doping glasses, especially HMF and chalcogenide glasses, with rare earth ions are discussed. Subsequently, we review the literature data pertaining to laser oscillation and amplification in rare earth doped HMF and chalcogenide glasses and fibers.

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9.2 INFRARED-TRANSMITTING GLASSES The IR-transmitting glasses discussed in this chapter are based on the heavy-metal fluoride glasses and the chalcogenide glasses, respectively. There are unique differences in the ways they are fabricated and in their structural, physical, chemical, and optical properties. The discovery of the first heavy-metal fluoride glass came about quite serendipitously in 1974 at the University of Rennes in France [1]. A research group led by Professor Jacques Lucas was trying to prepare single-crystal NaF ⋅ BaF2 ⋅ 2ZrF4 doped with neodymium (Nd 3⫹) for fluorescence experiments, but x-ray analysis of the product revealed that it was predominantly amorphous. Although this particular composition was relatively unstable, it did generate a considerable amount of interest, and other more stable compositions were eventually developed. The glasses were highly transmissive from approximately 0.2 to 7 µm (Fig. 1). Routine optical measurements soon revealed that these glasses possessed potential minimum attenuations of approximately 0.01 dB/km at longer wavelengths (2–3 µm) compared with the 0.12 dB/km obtained for silica. Therefore, the possibility arose that long lengths of fibers made from these glasses could be used in longdistance telecommunications networks, with potentially lower losses than those of silica fibers. This had economic considerations as well, because fewer boosters, repeaters, or signal regenerators would be required to amplify the signal. Currently, signal repeaters are used every few tens of kilometers or so in silica fibers. With HMF glasses this distance would be potentially increased by an order of magnitude. Chalcogenide glasses have been known for a long time. Their name originates from the fact that they contain the chalcogen elements sulfur, selenium, and tellurium (S, Se, and Te). One of the most common chalcogenide glasses, As 2S 3, was discovered more than 100 years ago [2]. Based on the wide transmission window of this glass, numerous other systems have been investigated [3]. Figure 1 shows the shift in the multiphonon edge to longer wavelengths due to decreasing phonon energy going from sulfide- to selenideto telluride-based glasses. Reasonably low losses (⬍100 dB/km) have been achieved in

Figure 1

The infrared transmission curves for silica, heavy-metal fluoride (ZBLAN), and chalcogenide glasses. The sample thickness is listed in parenthesis.

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traditional chalcogenide glass systems. However, more recent interest has focused on doping these glasses with rare earth (RE) ions to produce lasers and amplifiers in the IR because of the lower phonon energies of chalcogenide glasses compared with silica and HMF glasses. 9.2.1 Glass Compositions Heavy-Metal Fluoride Glasses Typically, the most stable heavy-metal fluoride glass is ZBLAN, made from the fluorides of zirconium, barium, lanthanum, aluminum, and sodium (Zr, Ba, La, Al, and Na) in the stoichiometry 53:20:4:3:20 mol%, respectively. This glass is called a fluorozirconate because its major component is Zr. For effective waveguide behavior, however, the optical fiber must consist of a core and cladding to give the desired numerical aperture (NA), in the 0.12–0.2 range. To this extent, other components can be added to ZBLAN to increase or lower its refractive index. Because, for example, the addition of PbF2 increases the index, ZBLAN is used as the cladding and the lead (Pb)-doped glass as the core (ZBLANPb or ZBLANP). On the other hand, partial substitution of Zr by hafnium (Hf) lowers the index, and thus ZBLAN is used as the core, whereas HZBLAN is used as the cladding glass. In addition to the fluorozirconate glasses, there are other glass compositions based on other fluorides. For example, fluoroaluminates are based on AlF3; they tend to be less stable toward crystallization [4]. Other glass systems include BIZYT (Ba, In, Zn, Yb, Th) [5], CLAP (Cd, La, Al, Pb) [6], and fluorozircoaluminates [7]. Unless otherwise stated, this chapter is concerned with the fluorozirconate glasses, which are the prevalent materials used among the different research groups in this field because their thermal stability is the highest of all the HMF glasses. Chalcogenide Glasses The traditional chalcogenide glasses such as As 2S 3-, As 2Se 3-, and GeAsS-based are stable toward crystallization and can be readily made into reasonably crystal-free fibers. However, a major drawback is that the rare earth solubility is very low in these glasses, typically less than about 100 ppm, which is not suitable for a practical device [8,9]. Larger quantities of rare earth ions tend to cluster in the glasses and lead to crystallization, especially on reheating during the fiber-drawing process. Therefore much effort has gone into developing glass compositions suitable for rare earth doping at levels of several hundred to a few thousand parts per million. Some examples of glass systems include Ga 2S 3 –La 2S 3 (GLS) [10], GeS 2 –Ga 2S 3 (GGS) [8,11], GeS 2 –As 2S 3 –Ga 2S 3 (GAGS) [12], BaS–GeS 2 – Ga 2S 3 (BGGS) [13], BaS–GeS 2 –Ga 2S 3 –As 2S 3 (BGGAS) [14], Cs–Ga–S–Cl [15], and Ga 2S 3 –Na 2S (GNS) [16]. Gallium increases the solubility of the rare earth ions and prevents clustering. The Ga/RE ratio is usually at least 10:1 which appears to be analogous to the Al/RE ratio in silica glass [17]. There are reports indicating that some chalcohalide glasses (Ge–S–I) may be useful to prevent clustering of the rare earth ions [8,18]. These glasses are called chalcohalides because they contain mixtures of the chalcogen and halogen elements [19]. Unlike HMF glasses, which are predominantly ionic, and chalcogenide glasses, which are predominantly covalent, the chalcohalide glasses are fundamentally interesting because they contain mixtures of covalent and ionic species. The core and cladding glass compositions can be made by slight modifications to

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the glass stoichiometry. For example, increasing the sulfur content or adding halides lowers the refractive index, whereas additives such as As and Sb raise the index. 9.2.2 Glass-Melting Techniques Heavy-Metal Fluoride Glasses The HMF glasses are obtained by melting the high-purity fluoride starting materials at about 850°C in precious metal crucibles such as Pt, Au, and Pt/Au, under an inert atmosphere, such as Ar or N 2, containing small quantities of an oxidizing gas. In the absence of an oxidizing atmosphere the Zr 4⫹ ion will reduce to Zr 3⫹ [20], which gives the glass a dark color and leads to an increased crystallization tendency. Consequently, an oxidizing gas, such as oxygen, is added to the inert gas [21]. The oxygen also serves to burn off any residual organic species or carbon present in the starting materials. If not eliminated, these impurities lead to unwanted scattering in the glasses. Instead of O 2 gas, some research groups use HF gas to serve both as an oxidizing agent and fluorinating agent of any oxide impurities in the starting materials [22]. In addition, several grams of ammonium bifluoride can be added to the batch before melting. Ammonium bifluoride is a well-known fluorinating agent and is considered to fluorinate any oxide impurities. With this in mind, several research groups start with oxide precursors because of their high purity and add excess ammonium bifluoride [23]. This additional ingredient is not necessary today, however, because high-purity fluoride precursors are commercially available. Research groups working on ultra–low-loss optical applications still purify the chemicals further. If the oxide impurities are not fluorinated, they also lead to extrinsic scattering in the glasses and fibers [24,25]. More recently, novel crucible materials, such as vitreous carbon, have been used, because melting in precious metals such as platinum leads to the inclusion of submicron platinum particles in the glass, which behave as strong scattering centers and limit the transmittance of these materials [26]. However, oxygen gas cannot be used in conjunction with vitreous carbon at elevated temperatures. Other oxidizing gases have been investigated. The most promising of these gases are SF6 and NF3 [27,28]. The glasses can be quenched (i.e., cooled) directly in the crucibles or cast into a mold for subsequent fiber fabrication. Chalcogenide Glasses Chalcogenide glasses can be fabricated using either elemental starting materials, compounds, or mixtures of elements and compounds. The commercially available chemicals are of insufficient purity to produce high–optical-quality glass, and they have to be further purified in-house by distillation–sublimation processes to eliminate hydrogen- and oxygen-related impurities (e.g. water, hydroxyl, H 2S, H 2Se), as well as transition metal and rare earth ion impurities [29]. The chalcogenide elements (S, Se, and Te) possess high vapor pressures at elevated temperatures and, therefore, cannot be melted in open crucibles [3]. Furthermore, they react with metals (even platinum and gold), and alternative crucible materials have to be used. Typically, high-purity starting materials are weighed out in a dry box under an inert atmosphere. The batches are loaded into tubular quartz ampoules that are evacuated to less than 10⫺5 torr, then sealed with an oxygen–methane torch. The ampoules are placed inside a furnace that rocks gently to facilitate mixing of the components during the melting


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Figure 2 Schematic of a rocking furnace for melting a silica ampoule containing the chalcogenide glass batch.

stage at elevated temperatures (Fig. 2). The melting temperatures and times vary from one glass system to another but are usually in the range of 750–1100°C and 10–36 h, respectively. After melting, the ampoules are quenched by either blowing cold air over them or by immersion in water, then annealed at close to the glass transition temperature. Chalcogenide glass rods can be obtained by cutting the ampoules open once they have cooled to room temperature. Some glass systems cannot be melted in quartz ampoules because some or all of the components in the melt react with quartz at elevated temperatures. Examples of these include glass melts containing alkaline earth metals (e.g., Ba) [14] and GLS [10] glass melts. For this, the glass melting is performed in vitreous carbon or graphite crucibles that are placed in quartz ampoules and evacuated and sealed as before. For GLS glasses, these melts possess very low vapor pressures, unlike other chalcogenide glass melts, and melting can be performed under flowing inert gas. 9.2.3 Fabrication of Infrared-Transmitting Glass Fibers Heavy-Metal Fluoride Glass Fibers Fluoride fibers are fabricated using one of two main processes. The first one is drawing from solid preforms, and the second one is the double-crucible process. In the first, the preform is a glass rod that consists of a central core rod and an outer cladding tube. There are essentially three different techniques to prepare fluoride preforms: the built-in casting, rotational-casting, and suction-casting processes. The built-in casting technique was first to be developed [30]. It consists of pouring the cladding glass melt into a mold and waiting a few seconds for it to cool. The mold is then inverted, allowing most of the melt to drip out of the mold, leaving behind a cladding glass tube. The core melt is subsequently poured into the mold and the resulting preform annealed. However, because this technique

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Figure 3 The rotational casting technique for fluoride glass preform fabrication: (1) pouring of the cladding glass melt, (2) rotation of the cladding glass melt, (3) cladding tube formation, and (4) casting of the core melt. (From Ref. 31.)

produces a tapered preform, it is limited to short lengths of optical fiber. On the other hand, the rotational-casting technique (Fig. 3) produces a preform of uniform geometry because the mold containing the cladding melt undergoes rotation at high speeds, typically greater than 5000 rpm [31]. Again, the core melt is poured in once the cladding glass tube has been formed. This whole process can be performed under a vacuum to minimize the incidence of microbubbles [32]. The suction-casting technique [33] has the same problem as the built-in–casting technique; that is, the production of a tapered preform. Preforms are subsequently drawn into fibers on a fiber draw tower (Fig. 4) under an inert atmosphere. A laser micrometer is used for monitoring fiber diameter fluctuations. The preform feed rate into the furnace, the furnace temperature and the capstan/winding drum speed are used to minimize these fluctuations. In the double-crucible technique (Fig. 5), the core and cladding glasses are remelted in concentric crucibles with small holes in their bases [34]. Once the core melt has softened sufficiently, it flows through the hole and into the cladding glass melt whereupon both core and cladding glasses flow out of the second hole in the bottom of the crucible. Under optimized processing conditions, the ensuing fiber possesses a defect-free and concentric core/clad structure. The processing is performed under an inert atmosphere of argon to prevent contamination from atmospheric moisture, which otherwise leads to undesirable crystals on the fiber surfaces. Pt–5%Au crucibles have been the most promising so far, with the view of minimizing crystallization. The lowest optical loss yet reported is about 0.45 dB/km at about 2.55 µm and was measured on a 60-m fiber fabricated by the vacuum rotational-casting technique [32]. The lowest loss reported using the double-crucible process is about 5 dB/km, measured on over 100 m of fiber [34]. Typical losses on long lengths (⬎ 50 m) are usually in the range of 1–10 dB/km. These low losses have been obtained on multimode fibers prepared mostly by rotational-casting and suction techniques. The attainment of lower losses has been limited by extrinsic defects, such as scattering by microcrystals and bubbles. Single-mode fibers are needed for ultra–low-loss telecommunications applications as well as for rare earth doped fiber laser and amplifier applications. For the latter, consid-


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Figure 4 Schematic representation of a fiber draw tower. erably higher power densities are required, which can be achieved at lower power levels in single-mode fibers. The double-crucible technique offers the potential for long lengths of single-mode fiber fabrication. However, poor core-cladding geometrical alignment, adverse crucible–melt interactions, and difficulty in controlling the feed rates of the glass materials, pose serious problems that need to be overcome. On the other hand, the casting techniques described in the foregoing cannot produce a fiber of single-mode dimensions. It is very difficult to cast core melts into cladding glass tubes with small inner diameters because the core droplets are finite sized, typically 2–3 mm in diameter, and thus the cladding tube must possess an internal diameter larger than this. Although this condition can be satisfied, it necessitates the use of ultrathick cladding tubes. For example, the fabrication of a single-mode fiber with a 10-µm–core and 150-µm–cladding diameter would necessitate a cladding diameter of approximately 7.5 cm for a 5-mm–core diameter. The low thermal conductivities of fluoride glasses lead to crystallization problems at the core– cladding interface owing to reheating of the interface when pouring the core melt. Hence, thick cladding tubes are not recommended because it takes longer to dissipate the heat from the core–cladding interface, which is a common place for crystallization. However, it is possible to stretch a typical preform obtained from the rotational-casting technique (‘‘typical’’ implies a 10- to 14-mm–thick preform with a core diameter of approximately 5 mm). This elongated preform is then inserted in a cladding glass tube, collapsed and the whole stretch-and-insert process repeated several times until the appropriate core/ cladding diameter ratio is attained (Fig. 6). While this technique appears simple, inherent

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Figure 5 The double-crucible technique used to fabricate fluoride glass fibers.

problems are associated with it. The most obvious ones are bubble removal and crystallization at the cladding–cladding interface. Overall, the fabrication of single-mode fibers is a difficult task that has been addressed only recently. Therefore, relatively little work has been published on these fibers, especially fibers doped with rare earth ions. Consequently, most of the work described in this chapter deals with doped multimode fibers, although some notable results obtained with single-mode fibers are also discussed. Chalcogenide Glass Fibers The chalcogenide glass fibers are also made by drawing preforms and from the doublecrucible process. However, chalcogenide glass melts possess high vapor pressures that lead to loss of components through volatilization during traditional casting-type processes. This causes changes in the glass composition, leading to refractive index changes as well as scattering at the core-cladding interface owing to bubble formation and glass soot deposition. Therefore, alternative preform fabrication processes have been developed, such as the rod-in-tube process [35]. In this process, core glass rods are obtained by direct melting and quenching in the quartz ampoules and, therefore, can be made to almost any diameter and length. If needed, they can be ground and polished down to the desired diameter. The cladding glass tubes are made by spinning the molten cladding glass in the quartz ampoule


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Figure 6 The fabrication of a single-mode fluoride glass fiber: step 1: a multimode preform is initially stretched; step 2: a cladding tube is cast; step 3: the stretched preform is inserted into the cladding tube. The structure is then collapsed and drawn into a single-mode fiber.

while cooling the assembly to the glass transition temperature, then annealing. The inner diameter of the cladding tube is slightly larger (⬃50 µm) than the outer diameter of the core rod that is subsequently inserted into the tube. The rod-in-tube assembly can be collapsed either before fiber drawing or during the fiber draw process. The preform fiberdrawing process is similar to that used for making HMF glass fibers (see Fig. 4). The fabrication of single-mode fibers can be achieved by the stretch-and-insert process described for HMF single-mode fibers (see Fig. 6). Chalcogenide glass fibers can be fabricated by the double-crucible process, but in this case quartz crucibles are used to minimize reaction with the melt [36]. The fiber diameter is controlled by independent pressure control above the core and cladding glass melts, respectively, as well as by the furnace temperature and draw speed. An outer polymer coating, such as a UV-curable acrylate or thermoset polymer, is applied on-line. By appropriate control of the parameters, the double-crucible process can be used to produce either multimode or single-mode fibers. Typical multimode and single-mode fiber losses of less than 0.5 dB/m [37] and 1 dB/m [38], respectively, have been obtained, compared with theoretical predictions of about 1 dB/km [37]. An extrusion process, similar to that used for fluorozircoaluminate glasses, has been used to fabricate preforms from core and cladding glass disks made from the GNS glass system with Pr in the core glass [39]. The preforms, which tend to possess tapered cores, have been drawn into single-mode fiber with a minimum background loss of about 1.2 dB/m at 1.3 µm. Even though this is a significant result, the question arises whether this particular technique is applicable to the production of long lengths of rare earth doped

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single-mode fibers with a uniform diameter. This is important from the viewpoint of commercialization of these doped fibers for 1.3-µm fiber amplifier systems in telecommunications. 9.2.4 The Mechanical Strength of Infrared-Transmitting Glass Fibers The strength of the IR-transmitting glass fibers is an important property, for the fibers must be handled and potentially made into relatively long cables. Typical bending strengths of HMF glass fibers are about 800 MPa, with champion values on select fibers of about 1.2 GPa [40]. Strength data for chalcogenide glass fibers is not as prevalent in the literature as that for HMF glass fibers. Nevertheless, arsenic–sulfide-based fibers have been obtained with strengths in excess of 700 MPa and with record values of about 2.5 GPa [41]. There is no strength data available for rare earth doped chalcogenide fibers, although it is expected that they are not as strong. Although the maximum theoretically estimated strengths of HMF (⬃10 GPa) and chalcogenide (⬃4 GPa) glass fibers are lower than the values obtained for pristine silica (⬃15 GPa), the strengths are further reduced by various extrinsic factors associated with crystals and other defects in the fibers as well as surface attack by moisture. It is envisioned that these strengths will increase with improved processing of the fibers and development of hermetic coatings. In the meantime, current strengths are quite adequate for most applications requiring short fibers. 9.3 WHAT ARE THE RARE EARTH IONS? Table 1 lists the rare earth elements in order of increasing atomic number. The actinide series is not shown because the present chapter focuses mainly on the lanthanides shown in Table 1. The lanthanides are best characterized by the observation that they possess incomplete inner 4f levels and, to a large extent, the lanthanides (Ln) form ions that exist solely in the 3⫹ state. The 3⫹ state is formed by the removal of two outer 6s electrons

Table 1 The Rare Earth Elements Atomic number 58 59 60 61 62 63 64 65 66 67 68 69 70 71

Element

Electronic structure

Ce—cerium Pr—Praseodymium Nd—neodymium Pm—promethium Sm—samarium Eu—europium Gd—gadolinium Tb—terbium Dy—dysprosium Ho—holmium Er—erbium Tm—thulium Yb—ytterbium Lu—lutetium

[Xe]4f 25d 06s 2 [Xe]4f 35d 06s 2 [Xe]4f 45d 06s 2 [Xe]4f 55d 06s 2 [Xe]4f 65d 06s 2 [Xe]4f 75d 06s 2 [Xe]4f 75d 16s 2 [Xe]4f 95d 06s 2 [Xe]4f 105d 06s 2 [Xe]4f 115d 06s 2 [Xe]4f 125d 06s 2 [Xe]4f 135d 06s 2 [Xe]4f 145d 06s 2 [Xe]4f 145d 16s 2


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and one inner 4f electron. However, because the 5s and 5p levels are still complete, these provide shielding to the inner 4f level electrons. This behavior becomes important in the presence of a ligand field, as the 4f energy levels of a rare earth ion undergo only a small amount of splitting. For contrast, the 3d energy levels of transition-metal ions undergo significantly more splitting because the outer levels are empty and thus not capable of shielding the inner 3d levels. Furthermore, there is less fine structure associated with the rare earth ion energy levels. Thus the absorptions are sharp and well defined, and they exhibit little dependence on the ligand field. In a glassy matrix, however, the local environment of the rare earth ions varies from site to site, leading to spatial variations in the crystal field and slight broadening of the energy levels. 9.3.1 Optical Properties of the Rare Earth Ions Figure 7 shows the electronic energy levels of the rare earth ions as reported by Dieke and Crosswhite [42]. As indicated in this chart, these levels are separated by specific amounts of energy. Depending on the energy difference, subsequent absorption of appropriate photons can lead to several interesting effects. Figure 8 shows the most important effect in rare earth ions, namely fluorescence. Absorption of photons excites the rare earth ion into a higher-energy state, from which it relaxes to a lower energy level. In the example shown in Figure 8, initial relaxation takes place by a nonradiative process (i.e., by lattice phonons); thereafter, the ion decays by the emission of a photon (fluorescence). Usually, the energy of the emitted photon is lower than that of the incident/absorbed photon, but in some instances, such as upconversion (which is outside the scope of this chapter), the emitted photon may possess more energy. 9.3.2 Applications of Rare Earth Doped Glass Fibers Although bulk glasses doped with rare earth ions exhibit fluorescence when pumped with an appropriate source, they are of little practical value as laser sources because their output powers are low. However, fibers are of practical importance because they can be subjected to high pump power densities over considerably longer distances than bulk glasses, and as a result, they exhibit greater performance as laser devices. Laser oscillation will occur only under certain specific conditions. One of these requirements is the choice of an appropriate pump wavelength. Because the rare earth ion has to absorb specific quantities of energy, corresponding to the excited upper states, the pump wavelength should correspond to a specific absorption level. Typical pump sources include solid-state or gas lasers, although for practical applications, high-power semiconductor diode lasers are more appropriate. Currently, the output wavelengths from diode lasers are limited to 0.63–0.7 µm from AlGaInP; 0.78–0.87 µm from AlGaAs; 0.91–1.02 µm from InGaAs; and 1.5–2.0 µm from AlGaInP. Besides laser sources, the other main application of rare earth doped fibers is optical amplifiers. It is envisioned that the fluoride and chalcogenide glass fibers will find practical applications as amplifiers in the IR because rare earth doped silica fibers are currently used in the visible to near-IR region. In a silica glass host, transitions with energies less than 5000 cm⫺1 (2 µm) lose energy nonradiatively, compared with a value of 3300 cm⫺1 (3 µm) in HMF glasses [43] and 2500–2000 cm⫺1 (4–5 µm) in chalcogenide glasses. Hence, HMF and chalcogenide glasses offer potential oscillation and amplification at longer wavelengths than silica. There are numerous applications requiring lasers and amplifiers in the infrared. For

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Figure 7 The electronic energy levels of the trivalent rare earth ions. (From Ref. 42.)


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Figure 8

Absorption of light causing initial excitation to higher-energy levels and subsequently giving rise to fluorescence in a hypothetical rare earth ion.

example, a suitable laser amplifier is required at 1.3 µm, which is important for telecommunications using silica fibers. In addition to silica-based fiber-optic communication systems, potentially new networks based on HMF glass fibers will also require laser amplifiers operating in the 2 to 3-µm region. Another area that exploits the optical properties of rare earth ions is fiber lasers for medical applications. A rare earth doped fiber laser operating in the 2.9-µm region could be used for surgery and cauterization. Because body tissue consists mainly of H 2O, which has a strong fundamental absorption at 2.9 µm, infected tissue can be ablated. Other applications, too, become possible based on the properties of the HMF and chalcogenide glasses. They will be addressed under the specific rare earth dopant sections that follow. 9.3.3 Historical Development of Rare Earth-Doped Fibers The addition of rare earth ions into a silicate glass to produce laser action in a fiber was first shown in 1964 by Snitzer and Koester [44]. Thereafter, phosphate and fluoroberyllate glasses doped with Nd 3⫹ were investigated. The fluoroberyllates were toxic and hygroscopic, whereas the phosphate glasses contained OH⫺ that interacted with the Nd 3⫹, thereby reducing the quantum efficiency. Hence, the fluoroberyllate glass research was practically halted, but new compositions based on fluorophosphate glasses were soon developed [45]. Their development was based on the observation that the Nd 3⫹ laser performance was hindered by the OH⫺ content which, in turn, was process-sensitive. It was envisioned that during melting of a fluorophosphate glass the fluoride ion would reduce the OH⫺ concentration according to OH⫺ ⫹ F

⫺

→ O2⫺ ⫹ HF

(1)

This process turned out to be effective and the lifetime of the Nd 3⫹ excited state was subsequently increased [45]. In fact, in 1966 fluorophosphate glasses doped with Er 3⫹ were also shown to produce laser oscillation at 1.55 µm [46]. Despite the advantages of the fluorophosphate glasses over the phosphate and fluoroberyllate glasses, they possess high-energy phonons (P-O vibration ⬃ 8.3 µm) so that nonradiative transitions are more likely to occur. Furthermore, the presence of OH⫺ ions

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limited the transmission of these glasses to about 2.6 µm, which again reduced the quantum efficiency of the rare earth ions. Interest in rare earth doped glasses was rejuvenated by the discovery that HMF and chalcogenide glasses can be doped with rare earth ions. These glasses transmit to longer wavelengths than the previously described glass systems, and they possess potentially higher radiative efficiencies owing to their lower energy phonons (⬃600 cm⫺1 in fluorozirconate glasses and ⬃400 cm⫺1 chalcogenide glasses). 9.3.4 Absorption Spectra of Rare Earth Ions in Infrared-Transmitting Glasses Because they can tolerate up to about 5 mol% of LaF3, heavy-metal fluoride glass fibers can be readily doped with several mole percent of rare earth ions. Rare earth doping of chalcogenide glass is dependent on the glass host. For example, GLS glass can be doped with high concentrations of rare earth owing to the presence of La in the glass structure. The RE substitutes for the La in the matrix. However, As 2S 3 glass does not have any appropriate sites for the RE ion and the solubility is consequently very low (⬍ 100 ppm). Although the absorption spectra of the rare earth ions do not vary significantly from one matrix to another, small changes are likely to occur, and it is important to have complete knowledge of the absorption levels. In practice, the spectra dictate the choice of pump wavelength for fluorescence–laser applications, as well as the signal wavelengths in amplification devices. (text continues on p. 472)

Figure 9 The absorption spectra of (a) Ce3⫹ and (b) Pr 3⫹ in ZBLANPb glass. (From Ref. 47.)


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The absorption spectra of (a) Nd 3⫹ and (b) Sm3⫹ in ZBLANPb glass. (From Ref. 47.)


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The absorption spectra of (a) Eu3⫹ and (b) Tb3⫹ in ZBLANPb glass. (From Ref. 47.)


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Figure 12 The absorption spectra of (a) Dy3⫹ and (b) Ho3⫹ in ZBLANPb glass. (From Ref. 47.)


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The absorption spectra of (a) Er 3⫹ and (b) Tm3⫹ in ZBLANPb glass. (From Ref. 47.)


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The absorption spectrum of Yb3⫹ in ZBLANPb glass. (From Ref. 47.)

Figures 9–14 show the reported [47] absorption spectra for the rare earth ions in a ZBLANPb glass. As pointed out earlier, most of the ions exist in the 3⫹ state in fluoride glasses, even under reducing conditions. The only exception is Eu, which exhibits both 3⫹ and 2⫹ states, the latter under reducing conditions. The spectra for Pm, Gd and Lu are not shown. Pm is radioactively unstable and short-lived. The electronic structure of Gd 3⫹ is 4f 7 and, therefore, the 4f transitions are spin-forbidden. Lu3⫹ contains a full 4f 14 shell; and therefore, no transitions are observed. The absorption transitions from Figures 9–14 are listed in Table 2. The absorption spectra for the rare earth ions in chalcogenide glasses are shifted to longer wavelengths from those found in fluoride glass hosts, owing to the nephelauxetic effect. This is attributed to the predominantly covalent-bonding character in chalcogenide glasses, unlike the predominantly ionic-bonding character in HMF glasses. Rare earth ions are a nuisance from the viewpoint of attaining ultralow loss in fluoride fibers because they possess strong absorptions close to the wavelength of predicted minimum attenuation of 2.5 µm. For example, Nd 3⫹ is the major contributor to absorption at 2.5 µm (22 dB/km ppm⫺1 at 2.5 µm), which places stringent requirements on the purity of the chemicals to obtain 0.01 dB/km. In the example given, the Nd concentration must be kept below 0.45 parts per billion (ppb) to attain a loss of 0.01 dB/km at 2.5 µm. When citing the concentration of rare earth ions present in their fibers, many of the publications cited in this chapter use the unit of parts per million (ppm) without specifying whether it refers to weight or mole parts per million, and whether it describes the concentration of the rare earth or of its compound. Because these various ppm units differ by a factor of up to close to 6, the implication is that such figures are not imprecise. They are nevertheless cited in this chapter to provide an order of magnitude of the concentrations involved.

Source: Ref. 47.

5.15 3.65 3.38 2.83 2.63 2.197 2.065 0.587 0.524 0.464 0.393 4.63 2.95 2.26 1.972 1.840 1.815 0.485 0.376 0.350

1,940 2,740 2,960 3,530 3,800 4,550 4,840 17,040 19,840 21,550 25,450

2,160 3,390 4,420 5,070 5,430 5,510 20,620 26,600 28,570

34.4

4.68 2.34 1.95 1.54 1.44 1.02 0.587 0.479 0.466 0.443

2,167 4,310 5,128 6,494 6,920 9,709 17,036 20,877 21,459 22,734 290

4.60

Wavelength (µm)

2,170

Frequency (cm⫺1) Neodymium 4 I9/2 → 4I11/2 4 I13/2 4 I15/2 4 F3/2 4 F5/2 4 F7/2 4 F9/2 2 I11/2 2 G7/2, 4G5/2 4 G7/2 2 G9/2 4 G9/2 2 D3/2 4 G11/2 2 P1/2 5 D5/2 2 P3/2 4 D1/2 Thulium 3 H6 → 3F4 3 H5 3 H4 3 F3 3 F2 1 G4 1 D2 3 P0 Dysprosium 6 H15/2 → 6H13/2 6 H11/2 6 H9/2, 6F11/2 6 6 H7/2, F9/2 6 H5/2 6 F7/2 6 F5/2 6 F3/2

Transition

2.83 1.695 1.28 1.10 0.973 0.906 0.804 0.752

1.667 1.209 0.790 0.683 0.658 0.463 0.356 0.283

6,000 8,270 12,660 14,640 15,200 21,600 28,090 26,110 3,530 5,990 7,810 9,090 10,280 11,040 12,440 13,300

5.06 2.52 1.71 0.865 0.794 0.740 0.676 0.063 0.574 0.520 0.509 0.473 0.467 0.459 0.426 0.417 0.379 0.352

Wavelength (µm)

1,980 3,970 5,850 11,560 12,590 13,510 14,790 16,050 17,420 19,230 19,650 21,142 21,410 21,786 23,470 23,980 26,385 28,410

Frequency (cm⫺1)

The Absorption Levels of the Trivalent Rare Earth Ions in Fluoride Glasses

Cerium 2 F5/2 → 2F7/2 Praseodymium 3 H4 → 3H5 3 H6 3 F2 3 F3 3 F4 1 G4 1 D2 3 P0 3 P1 3 I2 Europium 7 F0 → 7F1 7 F2 7 F3 7 7 F1 → F4 7 F0 → 7F4 7 F1 → 7F5 7 F0 → 7F5 7 F1 → 7F6 7 F0 → 7F6 5 D0 5 D1 5 D2 5 D3 Terbium 7 F6 → 7F5 7 F4 7 F3 7 F2 7 F1 7 F0 5 D4 5 D3 5 D2

Transition

Table 2

Samarium 6 H5/2 → 6H7/2 6 H9/2 6 H11/2 6 H13/2 6 F1/2 6 F3/2 6 H15/2 6 F5/2 6 F7/2 6 F9/2 6 F11/2 4 F5/2 Erbium 4 I15/2 → 4I13/2 4 I11/2 4 I9/2 4 F9/2 4 S3/2 2 H11/12 4 F7/2 4 F5/2 4 F3/2 2 H9/2 4 G11/2 2 G9/2 2 G7/2 2 P3/2 Holmium 5 I8 → 5I7 5 I6 5 I5 5 I4 5 F5 5 S2, 5F4 5 F3 5 F2 5 5 F1, G6 5 G5 M band

Transition

5,140 8,680 11,250 13,300 15,370 18,690 20,700 21,460 22,320 24,100 27,860

6,540 10,290 12,530 15,380 18,550 19,290 20,620 22,320 22,680 24,690 26,530 27,550 28,170 31,750

1,250 2,439 3,774 5,102 6,329 6,472 6,711 7,231 8,104 9,234 10,560 25,063

Frequency (cm⫺1)

1.946 1.152 0.889 0.750 0.639 0.535 0.483 0.466 0.448 0.415 0.359

1.529 0.972 0.798 0.650 0.539 0.519 0.485 0.448 0.441 0.405 0.377 0.363 0.355 0.315

8.0 4.10 2.66 1.96 1.58 1.545 1.46 1.383 1.234 1.083 0.947 0.399

Wavelength (µm)

Rare Earth Doped IR-Transmitting Glass Fibers 473

474

Sanghera et al.

Figure 15 3⫹

and Dy

The fluorescence spectra of the trivalent rare earth ions Pr 3⫹, Nd 3⫹, Sm3⫹, Eu3⫹, Tb3⫹ in ZBLANPb glass. (From Ref. 48.)


475

476

Sanghera et al.

The fluorescence spectra of the trivalent rare earth ions Ho3⫹, Er 3⫹, and Tm3⫹ in ZBLANPb glass. (From Ref. 48.)

Figure 16


477

9.3.5 Fluorescence Spectra of Rare Earth Ions in Infrared-Transmitting Glasses The fluorescence spectra of rare earth ions in ZBLANP are shown in Figures 15 and 16, and the fluorescence transitions are listed in Table 3 [48]. Ce3⫹, Gd 3⫹, and Lu3⫹ do not exhibit fluorescence over the wavelength range shown in HMF glasses. Yb3⫹ exhibits one fluorescence band at 1 µm when excited by high-energy electrons. The following sections describe the laser and amplification properties of the rare earth doped HMF and chalcogenide glass fibers. The subsections are grouped according to the different ions that have been incorporated into the glass fibers. The first section deals with Nd 3⫹, which was the first rare earth ion to be incorporated in a fluorozirconate glass fiber. 9.4 NEODYMIUM IN HEAVY-METAL FLUORIDE GLASS FIBERS Neodymium was originally added to a zirconium–fluoride-based glass in 1974 in an attempt to fabricate a single crystal for laser experiments [1]. However, the resultant material turned out to be a glass, which heralded the start of research into fluorozirconate and other heavy-metal fluoride glasses. Although it was already known in 1974 that fluorozirconate glasses could be doped with rare earth ions, the first HMF glass fiber laser containing Nd was not fabricated until 1987 [49]. 9.4.1 Neodymium-Doped Fiber Lasers Although Nd 3⫹ exhibits four fluorescence peaks in bulk HMF glasses at 0.867, 1.048, 1.318, and 1.945 µm (see Table 3), only the 1.048- and 1.318-µm transitions have exhibited laser oscillation. The laser characteristics at these wavelengths are listed in Table 4 [49–54]. From a telecommunications viewpoint, 1.3 µm is an important wavelength for amplification and lasers, but in silica, excited-state absorption (ESA) inhibits oscillation at this wavelength [50,51]. Therefore, an understanding of the energy levels involved and the mechanism responsible for oscillation at 1.3 µm (and also 1.048 µm) in a fluoride glass matrix is important. This is addressed in the next two subsections. 9.4.2 Lasers at 1.05 ␮m The first Nd-doped fluoride fiber laser, demonstrated by Brierley and France [49], used a multimode fiber doped with 180 ppm of Nd and a 35-µm core diameter. The core and cladding glass compositions were ZBLANP and ZBLAN, respectively, and the numerical aperture was 0.16. Initially, the fiber was pumped at 514 nm by an argonion laser to induce fluorescence at 880, 1050, and 1320 nm. Figure 17 shows a schematic energy level diagram for Nd with particular reference to absorption and fluorescence transitions. The absorption of 514-nm light excites the rare earth ions into the 2G 9/2 state. Thereafter, the electrons decay back to the 4F3/2 state, from which they relax down to the 4I states, with the emission of photons of characteristic wavelengths. After their initial fluorescence experiments, Brierley and France placed approximately 10 m of fiber in a Fabry–Perot fiber laser cavity and observed laser oscillation at 1050 nm with a threshold of 390 mW of launched pump power. The output at 1050 nm arises from the transition 4F3/2 → 4I 11/2 (see Fig. 17). The efficiency was only 0.03%, which

D2 → 3 F 4 1.014

3

G4 → 3 F 2 H6 → 3H4 2.300

1

1

1

G4 → 3H5 D2 → 1G4 1.326 (1.364) (1.406) (1.460)

1

3 P 0 → 1 G4 0.908 (0.883)

P0 → 3F4 0.717

Source: Ref. 48.

j

i

h

g

f

e

3

d

D2 → 3H5 0.695 (0.674)

1

c

4

4

F3/2 → 4I15/2 1.945

F3/2 → 4I13/2 1.318

F3/2 → 4I11/2 1.048

4

P0 → 3F2 0.635

3

b

F3/2 → I9/2 0.867 (0.891) 4

P 0 → H6 0.603

a

4

Nd

3

G5/2 → 6F9/2 1.162

G5/2 → 6F7/2 1.022

4

G5/2 → 6F11/2 1.376

4

4

G5/2 → 6F5/2 0.936

G5/2 → 6H15/2 0.896

4

4

G5/2 → 6H13/2 0.782

G5/2 → 6H11/2 0.704

G5/2 → 6H9/2 0.641

4

4

6

G5/2 → 6H7/2 0.595

4

4

Sm G5/2 → H5/2 0.560

4

5

5

5

7

D0 → 7F4 0.698

D0 → 7F2 0.615

D0 → F 1 0.591

Eu

Tb 7

D4 → F0 0.681

D4 → 7F1 0.668

D4 → 7F2 0.649

D4 → 7F3 0.621

D4 → 7F4 0.585

D4 → F5 0.543

5

5

5

5

5

5

4

4

4

F9/2 → 6F1/2 1.384

F9/2 → 6F3/2 1.294

F9/2 → 7F5/2 1.170

F9/2 → 6F7/2 1.000

F9/2 → 6H6/2 0.924

4

4

4

F9/2 → 6H7/2 F9/2 → 6F9/2 0.834

F9/2 → 6H9/2 F9/2 → 6F11/2 0.750

4

4

5

F9/2 → 6H11/2 0.661

4

6

Dy F9/2 → H13/2 0.575

4

5

5

I5 → 5 I6 3.9

I6 → 5 I7 2.848

I7 → 5 I8 2.039

S2 → 5I4 1.953

S6 → 5I5 1.381

I6 → 5 I8 1.191

I6 → 5 I8 1.154

S2 → 5I6 1.015

5

5

5

S2 → 5I7 0.750

5

5

Ho S2 → I8 0.543

5

5

5

5

The Fluorescence Transitions and Wavelength (in µm) of Rare Earth Ions in Fluoride Glasses

Pr

3

Peak

Table 3 Er 4

S3/2 → 4I13/2 0.847

I9/2 → 4I11/2 3.45

I11/2 → 4I13/2 2.719

I13/2 → 4I15/2 1.538

4

4

4

S3/2 → 4I11/2 1.219

I11/12 → 4I15/2 0.977 5

4

4

4 F9/2 → 4I15/2 0.655 (0.666)

S3/2 → I15/2 0.543 (0.550) 4

Tm 3

G4 → 3 H4 F3 → 3F4 3 H5 → 3 H6 1.184

G4 → 3 H5 H4 → 3 H6 0.799

G4 → F 4 0.649

3

F 4 → 3 H6 1.847

G4 → 3F3 H4 → 3F4 1.464

H4 → 3 H5 2.307

1

3

1

3

1

3

1

5

2

F5/2 → 2F7/2 1.0

Yb

478 Sanghera et al.

15,000 15,000 1,000 1,000 1,000 na

1340 1340 1354 1346 1345 1348

50/na 50/na 44/na 40/100 40/na na

35/80 50/na 50/na 44/na 40/100

Core/clad diameter (µm)

2.83 2.83 50.0 31.5 35.0 na

10.0 2.83 2.83 50.0 31.5

Length (cm)

b

na, not available. Output coupler reflectivity at the laser wavelength. c Unless stated otherwise (here or in the text): launched pump power. d Absorbed pump power.

a

180 15,000 15,000 1,000 1,000

Nd concentration (ppmw)

Nd-Doped Fluoride Glass Fiber Lasersa

1050 1050 1050 1050 1050

Laser wavelength (nm)

Table 4

na na 0.16 0.16 0.16 na

0.16 na na 0.16 0.16

NA

514 514 514 795 795 na

514 514 514 514 795

Pump (nm) 99 97.6 97.6 90 90 95 98.2 98.2 97 95 90 na

Output coupler (%R)b 390 190c 190c 33 22 3 670c 670c 84 60 60 5

Threshold (mW) 0.03 na na 16.8 70.0 37.0 2.6d 2.6d 3.2 57.0 57.0 12.0

Efficiency (%) na 22 22 40 55 16 9 9 4 30 30 na

Maximum output power (mW)

1,800 1,000c 1,000c 280 110 45 1,000d 1,000d 260 110 110 na

Pump power (mW)c

49 52 53 54 55 55 52 53 54 55 57 58

Ref.


480

Figure 17

Sanghera et al.

A schematic electronic energy level diagram for Nd 3⫹ ions in a fluoride glass.

is not unreasonable considering that the fiber and cavity parameters were far from optimized. As mentioned previously, the laser oscillation threshold and efficiency are defined relative to the launched pump power. As another example, Miniscalco et al. [52,53] observed laser oscillation at 1050 nm from a 2.83-cm multimode fiber pumped at 514.5 nm with an argon-ion laser. The Nd concentration was 1.5 mol%. The core and cladding compositions were ZBLANI and HZBLAN, respectively, and the core diameter was 50 µm. The threshold was 190 mW of launched pump power. This value is rather high and probably related to the high loss of the fiber (⬃10 dB/m) at 1 µm. Brierley and Millar [54] have also observed continuous-wave (CW) laser action at 1050 µm. A 50-cm fiber was doped with 1000 ppm Nd and pumped with 514-nm light. The core diameter and NA were 44 µm and 0.16, respectively. The laser had a threshold of 33 mW (launched pump power) and a slope efficiency of 16.8%. The lower threshold, compared with those discussed in the foregoing [52,53], presumably arises from the improved fiber quality. The use of a semiconductor diode laser to pump a fluoride fiber laser was initially demonstrated in 1989 by Brierley and Hunt [55], who achieved oscillation at 1050 and 1346 nm (Fig. 18). They used a Sony SLD 303 broad-stripe 500-mW diode laser for which the output was at 795 nm. The absorption by the fiber at this wavelength was approximately 39 dB. The fiber composition and NA were identical with those used by Brierley and Miller [54]; the length was 31.5 cm and the core and cladding glass diameters were 40 and 100 µm, respectively. Pumping was from the 4I 9/2 ground state to the 4F5/2 level. The threshold power was 3 mW (launched power) and the slope efficiency was 37% for the 1050-nm output. The maximum efficiency, defined as the ratio of the input photons to laser photons, was 75.7%, which gave a subsequent quantum efficiency (QE) of 92.5%.


481

Figure 18

The laser output powers at (a) 1050 nm and (b) 1346 nm, from a 31.5-cm–multimode Nd-doped HMF glass fiber laser pumped at 795 nm. (From Ref. 55.)

Small changes in the reflectivities of the output mirrors affected both the threshold and slope efficiencies. For example, replacing the 95% by 90% reflecting mirrors increased the slope efficiency from 37 to 70%, but also increased the threshold from 3 to 22 mW. The output powers were typically high, approaching 55 mW. Efficient tunable CW operation at 1.05 µm in ZBLAN fibers has been reported by Wetenkamp et al. [56]. Single-mode and multimode fibers exhibited laser oscillation. The fiber lasers were tuned utilizing a diffraction grating of 300 lines per millimeter and blazed at 1.0 µm. Tuning of the multimode fiber was in the range of 1.044–1.071 µm when pumped at 780 nm, 4.5 times above threshold. The single-mode fiber exhibited a wider tuning range. When pumped at 780 nm, 8.5 times above threshold, its tuning range extended from 1.041 to 1.078 µm. The spectral linewidths, given by the resolution of the spectrometer, were less than 1 nm. 9.4.3 Lasers at 1.3 ␮m From a telecommunications viewpoint, 1.3 µm is an important wavelength for amplifiers and sources. Unfortunately, in silica excited-state absorption (ESA) inhibits laser oscillation at this wavelength. The 1.3-µm fluorescence arises from the 4F3/2 → 4I 13/2 transition

482

Sanghera et al.

Comparison between the fluorescence spectrum and the laser emission of the Nd 3⫹doped ZBLAN free-running fiber laser of Figure 18 operated well above threshold. (From Ref. 52.)

Figure 19

(see Fig. 17), but there is a competing transition (4F3/2 → 4G 7/2) which absorbs the 1.3µm signal and generally represents a significant loss mechanism. In fact, Alcock et al. [50] observed pump-induced loss (ESA), rather than gain, at 1.32 and 1.34 µm in an Nd 3⫹doped silica fiber. Laser oscillation has been observed only at 1.4 µm in silica [51] on the edge of the ESA band, but this wavelength is too long for communication applications. The conditions of net gain or loss at a particular wavelength depend on both the spectral overlap between the competing transitions and their respective strengths, both of which are functions of the host composition. The ratio of the calculated line strength of the emitting transition to that of the ESA transition at 1.3 µm is estimated to be 0.92 in silica and 2.0 in a fluorozirconate glass [52]. Hence, the fluorozirconate glasses offer more favorable conditions for gain at 1.3 µm. As an example, Miniscalco et al. [52,53] have demonstrated laser oscillation at 1340 nm from a 2.83-cm, multimode HMF fiber pumped at 514.5 nm. The core and cladding compositions were ZBLANI and HZBLAN, and the core was 50 µm in diameter. The threshold and slope efficiency were 670 mW and 2.6%, and 10-mW–output power was obtained at 1.3 µm. Their use of short lengths was due to the high losses exhibited by their fibers, typically ⬎8 dB/m at 1300 nm. Furthermore, the laser output at threshold was at 1330 nm, well beyond the 1320-nm fluorescence peak, suggesting that a mechanism such as ESA was operating at less than 1330 nm. In addition, the free-running laser exhibited bimodal behavior, whereby the laser output intensity shifted from 1330 to 1340 nm with increased pump power [52,53]. Figure 19 shows a comparison between the luminescence spectrum and the free-running fiber laser at 1340 nm. From an amplification viewpoint, the fiber can potentially be tuned over a wide wavelength range, typically from 1270 to 1400 nm. Brierley and Hunt [55] have used semiconductor diode laser pumping to achieve laser oscillation at 1346 nm. Pumping was from the 4I 9/2 ground state to the 4F5/2 level (800 nm). The threshold power and slope efficiencies were 60 mW and 57%. The maximum efficiency as described by the ratio of the pump-to-signal photon numbers was 59%, which gave a quantum efficiency of 97% for the 1346-nm output. This is one of the highest QEs ever reported for a fiber laser. The authors noted that small changes to the reflectivities


483

of the output mirrors affected both the threshold and slope efficiencies at 1050 and 1346 nm. For example, at 1346 nm, changing the output mirror reflectivity from 95% to 97% lowered the threshold from 60 to 20 mW, but as expected, it also lowered the slope efficiency (to 12%). In addition, output powers of approximately 30 mW were obtained. If a multimode Nd-doped fluoride fiber, similar to the one used by Brierly and Hunt [55], is aligned in a straight line, the signal is sustained in the lowest-order transverse propagation mode, even up to pump values 1.95 times the threshold value of 60 mW [57]. The fibers were pumped at 795 nm by a semiconductor diode laser emitting up to 120 mW of power. In an optimized cavity, the slope efficiencies of 57% gave output powers of 30-mW continuous wave (CW) at 1345 nm. Up to 12 mW of this output power were coupled into a GeO 2 –SiO 2 single-mode fiber. The coupling loss was attributed to the coupling lens design and residual high-order modes in the oscillator at higher pump powers. Coupling efficiencies approaching unity should be possible with improved lens designs. Komukai et al. [58] have obtained highly efficient CW tunable operation close to the 1.3-µm band with a dielectric multicoated bandpass filter as the tuning element, laser oscillation was observed from 1.315 to 1.348 µm. The slope efficiencies at 1.32 and 1.348 µm were 6.7 % and 12%, respectively. The threshold power was estimated to be 5 mW for both wavelengths. Tuning of the laser to 1.315 or 1.316 µm resulted in simultaneous oscillation at 1.05 µm, but was suppressed on tuning to 1.318 µm. 9.4.4 Amplification Using Neodymium-Doped Fluoride Glass Fibers Brierley and Millar [54] showed the first example of amplification in an Nd-doped fluoride glass fiber. The signals for the gain experiments were provided by several temperaturetuned semiconductor lasers in the wavelength range from 1323 to 1365 nm, with typical output powers of 0.1 mW. The gain was measured as a function of pump power for several signal wavelengths. Gain was observed over a 40-nm wavelength range, with a maximum gain of 32% at 1354 nm for 688 mW of pump power (Fig. 20). In addition, the offset in

Normalized fluorescence spectrum (broken curve) and small-signal gain for a Nd 3⫹doped ZBLANP fiber for launched pump powers of (a) 688 mW, (b) 430 mW, and (c) 215 mW at 514 nm. (From Ref. 54.)

Figure 20

484

Table 5

Sanghera et al. Amplification at 1.3 µm in Nd-Doped Fluoride Glass Fibers

Nd concentration (ppmw)


Length (cm)

6.5/125 6.5/125 6.5/125 9/naa 5.8/na

1000 1000 200 140 75

1,000 1,000 2,000 500 500 a

NA

Pump (nm)

Gain (dB)

Wavelength of maximum gain (µm)

Range of gain (µm)

Ref.

0.15 0.15 0.15 0.16 0.16

496 780 820 795 795

10.0 10.0 5.5 5.0 6.5

1.33 1.33 1.339 1.33 1.337

1.31–1.36 1.31–1.38 1.319–1.339 1.310–1.370 1.320–1.337

59 60 61 62 63

na, not available.

the peak position between the fluorescence and the small-signal gain measurements indicates ESA operating on the short-wavelength side of the gain spectrum. In 1990, Miyajima and co-workers were successful in showing gain in the first single-mode fluoride fiber [59] (Table 5). The advantage of single-mode fibers is that the pump power intensity is greatly increased, which leads to higher gain coefficients. The fiber was doped with 1000 ppm Nd. The core and cladding glass diameters were 6.5 and 125 µm and the fiber was 10-m long. It was pumped with a 150-mW argon ion laser at 496 nm and the signal source at close to 1.3 µm was a tunable laser diode. They were able to use a relatively long fiber because their single-mode fiber possessed a loss of only 100 dB/km at 1.3 µm. The fiber exhibited wide gain between 1.31 and 1.36 µm, with a maximum gain of 10 dB at 1.33 µm (Fig. 21a). Gain saturation was observed above about 50 mW of pump power for a 1.33-µm signal (Fig. 21b). The signal level (dBm) was not given for Figure 21b. Following this initial work, Miyajima et al. [60] pumped a similar single-mode fiber with 150 mW of 780-nm light from a Ti:sapphire laser. The signal input was varied from ⫺30 to ⫺50 dBm and gain observed between 1.31 and 1.38 µm. A maximum gain of 10 dB was measured at 1.33 µm for a ⫺50-dBm input power. As previously observed, saturation occurred gradually above 50 mW of launched pump power. At a 1.339-µm signal wavelength, with an input level of ⫺10 dBm, a gain of 5.5 dB has also been observed by Miyajima et al. [61]. The sample was a 2-m, single-mode fluoride fiber doped with 2000 ppm Nd and pumped at 820 nm by a Ti:sapphire laser operating at 50 mW. The signal was supplied by an external cavity laser and an Nd:YAG ring laser (1.319 µm). Their results are shown in Figure 22. The pumping efficiency was 0.13 dB/mW. The gain decreased to 3.3 dB at 1.319 µm and became almost negative below 1.31 µm because of ESA (see Fig. 17). Gain saturation became evident above about 40 mW pump power because of amplification of stimulated emission (ASE) at 1050 nm on the 4F3/2 → 4I 11/2 transition. In addition, gain saturation did not occur for signal power levels less than 0 dBm. Brierley et al. [62] have measured a gain of 4–5 dB between 1320 and 1350 nm, but again, this was limited by saturation due to ASE from 1050 nm radiation (Fig. 23). However, the authors concluded that improvements are possible by restricting the buildup of the competing ASE and increasing the pump-to-signal field overlap using a truly singlemode fiber. In addition, they found a gain coefficient, at 1050 nm, of 0.03 dB/mW for up to 150 mW of pump power. Thereafter, saturation was present.


485

Figure 21

(a) The gain profile for a 10-m length of single-mode HMF glass fiber containing 1000 ppm of Nd. (b) Gain versus launched pump power for a signal at 1.33 µm; saturation is evident above about 50 mW. (From Ref. 59.)

A gain of 6.5 dB was obtained in a single-mode fiber similar to the composition used by Brierley and Hunt [55] except that the core diameter was 5.8 µm and the fiber was 75 cm long [63]. The Ti:sapphire laser pump power was 100 mW at 795 nm, whereas a 20-mW signal was provided by a diode-pumped Nd:YAG laser limited to 1320 and 1337 nm. Saturated output power levels in excess of 15 dBm were obtained.

486

Sanghera et al.

Relation between pump power and gain at 1.338 µm for an HMF glass fiber amplifier pumped at 0.82 µm. The fluorescence powers at 1.318 µm and at 1.048 µm are also plotted. The fiber was 2 m long and contained 2000 ppm of Nd. (From Ref. 61.)

Figure 22

Figure 23 Excited-state absorption spectrum evaluated as the difference between the emission spectrum of the 4F3/2 → 4I 13/2 transition and the scaled gain. (From Ref. 62.)


Figure 24

487

Laser spectrum of a Nd 3⫹-doped GLS glass fiber laser. (From Ref. 67.)

9.5 NEODYMIUM IN CHALCOGENIDE GLASSES Early work on Nd 3⫹ in chalcogenide glass was performed by Reisfeld and Bornstein [64,65]. They reported the visible and near-IR fluorescence spectra of Nd 3⫹ in gallium lanthanum sulfide (GLS) and aluminum gallium sulfide (ALS) glasses. Near-IR fluorescence at 786, 919, 1077, and 1370 nm was observed, corresponding to the transitions (2H 9/2, 4 F5/2) → 4I 9/2; 4F3/2 → 4I 9/2; 4F3/2 → 4I11/2; and 4F3/2 → 4I 13/2, respectively. Emission cross sections of 7.95 10⫺20 and 8.20 10⫺20 cm2 were calculated for the 1.080-µm transition of Nd 3⫹ in GLS and ALS glasses, respectively. Emission cross sections of 3.60 ⫻ 10⫺20 and 4.10 ⫻ 10⫺20 cm2 were calculated for the 1.37-µm transition in GLS and ALS glasses, respectively. To date, neodymium has been the only rare earth ion to successfully demonstrate laser oscillation in a chalcogenide glass. Schweitzer et al. [66,67] observed laser action at 1.08 µm on the 4F3/2 → 4I 11/2 transition in both bulk glass and chalcogenide glass fiber. In bulk, CW laser action was observed in a 1.42-mm–thick sample of GLS glass (Ga 2S 3 – La 2S 3) doped with 1.5 mol% of Nd situated in a simple hemispherical resonator and pumped with a Ti:sapphire at 890 nm [66]. The output power saturated, and at high pump power laser action ceased due to thermal problems of the glass. Laser action in fiber was observed in a GLS glass fiber doped with 0.05 mol% Nd under 815-nm pumping [67]. The doped, multimode fibers were about 20 mm in length. Under CW pumping, selfpulsing laser behavior was observed, which was not explained. The laser spectrum of this fiber laser is shown in Figure 24. Mori et al. [68] have shown amplification at 1.083 µm in an Nd 3⫹-doped GAGSbS (germanium–arsenic–gallium–antimony–sulfide) fiber. The 5-cm long fiber had a 5-µm core diameter, an index difference between the core and the cladding (∆n) of 1%, and a cutoff wavelength of 2.1 µm. The fiber loss was 10 dB/m at 1.3 µm. The fiber was pumped at 0.89 µm. A maximum internal gain of 6.8 dB was obtained with 180 mW of pump power.

488

Figure 25

Sanghera et al.

A schematic representation of the electronic energy levels and transitions of Er 3⫹ in

HMF glasses.

9.6 ERBIUM IN HEAVY-METAL FLUORIDE GLASS FIBERS Erbium in fluoride glasses exhibits six main fluorescence peaks in the IR, at 0.847, 0.977, 1.219, 1.538, 2.719, and 3.45 µm (Fig. 25). The transitions corresponding to these emissions are shown in Table 3. The emissions at 1.538 and 2.719 µm are of practical interest for optical communications and medical applications, respectively. Specifically, the 2.7µm emission also has a potential application in optical fiber communications using ultralow-loss fluoride glass fibers. The transition at 3.45 µm is of interest because it lies in an atmospheric transmission window. Emission at this wavelength could have potential applications in laser ranging and remote sensing. The following subsections describe the properties of the Er-doped fluoride glass fibers and are separated into fiber lasers and amplifiers. 9.6.1 Erbium-Doped Fiber Lasers In silica fiber hosts, the erbium system has exhibited only a single, but very important, laser line from the 4I 13/2 → 4I 15/2 three-level transition at close to 1530 nm, which is of interest in optical communications. However, in HMF glass fibers many more laser transitions have been observed, as listed in Table 6 and discussed in the following.

10,000 10,000 860 10,000 5,000 100,000 977 977 977 250 10,000 200 1,200 840 500

Er concentration (ppmw) 40/na 5/na 40/na 8/na 13/na 170b 40/80 40/80 40/80 40/na 8/na 30/na 11/na 40/na na

Core/clad diameter (µm) na na 75 150–300 50 2 40 40 40 5 48–61 30 44 75 300

Length (cm)

Er-Doped Fluoride Glass Fiber Lasersa

na 0.40 0.16 na 0.12 0.13 0.16 0.16 0.16 0.16 na na na na na

NA

b

na, not available. No cladding. c Unless stated otherwise (here or in the text): launched pump power. d Absorbed pump power.

a

3.45 3.45 2.702 2.714 2.71–2.78 2.71 1.72 1.68,1.66 1.60 1.56 1.0 0.99 0.983 0.85 0.85

Laser output (µm)

Table 6

655 650 476.5 476.5–647.1 792 802 514,488 514,488 514,488 488 488,514.5 488 647.1 476.5 801

Pump (nm) 96 90 99 99 95 99 99 99 na 90 98 na na 98 93

Output coupler (%R) 721 50 191 7 4 10d 150 150 400 230 600 700 19 500 200c

Threshold (mW) 2.8 na na na 3.0 8.0d na na na 0.5 na na 8.7 na 38.0d

Efficiency (%) 8.5 na na 0.02 0.12 1.0 na na na na 0.6 na 10.0 na 60.0


1050 na na 10.5 19 50d na na na na 750 na 300 na 350d

Pump power (mW)c

68 71 76 77 78,79 80 83,84 83,84 83,84 85 86 87 88 87 90

Ref.


490

Sanghera et al.

9.6.2 Lasers at 3.45 ␮m Laser action at 3.45 µm has been reported by Tobben [69] on the 4I 9/2 → 4I 11/2 transition of Er in ZBLAN. CW laser oscillation was achieved between ⫺80°C and room temperature. The fiber was a ZBLAN composition containing 1 mol% Er and had a 40-µm core diameter. The fiber was pumped with a DCM dye laser at 655 nm. At ⫺80°C, the laser exhibited a slope efficiency of 3–4% and threshold of 468 mW, with an output mirror reflectivity R ⫽ 96%. At room temperature, the laser exhibited a threshold of 996 mW and a slope efficiency of 2.8%. On chopping at 118 Hz, the threshold decreased to 721 mW and the fiber emitted nearly 8.5 mW of power with 1.05 W of absorbed power. The improvement with chopping may be due to the change in the nonradiative relaxation caused by the reduced duty cycle. Tunability at this wavelength was also demonstrated [70]. Laser oscillation was achieved in a ZBLAN fiber containing 1 mol% Er and with a 5-µm core diameter and an NA of 0.4. The fiber was pumped by a DCM dye laser operating near 650 nm and the output mirror reflectivity was 97%. Temperature tuning was achieved using a Peltier element to heat the fiber from 5° to 41°C, resulting in laser operation from 3.449 to 3.478 µm. Heating also resulted in a temperature-dependent decrease in the slope efficiency of the laser owing to a decrease in the upper laser level lifetime with increasing temperature. Schneider et al. [71] have observed laser oscillation at 3.45 µm in cascade mode, with the 2.7- and 1.55-µm transitions. The fiber was doped with 10,000 ppm Er and pumped at 650 nm with a DCM dye laser. The output coupler mirror had R ⬃ 75% at 1.55 µm, R ⬃ 50% at 2.78 µm and R ⬃ 90% at 3.45 µm. The threshold for both 2.78and 3.45-µm laser action was approximately 50 mW. Laser action at 1.55 µm occurred at launched powers of more than 250 mW. 9.6.3 Lasers at 2.7 ␮m Laser action at 2.7 µm is not possible in silica, but CW oscillation at this wavelength has been observed in several crystals doped with erbium, such as YSGG (2.707 µm) and YLF (2.66–2.85 µm) with Kr and Ar ion laser pumping, respectively [72,73]. Furthermore, CW operation in Er-doped YLF has also been realized by diode laser pumping [74]. The first report of a laser using erbium in fluoride glasses was in a bulk ZBLAN glass in which LaF3 was completely replaced by 4 mol% ErF3 [75]. The glass block was pumped by a xenon flash lamp and exhibited laser oscillation at 2.78 µm, with a threshold of 75 J. The 2.78-µm emission is close to the OH absorption band found in fluoride glasses and fibers. If the OH levels are high, the absorption band may limit the laser properties. In the foregoing example, the authors did not find any OH using IR spectroscopy and attributed this result to their processing conditions; namely, the use of high-quality chemicals and reactive atmosphere melting of the glasses. The bulk glass also exhibited fluorescence at 0.54, 0.66, 0.98, 1.56, and 2.7 µm. Esterowitz et al. [76] have also observed laser oscillation at 2.7 µm in a bulk glass doped with 3 mol% Er by pumping with an alexandrite laser at 797 nm. The threshold was 250 µJ of absorbed power. They also observed visible fluorescence from upconversion processes. The electronic energy level diagram of Er is shown in Figure 25. The lifetimes of the various states in a fluoride glass were determined to be 36 µs, 64 µs, 9 ms, and 14 ms for the 4S 3/2, 4I 9/2, 4I 11/2 , and 4I 13/2 levels, respectively. The 2.7-µm emission arises from the 4I 11/2 → 4I 13/2 transition. Because the lifetime of the lower level ( 4I 13/2) is longer than the lifetime of the upper laser level (4I 11/2), this transition is self-terminating and should


491

not exhibit CW oscillation. Nevertheless, laser oscillation at 2.7 mm was made CW by Brierley and France [77]. They pumped a multimode fluoride fiber containing 860 ppm Er at 476.5 nm. CW laser action was obtained at 2.702 µm, with a threshold of 191 mW. In this particular case, the lifetimes of the upper and lower levels were determined to be 7.8 and 10.2 ms, and the laser should be self-terminating. The authors attributed the CW laser action to ESA of the pump wavelength, which causes excitation from the lower level 4 I 13/2 to the upper levels 4G 7/2, 2K 15/2, and 4G 9/2. Hence, depopulation of the 4I 13/2 level and subsequent population of the 4I 11/2 level occurs, which leads to CW operation. Continuous-wave laser oscillation has been obtained at 2.714 µm in a single-mode fiber with an 8-µm core diameter pumped at 476.5, 501.7, or 647.1 nm [78]. The 1.5-, 2-, and 3-m fiber lengths were doped with 10,000 ppm of Er. The absorption of the fiber at 476.5 nm was 6.6 dB/m and the threshold power was only 7 mW, whereas the output power was 250 µW. The output line width was less than 2 nm (limited by the resolution of the monochromator). No fundamental dependence of the threshold on fiber length was observed. To test the proposed depopulation theory [77], Allain et al. [78] pumped their fiber with several different wavelengths including 488, 496.5, 514.5, and 676.4 nm. None of these wavelengths produced laser oscillation at 2.7 µm. From their observations and the electronic energy levels of Er, they concluded that ESA of the pump wavelength was the dominant mechanism for depopulation of the 4I 13/2 level. The pump absorptions that lead to laser oscillation correspond to the following known transitions from the 4I 13/2 level: 476.5 nm: 4I 13/2 → 4G 9/2, 2K 15/2, and 2G 7/2

(2)

501.7 nm: I 13/2 → G 11/2

(3)

4

4

647.1 nm: I 13/2 → F5/2 and F3/2 4

4

4

(4)

The 488-, 496.5-, 514.5-, and 676.4-nm wavelengths do not correspond to an ESA transition. Consequently, for these pump wavelengths depopulation of the 4I 13/2 level and subsequent laser oscillation do not occur. The argon-ion laser is a large and inefficient pump source for practical applications, and it would be desirable to use laser diode pumping for a compact and efficient laser system. To this extent, CW oscillation was achieved in a single-mode fiber at 2.7 µm by pumping with either a laser diode array at 792 nm or a Ti:sapphire laser at about 810 nm [79,80]. The laser diode pumps the 4I 9/2 level and the decay of the 4I 9/2 level into the 4 I 11/2 has an efficiency of nearly 100%. A threshold of 4-mW absorbed power and a 3% slope efficiency were obtained at 792 nm. The outputs occurred primarily at 2.71, 2.75, and 2.78 µm, but they varied with pump power and fiber length. CW operation was not possible when pumping between 806 and 815 nm. This was attributed to pump ESA from the 4I 11/2 level to the 4F3/2 level, which depopulates the upper state of the laser transition. CW operation was achieved at 820 nm, although no ESA was observed from the 4 I 13/2 level. This indicates that depopulation of the longer-lived 4I 13/2 level through ESA or upconversion may not be necessary for CW operation. Continuous wave oscillation has also been observed at 2.715 µm, using diode laser pumping at 802 nm, with both clad and unclad multimode fluorozircoaluminate fibers [81]. The threshold was 10 mW of absorbed pump power, the slope efficiency was 8%, and the maximum output power 2.1 mW. In addition, Allen et al. [79,80] found weaker outputs at 2.714, 2.716, 2.725, 2.758, and 2.782 µm, with lower stability in power. They also observed the emission of green light (545 nm) corresponding to the 4S 3/2 → 4I 15/2

492

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transition (see Fig. 25). This implies that ESA at the pump wavelength may be present and responsible for CW operation at 2.7 µm. However, the possibility of energy-transfer upconversion is also likely due to the high concentration of Er, in this case 10,000 ppm. In energy transfer upconversion, the energy from the relaxation of one ion can be absorbed by an adjacent excited ion, thereby exciting the latter to higher energy levels. A high concentration of the dopant is a prerequisite for energy transfer upconversion. This process can be distinguished from upconversion, in which the excited ion absorbs another pump photon, which excites the electron to a higher level. High power at 2.7 µm is desirable for medical applications. Bedo et al. [82] have studied the saturation of the 2.71-µm laser output in Er-doped ZBLAN fibers to identify the principal saturation mechanism by pumping at 791 nm. They determined that saturation occurs because of simultaneous laser action at 850 nm from the 4S 3/2 level, which is populated by the strong ESA. The 850-nm laser action from the 4S 3/2 effectively couples the 4 I 13/2, 4I 11/2, and 4S 3/2 levels. As a consequence, the 2.71-µm laser output saturates and additional pump power is compensated for by increased laser output at 850 nm. Tunability of the 2.7-µm laser emission has been demonstrated by Wetenkamp et al. using a diffraction grating of 150 lines per millimeter blazed at 2.5 µm [56]. Tunability from 2.70 to 2.83 µm was demonstrated under 650-nm pumping at four times the threshold power. The threshold was 197 mW, the slope efficiency 7.2%, and the maximum output power 26 mW. Pumping at 795 nm resulted in a slope efficiency of 9.2% with a threshold of 110 mW, and a maximum output power of 19.6 mW. The tuning range under 795-nm pumping at eight times the threshold power was 2.67–2.83 µm. 9.6.4 Lasers Between 1.66 ␮m and 1.72 ␮m This wavelength region is not currently available from silica glass fiber lasers, as it falls between the ranges presently covered by Er 3⫹-doped and Tm3⫹-doped silica fiber lasers. Interest in a source near this wavelength centers on the possibility of developing a compact sensor for CH 4 gas, exploiting the absorption close to 1.67 µm. Ideally, such a device would be pumped by a diode laser. Smart et al. [83,84] observed pulsed laser action in a multimode fiber at 1.72 and 1.66 µm at room temperature by pumping at 514 nm. Absorption of 514-nm light causes excitation from the 4I 15/2 ground-state to the 2H 11/2 level. Subsequent transitions from the 2 H 11/2 level to the 4I 9/2 level and from the 4S 3/2 level to the 4I 9/2 level give rise to the observed laser emissions at 1.66 and 1.72 µm, respectively (see Fig. 25). Fluorescence decay measurements on these emissions show an exponential decay with a 1/e decay time of approximately 500 µs. Because the lifetime of the 4I 9/2 level is about 1 ms, the 4S 3/2 → 4I 9/2 transition is expected to be self-terminating. The laser thresholds were approximately the same for both emissions lines, typically 150 mW of launched pump power. The same result was found when pumping at 488 nm. However, at 77 K they observed laser oscillation at 1.72, 1.68, and 1.66 µm. The 1.68-µm output has characteristics similar to the 1.66and 1.72-µm outputs and is probably due to a transition from the 2H 11/2 level to another Stark sublevel of 4I 9/2. The 4S 3/2 level can be populated by upconversion of pump light at about 800 nm, readily available from high-power diode lasers. The efficiency of populating the 4S 3/2 level by this process is about 20% of that by pumping at 514 nm [83]. Despite this disadvantage, the use of single-mode fibers would allow reasonable threshold powers for a laser at 1.7 µm using diode lasers.


493

Normalized fluorescence spectrum of an Er 3⫹-doped ZBLANP fiber and an Er 3⫹doped silica fiber. (From Ref. 85.)

Figure 26

9.6.5 Lasers at 1.55 ␮m The 1.5-µm emission of Er 3⫹ arises from the 4I 13/2 → 4I 15/2 transition (see Fig. 25). Figure 26 shows the fluorescence spectra close to 1.5 µm of an Er 3⫹:ZBLANP fiber and an Er 3⫹: silica fiber [85]. The fluoride glass host leads to a broader emission spectrum, which is a significant practical advantage for the gain bandwidth and noise performance of amplifiers, as well as for the tuning range of fiber lasers using a fluoride glass host. Surprisingly, a relatively low number of Er-doped lasers operating near 1.5 µm have been demonstrated in fluoride fibers. Continuous-wave laser oscillation has been demonstrated at 1.56 µm from a 50-cm–fiber doped with 250 ppm of Er, and pumped at 488 nm [85]. The threshold was 230 mW of launched pump power and the slope efficiency was only 0.5%. This low figure was related to extrinsic cavity losses primarily associated with hand-cleaved fiber ends. Smart et al. reported CW laser operation at 1.60 µm by cooling their fiber to 77 K [83,84]. The fiber was pumped at 488 nm. The 1.6-µm output was caused by the longwavelength tail of the three-level transition 4I 13/2 → 4I 15/2. 9.6.6 Lasers at 1 ␮m A fiber laser source operating close to 1 µm should find applications in many areas, including for spectroscopic measurements, for the generation of second-harmonic radiation in the blue, and as an efficient pump source for Er-doped silica fiber amplifiers. Continuouswave operation at 1 µm was first demonstrated in a single-mode fiber by pumping at either 488 or 514 nm [86]. Several fiber lengths were used with the same Er concentration of 10,000 ppm. Absorption of pump light at 488 and 514 nm causes excitation from the ground state to the 4F7/2 and 2H 11/2 levels, respectively. The 1-µm emission arises from the three-level transition between the 4I 11/2 level and the 4I 15/2 ground-state level (see Fig. 25). Output powers of approximately 1 mW were obtained for launched pump powers near

494

Sanghera et al.

900 mW. The laser wavelength varied as a function of fiber length, for example, from 1.002 to 1.006 µm for 26- and 61-cm lengths of fiber, respectively. Furthermore, the threshold powers increased with fiber length, such that fiber lengths of 48 and 61 cm had threshold powers of approximately 625 and 760 mW, respectively. In addition, a fiber several meters in length, doped with 500 ppm Er, exhibited oscillation when pumped at 488 nm but not at 514.5 nm, as the absorption was too low at the latter wavelength. Brierley et al. [87] have observed CW laser operation at 0.99 µm in a multimode fiber doped with less than 200 ppm Er and pumped at 488 nm. The laser had a threshold of 700 mW of launched pump power, corresponding to 205 mW of absorbed power. This high threshold was attributed to a nonoptimized fiber length. In addition, pumping at 488 nm led to 20 separate fluorescent transitions, ranging from 255 to 2700 nm. The quantum efficiency of pumping at 488 and 514 nm is not optimum because the excited states, 4F7/2 and 2H 11/2, respectively, decay readily to the 4S 3/2 level (which gives rise to subsequent emissions). For instance, there is a strong fluorescence at 0.85 µm owing to the 4S 3/2 → 4I 13/2 transition (see Fig. 25). However, exciting the 4F9/2 level at 647.1 nm using a krypton-ion laser avoids this disadvantage [88]. Based on this idea, Allain et al. [88] have observed CW laser operation at 0.983 µm with a threshold of 19mW launched pump power, efficiency of 8.7%, and an output power of approximately 10 mW. The laser wavelength can also be tuned between 981 and 1004 nm. The mechanism for the 0.983–µm emission using 647.1-nm light is as follows: NR NR R F9/2 → 4I 9/2 → 4I 11/2 → 4I 15/2

4

(5)

where NR and R stand for nonradiative and radiative relaxation, respectively. Although, the excited 4F9/2 level exhibits two radiative emissions at 650 and 1155 nm, corresponding to transitions to the 4I 15/2 ground-state level and the 4I 13/2 level, respectively, significant nonradiative deexcitation takes place at 300 K toward the 4I 9/2 level due to multiphonon quenching [89]. Furthermore, no radiative emissions have been observed from the 4I 9/2 level. This may be due to the small energy difference between the 4I 9/2 and 4 I 11/2 levels, leading to nonradiative relaxation. This difference is only 2250 cm⫺1. This energy could be absorbed by four 590-cm⫺1 phonons, which are the dominant phonons in ZBLAN glass. This is supported by the lifetime of the 4I 9/2 level, which has been measured to be 64 µs, compared with the 8.3 ms of the 4I 11/2 level. Next, radiative deexcitation from the 4I 11/2 level to the ground-state 4I 15/2 level gives rise to the 0.983-µm emission. It should also be pointed out that ESA at 647.1 nm from level 4I 13/2 to level 4F5/2 contributes to the repopulation of the 4I 11/2 level and can thus increase the laser efficiency. However, pumping at 800 nm using a diode laser should improve the efficiency. In addition, the same authors have demonstrated tunable Q-switched operation with pulses of 120-ns duration and 10-W peak power at a repetition rate of 50 Hz [88]. 9.6.7 Lasers at 0.85 ␮m A multimode Er-doped HMF glass fiber was first shown to exhibit CW laser operation at 0.85-µm by pumping at 476.5 nm [87]. The 0.85 µm emission arises from the 4S 3/2 → 4 I 13/2 transition (see Fig. 25), which is normally self-terminating owing to the long lifetime of the lower level. However, the fact that this level exhibits CW oscillation implies that another mechanism, such as pump ESA or energy transfer upconversion, may be playing a significant role. Energy transfer upconversion can be ruled out because the Er concentra-

495


tion was relatively low (840 ppm Er). However, ESA must be occurring based on the observation that the lower level (4I 13/2) in this emission is also the lower level in the 2.7µm emission. In that particular case, CW laser operation was made possible by pump ESA from the 4I 13/2 level, which depopulated this level. In the same manner, the CW operation at 0.85 µm is possible owing to pump ESA from the 4I 13/2 level. The high threshold (500 mW of launched pump power) that was reported is likely due to a lack of optimization of the cavity. Millar et al. [90] have pumped a multimode fluoride fiber at 801 nm using a Ti: sapphire laser with up to 350 mW of power. They observed CW operation at 0.85 µm, with a threshold of 200 mW and a slope efficiency of 38%. Again, as the lifetime of the lower level (4I 13/2) is long, this transition should be self-terminating. Hence, depopulation of this lower level has to occur for successful CW operation. Because the authors did not observe any laser operation close to 1540 nm, corresponding to the 4I 13/2 → 4I 15/2 transition as an alternative mode of operation, rapid depopulation of the lower level must be occurring through pump ESA. 9.6.8 Amplification Using Erbium-Doped Fluoride Glass Fibers Erbium-doped fiber amplifiers are very important optical devices that allow significant improvements in 1530-nm telecommunications systems through the application of optical power amplifiers, signal repeaters, and low-noise preamplifiers (see Chaps. 10 and 11). Although the most common host material for the active fiber has been silica, usually codoped with germania or alumina, the fluoride glasses have shown promise as candidate host materials. Millar et al. [85] were first to demonstrate gain at 1.5 µm in an Er-doped fluoride fiber similar to the one shown in Table 6, which exhibited laser oscillation at 1.56 µm, except that the length was 25 cm. The results from this and other literature data are summarized in Table 7. The pump source was an argon-ion laser operating at 488 nm, whereas the signal was provided by a tunable InGaAsP diode laser. The plot of the gain against launched pump power for different signal wavelengths is shown in Figure 27. Small-signal gain coefficients of 0.056 dB/cm at 1525 nm were recorded when all the ions were inverted with 500 mW of launched pump power. Furthermore, gain was available from 1480 to 1600 nm. A gain of 15 dB at 1532 nm for 25 mW of launched pump power at 1482 nm has been observed [91]. The single-mode fiber was pumped with up to 25 mW by an InGaAsP Table 7 Amplification at 1.5 µm and 2.7 µm in Er-Doped Fluoride Glass Fibers Er concentration (ppmw)

Core/clad diametersa (µm)

Length (cm)

40/na 7.1/na 7.1/na 13/105

At 1.5 µm 250 500 500 At 2.7 um 1170 a

na, not available.

NA

Pump (nm)

Gain (dB)

Wavelength of maximum gain (µm)

Range of gain (µm)

Ref.

25 230 500

0.16 0.16 0.16

488 1482 1485

1.4 15.0 18.0

1.525 1.53 1.554

1.48–1.60 1.524–1.572 1.520–1.600

85 91 92

300

na

647

18.3

na

na

93

496

Sanghera et al.

Figure 27

Small-signal gain versus launched pump power at various signal wavelengths in a 25-cm HMF glass fiber doped with 250 ppm of Er. (From Ref. 85.)

MQW laser. The signal was provided by a tunable long external–cavity semiconductor laser operating at 1532 nm. The absorption coefficient of the fiber at the pump and signal were 4.5 dB/m and 13 dB/m, respectively. The noise figure F can be determined from the following equation: F⫽

2µ(G–1) G

(6)

where µ is the inversion parameter (µ ⫽ 1.68, and is related to the noise spectral density) and G is the gain (G ⫽ 13 dB for 20-mW pump power). This leads to an expected noise figure of approximately 5 dB, which compares favorably with values obtained from silicabased fiber amplifiers. Spirit et al. [92] reported gain between 1520 and 1600 nm in a fiber that was similar to, but longer than, the one used by Millar and France [91]. The pump was a commercial semiconductor laser operating at 1485 nm so that pumping was from the ground state 4 I 15/2 to the 4I 13/2 level. The signal was provided by one of two tunable external-cavity semiconductor lasers to cover the ranges 1525–1570 and 1570–1620 nm. The amplifier noise figure was 3.6 dB and the small-signal amplifier gain was 18 dB at 1554 nm at an output power of 0 dBm. The gain varied by less than 1 dB from 1534 to 1561 nm, and by less than 3 dB from 1530 to 1565 nm. This bandwidth compares favorably with the 40-nm, 3-dB bandwidth obtained in alumina co-doped silica, and it is significantly higher than the less than 10-nm bandwidth obtained in germanosilica fibers. Furthermore, power amplification using the erbium-doped fluoride fiber was demonstrated using a 2 Gbit/s directly modulated laser transmitter. For 28 mW of launched pump power, the signal input power of ⫺8.2 dBm was amplified by 12.2 dB to ⫹4.0 dBm. No loss was apparent after transmission of the amplified signal over 100 km of silica fiber. In addition to gain at 1.5 µm, small-signal gain has also been observed at 2.7 µm [93]. The fiber was doped with 1170 ppm of Er and pumped at 647 nm using a krypton ion laser. The signal was provided by an HF laser tunable between 2.55 to 2.95 µm, and the input signal power was kept constant at ⫺16 dBm. The gain increased as a function

497


of pump power from 50 to 250 mW. The net gain increased as the signal wavelength decreased from 2.823 to 2.795, to 2.727 nm, and to 2.707 nm. Also, the 3-m–fiber amplifier exhibited gain saturation for pump powers of about 200 mW owing to incomplete absorption of the pump output by the fiber. This situation can be remedied by increasing the fiber length. A maximum gain of 18.3 dB was obtained. With 200 and 250 mW of pump power, the saturation power was approximately 2 mW; with a 150-mW–pump power, it was about 1.3 mW.

9.7 ERBIUM IN CHALCOGENIDE GLASSES The spectroscopy of erbium in chalcogenide glasses has been investigated extensively. Reisfeld and Bornstein first studied the visible and near-IR transitions of Er in GLS and ALS glass [94,95]. Fluorescence at 660, 822, 860, and 987 nm was observed corresponding to the transitions 4F9/2 → 4I 15/2; 4I 9/2 → 4I 15/2; 4S 3/2 → 4I 13/2; and 4I 11/2 → 4I 15/2, respectively. Radiative lifetimes were determined by the Judd–Ofelt theory and experimental lifetimes measured at room temperature and 77 K. The experimental lifetimes are summarized in Table 8. Ye et al. [96] have measured emission and absorption spectra and lifetimes of the lower-lying energy levels of Er in GLS glass. Fluorescence spectra of the 1.54-µm 4 I 13/2 → 4I 15/2 transition and the 2.7-µm 4I 11/2 → 4I 13/2 transition were reported as well as lifetimes of the 4I 13/2, 4I 11/2, 4I 9/2, and 4F9/2 levels. These measured lifetimes were 2.3, 1.23, 0.59, and 0.10 ms, respectively. Under 1.54-µm pumping, upconversion was observed to the 4I 11/2 level. Ye et al. [97] proposed a potential 980-nm laser pumped at 1.480 µm based on their measured spectroscopic values. Such a laser could find application as an in-line 980-nm pump source for EDFA amplifiers. It would take advantage of the low loss of the 1.480-µm pump and of the low noise factor of the 980-nm pump. Shaw et al. [98] and Schweitzer et al. [99] have studied the mid-IR transitions of Er in BIGGS (barium-indium-gallium-germanium sulfide) glass and GLS glass, respectively. The mid-IR transitions of interest for erbium in chalcogenide glass include the 4 I 11/2 → 4I 13/2 transition at 2.7 µm, the 4I 9/2 → 4I 11/2 transition at 4.5 µm, and the 4F9/2 → 4 I 9/2 transition at 3.5 µm. Both groups report similar lifetime and emission cross sections for the 4.5- and 3.5-µm transitions. Lifetimes of 500 and 100 µs and emission cross sections of 0.25 ⫻ 10⫺20 cm2 and 0.45 ⫻ 10⫺20 cm2 were found for the 4I 9/2 → 4I 11/2 and 4 F9/2 → 4I 9/2 transitions, respectively, for Er in BIGGS glass [98]. Lifetimes of 590 and 100 µs and emission cross sections of 0.25 ⫻ 10⫺20 cm2 and 0.43 ⫻ 10⫺20 cm2 were found for the 4I 9/2 → 4I 11/2 and 4F9/2 → 4I 9/2 transitions, respectively, for Er in GLS glass [99]. The fluorescence spectra of these two transitions are shown in Figure 28.

Table 8 Experimental Lifetimes of Er3⫹ in Chalcogenide Glassesa Glass ALS GLS GLS BIGGS a b

4

I13/2(µs) na na 2300 na

na, not available. 77 K.

4

I11/2(µs) na na 1230 na

4

I9/2(µs) b

232 262/297b 590 500

4

F9/2(µs) b

190/190 161/161b 100 100

Ref. 94,95 94,95 97,99 98

498

Figure 28

Sanghera et al.

Room temperature mid-IR fluorescence spectra of Er 3⫹ in BIGGS glass.

9.8 ERBIUM IN TELLURITE GLASS FIBERS Mori et al. [100] have demonstrated signal amplification and laser operation at 1.56 µm in Er-doped tellurite glass fibers. EDFAs based upon these glasses offer the advantages of potential broader band operation than is possible in silica-based EDFAs, because the emission cross section is larger over the whole wavelength region than that of Er in fluoride or silica (Fig. 29). By comparison, the cross section at 1600 nm is larger than that of Er in fluoride or silica glass by a factor greater than 2.

Stimulated emission cross section spectra of Er 3⫹ in Al/P-doped silica, in fluoride glass, and in tellurite glass. The cross section in tellurite is larger than that in fluoride and silica by a factor of about 1.3. (From Ref. 100.)

Figure 29


499

Figure 30 A schematic representation of the electronic energy levels and transitions of Tm3⫹ in an HMF glass.

Amplification was achieved in an 85-cm length of single-mode tellurite fiber with a 3-µm core, a ∆n of 0.7%, and a transmission loss of 3 dB/m at 1.3 µm. Under 978-nm pumping, 16 dB of gain was achieved at 1.56 µm for a pump power of 130 mW. The gain coefficient was 0.29 dB/mW. The signal gain increased linearly as pump power increased, and the gain saturated beyond 120 mW of pump power. Laser operation was demonstrated under 978-nm pumping in the same fiber using the reflections off the fiber end faces to form the fiber cavity. Because of the high index of the core (n ⫽ 2.083), the Fresnel reflection at each end was high, about 12.3%. The laser threshold was 120 mW, and the slope efficiency was 0.65%. 9.9 THULIUM IN HEAVY-METAL FLUORIDE GLASS FIBERS The energy level diagram of Tm3⫹ is shown in Figure 7. More recent theoretical work [101] has shown that the 3F4 and 3H 4 levels are incorrectly labeled and that it is more appropriate to reverse their assignment. Figure 30 shows the correctly labeled electronic energy level diagram. Although the old assignment is still used in the literature, through tradition more than anything else, in this chapter we adopt the new assignment. 9.9.1 Thulium-Doped Fiber Lasers Thulium laser operation using resonant pumping was first reported in Tm3⫹:YLF, with a ruby laser to pump the 3H 6 → 3F3 transition [102]. Thereafter, alexandrite and diode laser

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pumping were used to attain laser oscillation at 2.3 µm [103,104]. This wavelength is close to the wavelength of minimum attenuation in ultralow-loss fluoride fibers, so that lasers and amplifiers operating close to this wavelength are highly desirable for potential future optical communications systems, which are projected to require CW output powers on the order of a few milliwatts. Furthermore, Tm can be pumped by high-power diode lasers, such as AlGaAs, owing to the strong ground-state absorption of Tm near 790 nm. Laser sources operating in the near-infrared can be expected to find applications in areas, such as sensing of gas molecules and in medicine. Thulium is a candidate for such applications, because it emits at wavelengths between approximately 1.6 and 2.1 µm and, therefore, covers the absorption bands of water vapor (1.88 and 1.91 µm), liquid water (1.94 µm), carbon dioxide (1.96, 2.01, and 2.06 µm), and methane (C-H overtone at 1.688 µm). The fiber laser data for the Tm-doped HMF glasses discussed in the following are summarized in Table 9. Thulium-doped heavy-metal fluoride fibers can lase on one of three distinct wavelengths from the same 3H 4 metastable level: about 2.3 µm to the 3H 5 level, 1.48 µm to the 3F4 level, and at 0.82 µm to the 3H 6 level. One or the other of these laser lines can be selected by choosing the proper reflectivity spectrum for the two laser mirrors. 9.9.2 Lasers at 2.3 ␮m The initial laser experiments using thulium were performed on a bulk ZBLAN glass approximately 1.5-cm long and doped with 1 mol% of Tm [76]. The sample was pumped with an alexandrite laser at 785 nm, with a pulse width of 200 ns, and exhibited laser oscillation at 2.25 µm. Absorption of 785-nm pump wavelength leads to excitation into the 3H 4 level from the 3H 6 ground-state level. Thereafter, decay from the 3H 4 level to the 3 H 5 level gives rise to the 2.25-µm emission (see Fig. 30). The lifetime of the upper laser level was determined to be 1.1 ms, whereas the lower 3H 5 level lifetime was significantly shorter, typically less than 10 µs. Hence, the 2.25-µm emission is not self-terminating. The lifetime of the 3F4 level was also measured to be 12 ms [76]. The threshold for the 2.25-µm emission was 2 mJ of pump energy absorbed by the sample, but when the absorbed energy reached 3 mJ, laser emission at 1.88 µm was observed, corresponding to the 3F4 → 3H 6 transition. This is due to rapid depopulation of the 3H 5 level by nonradiative relaxation to the 3F4 level. Visible fluorescence was also noted owing to upconversion processes. It can be reduced by using single-mode fibers, in which lower rare earth concentrations can be utilized because of the higher pump intensity. Lower rare earth concentrations lead to reduced upconversion, as the efficiency of upconversion increases as the square of the rare earth concentration. Following this preliminary work, Esterowitz et al. [105] observed laser oscillation at 2.3 µm in a 50-cm fluoride fiber using an alexandrite laser operating at 786 nm and 10-Hz frequency as a pump. The onset of pulsed laser oscillation occurred at a threshold pump energy of 25 µJ launched into the fiber. The lifetime of the upper laser level was determined to be 1.55 ms. According to Esterowitz et al. [105], in a four-level system such as this one, CW operation should occur at 16 mW because the threshold pump power is given by the pulsed threshold energy divided by the fluorescence lifetime. Subsequent excitation using a laser diode array at 787 nm led to CW operation at 2.29 µm with a threshold of 6 mW [106]. Unfortunately, the core of this fiber was elliptical and scattering loss was high, about 100–200 dB/km at 0.63 µm. Therefore, improvements in fiber quality should further enhance the laser performance. Allen and Esterowitz [107] have pumped

b

a

1,000 1,000 1,000 1,250 740 740 740 740 1,250 1,250 1,250 1,250

Tm concentration (ppmw) 15/150 15/150 15/150 7.2/na 40/80 40/88 40/80 40/80 7.2/na 7.2/na 7.2/na 7.2/na

Core/clad diameter (µm) 50 35 35 150 86 86 86 30 150 177 150 150

Length (cm)

Tm-Doped Fluoride Glass Fiber Lasersa

na, not available. Output coupler reflectivity at the laser wavelength.

2.3 2.29 2.3 2.35 2.305 2.0, 1.96 1.942 1.972 1.88 1.51 1.48 0.82

Laser output (µm)

Table 9

0.122 0.122 0.122 0.186 0.16 0.16 0.16 0.16 0.186 0.186 0.186 0.186

NA 786 787 790 676.4 791 791 791 795 676.4 647.1 676.4 676.4

Pump (nm) 50 99.7 98 na 97 99 97 99 na na na na

Output coupler (%R)b 16 6 4 31 115 75 115 40 50 6 40 45

Threshold (mW) na na 10.0 3.8 18.8 5.3 8.3 0.3 3.3 na Poor 1.6

Efficiency (%) na 0.05 0.95 2.2 27.0 8.0 13.0 0.2 1.3 6.0 0.01 0.5


na 12 17 na 275 225 275 100 na na na na

Launched pump power (mW)

105 106 107 108 84 84 84 111,84 110 114 110 110

Ref.


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The output power at 2.3 µm as a function of launched pump power in a Tm3⫹-doped HMF glass fiber laser with a 2% output coupler. (From Ref. 107.)

Figure 31

similar fibers with a GaAlAs diode laser at 790 nm (Fig. 31) and observed thresholds of 4 mW and slope efficiencies of approximately 10% for less than 10 mW of launched pump power. Approximately 1 mW of output power was obtained, but saturation occurred at about 13 mW or more of launched pump power. The saturation is most likely caused by bottlenecking due to the rapid depopulation of the 3H 5 level to the long-lived 3F4 level. The population above threshold of the 3F4 level, N(3F4), can be obtained as follows for an optically thin medium [107]: N(3F4) ⫽ N 0(1 ⫹ P sat /P p)⫺1

(7)

where P sat is the saturation power, P p is the pump power above threshold, and N 0 is the total ion concentration. Furthermore, P sat is given by: P sat ⫽ hυ pA/(σ pτ)

(8)

where hυ p is the pump photon energy (2.5 ⫻ 10⫺19 J), A is the fiber core radius (7.5 µm), σ p the pump absorption cross section (3.5 ⫻ 10⫺21 cm2), and τ the lifetime of the 3F4 level (9.8 ms). Substituting the appropriate values into the equations gives a saturation power of approximately 13 mW, comparable with the data in Figure 31. The authors also report the tuning range of their system to be close to 2.2–2.5 µm based on the emission spectrum [107]. Continuous-wave laser oscillation has also been demonstrated at 2.32 µm with a threshold of 31 mW, a slope efficiency of 3.8%, and a maximum output power of 2.2 mW, limited by the pump power (200 mW) [110]. Unlike the result of Allen and Esterowitz [107], saturation of the output power was not present. This may be related to the choice of pump source [107]: 676.4 nm compared with 790 nm. The former pump wavelength causes excitation into the 3F3 level (see Fig. 30). The branching ratio of the 3F3,


503

The fluorescence (outer curve) and laser (inner curve) spectra close to 2.3 µm of Tm3⫹ in HMF glass. The laser spectrum was measured at 1.64 times above threshold. (From Ref. 110.)

Figure 32

F2 → 3H 4 transition is low; therefore, 790-nm pumping is more efficient simply because it pumps into the 3H 4 level directly. The tuning range was similar to that described [107], approximately 2.2–2.45 µm (Fig. 32). An attempt by Smart et al. [84] to induce laser oscillation by laser diode pumping was unsuccessful owing to the high fiber threshold and the low pump power availability (approximately 100 mW). Instead of a laser diode, they used a Ti:sapphire laser as a pump source, which allowed excitation wavelengths to be tuned over the entire 3H 6 – 3H 4 absorption band, unlike the diode laser where temperature tuning only allowed pump wavelengths as short as 795 nm. They observed laser oscillation at 2.305 µm with a threshold of approximately 115 mW and a slope efficiency of 18.8%. They did not observe the saturation of output power reported by Allen and Esterowitz [107]. They attributed this to laser emission from the 3F4 → 3H 6 (1.88-µm emission), which rapidly removed population from the 3F4 level to the ground state. Laser diode pumping has been achieved by McAleavey et al. [108]. The authors reported 2 mW of output power with a high slope efficiency at 2.31 µm by pumping with a low-power diode laser operating at 785 nm. Recently, McAleavey et al. [109] have demonstrated a narrow-linewidth tunable Tm3⫹-doped fiber laser with a tuning range of 140 nm and a linewidth smaller than 210 MHz. Such lasers are of great interest for hydrocarbon gas sensing. 3

9.9.3 Lasers at 1.9 ␮m Laser oscillation at 1.88 µm has been demonstrated with an output power of 1.3 mW by pumping with a krypton ion laser at 676.4 nm [110]. The threshold was 50 mW of launched pump power and the slope efficiency 3.3%. The 1.9-µm emission arises from the 3F4 → 3 H 6 transition shown in Figure 30. The authors found that the tuning curve more or less reproduced the fluorescence curve when the laser was pumped 1.7 times above threshold, and that laser operation could be tuned between 1.84 and 1.94 µm. As mentioned previously, Smart et al. [84] were unsuccessful in producing 2.3-µm

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lasers with a diode laser pump and low-output couplers (⬎1% transmission). They found a similar result when trying to obtain laser oscillation near 2 µm. This problem was alleviated using a Ti:sapphire laser operating at 791 nm, which supplied a higher pump power than the diode laser. They observed laser outputs ranging from 2.0 to 1.96 µm depending on the output coupler transmission, which ranged from 1 to 10%. These variations in laser wavelengths were due to the wavelength dependence of the mirror reflectivity. Carter et al. [84,111] have used diode laser pumping at 795 nm to obtain CW operation at 1.972 µm with a threshold of 40 mW of launched power (or 20 mW of absorbed power) and a slope efficiency of 0.3% when the mirror transmissions were smaller than 1%. The maximum output power from their diode laser was approximately 100 mW, yielding 200 µW of output power. Interestingly, the 1.972-µm output falls outside the tuning range of 1.84–1.94 µm quoted by Allain et al. [110]. Overall, the tuning range in a fluoride matrix is expected to be narrower than in silica (1.78–2.056 µm [112]) as the fluorescence linewidth is narrower in fluoride than in silica. The low slope efficiency (0.3%) found here arises from the small branching ratio for Tm3⫹ ions decaying to the 3 F4 level from the 3H 4 level. This is due to the low rate of nonradiative multiphonon decay from the 3H 4 level to 3H 5 level in fluorozirconate glass, compared with that of silica, which is directly related to the lower phonon energy of the fluoride matrix. Therefore, approximately 90% of the excited Tm3⫹ ions in the 3H 4 level decay radiatively to the 3H 6 ground state, whereas only about 10% decay to the 3F4 laser level [113]. Consequently, the threshold for laser oscillation is increased by a factor of about 10, and the slope efficiency is decreased by a similar factor. However, the threshold can be reduced by using a single-mode fiber. The slope efficiency can be improved by using a higher Tm concentration or by allowing simultaneous operation at 2.3 and 1.9 µm. The first approach allows a crossrelaxation mechanism to take place between neighboring Tm ions. This is the same mechanism as the energy transfer upconversion described earlier. In this manner, the radiative emission from an ion in the excited 3H 4 level, which decays to the 3F4 level, is absorbed by an adjacent Tm ion, which is thus excited from the ground state (3H 6) to the upper laser level (3F4). Thus, two ions end up in the upper laser level for each absorbed pump photon; consequently, the pumping efficiency is enhanced. In the second approach, using simultaneous laser oscillation at 1.9 and 2.3 µm, pumping at n times above threshold, increases the branching ratio of the 3H 4 → 3H 5 transition, and increases the decay to the 3 F4 level by a factor of n. By changing the mirrors in their laser resonator, Smart et al. [84] observed laser oscillation at both 2.305 µm and 1.942 µm. The laser at 1.942 µm had an increased slope efficiency of 8.3% and a threshold of approximately 115 mW of launched power. However, the authors do not rule out the possibility that the increased slope efficiency may be due to the reduced loss of the resonator. 9.9.4 Lasers at 1.51 ␮m Laser oscillation has been observed at 1.51 µm using a single-mode fluoride fiber cooled to 77 K and pumped at 647.1 nm [114]. Laser operation at 1.51 µm occurs by a multiphoton absorption mechanism, whereby initial absorption of a 647.1-nm photon causes excitation from the ground-state 3H 6 to the 3F3 level (see Fig. 30). Deexcitation then occurs from the 3 F3 level to the 3H 4 level by nonradiative relaxation, followed by absorption of a pump photon (ESA) into the 1D 2 level. Decay from the 1D 2 level to the 1G 4 level is radiative and gives rise to the 1.51-µm emission. Up to 6 mW of output power has been achieved.


505

9.9.5 Lasers at 1.48 ␮m Allain et al. [110] have shown laser oscillation at 1.48 µm in a single-mode fiber pumped at 676.4 nm. The emission at 1.48 µm arises from a four-level system, specifically from the 3H 4 → 3F4 transition (see Fig. 30). Absorption of a pump photon causes excitation from the ground-state 3H 6 to the 3F3 level (which is in equilibrium with the 3F2 level). Nonradiative decay from 3F3 to 3H 4 is followed by radiative emission from 3H 4 to 3F4, giving rise to the 1.48-µm emission. As the lifetime of the upper level (1 ms) is shorter than that of the lower level (10 ms), this transition should be self-terminating. This effect accounts for the high threshold power of 40 mW and the very low slope efficiency. However, the efficiency of this laser can be significantly improved by lowering the lifetime of the lower level (3F4) by changing the mirrors to allow co-oscillation at 1.9 µm on the 3 F4 → 3H 6 transition. Co-oscillation effectively depopulates the lower level 3F4, thereby increasing the slope efficiency of the 1.48-µm CW laser to 1.6%. The threshold was 63 mW and the maximum output power 0.2 mW. The tunability in this region ranges from 1.46 to 1.51 µm. The laser emission and fluorescence spectra are somewhat shifted, presumably because signal ESA appears to operate on the short wavelength side of the laser spectrum. Signal ESA is highly likely from 3F3 to 1G 4 because the energy difference between these two levels falls on the short wavelength side of the 3H 4 → 3F4 transition. Percival et al. [115] attempted to increase the efficiency of the 1.48-µm fiber laser by co-doping the glass with terbium. Using a fiber doped with 0.1% Tm and 1% Tb, the authors observed a minimum threshold of 5.5 mW and a maximum slope efficiency of 16%, corresponding to a photon conversion efficiency of 30%. The relatively low output efficiency was due to an energy match between thulium and terbium, which resulted in blue emission by upconversion. 9.9.6 Lasers at 0.82 ␮m Continuous-wave laser oscillation at 0.82 µm by pumping a single-mode fluoride fiber at 676.4 nm was first demonstrated in 1989 [110]. The laser had a threshold of 45 mW, a slope efficiency of 1.6%, and an output power of 0.5 mW. The tuning range was from 0.815 to 0.825 µm and could be improved by optimization of the cavity parameters. The 0.82-µm laser is from a three-level system. Initial absorption of a 676.4-nm photon leads to excitation to the 3F3 level. Nonradiative decay to the 3H 4 level is followed by radiative decay from 3H 4 to 3H 6 with the emission of a 0.82-µm photon. 9.9.7 Amplification Using Thulium-Doped Fluoride Glass Fibers Amplification at 1.46 and 1.65 µm has been achieved in Tm-doped HMF fibers. Amplification at 1.46 µm has been demonstrated by Sakamoto et al. [116] in a Tm–Ho ZBLAN fiber pumped at 0.79 µm. A maximum gain of 18 dB was achieved at 1.46 µm with 150 mW of pump power. The gain coefficient was 0.25 dB/mW. The 20-m fiber contained 0.05 wt% Tm and 1 wt% Ho, and had a 1.8-µm core diameter and a ∆n of 3.7%. By comparing the gain characteristics of the Tm–Ho co-doped fibers with fibers doped with Tm only, it was found that Ho3⫹ increased the gain and widened the gain spectrum. Amplifiers at 1.65 µm are of interest in optical transmission-line monitoring systems. Optical time-domain reflectometers (OTDRs) operating at 1.65 µm would allow testing of optical fibers transmitting at 1.3 and 1.5 µm without interruption of service. To this end, Sakamoto et al. [117] have demonstrated 35 dB of gain at 1.65 µm in a Tm-

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doped ZBLAN fiber. This amplifier utilizes the short-wavelength edge of the 3F4 → 3H 6 transition. A Tb-doped cladding was used to suppress ASE and laser oscillation in the 1.75- to 2.0-µm range. A gain efficiency of 0.75 dB/mW was achieved in a 2000-ppm Tm-doped ZBLYAN fiber with 4000 ppm of Tb doped in the cladding. The core diameter was 1.8 µm and the ∆n was 3.7%. Laser diodes at 1.22 µm were used as the pump source. The two-stage amplifier had a high gain of 35 dB at a pump power of 140 mW. Gain at 1.65 µm could not be achieved in a similar fiber with no Tb3⫹ doping in the cladding. This result demonstrates the effectiveness of ASE suppression by doping the cladding with Tb3⫹. 9.10 THULIUM IN CHALCOGENIDE GLASSES Shin et al. [118] have studied the spectroscopy of thulium in GAS (germanium–arsenic sulfide) and GGS (germanium–gallium sulfide) glasses. Four emission lines in the IR at 1.21, 1.45, 1.81, and 2.35 µm were reported, corresponding to the 3H 5 → 3H 6; 3H 4 → 3F4; 3 F4 → 3H 6; and 3H 4 → 3H 5 transitions, respectively. The large oscillator strengths and reduced multiphonon quenching of these transitions is promising for laser applications. Thulium in chalcogenide glass has also been studied as a sensitizer for holmium and dysprosium. Details of these studies are given in the following appropriate sections. 9.11 HOLMIUM IN HEAVY-METAL FLUORIDE GLASS FIBERS The fluorescence spectrum of Ho3⫹ contains nine major emission lines, corresponding to the transitions listed in Table 3. Although Ho-doped fluoride glass fibers have sustained laser operation, gain measurements have not yet been reported in the literature. 9.11.1 Holmium-Doped Fiber Lasers The electronic energy level diagram of Ho3⫹ is shown in Figure 33. To date, only six transitions have exhibited laser oscillation in Ho3⫹-doped fluorozirconate glass fibers in the infrared: at 3.9, 2.9, 2.08, 1.38, 1.2, and 0.75 µm. The characteristics of these lasers are listed in Table 10 and are discussed in the following. Other systems doped with Ho have exhibited laser oscillation. For example, pulsed laser operation by upconversion in BaY 2F8 co-doped with Yb and Ho has been obtained at 77 K [119]. Also, a 2.1-µm laser has been demonstrated in YAG [120] and in silica [121]. 9.11.2 Lasers at 3.9 ␮m Holmium-doped ZBLAN fibers have shown the longest wavelength laser oscillation to date at 3.9 µm on the 5I 5 → 5I 6 transition. Schneider et al. [122] have demonstrated CW operation of a fluorozirconate fiber doped with 2000 ppm of Ho and pumped at either 640 or 890 nm. Simultaneous laser action at 1.2 µm on the 5I 6 → 5I 8 transition was used to deplete the lower laser level of the 3.9-µm laser transition. Laser operation was at 77 K, although laser operation could still be observed to 145 K. Under 890-nm pumping, a maximum power of 11 mW at 3.9 µm was achieved with an efficiency of 1.7% and an estimated launching efficiency of 50%. The 1.2-µm laser had a slope efficiency of 6.9% and a maximum CW output power of 70 mW. These results were obtained with 1.7 W of launched pump power.


Figure 33

507

The electronic energy levels and transitions of Ho3⫹ in ZBLAN glass. (From Ref.

123.)

9.11.3 Lasers at 2.9 ␮m Wetenkamp [123] has demonstrated laser oscillation in the range of 2.83–2.95 µm in a multimode fiber pumped at 640 nm with a dye laser. The threshold was 65 mW of absorbed pump power, and an output power of 12.6 mW was obtained with a 90% output coupler. This fiber laser was also pumped at 750 nm by a Ti:sapphire laser and exhibited a threshold absorbed power of 35 mW. The 2.9–µm laser emission arises from the 5I 6 → 5I 7 transition. Various pump wavelengths could be used to populate the 5I 6 level: for example, 488, 640, 750, and 890 nm. These wavelengths cause excitation into the 5F3, 5F5, 5I 4, and 5I 5 levels, respectively, all of which decay nonradiatively into the 5I 6 level (see Fig. 33). The lifetimes of the 5I 6 and 5 I 7 levels are approximately 3.2 and 13.4 ms, respectively; therefore, the transition is selfterminating. However, CW operation was obtained at both pump wavelengths (640 and 750 nm) by depopulation of the 5I 7 level due to ESA at the pump wavelength. For example, ESA at 750 (and 640 nm) causes excitation from the 5I 7 level into the 5S 2 (and 5 F4) level and the 5F3 level, respectively (see Fig. 33). This is substantiated by the observation of green fluorescence from the 5S 2 → 5I 8 transition. The efficiency of the 2.9-µm laser pumped at 640 nm was further demonstrated by the observation of CW operation without an output mirror (i.e., with only the 4% reflectivity of the fiber end face). This laser exhibited a threshold power of 290 mW, a slope efficiency of 4.4%, and a maximum output power of 10.2 mW. These results were obtained with a 2.2-m fiber. Laser oscillation was also observed in a 10-m fiber pumped at 640 nm. Although the threshold remained unchanged because all the power was absorbed for both fiber lengths, the slope efficiency

na 30/125 40/na 40/na na

na 220 50 50 na

na 0.15 na na na

NA

b

na, not available. Output coupler reflectivity at the laser wavelength. c Unless stated otherwise (here or in the text): launched pump power. d Absorbed pump power.

a

2,000 1,000 993 993 2,000

3.9 2.9 2.08 1.38 1.2

Length (cm)

Ho concentration (ppmw)

Laser output (µm)


Ho-Doped Fluoride Glass Fiber Lasersa

Table 10

890 640 488 488 890

Pump (nm) na 90 95 98 na

Output coupler (%R)b

Efficiency (%) 1.7 2.9d na 0.28 6.9

Threshold (mW) ⬃1,000 65d 163 1,120 na

11.0 12.6 na na 71.0


1,700 500d na na 1,700

Pump power (mW)c

122 123 124 124 122

Ref.

508 Sanghera et al.


509

The tuning range of a Ho3⫹-doped fiber laser pumped four times above threshold at 640 nm. (From Ref. 123.)

Figure 34

and the output power increased slightly because the shorter fiber happened to exhibit a higher loss. Pumping the longer fiber at 750 nm yielded an output power of 0.8 mW and a slope efficiency of approximately 1% for 114 mW of absorbed pump power. Pumping at 750 nm is not as efficient as it is at 640 nm because of the weaker absorption of the 5 I 4 level, although the threshold was still only 35 mW. This is attributable to more efficient population of the 5I 6 level by multiphonon transfer from the excited state (5I 4). Pumping with an 890-nm diode laser should improve the characteristics of the 2.9-µm laser, as absorption of the 5I 8 → 5I 5 transition is stronger. As shown in Figure 34, tuning with the 640-nm pump at four times the threshold power was achieved over a range of 2.83–2.95 µm, and the laser was CW over the entire range. Individual laser lines were discernible at about 5-nm intervals by using a rotational diffraction grating. The linewidth of each line was at most about 2 nm (limited by the resolution of the monochromator). Figure 34 shows a good match between the discrete laser lines and the fluorescence spectrum of a similar fiber. 9.11.4 Lasers at 2.08 ␮m Laser oscillation has been observed at 2.08 µm in a 50-cm, multimode fiber by pumping at 488 nm using an argon-ion laser [124]. The laser threshold was 163 mW of launched

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pump power. The absorption of pump light at this wavelength was high, approximately 6.3 dB. Initial absorption of 488-nm photons causes excitation into the 5F3 level. After subsequent relaxation to lower levels, the 2.08-µm laser emission arises from the 5I 7 → 5 I 8 transition. Because the 5I 8 level is the ground state, this is a three-level laser system. A laser with a similar threshold was also demonstrated using a 457.9-nm pump [124]. In both cases, at room temperature the laser did not run CW but pulsed. The pulse frequency was 3 kHz near threshold and increased above threshold. This behavior was attributed to self-sustained relaxation oscillations caused by intracavity saturable absorption. The origin of this effect could be simultaneous ESA of laser photons. 9.11.5 Lasers at 1.38 ␮m The 1.38-µm emission of Ho3⫹ is of practical importance for the 1.3-µm telecommunications window. Brierley et al. [124] demonstrated a CW laser at 1.38 µm by pumping at 488 nm. A launched pump power of 1.12 W was required to reach threshold, and the slope efficiency was 0.28%. They also observed fluorescence at 0.55, 0.75, 1.01, 1.19, and 1.35 µm. The 1.38-µm emission arises from a transition from the 5S 2 / 5F4 levels to the 5 I 5 level. Furthermore, the laser wavelength (1.38 µm) is longer than the peak of the fluorescence spectrum (1.35 µm).

9.12 HOLMIUM IN CHALCOGENIDE GLASSES Reisfield et al. have reported the visible and near-IR spectra of Ho in GLS and ALS glass [95,125]. Emissions near 660, 760, and 910 nm were observed. The emission at 910 nm is attributed to the 5I 5 → 5I 8 transition. Shin et al. [126] observed fluorescence at 1.2, 2.0, and 2.9 µm from Ho-doped GAS and GGS glasses. These fluorescence emissions correspond to the 5I 6 → 5I 8; 5I 7 → 5I 8; and 5 I 6 → 5I 7 transitions, respectively, in a GAS glass doped with 0.5 and 1.5 wt% Ho and pumped at 905 nm. The large radiative transition probabilities for the 2.9-µm transition and the low multiphonon quenching for this transition are promising for 2.9-µm laser development. Kim et al. [127] studied energy transfer between thulium and holmium in GGS to determine the effect of thulium co-doping on the 2.02-µm fluorescence of holmium. Under 798-nm excitation into the 3H 4 level of Tm3⫹, the intensity of the 2.02-µm emission of Ho3⫹ increased with increasing Tm3⫹ concentration, while keeping the Ho3⫹ concentration constant. When the concentration of Ho3⫹ was increased, while keeping the Tm3⫹ constant, the intensity of the 1.8-µm emission of Tm3⫹ decreased sharply, with a corresponding increase in the 2.02-µm emission of Ho3⫹. The lifetime of the 5I 7 level of Ho3⫹ also decreased with increasing Tm and Ho concentrations. Lifetimes ranged from 4.1 to 2.6 ms. Rate equation modeling was utilized to determine the Tm–Ho energy transfer rate and the backtransfer rate. Figure 35 shows the energy transfer rate dependence on the Ho concentration in a Tm–Ho co-doped sample of GGS glass when the Tm concentration was kept at 1.0 wt%. Kim et al. calculated the emission cross section of the 5I 7 → 5I 8 transition to be 1.54 ⫻ 10⫺20 cm2. This value is three times larger than that of Ho in ZBLAN glass. It indicates that Ho in chalcogenide glass may produce more efficient lasers than in fluoride glass.


511

Dependence of energy transfer rates between (a) Tm3⫹ → Ho3⫹ and (b) Ho3⫹ → Tm3⫹ with increasing Ho3⫹ (acceptor) concentrations. Lines are drawn as guides to the eye. (From Ref. 127.)

Figure 35

9.13 PRASEODYMIUM IN HEAVY-METAL FLUORIDE GLASS FIBERS 9.13.1 Praseodymium-Doped Fiber Lasers Most of the work on HMF glass fiber lasers and amplifiers reported in the literature has dealt with the more commonly used rare earth ions, namely Nd 3⫹, Er 3⫹, Tm3⫹, and Ho3⫹. However, more recently, laser oscillation has been demonstrated in a praseodymium (Pr)doped HMF glass fiber [128]. Although Pr 3⫹ exhibits numerous fluorescence lines (see Table 3 and Fig. 36), only two transitions, at 885 and 910 nm, have demonstrated laser

Figure 36 Pr 3⫹ exhibits numerous fluorescence lines but only two transitions (885 and 910 nm) have demonstrated laser oscillation in the infrared.

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Table 11 Pr-Doped Fluoride Glass Fiber Lasers Laser wavelength (nm) 885 910

Threshold (mW) 600 590

Transition

Tuning range (nm)

P1 → 1G4 P0 → 1G4

880–886 902–916

3 3

Source: Ref. 128.

oscillation in the infrared. These transitions are shown in Table 11, along with the laser thresholds and tuning ranges. For comparison, only the 888-nm and 1080-nm laser wavelengths were reported in silica [129]. The fluoride fiber core diameter, fiber length, and refractive index difference were 12 µm, 60 cm, and 0.013, respectively. The fiber was doped with 1200 ppm Pr and pumped at 476.5 nm using an argon-ion laser. Absorption of 476.5-nm photons causes excitation into the 3P 0 level (see Fig. 36). The energy difference between the 3P 0 level and the 3P 1 level just above it is only about 600 cm⫺1, and the relative population of these two levels, obtained by the Maxwell–Boltzmann distribution law, is approximately 95 and 5%, respectively. This contributes to the observed fluorescence spectrum, in which each emission line from the 3P 0 level is accompanied by a weaker, blue-shifted line from the 3P 1 level. Furthermore, the lifetimes of both levels are 15 µs [128]. The emissions at 885 and 910 nm arise from the 3P 1 and 3P 0 levels, respectively. In addition, the line at 885 nm exhibits only two unique output wavelengths—880 and 886 nm—whereas all the other emissions show fine structure. Reducing the reflectivity of the output mirrors leads to increased output powers at the expense of higher threshold powers, although this situation can be improved by using a single-mode fiber with lower loss. 9.13.2 Praseodymium-Doped Fiber Amplifiers Perhaps the most important outgrowth of rare earth doped HMF glass research is the development of the praseodymium-doped fluoride fiber amplifier (PDFA) operating in the second telecommunication window at 1.31 µm where the dispersion of silica is minimum. The majority of the world’s fiber-optic communication systems operate in this window, and there is a strong need for an efficient optical amplifier in this region. Since the first demonstration of gain in 1991, the demand for this market has moved these devices from the laboratory to the commercial sector. Today, companies are beginning to offer highgain PDFAs as part of their product line. Owing to the large amount of work on the development and optimization of PDFAs over the years, this section will concentrate on the material’s development of PDFAs. A more complete summary of PDFA development can be found in Chapter 12. The PDFA operates on the 1G 4 → 3H 5 transition of Pr 3⫹. In a standard silica host, this transition is quenched nonradiatively; consequently, an amplifier is not viable. Owing to the lower phonon energy of HMF glass, the transition is active and fluorescence is possible from this transition. Quantum efficiencies of approximately 3% have been measured for Pr in ZBLAN glass. The earliest successful operations of a Pr-doped HMF optical amplifier at 1.3 µm


513

were reported by Ohishi et al. [130], Durteste et al. [131], and Carter et al. [132]. They observed modest gains at 1.3 µm in Pr-doped ZBLAN fibers. Ohishi et al. [133] were the first to demonstrate a high-gain and a high-output saturation in a PDFA. They reported a gain of 30.1 dB at 1.309 µm with a gain coefficient of 0.04 dB/mW and a saturation output power of 13 dBm in a ZBLAN fiber doped with 500 ppm of Pr. The Pr-doped fiber was 23-m long and had a core diameter of 3.3 µm, a cutoff wavelength of 0.65 µm, and a ∆n of 0.6%. Later on, Miyajima et al. [134] demonstrated 38.2-dB amplification at 1.31 µm in a ZBLAN fiber doped with 2000 ppm of Pr and pumped with 300 mW at 1.017 µm. The fiber core diameter was 2.3 µm, the cladding diameter was 125 µm, the cuffoff wavelength 1.26 µm, and the ∆n was 3.8%. Approximately 8 m of fiber was used in this demonstration. The gain coefficient was 0.21 dB/mW at 100 mW of pumping. Since then, significant improvements have been made on the fiber quality and on optimizing the fiber NA and the Pr concentration to maximize the fiber amplifier performance. Today, typical performance exceeds 30 dB of small-signal gain at 1.31 µm, and system demonstrations indicate that the PDFA offers excellent operational characteristics [135]. Research has continued on the material properties and on improving the efficiency of PDFAs, which is limited by the inherently low quantum efficiency and low absorption coefficient of the 1G 4 level of Pr in ZBLAN. Research includes development of alternative HMF fluoride glasses and chalcogenide glasses with increased quantum efficiency. Work on chalcogenide glass is detailed in the next section. The most significant development of alternative HMF compositions is the work of Nishida et al. [136], who have demonstrated amplification with a single-pass gain coefficient of 0.36 dB/mW in a Pr-doped high-NA PbF2 /InF3 fluoride fiber. The quantum efficiency in these fibers is twice that of ZBLAN fiber (6.1% compared with 3.4% in ZrF4-based glasses), and it yielded the highest gain coefficient in HMF fibers to date. A small-signal gain of 22.5 dB was achieved at 1.3 µm with 238 mW of pump power. These fibers have recently been used in a plug-in PDFA module for rack-mounted shelves [137]. Small-signal gains of 24 dB with a noise figure of 6.6 dB were achieved at 1.30 µm. Attempts have also been made to improve the pumping efficiency of Pr-doped amplifiers by co-doping the fiber with Yb as a sensitizer. Work by Allain et al. [138], Miyajima et al. [134], Ohishi et al. [139], and Xie et al. [140] indicate that Yb sensitization is possible. Co-doping with Er/Yb [141] and Nd/Yb [142] has also been explored. No highgain Pr co-doped fiber has yet been demonstrated. 9.14 PRASEODYMIUM IN CHALCOGENIDE GLASSES Praseodymium has received the most attention of all the rare earth dopants in chalcogenide glass owing to the 1G 4 → 3H 5 transition at 1.3 µm, which is important for telecommunication amplifier applications. Although praseodymium-doped fluorozirconate fiber amplifiers are commercially available, their efficiency is low. In contrast, chalcogenide glasses offer the advantage of larger radiative quantum efficiencies due to their lower phonon energy. Quantum efficiencies approaching 90% have been reported in chalcogenide glass fibers [143]. Another advantage is the increased oscillator strength of the 1G 4 → 3H 5 transition in chalcogenide glass because of the larger refractive index of this glass, which results in a larger emission cross section. The drawback is the slight shift toward longer wavelength of the Pr fluorescence peak away from the 1.31-µm telecommunication wavelength

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owing to the nephelauxetic effect. Nevertheless, fiber amplifiers developed from Pr-doped chalcogenide glasses are potentially more efficient than those based on fluorozirconate glasses because of this high relative quantum efficiency. Praseodymium in chalcogenide glass was first proposed as a potential 1.3-µm– amplifier material by Hewak et al. [10]. Since then, numerous researchers have studied this transition in a variety of chalcogenide glass compositions. Although many of the compositions show favorable spectroscopic properties for development of chalcogenidebased PDFAs, high fiber loss is the primary roadblock to successful fabrication of a fiber amplifier. The chalcogenide hosts studied by various groups include GLS [10,144], BGGS [145], CGSCl [15], GGS [143,146,147], GAS [143], GeSI [143,148], As-S [143,149,150] and GNS [16]. Table 12 summarizes the spectroscopic properties of the 1.3-µm transition of Pr in these glasses. Amplification at 1.34 µm has been demonstrated only by Tawarayama et al. [16] in Pr-doped GNS glass single-mode fiber. A gain of 30 dB was observed in a 6.1-m length of 750-ppm Pr-doped GNS fiber pumped at 1.0 µm with 100 mW of pump power. The gain coefficient was 0.81 dB/mW, which is the highest value reported for a Pr-doped amplifier. The loss of 1.3 dB/m in this fiber at 1.3 µm is the lowest yet reported for a rare earth doped single-mode chalcogenide fiber. The near-IR and mid-IR transitions of Pr in chalcogenide glass have also been studied for development of lasers, amplifiers, and sources in this region. Shaw et al. have reported fluorescence from the 3H 5, 3H 6, 3F2, 3F3, 3F4, and 1G 4 levels in the range from 1 to 5.5 µm in Pr-doped barium–indium–gallium–germanium–selenide (BIGGSe) glass [151] and modified germanium–arsenic selenide (m-GASe) compositions [152]. Figure 37 shows the fluorescence spectra of Pr in m-GeAsSe glass pumped at 1.0 µm. Because of the overlapping nature of many of these emission lines, the observed fluorescence is Table 12 Glass GLS BaGeGaS AsGaGeS CsGaSCl GeGaS GeGaS GeGaS GeSx GeAsS GeSI As2S3 As2S3 w/I As-S GNS a

Spectroscopic Properties of the 1.3-µm Transition of Pr3⫹ in Chalcogenide Glassesa Pr concentrationb

τ(µs)

η(%)

σe (⫻10⫺20 cm2)

σ eτ (⫻10⫺26 cm2s)

Ref.

⬍1000 ppm 0.01 mol% na 0.086 wt% PrCl3 500 ppm 100 ppm 100 ppm 100 ppm 500 ppm 350 ppm 350 ppm 350 ppm ⬍500 ppm 500 ppm

295 250 290 2460 360 377 320 360 322 360 250 277 250 370

58 43c 55c 24 70 71–93 59 90 12 82 na na na 56

na na na 0.198 1.33 na na na na na na na 1.05 1.08

250 na na 490 479 na 250d na na na na na 263 400

10, 144 145 145 15 146 143 147 147 143 143, 148 143 143 149, 150 16

na, not available. wt% of Pr2S3 (unless otherwise stated). c Value is radiative quantum efficiency of the 1G4 → 3H5 transition, which is equivalent to βη, where β is the branching ratio (β is approx. 0.5–0.6 for Pr3⫹ in chalcogenide glass). d Value is (σe ⫺ σESA). b


515

Figure 37

Room temperature mid-IR fluorescence spectra of Pr 3⫹ in m-GeAsSe glass pumped at 1.06 µm. The large band between 3.7 and 5.5 µm is attributed to mid-IR transitions originating from the 3 F4, 3 F3, 3 F2, 3 H 6, and 3 H 5 levels. Dips in this band are attributed to atmospheric CO 2 absorption and H-Se impurity absorption in the glass.

quite broad in the 3 to 5-µm wavelength region, and it is composed of transitions from all the lower-lying levels. This broad character lends itself well to high-brightness phosphor sources in the mid-IR region. Measured lifetimes and cross sections are listed in Table 13. They indicate that many of these transitions are promising for efficient mid-IR lasers and sources. Schweitzer et al. [153] have reported 3.4-µm emission on the 1G 4 → 3F4 transition in Pr-doped GLS glass. Other lines from the 1G 4 level were seen at 2.9, 2.1, 1.85, and 1.3 µm. Lifetimes and cross sections for these transitions in GLS glass are summarized in Table 13.

9.15 DYSPROSIUM IN CHALCOGENIDE GLASSES Figure 38 shows the energy level diagram for dysprosium. Dy-doped chalcogenide glass fibers have been proposed for optical amplifiers at 1.3 µm [154–156]. Amplification has been demonstrated at this wavelength with dysprosium in the low-phonon crystalline host LaCl 3 [157]. The transition of interest for amplification is from the 6H 9/2 – 6F11/2 doublet to the 6H 15/2 ground state. Because of the small energy gap of approximately 1800 cm⫺1, the transition is effectively quenched in oxide and fluoride glasses, and it is active only in the lower-phonon–energy chalcogenide glasses. Compared with Pr-based amplifiers, Dy-based amplifiers have several advantages for 1.3-µm telecommunication applications. First, numerous pump bands exist in the nearIR to populating the 6H 9/2 – 6F11/2 levels. Second, these pump bands have absorption coefficients more than ten times greater than that of the pump level (1G 4) of Pr 3⫹ in the same host. Third, the emission cross section from the 6H 9/2 – 6F11/2 levels is generally higher than

516

Figure 38

Table 13

Sanghera et al.

The electronic energy level diagram of Dy 3⫹.

Spectroscopic Properties of the IR Transitions of Pr3⫹ in Chalcogenide Glass

Glass

Transition

λ(µm)

τexp(ms)

β

η(%)

σe (⫻10⫺20 cm2)

Ref.

BIGGSe

3

H5 → H4 H6 → 3 H5 3 F3 → 3F2 3 F3 → 3H6 3 F3 → 3H4 1 G4 → 3F4 1 G4 → 3F3 1 G4 → 3 H5 3 H5 → 3 H4 3 H6 → 3 H5 3 F3 → 3F2 3 F3 → 3H6 3 F3 → 3H4 1 G4 → 3F4 1 G4 → 3F3 1 G4 → 3 H5 1 G4 → 3F4

4.9 4.5 7.2 4.8 1.6 3.4 3.0 1.3 4.9 4.5 7.2 4.8 1.6 3.4 2.9 1.3 3.4

2.5 0.29 0.10 0.10 0.10 0.18 0.18 0.18 7.0 4.1 0.23 0.23 0.23 0.21 0.21 0.21 0.295

1 0.45 0.0005 0.029 0.77 0.04 0.01 0.62 1 0.45 0.0005 0.029 0.77 0.04 0.01 0.62 na a

20 6 40 40 70 70 70 70 55 82 83 83 83 84 84 84 na a

4.3 1.4 0.1 2.6 5.0 1.3 0.2 2.0 4.3 1.4 0.1 2.6 5.0 1.3 0.2 2.0 0.86

151 151 151 151 151 151 151 151 152 152 152 152 152 152 152 152 153

3

m-GeAsSe

GLS a

na, not available.

3

517


Table 14

Spectroscopic Properties of the 1.3-µm Transition of Dy3⫹ in Chalcogenide

Glassesa,b Glass

Dy concentration

τ(µs)

η(%)

σe (⫻10⫺20 cm2)

σ eτ (⫻10⫺26 cm2s)

Ref.

GLS GLS GeGaS GeGaS GeAsS GeSI m-GeAsSe

500 ppm 1 mol% 500 ppm 0.1 wt% 0.1 wt% 0.1 wt% 1100 ppm Dy

59 25 38 38 20 45 310

29 6.9 16.8 13–17 4–9 8–12 90

3.8 na 4.35 na na na 2.7

220 na 165 na na na 864

154,155 158 156 143 143 143 159

a b

na, not available. wt% of Dy2S3 (unless otherwise stated).

that of the metastable level (1G 4) of Pr 3⫹ in the same host [154]. These factors promise much shorter devices and higher performance than is possible for Pr 3⫹-doped materials. Hewak et al. [155] were the first to study dysprosium for 1.3-µm optical amplifiers. Since then, the 1.3-µm transition of dysprosium has been studied in several chalcogenide hosts, including GLS [154,155,158], GGS [143,156], GAS [143], GeSI [143], and mGASe [159]. The spectroscopic properties of the 1.3-µm transition of Dy in these glasses are summarized in Table 14. Of these hosts, the m-GeAsSe-based composition shows the highest quantum efficiency, lifetime, and emission cross section for the 1.3-µm transition. The low quantum efficiency of the 1.3-µm transition in sulfide-based glass compositions can be attributed to more severe multiphonon quenching by the higher phonon energy of the sulfide host (⬃425 cm⫺1, compared with ⬃350 cm⫺1 for the selenide glass [160]). This higher quantum efficiency comes at the expense of greater residual absorption of the selenide host in the near-IR region. Although this larger absorption effectively negates the possibility of pumping into the higher-lying bands at 814 and 914 nm, the host absorption is minimal near 1.3 µm; consequently, in-band pumping near 1.3 µm is feasible. The absorption coefficient of the Dy pump band is still more than ten times larger than that for the Pr pump band at 1.01 µm. Gain has not yet been demonstrated in these materials owing to the high losses in fibers made with these glasses. Minimum losses of 4 dB/m at 4 µm have been reported in unclad oxygen-modified GLS fibers [99]. The lowest losses achieved for unclad mGeGaSe fibers are 2.4 dB/m at 1.5 µm and 0.82 dB/m at 6.6 µm [160]. Concerns have been raised over possible bottlenecking and ESA effects, which could hinder gain at 1.3 µm in Dy-doped chalcogenide materials [161]. Modeling of the theoretical performance of GLS fiber amplifiers indicates that the addition of Tb should prevent the bottlenecking effect. Modeling the performance of Dy-doped m-GASe fibers including bottlenecking and ESA effects indicates that gains as high as 40 dB are feasible with 100 mW of pump power [162]. The near-IR and mid-IR transitions of Dy in chalcogenide glass have been studied for possible lasers, amplifiers, and sources. Glasses studied include GLS [153,163], GASe [164], GGS [156,164], BIGGSe [98], and m-GASe [165]. Table 15 summarizes the spectroscopic properties of the near-IR and mid-IR transition of Dy in these glasses. Heo et al. [166] have studied the sensitizing effects of thulium on the 2.9-µm emis-

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Table 15

Sanghera et al. Spectroscopic Properties of the IR Transitions of Dy3⫹ in Chalcogenide Glassa

Glass

Transition

λ(µm)

τexp(ms)

β

η(%)

σe (⫻10⫺20 cm2)

Ref.

GLS

H13/2 → H15/2 H11/2 → 6H13/2 6 H11/2 → 6H15/2 6 H13/2 → 6H15/2 6 H11/2 → 6H13/2 6 H11/2 → 6H15/2 6 H13/2 → 6H15/2 6 H11/2 → 6H13/2 6 H11/2 → 6H15/2 6 H13/2 → 6H15/2 6 H11/2 → 6H13/2 6 H11/2 → 6H15/2 6 H13/2 → 6H15/2 6 H11/2 → 6H13/2 6 H13/2 → 6H15/2 6 H11/2 → 6H13/2 6 H11/2 → 6H15/2 6 H9/2-6F11/2 → 6H13/2 6 H7/2-6F9/2 → 6H13/2

2.9 4.3 1.8 2.9 4.3 1.8 2.9 4.3 1.8 2.9 4.3 1.8 2.9 4.3 2.9 4.3 1.8 2.3 1.8

3.6 1.3 1.3 4.55 0.728 0.728 6.0 1.13 1.13 6.0 1.13 1.13 na 0.4 5.9 2.3 2.3 0.32 0.03

1.0 0.86 0.14 1.0 0.154 0.846 1.0 0.16 0.84 1.0 0.115 0.885 1.0 0.18 1.0 0.15 0.85 0.08 0.32

57 7.4 44 86.0 32.8 32.8 90.4 38.4 38.4 81.8 38.4 38.4 na 7 ⬎90 79 79 ⬎90 9

0.92/1.16 1.17 0.57/0.64 na na na na na na 0.99 na 0.64 0.66 0.76 1.19 1.29 na na na

153, 163 153, 163 153, 163 164 164 164 164 164 164 156 156 156 98 98 165 165 165 165 165

6

6

6

GeAsS

GeGaS

GeGaS

BIGGSe m-GaAsSe

a

na, not available.

sion of dysprosium in chalcogenide glass. Efficient energy transfer was found between the excited thulium ion and the dysprosium ion. 9.16 TERBIUM IN CHALCOGENIDE GLASSES The energy level diagram of Tb3⫹ is shown in Figure 39. The mid-IR transitions of terbium have been studied by Shaw et al. [98] in BIGGSe glass and germanium–arsenic–telluridebased glasses (GAT). Interest in Tb is primarily due to its transitions in the 8- to 12-µm band from the 7F4 and 7F3 levels. In both hosts pumped at 2 µm, emission was observed at 4.8 µm on the 7F5 → 7F6 transition and at 3.0 µm on the 7F4 → 7F6 transition. Lifetimes of 180 µs were found for the 7F5 → 7F6 transition in both materials. Lifetimes of 90 and 180 µs were found for the 7F4 → 7F6 transition in BIGGSe and GAT, respectively. The fluorescence spectrum of these two transitions is shown in Figure 40. No emission was observed at 8.0 µm from the 7F4 level owing to the small branching ratio of this transition and limitations of the detection system. However, the 90- to 180-µs lifetime of the 7F4 level indicates that the transition is active in these glasses. The large calculated cross section of the 7F4 → 7F5 transition in these glasses opens the possibility for lasers at 8.0 µm. 9.17 MISCELLANEOUS Various groups have made contributions to the development of HMF, chalcogenide, and telluride fiber lasers in the IR. Some of these contributions are mentioned in the following. The reader is encouraged to consult the appropriate references for further information.


Figure 39

519

The energy level diagram of Tb3⫹.

Newhouse et al. [167] have studied the spectroscopic properties of the 1.3-µm transition of Pr-doped mixed halide glasses for optical amplifier applications. The cadmium– fluoride-based glass was composed of a mixture of chlorides and fluorides of Cd, Na, Ba, and K, with a fluorine anion ratio of 60% relative to the total anion content. The lifetimes of the Pr 3⫹-doped mixed halide glasses were 320 µs, compared with approximately 110 µs for a ZBLAN glass. Modeling indicated that a gain higher than 30 dB could be obtained with less than 150 mW of pump power. Unfortunately, these glasses are highly hygro-

Figure 40

The fluorescence spectrum of Tb in GAT glass.

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scopic and, therefore, are inappropriate for most practical applications. The development of appropriate hermetic coatings for these glasses has not been reported in the literature. Miura et al. [168] have demonstrated laser oscillation in Nd 3⫹-doped HMF glass microspheres. Laser action was observed at about 1.051 µm. The laser threshold was 5 mW for the 1.051-µm line, and 60 mW for the 1.334-µm, in 100-µm–diameter microspheres pumped at 800 nm. Single-frequency oscillation occurred when the exciting beam was ‘‘grazed’’ along the sphere. It was also observed that the laser wavelength could be shifted by changing the point of incidence on the sphere. Clare et al. [169] have shown that U3⫹-doped zirconium–fluoride-based glass exhibits a fluorescence peak close to 2.5 µm. This wavelength corresponds to the minimum loss of HMF fibers and could possibly be used as sources or amplifiers in a fluoride-based telecommunication network. One major problem is that the preferred oxidation state of uranium is 4⫹. The 3⫹ state required for this laser is only seen in reduced fluoride glasses, and reduced zirconium–fluoride-based glasses exhibit high scattering. On the other hand, alternative glasses, such as fluoroaluminates, do not contain reducible ions and may be more appropriate. Singh et al. [170] have studied the spectroscopic properties of Nd 3⫹ in various Nddoped tellurite glasses to determine the feasibility of a 1.06-µm fiber laser based on these materials. They found an emission cross section of approximately 9 ⫻ 10⫺20 cm2. From their calculations, they predict that the laser threshold for tellurite glasses under transverse pumping can be lower than that of Nd:YAG. Wang et al. [171] studied the 1.3-µm emission properties of Nd 3⫹-doped and Pr 3⫹doped tellurite-based glasses for optical amplifier applications. The fluorescence efficiency of the Pr 3⫹-doped tellurite glass increased with Yb co-doping. Bishop et al. [172–174] have studied the photoluminescence spectra of Pr 3⫹-, Er 3⫹-, and Dy3⫹-doped GASe glass, as well as Er 3⫹-doped As 2S 3 glass. A broadband photoluminescence excitation (PLE) spectrum was observed in these materials, which corresponded to absorption by below-gap defects and impurity-induced localized states in the host glass, and energy transfer to the rare earth dopants. Viens et al. [175] have reported luminescence at 1.08 µm in Nd-implanted As 2S 3 glass waveguides under pumping at 815 nm. As 24S 38Se 38 and As 2S 3 were used to produce multilayer waveguides and Nd 3⫹ was ion-implanted into the As 2S 3 layer. Such results are promising for the development of chalcogenide-based waveguide devices. 9.18 SUMMARY Since the first demonstration of laser oscillation in an Nd-doped HMF glass fiber in 1987, the field has grown tremendously. This effort has been spurred by the fact that infrared laser emissions in silica fibers are restricted to wavelengths shorter than 2 µm owing to multiphonon absorption. HMF glass fibers, which possess lower phonon energies, have demonstrated IR laser oscillation between 0.82 and 3.9 µm. Table 16 summarizes the laser oscillation and amplification wavelengths demonstrated to date in rare earth doped HMF glass fibers. Ho-doped HMF fibers have exhibited the longest laser oscillation wavelength of 3.9 µm. Laser oscillation has been reported in an Nd-doped HMF glass fiber with a quantum efficiency of 97%. This value is one of the highest reported for a fiber laser. Even more interesting is that this laser operated at 1.33 µm, a wavelength that has not been attained in Nd-doped silica fibers owing to pump ESA. Fiber amplifiers based on HMF glass have been developed at several wavelengths. Most notably, a 1.31-µm fiber amplifier is commercially available for telecommunication

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Table 16

The Wavelengths Demonstrated in a Laser or an Amplifier in HMF Glass Fibers

Rare earth ion Nd Er Tm Ho Pr Dy Tb

Laser oscillation wavelengths (µm)

Amplification wavelengths (µm)

1.05, 1.35 0.85, 1.00, 1.55, 1.7, 2.7 0.82, 1.48, 1.51, 1.9, 2.3 1.2, 1.38, 2.08, 2.9, 3.9 0.885, 0.91 — —

1.33 1.5, 2.7 1.46, 1.65 — 1.31 — —

applications with a typical small-signal gain in excess of 30 dB. Research and improvements will continue in the area of HMF glass fiber lasers and amplifiers as high-quality single-mode fluoride fibers and high-power laser diode pump sources become available. Furthermore, it is anticipated that other dopants and co-dopants will be investigated and both laser oscillation and amplification will be demonstrated at other wavelengths. More recent efforts have focused on the development of rare earth doped chalcogenide glasses and fibers, because of their even lower phonon energies compared with HMF glasses. Table 17 lists IR emission wavelengths as well as the wavelengths that have demonstrated laser oscillation and amplification in chalcogenide glasses and fibers. Although this is a relatively new area of research, a major result has already been obtained: a 1.3-µm fiber amplifier with higher performance than commercially available PDFAs. Also, preliminary laser oscillation has been observed at 1.08 µm. It is predictable that numerous other rare earth doped chalcogenide glass compositions will be developed, that other dopants and co-dopants will be explored, and that improvements will be made in the fabrication techniques of single-mode fibers. These advances will undoubtedly lead to the demonstration of many more laser wavelengths, especially at longer wavelengths. In addition, new and improved amplifiers will also become readily available. In summary, the area of rare earth doped low-phonon–energy glasses and fibers is anticipated to receive significantly more attention in the near future and continue to grow Table 17

The IR Emission Wavelengths and the Wavelengths That Have Exhibited Laser Oscillation and Amplification in Chalcogenide Glasses and Fibers

Rare earth ion Nd 3⫹ Er3⫹ Tm3⫹ Ho3⫹ Pr3⫹ Dy3⫹ Tb3⫹ a

Indirect evidence.

IR emission wavelengths (µm)

Laser oscillation wavelength (µm)

Amplification wavelength (µm)

0.786, 0.919, 1.08, 1.37 0.822, 0.860, 0.987, 1.54, 2.7, 3.5, 4.5 1.21, 1.45, 1.81, 2.35 0.76, 0.91, 1.2, 2.9, 3.9 1.3, 1.6, 2.9, 3.4, 4.5, 4.8, 4.9, 7.2a 1.3, 1.8, 2.3, 4.3 3.0, 4.8, 8.0a

1.08 — — — — — —

1.08 — — — 1.34 — —

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137. Y. Nishida, M. Yamada, J. Temmyo, T. Kanamori, Y. Ohishi. Plug-in type 1.3 µm fiber amplifier module for rack-mounted shelves. IEEE Photon. Techol. Lett. 9:1096 (1997). 138. J. Y. Allain, M. Monerie, H. Poignant. Energy transfer in Pr 3⫹ /Yb3⫹-doped fluorozirconate fibres. Electron. Lett. 27:1012 (1991). 139. Y. Ohishi, T. Kanamori, T. Nishi, S. Takahashi, E. Snitzer. Gain characteristics of Pr 3⫹ – Yb3⫹ co-doped fluoride fiber for 1.3 µm amplification. IEEE Trans. Photon. Technol. Lett. 3:990 (1991). 140. P. Xie, T. R. Gosnell. Efficient sensitization of praseodymium 1.31 µm fluorescence by optically pumped ytterbium ions in ZBLAN glass. Electron. Lett. 31:191 (1995). 141. B. J. Galagan, B. I. Denker, V. V. Motsartov, V. V. Osiko, S. E. Sverchkov. Erbium-sensitised glasses for praseodymium fibre laser amplifiers operating at λ ⫽ 1.3 µm. IEEE J. Quant. Electron. 26:105 (1996). 142. B. J. Galagan, B. I. Denker, L. N. Dmitruk, V. V. Motsartov, V. V. Osiko S. E. Sverchkov. Glasses for praseodymium laser amplifiers sensitized with neodymium and ytterbium. IEEE J. Quant. Electron. 26:99 (1996). 143. D. P. Machewirth, K. Wei, V. Krasteva, R. Datta, E. Snitzer, G. H. Sigel, Jr. Optical characterization of Pr 3⫹ and Dy3⫹ doped chalcogenide glasses. J. Noncryst. Solids 213–214:295 (1997). 144. D. W. Hewak, J. A. Medeiros Neto, B. Samson, R. S. Brown, K. P. Jedrzejewski, J. Wang, E. Taylor, R. I. Laming, G. Wylangowski, D. N. Payne. Quantum-efficiency of praseosymium doped Ga:La:S glass for 1.3 µm optical fibre amplifiers. IEEE Photon. Technol. Lett. 6:609 (1994). 145. R. S. Quimby, K. T. Gahagan, B. G. Aitken, M. A. Newhouse. Self-calibrating quantum efficiency measurement technique and application to Pr 3⫹-doped sulfide glass. Opt. Lett. 20: 2021 (1995). 146. K. Wei, D. P. Machewirth, J. Wenzel, E. Snitzer, G. H. Sigel, Jr. Pr 3⫹-doped Ge–Ga–S glasses for 1.3 um optical fiber amplifiers. J. Noncryst. Solids 182:257 (1995). 147. D. R. Simons, A. J. Faber, H. de Waal. Pr 3⫹-doped GeS x-based glasses for fiber amplifiers at 1.3 µm. Opt. Lett. 20:468 (1995). 148. V. Krasteva, D. Machewirth, G. H. Sigel, Jr. Pr 3⫹-doped Ge–S–I glasses as candidate materials for 1.3 µm optical fiber amplifiers. J. Noncryst. Solids 213–214:304 (1997). 149. Y. Ohishi, A. Mori, T. Kanamori, K. Fujiura, S. Sudo. Fabrication of praseodymium-doped arsenic sulfide chalcogenide fiber for 1.3-µm fiber amplifiers. Appl. Phys. Lett. 65:13 (1994). 150. J. Kirchoff, J. Kobelke, M. Scheffler, A. Schwuchow. As–S based materials and fibres towards efficient 1.3 µm fibre amplifiers. Electron. Lett. 32:1220 (1996). 151. L. B. Shaw, B. H. Harbison, B. Cole, J. S. Sanghera, I. D. Aggarwal. Spectroscopy of the IR transitions in Pr-doped heavy metal selenide glass. Opt. Express 1(4):87 (1997). 152. L. B. Shaw, B. Cole, D. T. Schaafsma, B. B. Harbison, J. S. Sanghera, I. D. Aggarwal. Rare earth doped selenide glass optical sources. Tech. Dig. of Conf. on Lasers and Electro-Optics 6:420 (1998). 153. T. Schweizer, D. W. Hewak, B. N. Samson, D. N. Payne. Spectroscopy of potential midinfrared laser transitions in gallium lanthanum sulphide glass. J. Lumin. 72–74:419 (1997). 154. D. W. Hewak, B. N. Samson, J. A. Medeiros Neto, R. I. Laming, D. N. Payne. Emission at 1.3 µm from dysprosium-doped Ga:La:S glass. Electron. Lett. 30:968 (1994). 155. B. N. Samson, J. A. Medeiros Neto, R. I. Laming, D. W. Hewak. Dysprosium doped Ga: La:S glass for an efficient optical fibre amplifier operating at 1.3 µm. Electron. Lett. 30:1617 (1994). 156. K. Wei, D. P. Machewirth, J. Wenzel, E. Snitzer, G. H. Sigel, Jr. Spectroscopy of Dy3⫹ in Ge–Ga–S glass and its suitability for 1.3 µm fiber-optical amplifier applications. Opt. Lett. 19:904 (1994). 157. R. H. Page, K. I. Schaffers, S. A. Payne, W. F. Krupke. Dy-doped chlorides as gain media for 1.3 µm telecommunications amplifiers. J. Lightwave Technol. 15:786 (1997).


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158. S. Tanabe, T. Hanada, M. Watanabe, T. Hayashi, N. Soga. Optical properties of dysprosiumdoped low-phonon-energy glasses for a potential 1.3 µm optical amplifier. J. Am. Ceram. Soc. 78:2917 (1995). 159. L. B. Shaw, B. J. Cole, J. S. Sanghera, I. D. Aggarwal, D. T. Schaafsma. Dysprosium doped selenide glass for 1.3 µm optical fiber amplifiers. Opt Fiber Communications, San Jose, CA, 1998; paper WG8. 160. B. Cole, L. B. Shaw, P. C. Pureza, R. Mossadegh, J. S. Sanghera, I. D. Aggarwal. Rare earth doped selenide glass fibers. J. Non-Cryst. Solids 256 & 257:253 (1999). 161. B. N. Samson, T. Schweizer, D. W. Hewak, R. I. Laming. Properties of dysprosium-doped gallium lanthanum sulfide fiber amplifiers operating at 1.3 µm. Opt. Lett. 22:703 (1997). 162. D. T. Schaafsma, L. B. Shaw, B. Cole, J. S. Sanghera, I. D. Aggarwal. Modeling of Dy3⫹doped GeAsSe glass for 1.3 µm optical fiber amplifiers. IEEE Photon. Technol. Lett. 10: 1548 (1998). 163. T. Schweizer, D. W. Hewak, B. N. Samson, D. N. Payne. Spectroscopic data of the 1.8-, 2.9-, and 4.3-µm transitions in dysprosium-doped gallium lanthanum sulfide glass. Opt. Lett. 21:1594 (1996). 164. J. Heo, Y. B. Shin. Absorption and mid-infrared emission spectroscopy of Dy3⫹ in Ge–As(or Ga)–S glasses. J. Noncryst. Solids 196:162 (1996). 165. L. B. Shaw, B. Cole, J. S. Sanghera, I. D. Aggrawal. Opt. Lett. (submitted). 166. J. Heo, W. Y. Cho, W. J. Chung. Sensitizing effect of Tm3⫹ on 2.9 µm emission from Dy3⫹doped Ge 25Ga 5S 70 glass. J. Noncryst. Solids 212:151 (1997). 167. M. A. Newhouse, R. F. Bartholomew, B. G. Aitken, L. J. Button, N. F. Borrelli. Pr-doped mixed-halide glasses for 1300 nm amplification. IEEE Photon. Technol. Lett. 6:189 (1994). 168. K. Miura, K. Tanaka, K. Hirao. Laser oscillation of a Nd 3⫹-doped glass microsphere. J. Mater. Sci. Lett. 15:1854 (1996). 169. A. G. Clare, J. M. Parker, D. Furniss, E. A. Harris, T. M. Searle. Applications. In: Fluoride Glass Optical Fibers. P. W. France, ed. CRC Press, Boca Raton, FL, 1990:249. 170. S. Singh, L. G. Van Uitert, W. H. Grodkiewicz. Laser spectroscopic properties of Nd 3⫹doped tellurite glass. Opt. Commun. 17:315 (1976). 171. J. S. Wang, E. M. Vogel, E. Snitzer, J. L. Jackel, V. L. da Silva, Y. Silberberg. 1.3 µm emission of neodymium and praseodymium in tellurite-based glasses. J. Noncryst. Solids 178:109 (1994). 172. D. A. Turnbull, S. Q. Gu, S. G. Bishop. Photoluminescence studies of broadband excitation mechanisms for Dy3⫹ emission in Dy:As 12Ge 33Se 55 glass. J. Appl. Phys. 80:2436 (1996). 173. S. Q. Gu, D. A. Turnbull, S. G. Bishop. Broad-band excitation of Pr 3⫹ luminescence by localized gap state absorption in Pr:As 12Ge 33Se 55 glass. IEEE Photon. Tech. Lett. 8:260 (1996). 174. S. Q. Gu, S. Ramachandran, E. E. Reuter, D. A. Turnbull, J. T. Verdeyen, S. G. Bishop. Novel broad-band excitation of Er 3⫹ luminescence in chalcogenide glass. Appl. Phys. Lett. 66:670 (1995). 175. J.-F. Viens, C. Meneghini, A. Villeneuve, E. J. Knystautas, M. A. Duguay, K. A. CerquaRichardson, S. Schwartz. Neodymium luminescence from ion-implanted As 2S 3 chalcogenide glass waveguides. OSA Tech. Dig. Ser. 11:249 (1997).

10 Erbium-Doped Fiber Amplifiers: Basic Physics and Characteristics E. DESURVIRE Columbia University, New York, New York

10.1 INTRODUCTION The field of erbium-doped fiber amplifiers (EDFAs) has, in a relatively short time, come to the forefront of research in fiber-optic technology. The abundant literature published every month and the growing number of conference papers on this subject indeed reveal a worldwide interest and an intense research effort in a domain that was little known only a few years ago. Not surprisingly, this recently appearing technology rests on concepts and achievements dating as far back as 1964, with the first amplification experiments in rare earth doped fiber lasers [1,2]. As early as 1974, following the development of GaAs semiconductor diode lasers, the first laser-diode-pumped fiber lasers were developed to achieve compact sources for optical communications [3]. The reduction of fiber transmission loss and the progress in reliability of InGaAs and InGaAsP diode lasers made in the 1970s led to the development of modern 1.3- and 1.55-µm fiber communication systems, thus leaving the field of rare earth doped fiber devices in the background. Semiconductor optical amplifiers were also investigated experimentally for increasing receiver sensitivity (as preamplifiers) or transmission length (as repeaters) and for multichannel amplification in communication systems. During the same period, however, much attention was given to nonlinear effects in single-mode fibers (e.g., Raman and Brillouin scattering, four-photon mixing) because of their potential for signal amplification, the standard silica-based optical fiber being the gain medium itself [4]. During the years 1982–1985, studies were continuing in the characterization of rare earth doped fibers, for lasers and amplifier applications [5] or for the investigation of photon echoes [6]. In 1985 Southampton University reported an extended vapor deposition process (i.e., modified chemical vapor deposition; MCVD) for the fabrication of single-mode rare earth 531

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doped fibers [7], leading to, among many other developments, the demonstration of erbium-doped fiber lasers (1986) [8] and traveling-wave amplifiers (1987) [9] operating near 1.5 µm. This first reported EDFA, pumped with a dye laser at 665 nm, exhibited a gain of 20 dB for 20 mW of absorbed pump power. From this period to the present, the field of EDFAs has gained considerable attention around the world and is still progressing at a rapid pace. In 1989 the first efficient laser-diode-pumped devices were reported [10,11], making possible numerous breakthroughs in 1.5-µm optical fiber communications [for a detailed review, see, e.g., Ref. 12]. In 1990, packaged Er fiber amplifier modules and related devices started to appear in the catalogs of optoelectronics component manufacturers. Such a rapidly expanding technology makes it clear that EDFAs are bringing about a revolution in communications systems [13]. This chapter reviews several aspects of erbium-doped fiber amplifiers, in an attempt to provide the reader with a comprehensive insight into their basic physics, principles of operation, and device performance. The systems applications are dealt with in detail in Chapter 12. This chapter has five main sections Section 10.2 describes the Er:glass laser system and related spectroscopic data. In Section 10.3, the basic equations modeling Er fiber amplifiers are derived. Section 10.4 deals with the analysis of EDFA noise and noise figure characteristics. Section 10.5 analyzes the spectral properties of the EDFA complex susceptibility as well as the effect of inhomogeneous broadening. The characteristics of gain, pumping efficiency, and saturation in the steady state and transient regimens are considered in Section 10.6. These sections can be read independently; Sections 10.3–10.5 are mostly theoretical, whereas Sections 10.2 and 10.6 focus mainly on experimental results and device characteristics. A large number of references are made to published work, to give an account as comprehensive as possible of the wide range of issues involved in the field of EDFAs, and of the experimental data now available, as well as to direct the reader toward relevant and in-depth study material. 10.2 DESCRIPTION AND SPECTROSCOPY OF THE ERBIUM–GLASS LASER SYSTEM A comprehensive review of the physical properties of erbium glass is beyond the scope of this chapter. Many books [see, e.g., Refs. 14–17] are dedicated to this complex subject, which is essentially based on the atomic physics description of rare earths (REs) in vitreous state hosts (Judd–Ofelt theory [17]), as well as on a large amount of spectroscopic studies of the radiative–nonradiative relaxation processes in RE glasses. A review of various spectroscopic investigation techniques of RE:glass can be found elsewhere [18]. However, some background of Er:glass spectroscopy is necessary for an understanding of the role played by the different laser parameters used in the EDFA theoretical models. This section includes a description of basic spectroscopic features and data relevant to silica-based Er:glass, showing that the Er3⫹ ion behaves in a way similar to a quasi-three-level laser system, which is used for the theory detailed in Section 10.3. The issues of inhomogeneous broadening in Er:glass are addressed in Section 10.4. Figure 1 is a diagram of the relevant Er:glass energy levels and associated transitions [19–22]. The two main processes contributing to the population of these energy levels are the radiative absorption or decay and the nonradiative decay, where the excitation energy is converted into one or several vibrational quanta (phonons) of the surrounding crystal lattice [17] (we overlook here other ion–ion interaction processes, such as nonradia-

Erbium-Doped Fiber Amplifiers

533

Figure 1 Energy level diagram of Er :glass showing the pump absorption bands, as well as the radiative and nonradiative transitions. The numbers correspond to the associated decay rates (s⫺1 ) measured for a variety of Er : glass samples. (From Refs. 19–22.)

tive energy transfers and cooperative upconversion). The one-phonon process is caused by random fluctuations of the crystal field associated with lattice vibrations, whereas the less probable multiphonon relaxation is related to a higher-order process [20]. Figure 1 shows the range of radiative and nonradiative rates in reciprocal seconds, measured on each level in various glasses, including silicate, germanate, and fluorophosphate types [20,21], and fluorozirconate or ZBLA glasses [22]. The levels are labeled with the spectroscopic notation 2S⫹1 L J where J is the total angular momentum [see, e.g., Ref. 16 for definitions]. Figure 1 shows that except for the ZBLA glasses, the relaxation process between the 2 H11/2 and 4 I 13/2 energy levels is strongly dominated by fast nonradiative decay, while the 4 I 13/2 → 4 I 15/2 transition near the 1.5-µm wavelength is 100% radiative, with a fluorescence lifetime of the order of 10 ms. Thus, a three-level system approximation is justified for Er:glass (other than ZBLA) where the ion is pumped from the ground level (A), or 4 I 15/2, to an excited level (C), and relaxes to the metastable level (B), or 4 I 13/2, which is characterized by a long fluorescence lifetime. The different pump wavelengths corresponding to the excited energy levels are shown in Figure 1. In pump excited-state absorption (ESA), the existence of resonant upper-energy levels (D) (not shown in Fig. 1) permits the absorption of pump light from the metastable level (B); this phenomenon occurs, in particular, at the 514- and 800-nm pump wavelengths [23,24]. The rate equations for the atomic populations are derived in Section 10.3. 10.2.1 Stark Levels In the presence of an external electric field perturbation, such as that caused by the crystal field of the glass host, the LSJ energy levels (J ⫽ half-integer) split into a maximum of

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Desurvire

J ⫹ 1/2 Stark components [16]; this maximum number being 8 and 7 for the ground (4 I 15/2 ) and upper (4 I 13/2 ) levels, respectively. The actual number of the Stark levels depends on the type of symmetry of the crystal field and increases with decreasing symmetry [16,25]. Knowing the Stark levels, it is possible to deduce the symmetry of the unknown crystal field. Low-temperature spectroscopic investigation by fluorescence line narrowing (FLN) in Er3⫹ alkali silicate glass [26] enabled a determination of five Stark components in each of the 4 I 13/2 and 4 I 15/2 manifolds, showing that in this glass Er3⫹ occupies a principal site with near-octahedral symmetry. The type of site corresponding to different Er ion coordination also varies with glass composition. Other studies have determined larger number of Stark levels in various types of silicate, fluoride, and fluorophosphate glass [27]. The Stark levels and related fluorescence and absorption transitions are shown in Figure 2 for aluminosilicate Er:glass [28]. The spectral positions of the transitions are

Figure 2

Energy level diagram of the 4 I 15/2and 4 I 13/2 Stark levels evaluated for Er-doped aluminosilicate glass with assignment of (a) fluorescence and (b) absorption transitions. (From Ref. 28.)


535

Figure 3 Absorption and emission cross section spectra at T ⫽ 295 K for an aluminosilicate fiber showing locations of the laser transitions Al–A12 (absorption) and F1–F12 (emission) assigned from the 4 I 15/2 → 4 I 13/2 energy level diagram of Figure 2. (From Ref. 28.)

indicated in Figure 3, which shows the room temperature fluorescence and absorption cross section spectra measured for this type of glass. As Figure 3 indicates, the fluorescence and absorption lines are closely spaced, thus having a strong spectral overlap, which is confirmed by the homogeneous broadening analysis detailed in Section 10.5. As seen in Figure 2, the Stark splitting of the ground and metastable states is about 250 cm⫺1, corresponding to an average spacing between adjacent Stark sublevels of ∆E ⬇ 50 cm⫺1. At thermal equilibrium, the ratio between two adjacent sublevel populations is exp (⫺∆E/kb T) ⫽ 0.78, which indicates that a large thermal population exists within each J manifold. Because the nonradiative decay rate between adjacent energy levels decreases exponentially with the energy gap [17,20], intramanifold relaxation leading to thermal equilibrium is a process much faster than the nonradiative decay occurring between adjacent J manifolds shown in Figure 1. 10.2.2 Cross Sections The emission and absorption cross sections σ a,e characterizing the 4 I 13/2 ⫺ 4 I 15/2 manifold of laser transitions are fundamental parameters for the EDFA. For electric-dipole transitions (as in RE: glass [17]), the Judd–Ofelt theory relates the integrated cross sections to the radiative transition probability A(L′S′; LSJ) ⫽ 1/τ rad (τ rad ⫽ fluorescence lifetime), which leads to the so-called Fuchtbauer–Ladenburg (FL) relation [29–33]: σ a, e (λ) ⫽

λ 4s I a, e (λ) 8πcn τ rad ∆λ aeff,e 2

(1)

where n is the medium refractive index and ∆λ aeff,e is an effective line width defined by: ∆λ aeff,e ⫽ ∫I a , e (λ)d λ

(2)

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Desurvire

where I a, e (λ) is the absorption or fluorescence spectrum with unity peak value. The use of Eq. (1) constitutes one out of four usual methods [32–37] for determining the cross sections which, for most, are not capable of better than 20% accuracy [32]. Indeed, it was observed that the value of the ratio σ a /σ e of Er :glass fibers, as calculated through the FL relation, disagrees with the experimental measurement of the absorption/gain coefficient ratio [38]. A recent study [39] based on McCumber’s theory [40] has shown, actually, that the Er3⫹ cross sections can be very accurately determined (within 3%), provided the electronic structure of the Stark sublevels is known; some approximations can be made with such a model, however, without use of the knowledge of the actual electronic structure, leading to a determination of cross sections far more accurate than is obtainable using the FL method [39]. We emphasize that throughout this chapter, the cross section values (such as plotted in Fig. 3) and theoretical expressions are based on the simpler approach of the FL method, which does not affect the validity of the theoretical models for the EDFA. Further discussions and analysis of the cross sections are given in Section 10.5. Spectroscopic studies of fluorescence and absorption in Er-doped preforms and fibers [23–25,42–47] are an important tool for understanding the role played by the glass co-dopant composition and stoichiometry in the fiber amplifier characteristics (gain spectrum and homogeneity, pumping efficiency, saturation intensity, and such), and many systematic studies remain to be done in this field. The study of homogeneous and inhomogeneous components in Er:glass, as detailed in Section 10.5, is also important for the modeling and analysis of saturation effects in EDFAs. 10.3 BASIC EQUATIONS FOR THE ERBIUM-DOPED FIBER AMPLIFIER Achieving a comprehensive theoretical model of the EDFAs is a complex task because of the wide range of issues associated with the basic physics of Er:glass, as well as the variety of experimental conditions. The evolution in fiber fabrication, waveguide design, and Er:glass materials makes theoretical models evolve as well. For instance, EDFAs based on silica glass have initially been described from three-level laser system approximations [see, e.g., Refs. 48–52], but the theory had to be extended to the case of the pump being in the 4 I 13/2 band (near 1.48 µm), at which the EDFA actually behaves similar to a quasi-two-level system [53]. On the other hand, with the development of EDFAs based on fluorozirconate glasses [54], where several excited-state levels can have long metastable lifetimes, the two- or three-level models do not apply. The theoretical descriptions of EDFAs found in the literature so far also make large use of approximations relevant to particular experimental conditions or types of study (e.g., gaussian approximation for mode envelopes, confined Er-doping, small-signal, or unsaturated gain regimen, and such). General rate equation descriptions of three- and four-level laser systems can be found [55–57]. Analyses of single- and multimode fiber lasers and amplifiers with three- and four-level RE ions have been developed [58–60]. Theoretical studies of the EDFA gain characteristics and gain optimization with waveguide and doping design [48–61], as well as comparisons between the different pump band efficiencies [62], are expected to expand as progress is made in alternative laser materials and EDFA designs. The purpose of this section is to show how such a complex multilevel laser system as Er: glass can eventually—within some simplifying assumptions—be described by basic equations that are


537

applicable to all pump bands, as well as to provide a background for the analysis developed in the following sections. The different types of approximation used in several theoretical studies may be a source of some confusion, because of the resulting variety of theoretical formulations. We provide here a most general formulation that can be applied to a broad range of studies. The EDFA basic equations generally need to be solved by numeric integration, as has been done in most studies so far [48–53]. Because of the nonlinear nature of the interaction between pump and signals in the EDFA, obtaining analytical formulations remains a challenge that is open to future work. However, there already exist analytical models for the EDFA that are useful to study the gain and saturation with bidirectional pump and signals [63] or to study the forward- and backward-amplified spontaneous emission (ASE) noise in the unsaturated gain regimen, that, in turn, can be used to model lowgain, distributed fiber amplifiers [64]. Such models are also described in this section. 10.3.1 Derivation of the Rate Equations of Quasi-Three-Level Systems The schematic energy diagram of a quasi-three-level system with Stark-split sublevels is shown in Figure 4. Let N A, N A, and N C be the total population density of the ground (A), upper (B), and pump (C) levels, respectively, with the relation N A ⫹ N B ⫹ N C ⫽ ρ, where ρ is the Er 3⫹ density. Each of the levels of population N D (D ⫽ A, B, C) is actually made of a manifold of g D Stark-split sublevels. In this section and Section 10.5, the indices j, k, and ᐉ will be used to number the sublevels of manifolds A, B, and C, respectively (i.e., j ⫽ 1 . . . g A, k ⫽ 1 . . . g B, ᐉ ⫽ 1 . . . g C ), and the populations of the sublevels will be denoted by N Dm (D ⫽ A, B, C; m ⫽ j, k, ᐉ ). The thermalization process within each manifold is characterized by the nonradiative rates A ⫹NR and A ⫺NR, which correspond the excitation or de-excitation of the Er 3⫹ ions, respectively, with absorption or creation of

Figure 4

Energy level diagram of a quasi-three-level system with Stark manifolds (A, B, C) of degeneracy g A, g B, g C, showing notations used in the text (see Sec. 10.3.)

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a lattice phonon (see Fig. 4). Thermal equilibrium within each manifold is represented by the condition: A ⫺NR NDm ⫽ A ⫹NR N D,m⫺1

(3)

with A ⫹NR /A ⫺NR ⫽ exp[⫺(E m ⫺ E m⫺1 )/kT], where E m ⫺ E m⫺1 is the energy difference between adjacent levels and kT, the quantum of phonon energy. A recurrence calculation from Eq. (3) leads to the well-known relation between the sublevel population N Dm and the total manifold population N D: ND m ⫽

exp[⫺(E m ⫺ E 1 )/kT ]

冱 exp[⫺(E

n

ND ⬅ p Dm ND

⫺ E 1 )/kT]

(4)

n

where p Dm is the Boltzmann distribution. The other relevant nonradiative process is the multiphonon decay [20] between the pump manifold (C) and the manifold B with rate A CB (cf., Fig. 4). For simplicity, this multiphonon decay is assumed to occur only between levels C 1 and B gB (see Fig. 4), which correspond to the smallest energy gap between the two manifolds. The radiative rates shown in Figure 4 and relevant to this study are the pumping rates R ᐉj (between manifolds A and C), the stimulated and spontaneous emission rates w kj and A kj (between manifolds A and B). The pumping rates and stimulated emission rates satisfy R ᐉj ⫽ R jᐉ and w kj ⫽ w jk, respectively [57]. The particular case of the pump level that belongs to the manifold B (i.e., the fiber is pumped directly in the 4 I 13/2 manifold) is analyzed later. The pumping rates and stimulated emission rates are given by: Rᐉ j ⫽

ψ p (x, y) ∫n p(ν′)hν′σ ᐉj (ν′)dν′ hν ᐉj

(5)

w kj ⫽

ψ s (x, y) ∫n s(ν′)hν′σ kj (ν′)dν′ hν kj

(6)

where ψ p (x, y), ψ s (x, y) are the normalized transverse mode envelopes of the pump and the signal, respectively (i.e., ∫∫ψ p, sdx dy ⫽ 1), n p, s (ν) are the corresponding photon number densities, ν mn ⫽ ω mn /2π is the center frequency of the transition between upper level m and lower level n, and σ mn (ν) is the homogeneous cross section associated with this transition. The rate equations relevant to each sublevel N Aj, B Bk, and N Cᐉ are detailed in Appendix A, where summation of Eqs. (73)–(75), (76)–(78), and (79)–(81) using the relation ∑ m N Dm ⫽ N D (D ⫽ A, B, C), yields the rate equations:

冱冱 R (N

dNA ⫽⫺ dt

ᐉj

j

Aj

⫺ N Cᐉ ) ⫹

ᐉ

dNB ⫽ A CBN C1 ⫺ dt

dNC ⫽ ⫺A CBN C1 ⫹ dt

kj

j

冱冱{A N kj

k

冱冱 {A N

Bk

Bk

⫹ w kj (N Bk ⫺ N Aj )}

(7)

k

⫹ w kj (N B k ⫺ N Aj )}

(8)

j

冱冱(N ᐉ

Aj

⫺ N Cᐉ )

(9)

j

Note the conservation relation d(N A ⫹ N B ⫹ N C )/dt ⫽ 0. Simplifications can be made in Eqs. (7)–(9) by assuming that the pump is monochromatic, in which case the pump spectral density is defined by n p (ν) ⫽ P pδ(ν ⫺ ν p )/hν p, where P p and ν p are the pump power and

539


frequency, respectively, and δ(ν ⫺ ν p ) is the delta function (the case for which the pump frequency ν p is close to the frequencies ν kj of the laser transition between B and A manifolds, is analyzed later). Replacing the expression of n p (ν) in Eq. (5) yields the pumping rate: Rᐉ j ⫽

ψ p Ppσᐉj (νp ) hνᐉ j

On the other hand, the radiative decay rates A kj can be assumed to be all equal to A kj ⬅ A R /g B, where A R ⫽ 1/τ is an average spontaneous decay rate corresponding to the overall fluorescence lifetime τ of the upper manifold B [57]. Using the foregoing results and Eq. (4), Eqs. (5)–(7) yield: dNA ⫽ ⫺R AC N A ⫹ R CA N C ⫹ A R N B ⫹ W BA N B ⫺ W AB N A dt

(10)

dNB ⫽ A CB p C1 N C ⫺ A R N B ⫺ W BA N B ⫹ W AB N A dt

(11)

dNC ⫽ ⫺A CB p C1 N C ⫹ R AC N A ⫺ R CA N C dt

(12)

with the following definitions: R AC , CA ⫽ ψ p Pp

冱冱 j

W AB, BA ⫽

ᐉ

冱冱w p kj

j

σ ᐉ j (νp ) pAj ,C ᐉ hνᐉ j

(13) (14)

A j ,B k

k

The more compact Eqs. (10)–(12) are the rate equations governing the changes in the total populations of manifolds A, B, and C, respectively. A further simplification can be introduced in the definition of the pumping rates R AC and R CA by the approximation ν ᐉj ⬃ ν p, which is equivalent to assume that the energy gap between the A and C manifolds is large compared with the Stark splitting. In this case, Eq. (13) becomes: R AC , CA ⬇

ψ p Pp hνp

冱冱 σ (ν )P ᐉj

j

p

Aj , Cᐉ

ᐉ

⬅

ψ p Pp a, e σ (νp ) hνp

(15)

In Eq. (15), σ a and σ e are, by definition, the pump absorption and emission cross sections (see Sec. 10.5). Resolution of the rate Eqs. (10)–(12) in the steady-state regimen is also detailed in Appendix A. In the limit where the pumping rates R AC,CA are negligible in comparison with the multiphonon rate A CB (which is the case of Er: glass [20]), the total populations of the upper (B) and ground (A) manifolds take the form (see Appendix A): NA ⫽ ρ

1 ⫹ WBAτ 1 ⫹ Rτ ⫹ (WAB ⫹ WBA )τ

(16)

NB ⫽ ρ

Rτ ⫹ WABτ 1 ⫹ Rτ ⫹ (WAB ⫹ WBA )τ

(17)

540

Desurvire

where R ⬅ R AC ⫽ ψ p P pσ a (ν p )/hν p after Eq. (15). The solution for N C is given by N C ⫽ ρ ⫺ N A ⫺ N B, and the sublevel populations NDm (D ⫽ A, B, C) are given by Eq. (4). We now consider the case of pump frequency lying in the 4 I 13/2 absorption band. When the fiber is pumped in this band, the foregoing results for the steady-state populations N A,B still apply, but some additional definitions are necessary. The spectral density n s (ν) involved in the integrant in Eq. (6) can be expressed as n s (ν) ⫽ n pump (ν) ⫹ n sig (ν), where n pump (ν) ⫽ P pδ(ν ⫺ ν p )/hν p. In this case, we find from Eq. (14) for the total stimulated emission (or absorption) rates W TAB, BA : sig W TAB ,BA ⫽ W pump AB, BA ⫹ W AB, BA

(18)

where W pump AB, BA ⫽

ψ s (x, y) Pp hν p

冱冱 σ (ν )P kj

j

p

k

A j ,B k

⬅

ψ s (x, y) Ppσ Ha, e (νp ) hν p

ψ s (x, y) ∫n sig (ν′)hν′ σ kj (ν′)P Aj , B kdν′ hν s j k ψ s (x, y) ∫n sig (ν′)hν′σ Ha, e (ν′)dν′ ⬅ hν s

冱冱

W sig AB ,BA ⫽

(19)

(20)

where σ Ha, e (ν) are, by definition, the homogeneous absorption and emission cross sections of the 4 I 13/2 → 4 I 15/2 band (see Sec. 10.5). The steady-state solutions of Eqs. (10)–(12), using R ⫽ 0, now take the forms: NA ⫽ ρ NB ⫽ ρ

sig 1 ⫹ W pump BA τ ⫹ W BAτ pump sig ⫹ W BA τ) ⫹ (W sig AB ⫹ W BA )τ

(21)

pump W AB τ ⫹ W sig ABτ pump sig ⫹ W BA )τ ⫹ (W sig AB ⫹ W BA )τ

(22)

1 ⫹ (W

pump AB

1 ⫹ (W

pump Ab

which will be used later for the 4 I 13/2 pump band. A detailed rate equation analysis including the effect of pump excited-state absorption and involving a four-level laser system can be found elsewhere [52], with corresponding steady-state solutions for the populations N A, N B, N C, and a fourth level, N D. It is shown, in particular, that when the nonradiative decay between the fourth and the third energy levels is fast, as in Er:silicate glass, these solutions reduce exactly to that of the three-level system described here. Thus, the only change introduced by the effect of pump ESA is an increase of the pump absorption coefficient, proportional to N B, and resulting in a reduced degree of inversion along the fiber [52]. However, for Er:fluoride glasses [65–67], which are also amenable to applications to 1.5-µm fiber amplifiers [54], the existence of upper energy levels with comparatively long lifetimes, fluorescence branching ratios, and excited-state absorption processes makes the analysis of such laser systems far more complex. We emphasize that the theory developed throughout this chapter is essentially relevant to silica-based EDFAs and that further theoretical modeling is necessary to model EDFAs based on hosts of other types such as fluorozirconate glass. 10.3.2 Homogeneous Signal Gain and Pump Absorption Coefficients The homogeneous signal gain coefficient γ Hs at frequency ν and fiber transverse coordinates (x, y) can be expressed as follows:


541

γ Hs(ν, x, y) ⫽ σ He (ν)N B(x, y) ⫺ σ Ha (ν)N A(x, y) where σ Ha,e represents the absorption and fluorescence cross sections corresponding to the I 15/2 → 4 I 13/2 manifold of laser transitions. The validity of this expression for the net gain coefficient is demonstrated in Section 10.5. We distinguish now the two cases in which the pump level does or does not belong to the 4 I 13/2 manifold, the corresponding populations being given by Eqs. (16) and (17) and (21) and (22), respectively. Introducing the H H H notations R * ⫽ W pump AB ⫽ ψ P P p σ a (ν p )/hν p and s(ν) ⫽ σ a (ν)/σ e (ν), we obtain the following gain coefficients from these equations: 4

sig R *τ[1 ⫺ s(ν)/s(ν p )] ⫺ s(ν) ⫹ [W sig AB ⫺ s(ν)W BA]τ γ Hs(ν, x, y) ⫽ ρσ He (ν) sig sig 1 ⫹ R *τ[1 ⫹ 1/s(ν p )] ⫹ (W AB ⫹ W BA )τ

(23)

(pump in the 4 I 13/2 absorption band), and γ Hs(ν, x, y) ⫽ ρσ He (ν)

sig Rτ ⫺ s(ν) ⫹ [W sig AB ⫺ s(ν)W BA]τ sig 1 ⫹ RT ⫹ (W sig AB ⫹ W BA )τ

(24)

(pump in absorption bands other than 4 I 13/2 ). sig For clarity, the x, y dependence of ρ, R, R*, W sig AB, W BA was not made explicit in the foregoing equations. When the signal power P s (z, ν) propagating along the fiber is much greater than the ASE noise (see Sec. 10.4), the stimulated emission coefficients W sig AB,BA in Eq. (20) take a simpler form. Indeed, assuming a monochromatic input signal distributed in one (or K) optical channels, the photon number at coordinate z in Eq. (20) is given by n sig (ν) ⫽ P s (z, ν)δ(ν ⫺ ν s )/hν s[or n sig (ν) ⫽ ∑ K P SK (z, ν)δ(ν ⫺ ν SK )/hν SK ], and sig H H the stimulated emission rates are W sig AB ,BA ⫽ ψ s P s σ a , e /hν s[or W AB , BA ⫽ ψ s∑ K P SK σ a,e (ν SK )/ hν SK ]. As seen from Eqs. (23) and (24), the signal gain coefficients γ Hs (ν) for the two types of pump band have similar expressions, differing only by terms involving the ratio s⫺1 (ν p ) ⫽ σ He (ν p )/σ Ha (ν p ). When σ He (ν p ) is much less than σ Ha (ν p )—that is, when the fluorescence cross section at the pump wavelength is negligible in comparison with the absorption cross section—the two gain coefficients become identical; as the terms proportional to s⫺1 (ν p ) vanish. In this case, the Er: glass laser system behaves similarly to a three-level system, regardless of whether the pump is in the 4 I 13/2 band. The case of s⫺1 (ν p ) not negligible has been analyzed theoretically [53]. The pump absorption coefficient γ Hp is given by γ Hp (x, y) ⫽ σ Ha (ν p )N A. When pump ESA is significant, the pump absorption coefficient is γ Hp ⫽ σ Ha (ν p )N A ⫹ σ Ha,esa (ν p )N B [52], where σ Ha,esa is the pump excited-state absorption cross section. For simplicity, pump ESA is overlooked here, the modification of equations to include ESA effect being straightforward. From Eqs. (16) and (21), we find the pump absorption coefficient γ Hp. γ Hp (νp) ⫽ ρσ Ha (νp)

1 ⫹ R *τ/s(νp) ⫹ W sig BAτ sig 1 ⫹ R *τ[1 ⫹ 1/s(ν p )] ⫹ (W sig AB ⫹ W BA )τ

(25)

(pump in the 4 I 13/2 absorption band), and γ Hp ⫽ ρσ Ha (νp)

1 ⫹ W sig BAτ sig 1 ⫹ Rτ ⫹ (W sig AB ⫹ W BA )τ

(pump in absorption bands other than 4 I 13/2 ).

(26)

542

Desurvire

The total signal gain and pump absorption coefficients γ Hs (ν) and γ Hp (ν p ) are obtained by integration of γ Hs (ν, x, y) and γ Hp (γ p, x, y) over the transverse plane (x, y) weighted by the signal and pump modal distributions ψ p,s (x, y): γ Hs (z, ν) ⫽ ∫∫dx dy γ Hs(ν, x, y, z)ψ s(x, y) ⫽ ∫∫dx dyψ s{σ He N B ⫺ σ Ha N A}

(27)

γ Hp (z, νp) ⫽ ∫∫dx dy γ Hp (νp, x, y, z)ψ p(x, y) ⫽ ∫∫dx dyψ pσ Ha (νp)N A

(28)

From the expressions of the gain and absorption coefficients [see Eqs. (27) and (28)], two differential equations describing the evolution at fiber coordinate z of the pump power P(z) and the signal power P(z, ν) have to be solved, that is: dPp (z) ⫽ ⫺ γ Hp (z, νp)Pp(z) dz

and

dPs(z, ν) ⫽ γ Hs (z, ν)Ps(z, ν). dz

The signs ⫾ in the pump equation correspond to forward (⫺) or backward (⫹) pumping configurations. Note that amplified spontaneous emission noise, overlooked so far, is treated in detail in Section 10.4. Different assumptions can be made at this stage. For the mode envelopes ψ(x, y), one can use the LP mn mode solutions involving Bessel functions [68,48,51,58,61], or a gaussian mode approximation [49,52,53,60]. The Er 3⫹ density profile ρ(x, y) can be assumed to be either uniform across the fiber core [50,52,60], or confined near the core center [48,53,61]. The foregoing last three assumptions make it possible to carry out the integration in Eqs. (27) and (28). The effect of mode overlap with the active region leads to various useful expressions of ‘‘overlap’’ or ‘‘filling factors’’ [49,52,53,58,60]. However, numeric integration of the coefficients in Eqs. (27) and (28) using the LP mn mode envelopes solutions—or the mode profiles experimentally measured—is necessary for accurate modeling and optimization of fiber design [61]. Two regimens must be considered next: the small-signal regimen, where the pumping rate R (or R*) dominates over the stimulated emission rates W sig AB,BA [see Eqs. (23)– (26)], and the high-signal or saturated gain regimen, where these rates are of the same order of magnitude. In the first case, the ASE noise can be neglected, and solutions for the pump and signal equations can easily be obtained, either by numeric integration or by numeric solution of a transcendental equation, as shown at the end of this section. In the ASE–saturated gain regimen, however, resolution of the pump and signal equations is more difficult because the bidirectional propagation of the ASE noise in the EDFA causes a two-boundary–conditions problem. Note that the same problem occurs when bidirectional pumping is considered, as each pump signal affects the ground-state absorption of the other. In either situation, the resolution can be obtained numerically by iterative integration [51,52] with an appropriate convergence algorithm. Note that the computation time is greatly reduced by using approximations for the mode envelopes, as discussed earlier. In the high-gain regimen, however, the two-boundary–conditions problem of the ASE noise is alleviated if the input signal power P s (0, ν) is much greater than the equivalent input noise power, which is approximately the power of one photon in the EDFA effective bandwidth [53]. In this case, the saturation effect by both forward and backward ASE noise is negligible, and resolution of the pump and signal equations is easily performed. 10.3.3 Analytical Solutions for Bidirectional Pump and Signals Recent work [63] showed that analytical solutions are possible for the EDFA output pump and signal. This analysis, which is valid for pump bands free from ESA, assumes nonsatu-

543


rating ASE noise (high-signal or low-gain regimen). In particular, such analytical solutions make it possible to describe the complex case of bidirectional pumping and multichannel be the input or output power at frequency ν J and normalized to input signals. Let P in,out J the photon energy hν J, corresponding to either a pump or a signal optical channel ‘‘J.’’ The solution for P Jout at z ⫽ L is [63] (see Appendix B):

冦

P Jout ⫽ P Jin exp ⫺α J L ⫹

P in(⫹) ⫺ P out {⫹} P sat J

⫹

in out P (⫺) ⫺ P (⫺)

P sat J

冧

(29)

in out out where P in(⫹), P (⫺) , P (⫹) , and P (⫺) represent the total power input at z ⫽ 0, input at z ⫽ L, output at z ⫽ L, and output at z ⫽ 0, respectively. In Eq. (29), α J represents the fiber absorption coefficient and P sat J the intrinsic saturation power at frequency ν J (see Appendix B for definition). When the optical channel J represents a pump in an absorption band th other than 4 I 13/2, the definition of P sat J coincides with that of the pump threshold P p [53]. th Further discussion on the definitions of P sat and P is made in Section 10.6. J p Considering, for instance, the forward-pumping configuration, summation of Eq. (29) over J yields a transcendental equation for the total output power P out at z ⫽ L:

P out ⫽

冱P

out J

⫽

J

冱A

J

J

冢冣

P out exp ⫺ sat PJ

(30)

with

冦

A J ⫽ P Jin exp ⫺α J L ⫹

冧

P in P sat J

(31)

Because the A J factors are constants that can be determined experimentally [63], Eq. (30) can be solved for the total power output Pout. The output power P Jout of channel J is then given by Eq. (29), that is:

冦

P Jout ⫽ P Jin exp ⫺α J L ⫹

冧

P in ⫺ P out P sat J

(32)

Comparison between the theoretical solutions (see Eq. 32) for a 1.48-µm pump and a 1.55-µm signal with experimental measurements shows excellent agreement, as illustrated in Section 10.6 (see Fig. 19). Such a model, valid independently of the propagation directions of various pump and signal waves, represents a powerful tool to characterize EDFAs. Solving Eq. (30) numerically is also far simpler than solving the differential equations described previously. Yet, numeric integration is required when at high gains, ASE noise saturates the EDFA, or when more complex inhomogeneous broadening effects must be taken into account. Analytical solutions for the ASE noise, as applicable to unsaturated gain regimen, are described in Section 10.4. 10.4 FIBER AMPLIFIER NOISE The generation of noise associated with the amplification of light is a rather fundamental subject which, from semiclassic descriptions to fully quantized theories, can be approached from many levels of complexity [69–74]. The noise characteristics of EDFAs are of crucial

544

Desurvire

import for applications in optical communications, because they ultimately determine the performance of these devices and their limitations as optical preamplifiers or repeaters in lightwave systems. Two key aspects of noise relevant to EDFAs are the amplification of spontaneous emission and the fluctuation of signal light intensity (variance) at the amplifier output. The spontaneous initiation and buildup of ASE noise in optical amplifier cavities (or ‘‘mirrorless lasers’’) has been the subject of numerous theoretical studies [75–80], applied later to fiber laser waveguides [49,58–60]. So far, only a few theoretical descriptions have been made for the intensity noise and noise figure of the EDFA [81,82], these being based on the linear theory by Shimoda, Takahasi, and Townes (STT theory) [69]. In the nonlinear regimen of gain saturation, the analysis of the light photon statistics is far more complex, as discussed at the end of this section. The equations derived earlier for light amplification can now be extended to include the effect of ASE generation, which permits the study of the ASE noise spectrum under different regimens of pump and signal levels. The gain medium is assumed here to be homogeneous, which is a good approximation for aluminosilicate-based EDFAs [52] (for a model of inhomogeneous broadening and a comparison with experimental results obtained with ASE spectra, see Sec. 10.5). This section reviews the STT theory as applied to EDFAs and the study of the amplifier noise figure. Additionally, analytical solutions for the ASE noise that apply to low-gain distributed EDFAs are detailed. 10.4.1 Linear Theory of ASE Noise The interaction of light with atoms, resulting in the generation of ASE in the EDFA, can actually be described through a simple quantum model that uses the ‘‘photon number states’’ representation [73]. This representation, useful to model the photon statistics of light, cannot predict AM and FM noise spectral properties, which are relevant to more elaborate theoretical formulations (e.g., based on Langevijn, Van der Pol, or Fokker– Planck equations [74]). For describing the noise power spectrum at the amplifier output, other models [83] use a classic electromagnetic field description, where the ASE is introduced phenomenologically. We focus first on the STT model as applied to a fiber amplifier, and use the results to describe the EDFA signal-to-noise ratio (SNR) and noise figure (NF) characteristics. The signal electric field consists of the superposition of discrete radiation modes k of characteristic frequency ν k. Let P n (ν k ) be the probability of finding n photons in the kth mode. The change in number of photons in this mode, owing to the events of emission or absorption by atoms, can be viewed as transitions, or probability flows, occurring between the energy levels of the radiation field (n ⫺ 1)hν k, and nhν k and (n ⫹ 1)hν k [73]. It can be shown easily that the probability functions P n⫺1, P n, and P n⫹1 are coupled through the time-dependent rate equation [69,73]: dP n ⫽ g e[nP n⫺1 ⫺ (n ⫹ 1)P n] ⫹ g a[(n ⫹ 1)P n⫹1 ⫺ nP n] dt

(33)

where g e ⬃ σ He N B and g a ⬃ σ Ha N A are emission and absorption coefficients, respectively. Equation (33) is referred to as the ‘‘photon statistics master equation’’ [84,85] or ‘‘forward Kolmogorov equation’’ [86]. Let 〈nk〉, the kth moment of the distribution, P n, be defined as 〈n k〉 ⫽ ∑ n n k P n. From Eq. (33), we find (see Appendix C) [87]:

545


d〈n k〉 ⫽ dt

冱冢p ⫺ 1冣 [〈g (n ⫹ 1)n j

k

e

〉 〈 ⫹ (⫺1)k⫹p〈g an p〉]

p⫺1 ⫺1

(34)

p⫽1

In the linear regimen, the emission and absorption coefficients in Eq. (34) are independent of n and can be taken out of the brackets. In this case, the first two moment equations for k ⫽ 1 and 2 (mean and mean square photon number values) are given by: d〈n〉 ⫽ g e(〈n〉 ⫹ 1) ⫺ g a〈n〉 dt

(35)

d〈n 2〉 ⫽ 2(g e ⫺ g a)〈n 2〉 ⫹ (3g e ⫹ g a)〈n〉 ⫹ g e dt

(36)

Resolution of linear Eqs. (35) and (36), while assuming the coefficients g a,e to be constant, leads to the well-known solutions for the mean n ⫽ 〈n〉 and variance σ 2 ⫽ 〈n2〉 ⫺ 〈n〉2, after time t (or at fiber length L) [69,84,86]: n ⫽ Gn(0) ⫹

ge (G ⫺ 1) ⬅ Gn(0) ⫹ N ge ⫺ ga

(37)

σ 2 ⫽ G 2{σ 2(0) ⫺ n(0)} ⫹ {Gn(0) ⫹ N} ⫹ {2Gn(0)N ⫹ N 2}

(38)

where G ⫽ exp[g e ⫺ g a )L/c] is the amplifier gain, c the speed of light in the amplifier medium, and N the average number of ASE noise photons. In Eq. (38), n(0) and σ 2 (0) correspond to the input statistics conditions. The terms in curly braces in Eq. (38) are called the excess noise, shot noise, and beat noise, respectively [84]. Solutions (37) and (38) represent the foundation of the SNR analysis of semiconductor amplifiers [84,85]. In the case of fiber amplifiers, the same analysis also applies, but the variation of the emission and absorption coefficients along the fiber due to pump decay must be taken into account. With the identification g a,e /c ⬅ Γ sσ Ha,e N B,A (see Sec. 10.3), the EDFA gain G and ASE noise N in Eq. (37) are given from Eq. (35) by [81,82]:

冦冮

冧

z

G(z, ν) ⫽ exp Γ s [σ e(ν)N B (z′) ⫺ σ a(ν)N A (z′)]dz′ 0

(ν)N (z′) dz′ 冮 σ G(z′, ν)

(39)

z

N(z, ν) ⫽ Γ sG(z, ν)

e

B

(40)

0

Equation (36) for d〈n 2〉/dz has new variable coefficients g a,e (z) and depends on the more complex solution n(z) defined by Eqs. (37)–(40). Its integration may seem arduous, but remarkably, the solution for the output variance σ 2 (z) takes the same canonical form found in Eq. (38), provided one uses the definitions of Eqs. (39) and (40) for G and N. For demonstration of this see Ref. 82. We focus now on the characteristics of the signal and ASE noise spectrum evolution. The EDFA light spectrum at fiber coordinate z can be decomposed into ‘‘bins’’ of width δν with power P s (z, ν) ⫽ n(ν)hνδν. From the foregoing results and from the analysis in Section 10.3, the power spectrum rate equation takes the form [49]: dP ⫾s (z, ν) ⫽ ⫾∫∫dx dy ψ s(x, y) dz {σ He (ν)N B (x, y, z)[P ⫾s (z, ν) ⫹ P 0 (ν)] ⫺ σ Ha (ν)N A (x, y, z)[P ⫾s (z, ν)}

(41)

546

Desurvire

Figure 5 Output ASE spectra near 1.54 µm obtained both experimentally (top row) and theoretically (bottom row), in the forward and backward directions, for different launched pump power conditions, the pump power increasing from left to right linear and arbitrary scales. (From Ref. 49.) where the signs (⫾) apply to signals propagating in the forward (⫹) or the backward (⫺) directions of the fiber, and P 0 (ν) ⫽ 2hνδν is the power of two photons per mode (accounting for the polarization mode degeneracy). The populations N A,B in Eq. (41) are given by Eqs. (16) and (17) or (21) and (22), depending on the pump band, whereas the stimulated emission coefficients W sig AB,BA in these equations are, from Eq. (20): W sig AB,BA (x, y, z) ⫽

ψ s (x, y) ∫[P ⫹s (z, ν′) ⫹ P s⫺(z, ν′)] σ Ha,e (ν′)dν′ hν s

(42)

Note that the factor of 2 in the definition of P 0 (ν) is important when ASE noise is studied in the saturated regimen (since both polarization modes contribute to saturation through the coefficients W sig AB,BA ), but can be omitted in the study of strong-signal regimens, in which the saturating effect of ASE is negligible. The validity of applying the results of the linear analysis made so far to the saturated gain regimen is discussed in the following. Other approaches are possible for describing the effect of ASE noise. For instance, the ASE can be treated in a separate rate equation as an extraneous signal at frequency ν s propagating in the two directions [51] or in only one direction [53,61], its effective bandwidth ∆ν ASE being chosen for best match with experimental results. These approaches greatly simplify the computation, at the expense of accuracy and generality for the calculated results. By using the cross section spectra σ Ha,e (ν), such as shown in Figure 3 (aluminosilicate EDFA), the set of equations (dP s (z, ν k )/dz, k ⫽ 1 . . . N) combined with the pump equation (dP p (z, ν p )/dz) can be solved numerically and compared with experimental measurements.


547

Figure 5 Continued.

Figure 5 shows experimental and theoretical output ASE spectra obtained for various launched pump power conditions (the power increasing from left to right) in the forward and in the backward directions. As the figure shows, the ASE noise undergoes significant changes when the pump power is increased. From Eq. (41), it is clear that the ASE spectral evolution follows that of the net gain coefficient σ He (ν)N B ⫺ σ Ha (ν)N a. For low pump powers, absorption by the 4 I 15/2 ground level of Er 3⫹ occurs along most of the fiber length. At high pump powers, emission from the upper level 4 I 13/2 takes over absorption, and the ASE noise spectrum follows that of the emission cross section profile σ Ha (λ). The finite spectral overlap between the two cross sections (see Fig. 3) causes the ASE noise to exhibit peak features near 1.53 and 1.56 µm, the magnitude changes of which depend on both pumping conditions and fiber length [49]. Note that in this example a good qualitative agreement between theory and experiment is obtained simultaneously for both forward and backward ASE spectra. It is also observed that the ASE noise is generally higher in the backward direction [49]. It is expected then that the backward pumping scheme will give an SNR degradation higher than the forward pumping, as discussed in the following. 10.4.2 Amplifier Noise Figure The canonical formula (Eq. 38) of the output photon number variance σ 2 is an essential result for the analysis of the SNR and the NF of the EDFA. The detailed study of the amplifier SNR and of the bit error rates (BERs) associated with digital signal detection [83–85,88] is beyond the scope of this chapter. We shall address here only the basic issues for the noise figure, relative to pumping configurations, pumping bands, and fundamental limits. The NF is defined as the ratio of the amplifier input SNR to its output SNR [i.e.,

548

Desurvire

NF ⫽ (SNR) in /(SNR) out] and is always greater than unity [72]. The two SNRs can be defined as SNR in ⫽ n(0) 2 /σ 2 (0) and (after photodetection) SNR out ⫽ n 2D /σ 2D, where n D and σ 2D are the mean and variance of the detector photoelectron count (note that for digital on–off signals, the SNR definition is more complex [83–85,88]). It can be shown that in the limit of large amplified signals, NF D takes the form [82]: NF ⬇

2N(νs) ⫹ [η Cη Dη F(ν s)]⫺1 G(ν s)

(43)

where η C is the fiber-to-detector coupling efficiency, η D the detector quantum efficiency, and η F (ν s ) the transmission at ν s of an optical filter placed between the fiber and the detector (ideal detection conditions correspond to the case η C ⫽ η D ⫽ η F ⫽ 1). With the definition of the spontaneous emission factor [81,82], n sp (ν s ) ⫽ N(ν s )/[G(ν s ) ⫺ 1], N and G being defined in Eqs. (39) and (40), and with ideal detection, the noise figure in Eq. (43) reduces to NF ⫽ [2n sp (G ⫺ 1) ⫹ 1)]/G. In the high-gain regimen (i.e., G ⬎⬎ 1), NF ⬇ 2n sp. When maximum inversion is achieved along the EDFA, n sp is close to unity and NF ⫽ 2 or 3 dB. This corresponds to a dominant contribution from the signal/spontaneous beat noise 2Gn(0)N in Eq. (38). The 3-dB value represents the lowest NF achievable at high amplifier gain. For this reason, it is referred to as the quantum limit [88], or signal/ spontaneous emission beat noise limit. Through a numeric integration of the foregoing equations, it was shown that when the EDFA is operated as a three-level system and pumped in the forward direction, the noise figure at the peak gain wavelength can be theoretically as low as 0.2 dB above the quantum limit (i.e., NF ⬇ 3.2 dB) [81]. The same study showed that the NF is higher in the backward-pumping configuration, as expected from the difference observed between forward and backward ASE noises. An analysis of the spectral changes in NF with pumping conditions [82] showed that the quantum limit actually can be achieved with both pumping configurations, provided the fiber length is not optimized for maximum gain. Figure 6 shows the calculated spectra of n sp for forward and backward pumping and different input pump conditions γ ⫽ P inp /P pth [82]. It is clear that at high pump power (γ ⱖ 20) the spontaneous emission factor tends toward unity, which occurs over a broad

Figure 6 Spontaneous emission factor spectrum n sp (λ) corresponding to the forward and backward pumping configurations for values of input pump powers (normalized to pump threshold) γ ⫽ 2.5–50, the pump wavelength being λ p ⫽ 980 nm. (From Ref. 82.)

549


Noise figure spectra shown for the highest pump regimens in Figure 6 (i.e., γ ⫽ 2.5– 50 with λ p ⫽ 980 nm). (From Ref. 82.)

Figure 7

spectral range. Note that the difference between forward and backward pumping also disappears in this regimen. Figure 7 is a plot of the corresponding noise figure spectra, which shows at high pump powers a flattening of NF close to the 3-dB quantum limit value: clearly the NF can be ⫾0.2 dB near this limit in a spectral range of about 50 nm (the gain G being in this range greater than 10 dB). Outside this range, the NF tends toward unity, reflecting the characteristics of an absorption-free and noise-free transmission medium. Note that the limit NF p ⬃ 2n sp applies only in the high-gain regimen, whereas the definition of Eq. (43) is applicable over the whole spectral range. The theoretical results just described apply when the EDFA is operated as a threelevel laser system: that is, the population N C of the third level is negligible. As a result, full inversion is possible, with N B ⬃ ρ and N A ⬃ 0. However, when the pump is in the 4 I 13/2 pump band (i.e., near 1.48-µm wavelength), the EDFA is comparable with a quasitwo-level system, and complete medium inversion is not possible [53]. Therefore, the NF is expected to be higher with this pump band, as discussed elsewhere [82,89]. From the analysis of Ref. [53], the spontaneous emission factor at ν s and fiber coordinate z are given by: n sp (ν s, z) ⫽

冦

⫺1

冧

s(ν s ) P th N B (z) ⫽ 1⫺ ⫺ s(ν s ) p N B (z) ⫺ s(ν s )N A (z) s(ν p ) P p (z)

(44)

with s(ν o ) ⫽ σ a (ν)/σ e (ν). For a three-level system, σ e (ν p ) ⬃ 0, and at high pump powers (P p (z) ⬎⬎ P thp ) Eq. (44) gives n sp ⬃ 1. For a quasi-two-level system with σ e (ν p ) ≠ 0, the lowest NF achievable at high pump power NF ⬇ 2n sp ⫽ 2/[1 ⫺ σ a(ν s)σ e(ν p)/σe(νs)σa(νp)] [82,89]. Evaluation of NF as a function of pump wavelength near 1.48 µm [82] shows NF penalties of 0.3–1.5 dB relative to the 3-dB quantum limit. Such an NF evaluation for the 4 I 13/2 pump band rests on the accuracy of the measurement of the cross section spectra and, in particular, to the cross section ratio s(ν). Recent studies [38,39] have shown that the experimental value of s(ν) actually differs from that calculated by the Fuchtbauer– Ladenburg relations (see Secs. 10.2 and 10.5) and used elsewhere [82]. From the experimental measurement of the gain and absorption coefficients (leading to an exact determination of s(ν) for the 4 I 13/2 pump band), a more accurate prediction of the NF dependence on pump and signal wavelengths can be obtained [89].

550

Desurvire

Experimental measurements of n sp and NF were made for the 980-nm and 1.48- to 1.49-µm pump wavelengths [90,91]. The NF can be evaluated by two independent ways, consisting in measuring the gain and ASE optical power, or in measuring the output noise through an rf spectrum analyzer [90,91]. Figure 8 shows an experimental measurement of the gain G and noise factor 2n sp for 1.49-µm pump and 1.531-µm signal, using the first method. In agreement with the theory, n sp is seen to be independent of gain over a broad spectral range (see Fig. 6), the lowest noise factor value being 2n sp ⫽ 5.3 dB (which is equal to the NF). With improved pumping and filtering conditions and a longer signal wavelength (1.537 µm), a lower noise figure of 4.1 dB was measured for this pump wavelength [90]. This value was also reported [91] for 1.48-µm pump, whereas using the 980nm pump band in the same fiber gave an NF of 3.2 dB. The 980-nm result confirms the prediction of a near–quantum-limited regimen (NF ⬃ 3 dB) when the EDFA is pumped as a three-level system, whereas some noise penalty (NF ⬃ 4 dB) is introduced when it is pumped as a quasi-two-level system (i.e., near 1.48 µm). In spite of worse noise performance with 1.48-µm pump, the EDFA used as a preamplifier can provide highly sensitive detection. For instance, a sensitivity of 215 photons per bit (as referred to the EDFA input end) was shown at 1.8 Gb/s [90]. These results also show that broadband amplification of wavelength division multiplexed (WDM) signals with a near–quantum-limited regimen is theoretically possible with EDFAs. 10.4.3 Analytical Solutions for ASE Noise and Distributed Amplifiers An important potential application of optical amplifiers is to replace digital repeaters in long-distance communication links, particularly in submarine optical fiber cable systems [92], which span intercontinental lengths in the 10,000-km range. For such systems, successive amplification stages are needed to compensate for fiber loss (⬃20 dB/100 km at 1.5 µm). As a result of the loss compensation, the ASE noise generated accumulates at each state, and builds up along with the signals, thereby setting fundamental limits to the maximum system length. Theoretical studies of noise accumulation in optical amplifier

Figure 8 Gain and noise factor 2n sp spectra measured in an EDFA for a 34-mW input pump at 1.49 µm. (From Ref. 90.)

551


chains so far have assumed discrete or lumped amplification stages (as in the use of semiconductor amplifiers) [85,93]. With EDFAs, as well as Raman fiber amplifiers, however, distributed gain, as opposed to lumped gain, can be achieved [94–96]. Distributed amplification actually results in lower noise accumulation [95], at the expense of higher pump power requirement. Analytical solutions for the gain and ASE noise can be derived [64] in the case of low gain, unsaturated EDFAs, which corresponds to distributed gain conditions. Such an analytical model must include the effect of fiber background loss, which affects both pump and signals. Let P⫾ be the case and ASE powers at frequency ν s and fiber coordinate z, propagating in the forward (⫹) or the backward (⫺) directions. The corresponding rate equation for the unsaturated gain regime is [64]:

冤

冣冥

冢

dP⫾ η pq 1⫹q ηsq α (P⫾ ⫹ P0 ) ⫺ 1 ⫹ ⫹ α′s P⫾ ⫽⫾ s dz 1 ⫹ q 1 ⫹ ηp 1 ⫹ ηp αs

(45)

In Eq. (45) α s and α′s represent the Er 3⫹ absorption coefficient and the fiber background loss coefficient, respectively, and q is the ratio of pump power P p (z) to pump threshold P pth. The pump threshold is defined by P thp ⫽ hν p A/σ a (ν p )τ[1 ⫹ η p], where A is the pump effective mode area [61]. The parameters η p,s are defined by η p,s ⫽ σ e (ν p,s )/σ a (ν p,s ). Note that η p,s ⫽ 1/s(ν p,s ) as defined in preceding subsection. The pump rate equation (forward pumping) is

冤

冥

α′p dq 1 ⫽ ⫺α p q ⫹ dz 1 ⫹ q αp

(46)

Substituting the relation (1 ⫹ q)⫺1 ⫽ ⫺(dq/dz)[q(α p ⫹ α′p ⫹ α′p q)] in Eq. (45) and eliminating dz yields the equation: αs dP⫾ ⫽⫾ dq α p ⫹ α′p(1 ⫹ q)

冦冤η1 ⫹⫺ηη ⫹ αα′ ⫹ 1q α α⫹ α′冥P p

s

p

s

s

s

s

s

⫾

⫺

冧

ηs P0 1 ⫹ ηp

(47)

The solutions of Eq. (47) for P⫾ (q) are:

冦

αs ηs f⫹(q 0, q L ) αp 1 ⫹ ηp

冦

αs ηs f⫺(q 0, q L ) αp 1 ⫹ ηp

P ⫹ (q L ) ⫽ G ⫹ (q L ) P ⫹ (q 0 ) ⫹ P0

P ⫺ (q 0 ) ⫽ G ⫺ (q 0 ) P ⫺ (q L ) ⫹ P0

冧

(48)

冧

(49)

where the gain G ⫹ (q L ) ⫽ G ⫺ (q o ) and the functions f ⫾ (q 0, q L ) are given by integrals defined in Appendix D. In Eqs. (48) and (49), P⫾ (q 0 q L ) represent the input signal powers at z ⫽ 0 and z ⫽ L, respectively, while the other terms in braces represent equivalent input noise signals. We can define the spontaneous emission factors through n ⫹sp ⫽

G αs ηs f⫹(q 0, q L ) G ⫺ 1 αp 1 ⫹ ηp

(50)

n ⫺sp ⫽

G αs ηs f⫺(q 0, q L ) G ⫺ 1 αp 1 ⫹ ηp

(51)

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Desurvire

Thus, the output ASE noises are given by P ⫾out ⫽ P 0n ⫾sp (G ⫺ 1), where G ⫽ G ⫹ (q L ) ⫽ G ⫺ (q 0 ). The expressions in Eqs. (48)–(51) contain the functions f ⫾ (q 0, q L ) which, in the general case, do not take a simple analytical form (see Appendix D). However, the integrals involved in f ⫾ can be evaluated either numerically or through Taylor developments of the integrands. For the computation of solutions (48) and (49), the boundary conditions q 0, q L must be known. Straightforward integration of the pump Eq. (46) yields the transcendental relation between q o and q L:

2 Arth

冦q ⫹ qq ⫹⫺ 2εq q q 冧 ⫹ ε′1 ⫹ ln冦11 ⫹⫹ ε′ε′qq 冧 ⫽ ⫺(α ⫹ α′ )L L

0

p L

p

L

0

p

L

0

p

p

p

(52)

0

where ε′p ⫽ ε p /(1 ⫹ ε p ) and ε p ⫽ α′p /α p. The transcendental Eq. (52) must be solved numerically to evaluate q L ⫽ P p (z ⫽ L)/P thp for a given q 0 ⫽ P p (z ⫽ 0)/P thp. The case in which the fiber background loss is negligible (α′p,s ⬍⬍ α p,s or ε′p,s ⬍⬍ 1) leads to a more simple equation for the pump solution, that is: q L ⫺ q 0 ⫹ Ln(q L /q 0 ) ⫽ ⫺α p L; computation of the ASE powers, however, still requires the determination of the definite integrals f ⫾ (q 0, q L ) as shown elsewhere [64]. Such analytical solutions for the gain and ASE noises are particularly useful in the study of distributed fiber amplifiers, where unsaturated gain conditions can be achieved. 10.4.4 Nonlinear Amplifier Noise Theory As mentioned earlier, the description of ASE noise and noise figure of the EDFA made so far in this section is based on the linear STT model [69]. Some of the issues related to noise in the nonlinear or saturated gain regimen, which prevails in most EDFA applications, must therefore be also addressed here. The rate equation model used earlier was based on the assumption that the atomic populations N A (z), N B (z) are fixed by the external influence of pump and signal light. The photon and atomic populations, however, form two closely coupled systems, which makes the probability distribution of light P n (t) interacting with atoms difficult to calculate. Because the two systems reach equilibrium at different rates, the problem can yet be simplified by ‘‘adiabatic decoupling’’ [73]. More complex and rigorous treatments using the density matrix operator formalism [70,97] lead to a modified rate equation for P n that accounts for the nonlinear statistics of light emission [70,74,98–100]. For the EDFA, such equation can be shown to take the form [101]:

冤

冥

n⫹1 dP n n ⫽ ge P n⫺1 ⫺ Pn dt 1 ⫹ ns 1 ⫹ (n ⫹ 1)s ⫹ ga

冤1 ⫹n(n⫹⫹1 1)s P

n⫹1

⫺

n Pn 1 ⫹ ns

冥

(53)

⫹ g c [(n ⫹ 1)(P n⫹1 ⫺ P n ) ⫹ n(P n⫺1 ⫺ P n )] with the coefficients g e, g a defined by: g e ⫽ ρΓ sσ He

冢

冣

Rτ σH ⫺ H a H 1 ⫹ Rτ σ a ⫹ σ e

(54)

553


冦1 ⫹1 Rτ ⫺ σ σ⫹ σ 冧

g a ⫽ ρΓ sσ Ha

H e

H a

(55)

H e

and g c ⫽ ρΓ sσ Heσ Ha /(σ He) and s ⫽ hνδν/P sat. It can be easily shown with these definitions that in the linear regimen (s ⫽ 0) Eq. (53) takes the same form as Eq. (33). Direct resolution of Eq. (53) is actually a difficult task, because of instabilities in the differential equation system as well as the need to extrapolate the tail of P n for increasing values of n [98]. A simpler approach consists of considering the mean 〈n〉 and mean square 〈n 2〉 photon numbers of the distribution P n, which are found from Eq. (53) to be solutions of the equations [99]:

冬

冭冬

冬

冭冬

冭

n⫹1 n d〈n〉 ⫽ ge ⫺ ga ⫹ gc dt 1 ⫹ s(n ⫹ 1) 1 ⫹ sn

冭

2n 2 ⫹ 3n ⫹ 1 2n 2 ⫺ n d〈n 2〉 ⫺ ga ⫹ g c〈4n ⫹ 1〉 ⫽ ge dt 1 ⫹ s(n ⫹ 1) 1 ⫹ sn

(56)

(57)

Resolution of Eqs. (56) and (57) leading to a determination of 〈n〉, σ 2, SNR, and NF of the amplifier output light in the nonlinear regimen can be performed in several ways through Taylor developments about 〈n〉 [99], or through deconvolution approximations [98]. Note that when saturation is negligible (s ⫽ 0), Eqs. (56) and (57) reduce to Eqs. (35) and (36), which correspond to the linear STT theory. Resolution of Eqs. (53), (56), (57), and their solutions are discussed elsewhere [101]. Many important studies remain to be done to investigate the quantum noise properties of the EDFAs in linear and nonlinear gain regimens from both theoretical and experimental standpoints, and to relate these characteristics to the performance of optical communications systems using EDFAs. 10.5 COMPLEX SUSCEPTIBILITY AND INHOMOGENEOUS BROADENING The basic equations derived in Sections 10.3 and 10.4 represent the elementary tool that is necessary to model the EDFA in most applications of interest. We have shown that in spite of the complexity associated with the Stark-split Er: glass laser, the assumption of a three-level system with homogeneous gain coefficient g(ν) ⫽ σ e (ν)N B ⫺ σ a (ν)N A leads to a satisfactory description of the EDFA characteristics. In some cases, however, this representation can turn out to be oversimplified. For instance, if inhomogeneous broadening [57,71] is largely dominant, gain saturation effects cannot be accurately modeled by the homogeneous theory. For durations falling in the short time scale associated with intramanifold relaxation or thermalization processes, the steady-state expression g(ν) for the EDFA gain coefficient is likewise not applicable. Thus, this section outlines the basic assumptions leading to the definition of the cross-sections σ a,e (ν) and the EDFA gain coefficient g(ν), and provides some extension of the EDFA model to the case of inhomogeneous broadening. 10.5.1 Amplifier Gain Coefficient Some confusion may exist over a definition of the EDFA gain coefficient (i.e., g ⫽ ln G) and cross sections, because different formulations can be found in textbooks (e.g.,

554

Desurvire

[56,57,71]), which apply to various laser materials and transition line shapes. In particular, multilevel laser systems are usually shown in textbooks to have a gain coefficient g*(ν) ⫽ σ(ν)[N A ⫺ (g B /g A )N A], where g B and g A represent the degeneracies of the upper and lower manifolds, respectively. This formula is in contradiction to the observation that for Er: glass the emission and absorption line shapes are spectrally different (see Fig. 3), and that the ratio σ a /σ e is not constant, nor nearly equal to g B /g A ⫽ 7/8 [38,89]. Another description of the frequency dependence of the gain coefficient in Stark-split laser systems can be found in McCumber’s theory of ‘‘phonon-terminated optical masers’’ [40]. It can be shown [100] through an analysis of the complex atomic susceptibility of the EDFA, that the net gain coefficient g(ω) at frequency ω ⫽ 2πν is given by the expression: Γω g(ω) ⫽ ⫺ s χ″E (ω) nc

(58)

with χ″E being the imaginary part of the complex susceptibility: nc χ″E (ω) ⫽ ⫺ (σ He N B ⫺ σ HA N A ) ω

(59)

In Eq. (59), σ He and σ Ha are the emission and absorption cross sections defined by gB

σ

H e,a

⫽

gA

冱冱 σ (ω)p H jk

k⫽1

(60)

B k ,A j

j⫽1

where p A k, p B j are the Boltzmann distributions in manifolds A, and B (see Eq. 4), and σ jk (ω) is the cross section associated with the laser transition j ↔ k. The cross section line shape σ Hjk (ω) is a lorentzian, having full width at half-maximum (FWHM) ∆ω jk and peak value σ jkpeak. Such an expression for the gain coefficient g(ω) in Eq. (58) rests on the assumption that thermal equilibrium is maintained within each laser level manifold for the duration of the signal and pumps that interact in the fiber: that is, the sublevel populations are given by Eq. (4). With this assumption, the total complex susceptibility can be expressed as the sum of the susceptibilities associated with all possible transitions [57,100]. The integrated cross section corresponding to electric–dipole transitions is related [57] to the radiative emission probability A jk ⫽ τ⫺1 jk through ∫σ Hjk (ω)dω ⫽

π λ2 ∆ω jkσ jkpeak ⫽ 2 jk 2 4n cπ jk

(61)

By integrating the total cross sections σ He,a in Eq. (52) with Eq. (61) and using the definition 〈λ 〉 e,a ⫽ τrad 2

g2

g1

k⫽1

j⫽1

冱冱

λ 2jk p B ,A τ jk k j

(62)

where τ rad is the 4 I 13/2 radiative or fluorescence lifetime, we have: eff ∫σ Ha,e (ω)dω ⬅ σ peak e,a ∆ω e,a ⫽

〈λ2〉 e,a 4n 2τ rad

(63)

⫽ Thus, the ratio of peak absorption to emission cross sections is given by σ apeak / σ peak e eff 2 2 (∆ω eff e /∆ω a ) 〈λ 〉 a /〈λ 〉 e.

555


If the assumption 〈λ2〉 a ⬃ 〈λ2〉 e ⫽ λ 2s was made, which is justified when the Starksplitting of each manifold is small in comparison with the energy gap separating them, eff 2 Eq. (55) can be rewritten as follows, using ∆ω eff a,e ⫽ 2πc∆λ a,e /λ s : σ peak e,a ⫽

λ 4s 8πn 2cτ rad∆λ eff a,e

(64)

This equation constitutes the Fuchtbauer–Ladenburg relation [29–33] shown in Eqs. (1) and (2) of this chapter, which was widely used throughout the literature of RE:glass spectroscopy. On the other hand, if the approximations τ jk ⬃ τ′ and λ jk ⬃ λ s are made in Eq. (62) (all transition have the same decay rate and wavelength), one finds 〈λ2〉 e ⫽ λ2a and 〈λ2〉 a ⫽ λ 2 g A. Then, if the line shapes are assumed to be identical (i.e., if σ Ha,e (ω) ⬃ σ(ω)), the ratio of peak cross sections becomes σ apeak /σ epeak ⫽ g B /g A, which leads to the usual expression for the gain coefficient found in textbooks, namely

冤

g*(ω) ⫽ σ(ω) N B ⫺

gB NA gA

冥

In reality, however, the approximations of τ jk ⬃ τ′ and all σ Hjk (ω) being equal are not valid, because low-temperature absorption and emission measurements show that the individual transition strengths actually depend on the Stark levels involved [27,39]. Thus, the discrepancy observed between the ratio σ a /σ a predicted by the FL formula and the value measured from gain and absorption coefficients [38,89] is expected. Note that several alternative methods exist for cross section evaluation [32– 37,39,102], differing in complexity and accuracy. The most accurate methods are based on the McCumber theory [39,40] or on direct measurements requiring the knowledge of fiber waveguide parameters and Er density profile [102]. For the sole purpose of modeling the EDFA, the most simple approach consists of utilizing the absorption and gain coefficients that can be measured directly in the specific EDFA considered. This approach is accurate to the extent that the Er-doping profile is confined near the center of the fiber core, for which mode–core overlap effects are simple to model. The EDFA gain is given by [100]:

冦冢冣冮 χ ″(ν)dz冧

G(L, ν) ⫽ exp ⫺

Γsω nc

L

E

Figure 9 shows that the spectral shape of χ″E (ν) (see Fig. 9b) is strongly dependent on the ratio P p /P pth at low pump powers, whereas the dependence vanishes in the high pump regimen. For each pump power level at fiber coordinate z, the EDFA is absorbing (⫺χ″E (λ) ⬍ 0) in the short-wavelength region and amplifying [χ″E (λ) ⬎ 0] in the longwavelength region. The net spectral gain is given by the foregoing integral, which accounts for the decay of the pump power along the fiber. This spectral dependence of the gain coefficient with pump power is reflected in the changes in ASE spectra shown in Figure 5. Similar spectral changes were measured for the EDFA gain [103]. The pump threshold P pth is defined by P thp ⫽ hν p A p /σ a (ν p )τ (see also Secs. 10.2 and 10.6), where A p ⫽ πω 2p is the pump-effective mode area. This threshold corresponds to the pump power for which the ground and upper populations are equal (i.e., N B ⫺ N A ⫽ 0: see Eqs. 16 and 17). The parameters P thp should not be confused with the pump power P′p, for which the gain coefficient vanishes [i.e., g(ν) ⫽ σ e (ν)N B ⫺ σ a (ν)N A ⫽ 0], which varies with signal frequency

556

Desurvire

Figure 9 (a) Real and (b) imaginary parts of the complex atomic susceptibility of the EDFA at T ⫽ 295 K calculated for different values of pump power normalized to pump threshold (i.e., P p / P thp ⫽ 1–10). (From Ref. 100.)

ν as shown in Figure 9b. The relation between the two parameters is simply P ′p (ν) ⫽ [σ a (ν)/σ e (ν)]P pth [49]. These two parameters, in turn, should not be confused with the input pump power P trans required to reach transparency for a given fiber length (see Sec. p 10.6). This power is the solution of the equation G(L, ν, P trans p ) ⫽ 0 and depends on both fiber length and signal wavelength. The real part χ′E of the complex susceptibility can, similar to the imaginary part χ″E , be defined analytically [100], but it also can be determined by a Kramers–Kronig transform of χ″E [71]. Figure 9 shows plots of χ′E and ⫺ χ″E spectra for different pumping conditions Rτ ⫽ P p /P pth, with the assumptions Γ s ⫽ 1, ρ ⫽ 1.0 ⫻ 10⫺19 ion/cm3 (see Eqs. 16 and 17 for definition of N A and N B in Eq. 59). The gain-induced refractive index change at z ⫽ L is related to χ′E through δn ⫽ (Γ s /2nL) ∫Lχ′E dz, where L is the EDFA length. Thus, in the highest pumping conditions, δn(ν, L) ⬃ Γ sχ′E (ν)/2n, and Figure 9a shows that the refractive index change is of the order of δn ⬃ 5 ⫻ 10⫺7. Note that this value corresponds to an example of relatively high Er 3⫹ concentration, which nears the level at


557

which unwanted fluorescence quenching and cooperative upconversion mechanisms occur [41,104], and it can be reduced by several orders of magnitude by using lower concentrations. The result shows that gain-induced refractive index changes in EDFAs represent a negligible perturbation of the propagation constants of guided modes, for the index difference in fibers is in the ∆n ⫽ 10⫺3 –10⫺2 range. For comparison, gain-induced index changes in AlGaAs semiconductor amplifiers are of the order of ⫺4 ⫻ 10⫺2 at high carrier densities [105,106]. Note that the integrated phase change δφ ⫽ δnωL/c for both types of amplifier is nearly identical, because the EDFA length is usually five orders of magnitude longer than that of semiconductor amplifiers. 10.5.2 Gain Inhomogeneity The theory described so far is based on the assumption that the EDFA gain medium is primarily homogeneous. Such an assumption is validated by the observation of spectrally uniform gain saturation effects in Al 2O 3 /SiO 2 fibers [52], as well as by low-temperature spectroscopy of Er :glass [27]. Figure 10 shows EDFA output spectra obtained experi-

Figure 10

Output spectra obtained experimentally and theoretically for input signal power varying from 0 to 25 µW. Note uniform compression effect of the ASE spectrum. (From Ref. 52.)

558

Desurvire

mentally and theoretically when the input signal power at λ ⫽ 1.537 µm is varied from Pin s ⫽ 0–25 µW [52]. Note that the ASE spectral power decreases uniformly as the input signal is increased (see Fig. 10a). This effect is well reproduced with theory using the homogeneous gain approximation (see Fig. 10b). For aluminosilicate EDFAs, such a homogeneous model provides good agreement between theory and experimental data in oneand two-channel saturation experiments [52]. On the other hand, low-temperature spectroscopy showed that for a variety of bulk Er: glasses, site-to-site variation of the Stark level energies (inhomogeneous broadening) is of the same order of magnitude as the Stark splitting [27,28]. As a result, there exists a strong overlap between emission coming from different atomic sites, which indicates that homogeneous broadening is a valid approximation. It was observed, however, that EDFAs based on SiO 2 and GeO 2 /SiO 2 glasses exhibit some degree of inhomogeneity in the gain profile [107,108]. Because inhomogeneity is undesirable for multichannel applications of EDFAs, systematic spectroscopic studies should be pursued to determine the glass hosts and compositions that present the most homogeneous characteristics. The evaluation of homogeneity in optical transitions of RE glasses can be made through a variety of spectroscopic techniques, including fluorescence line narrowing, photon echoes, and hole-burning [109,110]. Among them, spectral gain hole-burning permits the determination of the homogeneous line widths in EDFAs [111,112]. The technique consists of measuring the temperature dependence of the width of a spectral hole generated in the ASE spectrum in the presence of a saturating signal. The homogeneous line width ∆λ H is simply related to the hole width ∆λ hole through ∆λ H ⬃ ∆λ hole /2 [57]. Figure 11 shows such output spectra, and the effect of hole-narrowing with decreasing temperature [110] (note that for accurate measurements, the spectra must be monitored in the polarization direction perpendicular to that of the output saturating signal). Figure 12 shows plots of ∆λ hole as a function of temperature measured at the peak gain wavelength of aluminosilicate and germanosilicate EDFAs [111,112]. For these two

Figure 11

Unpolarized output spectra of an EDFA at temperatures 77, 51, 34, and 4.2 K showing spectral gain hole-burning by saturating signal near 1.53 µm. (From Ref. 111.)


559

Hole width ∆λ hole plotted as a function of temperature, for aluminosilicate and germanosilicate EDFAs at peak gain wavelengths 1.531 and 1.535 µm, respectively. (From Refs. 111 and 112.)

Figure 12

types of fiber, the homogeneous width is observed to follow a near-quadratic temperature dependence (i.e., T 1.73 and T 1.61, respectively) characteristic of RE glasses [110]. The room temperature widths, obtained by extrapolation at T ⫽ 300 K of these power laws, are found to be ∆λ H ⫽ 11.5 and 4 nm for the respective fiber types. Calculation of the Voight line shapes [57] that give the best-fit to the emission cross section profiles yields corresponding inhomogeneous line width values of ∆λ I ⫽ ⫹11.5 and 8 nm, for the two fiber types, respectively [111,112]. Thus, at the signal wavelengths considered, the aluminosilicate EDFA has equal amounts of inhomogeneous and homogeneous broadening, whereas for the germanosilicate EDFA the homogeneous width is about three times narrower, and its inhomogeneity/homogeneity ratio is twice as important. Note that homogeneity in RE glass may vary across the gain profile [18] and that accidental coincidences of laser transitions can result in apparently broader homogeneous line widths. The values of ∆λ H ⫽ ∆λ I ⫽ 11.5 nm (⫽ 49 cm⫺1 ) are nearly equal to the energy spacing of Stark levels (50 cm⫺1 ) [28] for the aluminosilicate fiber type, which is an indication of strongly homogeneous characteristics. 10.5.3 Modeling Inhomogeneous Gain Broadening The theoretical model developed earlier for homogeneous EDFAs can be extended to the case in which inhomogeneity cannot be neglected. The cross sections measured experi-

560

Desurvire

H mentally σ exp a,e can be related to the homogeneous cross sections σ e,a defined in Eq. (52) through the convolution integral [113]:

σ exp e,a (ν) ⫽

冱冱p j

Bk , Aj

∫σ Hkj (ν ⫺ ν′)f(ν′ ⫺ ν jk )dν′

(65)

k

The normalized function f(ν) in Eq. (65) models the random variation of the energy spacing E j ⫺ E k owing to inhomogeneous broadening. In the homogeneous case f(ν′ ⫺ ν jk ) ⫽ δ(ν′ ⫺ ν jk ) and Eqs. (60) and (65) are identical. Assuming that f(ν) is the same for all transitions j ↔ k, the change of variables ν″ ⫽ ν′ ⫺ ν ⫺ ν jk in Eq. (65) leads to: H σ exp e,a (ν) ⫽ ∫ σ a,e (ν″) f (ν ⫺ ν″)dν″

(66)

If one assumes a gaussian function of width ∆ν I for f(ν), deconvolution by Fourier transformation of Eq. (66) yields the homogeneous cross sections σ He,a (ν). Figure 13 shows, for aluminosilicate, the experimental cross sections σ exp e,a (λ) and their homogeneous counterexp in Fig. 13a are part σ He,a (λ) obtained by using ∆λ I ⫽ 11.5 nm (note that values for σ e,a calculated by the FL relations, with improved accuracy in the experimental measurement of the line shapes as compared with that of Fig. 3). The well-resolved peaks in the homogeneous cross section profiles in Figure 13b can be attributed to the contributions of individual Stark transitions. The EDFA gain coefficient at fiber coordinate z can now be written as follows [113]: g(z, ν) ⫽ Γs ∫f(ν′)[σ He )(ν ⫺ ν′)N B(z, ν) ⫺ σ Ha )(ν ⫺ ν′)N A(z, ν′)]dν′

(67)

with the populations N A, N B defined in Eqs. (21) and (22), and the associated stimulated emission coefficients in Eq. (18) being now defined by: W TAB,BA(z, ν′) ⫽

1 ∫[Pp(z, ν′) ⫹ Ps(z, ν′)]σ Ha,e (ν″ ⫺ν′)dν″ hν sδνπω 2s

(68)

where P p (z, ν) and P s (z, ν) represent the power spectra of the pump and the signal.

Figure 13 (a) EDFA experimental absorption cross sections of aluminosilicate fiber and (b) theoretical homogeneous cross section obtained after deconvolution of experimental cross sections using inhomogeneous width of ∆λ i ⫽ 11.5 nm. (From Ref. 113.)


561

Figure 14 Polarized output spectra obtained experimentally and theoretically, using the homogeneous and inhomogeneous models, for different values of input signal power at a wavelength of 1.531 µm for P ins ⫽ 0–1000 µW. Bottom row shows gain compression curves obtained by subtraction of the ASE spectra with first spectrum in top row, corresponding to P ins ⫽ 0. (From Ref. 113.)

Figure 14 shows plots of output spectra of the EDFA pumped at λ p ⫽ 1.56 µm with saturating input signal at λ s ⫽ 1.531 µm, as obtained experimentally and theoretically [113]. Both homogeneous and inhomogeneous models (using the foregoing equations) were used for comparison. As Figure 14 shows, gain compression is stronger near the peak gain wavelength λ s, which is explained by the frequency dependence of the saturation power P sat (see next section for definition). Comparison of the spectra calculated through the two models, however, shows that the inhomogeneous model predicts, far from the saturating signal, a compression effect that is smaller than that in the homogeneous signal, in closer agreement with the experimental result. The inhomogeneous model also predicts a gain compression effect near the saturating signal that is narrower than that in the homogeneous one, in closer agreement with the experiment. From this comparison it is clear, however, that in spite of this fair agreement, neither homogeneous nor inhomogeneous models provide a truly accurate description of the EDFA under high saturation conditions. This indicates the need for further spectroscopic data on the line-broadening effects in EDFA, as well as refinements in the theoretical model, including data on the homogeneity and inhomogeneity of the individual Stark components. 10.6 FIBER AMPLIFIER GAIN, EFFICIENCY, AND SATURATION CHARACTERISTICS The characteristics of the Er-doped fiber amplifier as a device are reviewed in this section. These basic characteristics can be grouped in three main categories: the EDFA gain (as a function of pump power, signal wavelength, fiber length, Er 3⫹ concentration, and such), the EDFA pumping efficiency (as a function of pump band, pump and signal wavelengths, glass host, fiber design, or others), and the EDFA saturation power. All these aspects are essential for practical applications. In only a few years, EDFA performance in gain, efficiency, and saturation has progressed very fast, and now one may view the EDFA as being a nearly optimized device, ready for manufacturing. More progress can yet be antici-

562

Desurvire

pated, given the intensive research currently taking place in the investigation of alternative materials, dopings, and fiber designs for the EDFA. This section outlines the issues related to the EDFA characterization and optimization. Following the demonstration of low-threshold Er fiber lasers [8], the first experiments with EDFAs used visible light for the pump (i.e., λ p ⫽ 665 nm from a dye laser [9] and λ p ⫽ 514 nm from an argon ion laser [114]). The pump powers required for a gain of 20 dB were 20 and 70 mW at these two pump wavelengths, respectively, whereas for 30-dB gain they were 100 [9] and 220 mW [52]. As an illustration of the drastic evolution in pumping efficiency, gains of 30 dB can now be obtained with nearly 5 mW at λ p ⫽ 980-nm pump wavelength [115]. A look at the energy level diagram shown in Figure 1 shows that there are indeed many possible pump bands for the EDFA. Initially, the 810-nm band was considered to be attractive because of its compatibility with high-power AlGaAs laser diodes (LDs). The first LD-pumped EDFA used an injection-locked semiconductor array operating near this wavelength [116]. It was observed, however, that in SiO 2 glass hosts, such a pump band is subject to the effect of pump excited-state absorption, resulting in decreased pumping efficiency [23,24]. With recent improvements of fiber design, gains up to 30 dB with a 100-mW pump at 800 nm are possible [117], this power requirement being compatible with currently available high-power AlGaAs LDs. The other possible bands with wavelengths of 532 nm (where ESA is minimized) and 980 nm (where ESA is absent) provide efficient pumping [118,119]. One advantage of 532-nm pump is the compatibility with miniaturized LD-pumped frequency-doubled Nd:YAG or Nd:YLF laser sources, and the 980-nm wavelength can be generated by strained-layer InGaAs/Al GaAs quantum well LDs [120]. The remaining pump band close to 1.48 µm, which nears the 4 I 13/2 → 4 I 15/2 laser transition at 1.55 µm, corresponds to the operation of the EDFA as a quasi-two-level system [53]. The early report of signal amplification using this pump band [121] led to the first demonstration of an efficient LDpumped EDFA [10,122], for which gains in excess of 12 dB could be obtained with 32mW launched pump power [10]. The first LD-pumped EDFA at 980 nm showed an advantage in efficiency for this pump band, as a gain twice as high (24 dB) could be achieved with only 6.5-mW pump power [11]. Yet, these results have continued to show improvement, as demonstrated later. Because of their low pump power requirement, the two pump bands of 980 nm and 1.48 µm have retained most of the attention for system applications and the realization of practical integrated EDFA modules. For this reason, this section focuses on the results obtained at these two pump wavelengths. 10.6.1 Gain Versus Pump Power The EDFA gain dependence with pump power near λ p ⫽ 1.48 µm is shown in Figure 15. The experimental points were obtained with a color-center (CC) laser pump and with an LD pump [122,123] for comparison purposes. Figure 15 shows that there exists a launched pump power level (i.e., P inp ⫽ P ptrans ⫽ 4–5 mW) for which transparency is achieved (G ⫽ 0 dB). This power, which should not be confused with the pump threshold P pth (see Sec. 10.5), actually depends on the signal wavelength and the EDFA length. The value of P ptrans is lower for long-signal wavelengths (i.e., 1.54 µm), consistent with the decrease with wavelength of the absorption by the ground level (see Fig. 3). For increasing pump above P trans p , the gain increases steeply, then levels off. This last regimen corresponds to the case in which near-complete inversion is achieved along the whole fiber length. The


563

Figure 15

Signal gain obtained in an EDFA 40 m long as a function of launched pump power near λ p ⫽ 1.49 µm, the pump being a color-center laser or a laser diode, for different signal wavelengths in the λ s range of 1.531–1.547 µm. The dashed lines show pumping efficiencies of 2.3 and 2.6 dB/ mW for the 1.531- and 1.544-µm signal wavelengths, respectively. (From Refs. 123 and 126; and courtesy of T. W. Cline et al., AT&T Bell Laboratories.)

maximum gain occurs at the peak wavelength of the emission cross section (i.e., λ s ⫽ 1.531 µm; see Fig. 3). One way to characterize the EDFA pumping efficiency is to measure the maximum ratio of gain to launched pump power. This ratio, called by several authors gain coefficient, is the slope of the tangent to the gain curve that intersects the origin, as shown by the dashed lines in Figure 15. The maximum gain coefficient is obtained at is minimized) and is 2.6 dB/mW at λ s ⫽ 1.544 µm in long signal wavelengths (as P trans p this example. For comparison, the best gain coefficients yet reported for the 980-nm and 1.48-µm pumps are 10.2 dB/mW [124] and 5.9 dB/mW [125], respectively. The EDFA gain coefficient strongly depends on fiber design [61], rather than on the choice between 980-nm and 1.48-µm pump bands [62]. The gain coefficient g (dB/mW) was increased by concentrating the Er-doping region near the center of the fiber core, where the pump intensity is maximum [48,61]. A study of the dependence of g (dB/mW) on the Er-doping confinement shows that for fibers with high numerical aperture, gain coefficient values up to 8 dB/mW, at both pump wavelengths, are theoretically predicted [61], which is consistent with the experimental results [124,125]. Gain coefficients up to 20 dB/mW are likely to be achieved in the future with improved confinement and control of the Er density profile. As Figure 15 shows, the gains obtained with a Fabry–Perot LD as a pump are very similar to those obtained with the CC pump. Thus, multimode LDs are as efficient pumps as narrow-spectrum CC lasers, which indicates a weak dependence of gain on pump detuning about 1.48 µm. This fact, predicted theoretically for the 1.48-µm band [53], was confirmed experimentally for both 1.48-µm and 980-nm bands [126–129]. The weak dependence (⬃20 nm) of gain on pump wavelength near 1.48 µm and 980 nm is illustrated in Figure 16.

564

Desurvire

Signal gain obtained in an Er-doped fiber for 10-mW launched pump power at λ p ⫽ 980 nm and λ p ⫽ 1.48-µm wavelengths, as a function of pump wavelength detuning about λ p. (From Refs. 126 and 129.)

Figure 16

10.6.2 Gain Saturation Next to the pumping efficiency, the most important feature of the EDFA is its gain saturation characteristics. In Figure 17, for example, the EDFA gain is plotted as a function of the output signal power [123]. The saturation output power P out sat is, by definition, the output power at which the gain is 3 dB below its unsaturated value. The saturation output power out should not be confused with the saturated output power, which some authors designate P sat

Figure 17

Signal gain versus output signal power for different input pump powers. The corresponding optimal lengths L opt, unsaturated gains G max, and output saturation power P out sat are also shown. (From Ref. 123.)


565

Output saturation power at λ s ⫽ 1.531 µm versus launched pump power for the two pump wavelengths of λ p ⫽ 975 nm and 1.49 µm, showing linear increase with 0.25 slope. (From Ref. 123; courtesy of P. C. Becker et al., AT&T Bell Laboratories.)

Figure 18

as the maximum output power that can be achieved with the EDFA, given an input signal P sin. In theory, this maximum output power can be, at most, as high as the input pump power when complete power conversion between pump and signal occurs. The value of out P sat is more relevant to characterizing the EDFA, since it represents a threshold value for the transition between linear and nonlinear gain regimens of the amplifier. As Figure 17 in shows, the value of P out sat depends on the input pump power P p , the best value being out in P sat ⫽ ⫹11.3 dBm for P p ⫽ 53.5 mW (where dBm is decibels over 1 mW). Note that for this pump power, the highest saturated output power was ⫹15 dBm, which represents about η ⫽ 60% power conversion between pump and signal. The maximum power conversion that can be achieved is given by the quantum limit η ⫽ hν s /hν p, which depends on the pump and signal wavelengths. The increase of output saturation power P out sat with input pump power has a linear dependence with a slope of ⬃0.25 for both 975 nm and 1.48 µm pump wavelengths, as illustrated in Figure 18, for the case of an aluminosilicate EDFA. Such dependence can be explained from the three-level system model developed in Section 10.3. The signal gain coefficient at fiber coordinate z and frequency ν can be expressed from Eq. (24) as follows: γ Hs ⫽ ρσ He (ν)

sig Rτ ⫺ s(ν) 1 ⫹ [ω sig AB ⫺ s(ν)W BA ]τ/[Rτ ⫺ s(ν)] sig 1 ⫹ Rτ 1 ⫹ (W AB ⫹ W sig BA )τ/(1 ⫹Rτ)

(69)

If we assume a strong monochromatic signal at frequency ν s, the stimulated emission s H coefficients take the form W sig AB,BA ⫽ P s /[hν A s /σ a,e (ν s )τ], where P s /A s is the signal intensig ⫹ W ) τ ⫽ P /P sity. Using the relation (W sig AB s sat, where P sat ⫽ hν s A s /[σ a (ν s ) ⫹ σ e(ν s )]τ BA is the intrinsic saturation power,* and Rτ ⫽ P p /P pth, where P p is the pump power, the gain coefficient at ν s can be expressed from Eq. (69) as follows: * The definition for the intrinsic saturation power P sat is identical with that of Appendix B, with P sat ⫽ hν JP sat J . Note that the definitions of P* sat in the appendix in Ref. 52 and P sat are identical, with the correction of a typographical error in the definition of the saturation intensity in Ref. 52, which should read I sat 12,21 ⫽ hν s /2σ a,eτ.

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Desurvire

P p /P pth ⫺ s(νs) 1 γ Hs(νs) ⫽ ρσ He (ν s) 1 ⫹ P p /P thp 1 ⫹ P s /P s*at

(70)

where P s*at ⫽ P sat (1 ⫹ P p /P thp ). Equation (70) shows that the signal gain coefficient γ s * )⫺1, where for high pump powers (P p ⬎⬎ P pth ), P *sat is proportional saturates as (1 ⫹ P s /P sat to P p. Thus, for a given signal power P s, the EDFA gain saturation can be compensated by an increase in pump power. As Figure 18 shows, the increase in saturation output power P out sat of the EDFA corresponds to increasing launched pump power. A factor of 2 increase of the saturation power P out sat represents an increase of ⬃15 mW of pump power P pin. Assuming a range launched pump power P inp 100 mW (which is within the capability of current 1.48-µm laser diodes), the EDFA saturation output power range can be projected for most practical applications to be P out sat ⫽ ⫹12 to ⫹14 dBm. Exact analytical solutions for the EDFA gain with bidirectional pump and signals were derived in Section 10.3. Figure 19 shows the gain dependence on pump power measured experimentally for two input signal powers, with theoretical curves derived from Eq. (32). Note the excellent agreement between theory and experiment. The values of P sat J ⬃ P sat (λ s or λ p ) used in Eq. (32), which are necessary to such a theoretical fit, can be derived experimentally through a method shown elsewhere [63]. The saturation characteristics of EDFAs also depend on the pump band, the saturaout tion power P sat being greater for 1.48-µm pumps, as Figure 18 indicates. Figure 20 shows a plot of experimental values of unsaturated gain versus saturation output power measured with the two different pump bands, different pump powers, and two types of glass fiber.

Signal gain at λ s ⫽ 1.55 µm versus launched pump power at λ p ⫽ 1.48 µm for two input signal powers of P ins ⫽ ⫺27 and 0 dBm, obtained experimentally and theoretically, using analytical solutions developed in Section 10.3. (From Ref. 63.)

Figure 19


567

Figure 20

Unsaturated signal gain versus output saturation power reported for the pump wavelengths near 980 nm (curves A, B) and 1.48 µm (C, D) in germanosilicate (A, C) and aluminosilicate (B, D) fiberglass types. The range of pump powers is shown below each set of experimental points. (From Refs. 11, 123, and 130; courtesy of A. Lidgard et al., AT&T Bell Laboratories.)

Several observations can be made from this plot. First, identical gains and saturation powers (e.g., G ⬃ 40 dB, P out sat ⬃ 0 dBm) can be obtained with either pump band, the required pump power at 1.48 µm being twice as high as at 980 nm (curves A and C). Second, the saturation output power can vary significantly from one fiber type to the other for fixed gain and pump power (e.g., P inp ⬃ 55 mW, λ p ⬃ 1.48 µm, curves C and D); alternatively, the gain can vary significantly with comparable saturation power for a fixed pump power (e.g., P inp ⬃ 20 mW, λ p ⬃ 980 nm, curves B and C). For a given pump power level, the maximum gains or saturation powers are observed to depend on fiber designs and glass types. The highest gain and saturation performance yet achieved with LD pumping, represented in the upper right-hand side in Figure 20, includes G ⫽ 46.5 dB and P out sat ⫽ 10.7 dBm, with 133-mW pump power at 1.48 µm [130]. More studies are now needed to fully characterize the combined effects of pump wavelength, fiber design, and fiber glass composition on the gain/saturation characteristics of EDFAs. 10.6.3 Transient Gain Dynamics When several signals are simultaneously amplified, the effect of gain saturation causes cross talk, or interchannel interference. This interference effect occurs for amplitudemodulated (ASK) signals (gain–saturation-induced cross talk), or frequency-modulated (FSK) signals (intermodulation distortion). Intermodulation distortion, observed in semiconductor amplifiers [131,132], is caused by the gain modulation at the beat frequency of closely spaced optical signals. In both cases, cross talk generated in each of the optical channels results in the degradation of signal/noise ratio. The dynamics of gain saturation for each type of optical amplifier determines the magnitude of cross-talk effects, and eventually the maximum number of optical channels that can be simultaneously amplified. Transient gain dynamics in EDFAs can be characterized by measuring the timedependent gain modulation generated by a saturating signal [133–135]. Figure 21 shows

568

Desurvire

Figure 21 Experimental and theoretical output signals obtained with a saturating input signal at

λ 1 ⫽ 1.531 µm having a square pulse envelope: (a) Input signal peak power is constant, whereas the pump power is varied. (b) Pump power is constant whereas input signal peak is varied. (c) Output signal at λ 1 (square pulse input) and output probe at λ 1 ⫽ 1.537 µm (cw input). Note the long time constants (0.1- to 1-ms range) associated with transient gain saturation and recovery. (From Refs. 135 and 136.)


569

output signal pulses measured and calculated under such conditions [130]. The case in which the input signal is a square pulse, with the input pump or signal powers being varied, is illustrated in Figure 21 a, b. The output pulses are characterized by an overshoot at the leading edge, corresponding to a transient of the unsaturated gain regimen, followed by a decrease corresponding to the steady-state gain conditions. The time constants associated with this dynamics are seen to be shorter with the highest pump or signal powers. Figure 21c illustrates the dynamics of gain compression and recovery experienced by a continuous-wave (CW) signal probe at a neighboring wavelength. Both effects of saturation and recovery have very slow dynamics, the associated time constants being in the range of 100 µs to 1 ms. The same experiment can be done with the saturating signal being sinusoidally modulated, the measure of cross talk being the peak to-peak gain variation induced by a CW probe. It was observed that such a cross talk effect vanishes with the increase in the frequency of the saturating signal, the 3-dB cross talk reduction occurring at frequencies between 100 Hz and 10 kHz, depending on the pump and signal power conditions [133–135]. Figure 22 shows this effect, as measured experimentally and calculated theoretically. The theoretical curve is obtained by solving time-dependent rate equations for the atomic populations and the optical signals [135,136]. An analysis of transient dynamics [137] shows that for a 101010 bit sequence at rate B, the time-dependent modulation δ(N B ⫺ N A ) of the population inversion N B ⫺ N A can be expressed as follows: δ(N B ⫺ N B ) ⬃

e

⫺ω/B

(1 ⫺ e⫺ω/B )(1 ⫺ e⫺ω′/B ) ⫺ e⫺ω′/B ⫹ K(1 ⫺ e⫺ω⫹ω′/B )

(71)

where ω ⫽ ω′ ⫹ (P s /P sat )/τ and ω′ ⫽ (1 ⫹ P p /P pth )/τ are the characteristic frequencies of the gain dynamics, which depend on the pump and the signal powers, and K is a function of ω, ω′. A plot of Eq. (71) versus bit rate B [137] shows that the inversion modulation δ vanishes at bit rates near 1 kHz; the specific frequency at which the cross talk effect decreases by 3 dB is determined by the values of P p /P pth and P s /P sat, in agreement with experimental observation. The rate at which the cross talk vanishes is typically 10 dB per order of magnitude increase in the modulation frequency [135,137].

Figure 22

Experimental and theoretical peak-to-peak gain variation or cross talk in a probe channel. (B) as a function of the frequency of a saturating signal in channel (A), showing that the effect vanishes at frequencies near 10 kHz. (From Refs. 135 and 136.)

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Desurvire

Figure 23

Bit error rate at 2 Gb/s in a two-channel amplification experiment, for channel A at λ a ⫽ 1.537 µm when signal power in channel B at λ b ⫽ 1.539 µm is increased from P inp ⫽ 0 (⫹) and P inb ⫽ ⫺32 dBm (䊊) and ⫺20 dBm (⫻), causing, in the last case, a 3-dB–gain compression in channel A. (From Ref. 52.)

The advantage of the slow gain dynamics in EDFAs is, for ASK signals, the immunity to patterning effects (single channel) or intersymbol interference (multiple channels), and for FSK signals, the immunity to intermodulation distortion. The effect of saturationinduced cross talk, which can be significant at frequencies lower than 1 kHz, can be alleviated by automatic gain control (AGC) loops. Feedforward compensation loops acting on the pump power source have been demonstrated [135]. This AGC method, similar to that used for semiconductor amplifiers [138], requires a comparatively small electronic bandwidth. An alternative scheme for AGC consists of maintaining a constant level of saturation in the EDFA, by means of a compensating input signal [139]. At high bit rates, the advantages of negligible patterning effects and cross talk are demonstrated by the early ASK signal amplification experiments at 2 Gb/s [52]. The bit error rates plotted in Figure 23 show that the multichannel cross talk penalty for ASK signals under saturation conditions (∆G ⫽ G(unsat) ⫺ G(sat) ⫽ 3 dB) is small and can be attributed to the effect of steady-state gain compression. A simple explanation for such a BER penalty is that gain saturation results in an decrease of the inversion along the fiber, corresponding to an increase of the spontaneous emission factor n sp (see Sec. 10.4), hence, of the EDFA noise figure. In a recent experiment [140] it was shown, however, that other factors contribute to such BER degradation. It can be shown, indeed, that the BER penalty P caused by saturated gain conditions takes the form [140]: P(dB) ⫽ 10 log

冢

冣

冢冣

冢

冣

G G′ ⫺ 1 n′ √1 ⫹ x′ ⫹ √x′ ⫹ 10 log sp ⫹ 20 log G ⫺ 1 G′ n sp √1 ⫹ x ⫹ √x

(72)


571

where G and G′ are the unsaturated and saturated gains, respectively, n sp and n′sp are the corresponding spontaneous emission factors, and x ⫽ (σ 2sp⫺sp ⫹ σ 2cir )/σ 2s⫺sp where σ 2s⫺sp, σ 2sp⫺sp, and σ 2cir are the signal–spontaneous beat noise, the spontaneous–spontaneous beat noise, and the circuit noise, respectively. Equation (72) shows that the BER penalty is made of these contributions. The first term in the right-hand side of Eq. (72) is negligible if the saturated gain is high (i.e., G′ ⬎⬎ 1); the second term involves, as expected, the ratio of the spontaneous emission factors (e.g., a relative increase of n sp by 3 dB corresponds to a 3-dB near-figure increase; hence, the input signal must be increased by 3 dB to achieve the same BER as in the unsaturated conditions). The third term is a function of x, which is the ratio of the EDFA noises without signal to the signal–spontaneous beat noise σ 2s⫺sp; as the gain saturates, the received signal decreases, and at some point the receiver noise is no longer dominated by the signal–spontaneous noise. The ratio σ 2sp⫺sp /σ 2s⫺sp can be reduced by use of narrow filtering, but the term from the circuit noise σ 2cir /σ 2s⫺sp is fixed by the receiver. Thus, the BER penalty owing to saturation is ultimately determined by both increase in spontaneous emission factor (reduced inversion) and departure from the signal–spontaneous beat noise regime (spontaneous–spontaneous noise and circuit noise dominant). The validity of Eq. (72) was checked with accuracy over a 12-dB gain compression range, using 1-Gb/s FSK signals with 30-dB unsaturated gain [140]. The BER penalties associated with gain saturation ∆G ⫽ 6–12 dB were P ⫽ 1.5–5 dB, in agreement (within 0.5 dB) with values predicted by Eq. (72). Thus, BER penalties cause by steadystate gain saturation are relatively small, which makes possible the use of many optical channels limited only by the amount of gain saturation that can be tolerated in a system application (Fig. 24). Quantitative interpretation and in-depth analysis of BER degradation with gain saturation ultimately requires knowledge of the EDFA photon statistics (probability distribution) in the nonlinear regime, as discussed in Section 10.4. The BER penalty formula (Eq. 72) is based indeed on phenomenological parameters (n sp, σ 2s⫺sp, σ 2sp⫺sp ) that cannot be predicted by the linear theory. Because of its important complexity, and its implications for systems applications, the issue of nonlinear photon statistics remains open to future experimental as well as theoretical investigations.

Figure 24

Bit error rate penalty at 1 Gb/s for an FSK signal in a saturated EDFA, plotted as a function of gain compression δG. (From Ref. 140.)

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10.7 CONCLUSION This chapter reviewed several aspects of erbium-doped fiber amplifiers: spectroscopic characteristics of Er :glass, theoretical analysis of signal and spontaneous emission noise amplification, and device performance in gain, pumping efficiency, and saturation. Many selected references were provided on each of these issues, to direct the reader toward further experimental data and theoretical insights. We also indicated several issues of interest on which research work on EDFAs remains to be done. We are now witnessing a large-scale research effort in the field of 1.5-µm fiber amplifiers, which indicates how important their potential applications have become for optical communications. Chapter 11 provides a detailed description of the advanced issues relating to EDFAs as they relate to the field of communication systems. From both the device and system perspectives, much progress is still to be anticipated. Novel rare earth combinations with alternative glass hosts, improvements in fiber fabrication techniques and design, and developments in high-power pump laser diodes and optical fiber components, all will likely give way to new generations of fiber amplifiers covering the 1.3- to 1.55-µm optical communications window. On the other hand, the study of the fundamental limits imposed by noise and sources of nonlinearities in optical fiber amplifiers will be necessary for the development of communication systems with hauls in the 10,000-km range. Such future systems, in which EDFAs will play a central role, will permit multigigabit optical communications over intercontinental distances. ACKNOWLEDGMENTS The author is indebted to J. R. Simpson, P. C. Becker, C. R. Giles, D. J. DiGiovanni, J. L. Zyskind, and J. W. Sulhoff for many collaborations in experimental work. He is also grateful to I. P. Kaminow and A. A. M. Saleh for their support and for many stimulating discussions. APPENDIX A Rate Equations of Quasi-Three-Level System Shown in Figure 4 One finds for the ground manifold A: dN A1 dt

⫽ ⫺A ⫹NR N A1 ⫹ A ⫺NRN A2 ⫹

冱A N k1

Bk

⫺

⫹

冱 w (N k1

Bk

冱 R (N ᐉ1

⫺ NCᐉ)

A1

ᐉ

k

(73)

⫺ N A1 )

k

dN Aj dt

冱A N

⫺ ⫽ ⫺A ⫹NRN Aj ⫹ A ⫺NkN A ,j⫹1 ⫺ A NR N Aj ⫹ A ⫹NRN A, j⫺1 ⫹

⫺

冱 R (N ᐉj

Aj

⫺ N Cᐉ ) ⫹

ᐉ

dN A,g1 dt

kj

Bk

k

冱 w (N kj

Bk

⫺ N Aj )

1 ⬍ j ⬍ g1

k

冱A N ) ⫹ 冱 w (N

⫺ N A,g1 ⫹ A ⫹NRN A ,g1⫺1 ⫹ ⫽ ⫺A NR

k,g 1

Bk

(75)

k

⫺

冱R ᐉ

(74)

(N A, g1 ⫺ N C ᐉ

ᐉ ,g 1

k ,g 1

k

Bk

⫺ N A, g1 )

573


Upper manifold B: dN B1 dt dN Bk dt

⫹ ⫽ ⫺A NR N B 1 ⫹ A ⫺NRN B2 ⫺

冱A N 1j

B1

⫺

j

冱 w (N 1j

B1

⫺ N Aj )

(76)

j

⫽ ⫺A ⫹NR N B k ⫹ A ⫺NRN B ,k⫹1 ⫹ A ⫹NR N B , k⫺1 ⫺ A ⫺NRN Bk ⫺

冱A N kj

Bk

j

⫺

冱w (N kj

Bk

⫺ N Aj )

(77)

1 ⬍ k ⬍ g2

j

dN B,g2 dt

⫺ ⫹ ⫽ A NR CB N C 1 ⫺ A NR N B ,g2 ⫹ A NR N B ,g2⫺1 ⫺

冱A

g2 , j

N B,g 2

j

⫺

冱w

g 2 ,j

(78)

(N B ,g 2 ⫺ N Aj )

j

Pump manifold C dN C1 dt dN Cᐉ dt

冱 R (N

⫹ ⫺ ⫽ ⫺A NR CB N C 1 ⫺ A NR N C 1 ⫹ A NR N C 2 ⫹

1j

Aj

⫺ N C1 )

j

⫹ ⫽ ⫺A NR N C ᐉ ⫺ A ⫺NR N C ᐉ ⫹ A ⫺NRN c,ᐉ⫹1 ⫹ A ⫹NRN c,ᐉ⫺1

⫹

冱 R (N ᐉj

Aj

(79)

(80)

⫺ NCᐉ) 1 ⬍ ᐉ ⬍ g3

j

dN C,g3 dt

⫽ A ⫺NRN C,g3 ⫹ A ⫹NRN C ,g3⫺1 ⫹

冱R

g3 , j

(N Aj ⫺ N C, g3 )

(81)

j

Solution of Rate Equations for Total Manifold Populations in the Steady-State Regimen In the steady-state regimen, we have dN D /dt ⫽ 0, and Eqs. (11) and (12) yield: A NR CB p C 1N C ⫺ (A R ⫹ W BA )N B ⫹ W AB N A ⫽ 0

(82)

⫺(R CA ⫹ A CBp C1 )N C ⫹ R ACN A ⫽ 0

(83)

Let a ⫽ R CA ⫹ A CBp C 1 and b ⫽ W BA ⫹ A R. Using these expressions and replacing N C ⫽ ρN A ⫺ N B in Eqs. (82) and (83) yields: (W AB ⫺ A CB p C 1 )N A ⫺ (b ⫹ A CBp C 1 )N B ⫽ ⫺A CB p C1ρ

(84)

(a ⫹ R AC )N A ⫹ aN B ⫽ aρ

(85)

Resolution of Eqs. (84) and (85) leads to: NA ⫽ ρ

ab b(a ⫹ R AC ) ⫹ aWAB ⫹ R AC A CBp C 1

(86)

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Desurvire

NB ⫽ ρ

R AC A CBp C 1 ⫹ aWAB b(a ⫹ R AC ) ⫹ aWAB ⫹ R AC A CBp C1

(87)

Replacing the definitions of a and b in Eqs. (86) and (87) gives: NA ⫽ ρ NB ⫽ ρ

(A R ⫹ W BA )(1 ⫹ R CA /A CBp C 1 ) (A R ⫹ W BA )(1 ⫹ R AC ⫹ R AC /A CBp C 1 ) ⫹ W AB (1 ⫹ R CA /A CBp C 1 ) ⫹ R AC R AC ⫹ W AB (1 ⫹ R CA /A CBp C 1 )

(A R ⫹ W BA )(1 ⫹ R AC ⫹ R CA /A CBp C1 ) ⫹ W AB(1 ⫹ R CA /A CBp C1 ) ⫹ R AC

(88)

(89)

Letting ε ⫽ R AC /A CB p C1 ⬇ R CA /A CB p C1 and multiplying the top and bottom of Eqs. (88) and (89) by τ ⫽ A R⫺1, yields finally: NA ⫽ ρ

(1 ⫹ W BAτ)(1 ⫹ ε) (1 ⫹ W BAτ) (1 ⫹ 2ε) ⫹ W ABτ (1 ⫹ ε) ⫹ R ACτ

(90)

NB ⫽ ρ

R ACτ ⫹ W AB(1 ⫹ ε) (1 ⫹ W BAτ)(1 ⫹ 2ε) ⫹ W ABτ (1 ⫹ ε) ⫹ R ACτ

(91)

In the limit ε ⬍⬍ 1 (pumping rate negligible in comparison with multiphonon rate between manifold C and B), Eqs. (90) and (91) yield the well-known solutions of threelevel laser systems shown in Eqs. (16) and (17). APPENDIX B The equation governing the power evolution in channel K is dP K ⫽ u K P K ∫∫(σ Ke N B ⫺ σ Ka N A )ψ K dx dy dz

(92)

where u K ⫽ ⫾1 corresponds to the forward (⫹) or the backward (⫺) propagation directions, and σ Ka,e D σ Ha,e (ν K ). Note that when the optical channel is not in the 4 I 15/2 → 4 I 13/2 band (as in a λ k ⫽ 980-nm pump), this model still applies, but with σ Ke ⫽ 0. Assuming the Er 3⫹ density profile ρ(x, y) is uniform with a radius a of small dimension in comparison with the size ω K of the mode envelope ψ K (x, y) and integrating Eq. (92), one obtains: uK

dP K ⫽ Γ K P K(σ Ke N B ⫺ σ Ka N A ) dz

(93)

where Γ K ⫽ a 2 /ω 2K is a filling factor [53]. In the steady-state regimen the atomic populations N A and N B satisfy: dN 1 dN A N ⫽⫺ B⫽ B⫹ dt dt τ A

冱 Γ P (σ N K

K

K e

B

⫺ σ Ka N A) ⫽ 0

(94)

K

where A ⫽ πa2. Using Eq. (93), Eq. (94) yields N B ⫽ ⫺(τ/ρA)∑ k u K dP k /dz ⫽ ρ ⫺ N A, and replacing this result in Eq. (93) leads to: uJ

冢

1 dP J ⫽ ⫺ α J ⫹ sat PJ PJ

冱u K

K

冣

dP K dz dz

(95)

575


J J where α J ⫽ ρΓ Jσ Ja is the fiber absorption coefficient at ν J and P sat J ⫽ A/Γ J(σ a ⫹ σ e )τ is the intrinsic saturation power [61,63], normalized to the photon energy hν J. If channel J J represents a pump in an absorption band other than 4 I 13/2, P sat J ⫽ A/Γ Jσ a is the pump th threshold P P [61]. Solving Eq. (95) yields the solution at z ⫽ L shown in Eq. (29).

APPENDIX C Derivation of the Moment Equation Multiplying Eq. (33) by n k and summing over n yields:

冱n dPdt k

n

⫽

n

⫽

d〈n k〉 dt

冱 {g [n e

k⫹1

P n⫺1 ⫺ n k (n ⫹ 1)P n] ⫹ g a[n k (n ⫹ 1)P n⫹1 ⫺ n k⫹1 P n]} (96)

n

By using the relations ⌺ n n p P n⫺1 ⫽ ⌺ n (n ⫹ 1)p P n and ⌺ n n p P n⫹1 ⫽ ⌺ n (n ⫺ 1)p P n [69,73] in Eq. (96), one obtains: d〈n k〉 ⫽ 〈g e n k(n ⫹ 1)〉 ⫺ 〈g an k⫹1〉 dt

(97)

⫹ 〈g e(n ⫹ 1)(n ⫹ 1) ⫹ g an(n ⫺ 1) 〉 k

k

Finally, using the binominal formula (n ⫾ 1)k ⫽ ⌺ j (k j )n j (⫾1)k⫺j in Eq. (97) yields the result shown in Eq. (34). Note that (⫺1)k⫺p⫹1 ⫽ (⫺1)k⫹p⫺1 APPENDIX D Analytical Solutions for the Gain and ASE Noise in Unsaturated Gain Regimen, with Effect of Fiber Background Loss The solutions of linear Eq. (47) take the form:

冦

αs ηs αp 1 ⫹ ηp

冮

q0

冦

αs ηs αp 1 ⫹ ηp

冮

q0

P⫹(q L ) ⫽ G ⫹ (q L ) P⫹(q 0 ) ⫹ P0

P⫺(q 0 ) ⫽ G ⫺ (q 0 ) P⫺(q L ) ⫹ P0

qL

qL

冧

(98)

冧

(99)

dq′ [1 ⫹ (1 ⫹ q′)α′p /α p]G ⫹ (q′) dq′ [1 ⫹ (1 ⫹ q′)α′p /α p]G ⫺ (q′)

with the forward and backward gains G ⫹ (q) defined by:

冦冮

G ⫾ (q) ⫽ exp ⫾

αs αp

q

q 0,q L

冤

冥冧

α ′ ⫹ αs dq′ η p ⫺ η s α′s ⫹ ⫹ s 1 ⫹ (1 ⫹ q′)α ′p /α p 1 ⫹ η p αs α s q′

(100)

576

Desurvire

Straightforward integration of Eq. (100) leads to:

冦 αα 冤冢η1 ⫹⫺ ηη ⫹ ε 冣ε1 ln 冦 11 ⫹⫹ εε (1(1 ⫹⫹ qq) )冧 1⫹ε q⫺q Arth 冦 ⫹2 1⫹ε q ⫹ q ⫹ 2qq ε /(1 ⫹ ε )冧冥冧

G ⫾ (q) ⫽ exp ⫾

s

p

s

p

s

p

p

p

p

s

in

(101)

in

p

in

in p

p

where ε s,p ⫽ α′s,p /α s,p and q in ⫽ q 0 for G ⫹ (q) and q in ⫽ q L for G ⫺ (q). Note from Eq. (101) that G ⫹ (q L ) ⫽ G ⫺ (q 0 ) ⫽ G. The gains in Eq. (101) can also be put under the form: ⫾A

冢冣冤

q G ⫾ (q) ⫽ q in

1 ⫹ ε p(1 ⫹ q) 1 ⫹ ε p(1 ⫹ q in )

冥

⫾B

(102)

where A ⫽ α s (1 ⫹ ε s )/α p (1 ⫹ ε p ) and B⫽

αs αp

冦冢η1 ⫹⫺ηη ⫹ ε 冣ε1 ⫺ 11 ⫹⫹ εε 冧 p

s

s

(103)

s

p

p

p

The integrals in Eqs. (98) and (99) can now be expressed as follows: f ⫾ (q 0, q L ) ⫽

冮

q0

qL

dx [1 ⫹ ε p (1 ⫹ x)]G ⫾ (x)

⫾B ⫽ q ⫾A in [1 ⫹ ε p (1 ⫹ q in )]

冮

q0

qL

(104) dx x [1 ⫹ ε p (1 ⫹ x)]1⫾B ⫾A

Because usually the exponents A and B do not have integer values, integration in Eq. (104) must be performed numerically. Approximate analytical form of Eq. (104) can also be obtained by effecting a Taylor development of the integrand and carrying the integration over as many terms as needed for accuracy. The output ASE power spectra are then given analytically by: P ⫾out ⫽ P0 G

αs ηs f ⫾ (q 0, q L ) αp 1 ⫹ ηp

(105)

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106. Manning, J., R. Olshansky, C. B. Su. The carrier-induced change in AlGaAs and InGaAsP diode lasers. IEEE J. Quant. Electron. QE-19:1525 (1983). 107. Laming, R. I., L. Reekie, P. R., Morkel, D. N. Payne. Multichannel crosstalk and pump noise characterization of Er 3⫹-doped fibre amplifier pumped at 980 nm. Electron. Lett. 25:455 (1989). 108. Inoue, K., H. Toba, N. Shibata, K. Iwatsuki, A. Takada. Mutual signal gain saturation in Er 3-doped fibre amplifier around 1.54 µm wavelength. Electron. Lett. 25:594 (1989). 109. MacFarlane, R. M., R. M. Shelby. Homogeneous line broadening of optical transitions of ions and molecules in glasses. J. Lumin. 36:179 (1987). 110. Yen, W. M., R. T. Brundage. Fluorescence line narrowing in inorganic glasses: linewidth measurements. J. Lumin. 36:209 (1987). 111. Desurvire, E., J. L. Zyskind, J. R. Simpson. Spectral gain hole-burning at 1.53 µm in erbiumdoped fiber amplifiers. IEEE Photon. Technol. Lett. 2:246 (1990). 112. Zyskind, J. L., E. Desurvire, J. W. Sulhoff, D. J. DiGiovanni. Determination of homogeneous linewidth by spectral gain hole-burning in an erbium-doped fiber amplifier with GeO 2 –SiO 2 core. IEEE Photon. Technol. Lett. 2:869 (1990). 113. Desurvire, E., J. W. Sulhoff, J. L. Zyskind, J. R. Simpson. Study of spectral dependence of gain saturation and effect of inhomogeneous broadening in erbium-doped aluminosilicate fiber amplifiers. IEEE Photon. Technol. Lett. 2:653 (1990). 114. Desurvire, E., J. R. Simpson, P. C. Becker. High-gain, erbium-doped traveling-wave fiber amplifier. Opt. Lett. 12:888 (1987). 115. Shimizu, M., M. Horiguchi, M. Yamada, M. Okayasu, T. Takeshita, I. Ishi, S. Uehara, J. Noda, E. Sugita. Highly efficient integrated optical fiber amplifier module pumped by a 0.98 µm laser diode. Electron. Lett. 26:498 (1990). 116. Whitley, T. J. Laser-diode pumped operation of Er 3⫹-doped fibre amplifier. Electron. Lett. 24:1537 (1988). 117. Nakazawa, M., Y. Kimura, K. Suzuki. High gain erbium fibre amplifier pumped by 800 nm band. Electron. Lett. 26:548 (1990). 118. Laming, R. I., M. C. Farries, P. R. Morkel, L. Reekie, D. N. Payne. Efficient pump wavelengths of erbium-doped optical fiber amplifier. Electron. Lett. 25:12 (1989). 119. Choy, M. M., C. Y. Chen, M. Andrejco, M. Saifi, C. Lin. A high-gain, high output saturation power erbium-doped fiber amplifier pumped at 532 nm. IEEE Photon. Technol. Lett. 2:38 (1990). 120. Bour, D. P., G. A. Evans, D. B. Gilbert. High-power conversion efficiency in a strained InGaAs/AlGaAs quantum well laser. J. Appl. Phys. 65:3340 (1989). 121. Snitzer, E. A., H. Po, F. Hakimi, R. Tuminelli, B. C. MacCollum. Erbium fiber laser amplifiers at 1.55 µm with pump at 1.49 µm and Yb-sensitized Er oscillator. Proc. OFC ’88, 1988; PD2. 122. Becker, P. C., J. R. Simpson, N. A. Olsson, N. K. Dutta. High-gain and high-efficiency diode laser pumped fiber amplifier at 1.56 µm. IEEE Photon. Technol. Lett., 1(9), 267 (1989). 123. Desurvire, E., C. R. Giles, J. R. Simpson, J. L. Zyskind. Efficient erbium-doped fiber amplifier at 1.53 µm wavelength with a high output saturation power. Opt. Lett. 14:1266 (1989). 124. Nakazawa, M., Y. Kimura, K. Suzuki. An ultra-efficient erbium-doped fiber amplifier of 10.2 dB/mW at 0.98 µm pumping and 5.1 dB/mW at 1.48 µm pumping. In: Proceedings of the IEE/LEOS/OSA Topical Meeting on Optical Amplifiers and Applications, 1990;PDP1. 125. Zyskind, J. L., D. J. DiGiovanni, J. W. Sulhoff, P. C. Becker, C. H. Brito–Cruz. High performance erbium-doped fiber amplifier pumped at 1.48 µm and 0.97 µm. In: Proceedings of the IEE/LEOS/OSA Topical Meeting on Optical Amplifiers and Applications, 1990; PDP6. 126. Zyskind, J. L., C. R. Giles, E. Desurvire, J. R. Simpson. Optimal pump wavelength in the 4 I 15/2 → 4 I 13/2 absorption band for efficient Er 3⫹-doped fiber amplifiers. IEEE Photon. Technol. Lett. 1:428 (1989).

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127. Kimura, Y., K. Suzuki, M. Nakazawa. Pump wavelength dependence of the gain factor in 1.48 µm pumped fiber amplifiers. Appl. Phys. Lett. 56:1611 (1990). 128. Suzuki, K., Y. Kimura, M. Nakazawa. Pumping wavelength dependence on gain factor of a 0.98 µm pumped Er 3⫹ fiber amplifier. Appl. Phys. Lett. 55:2573 (1989). 129. Becker, P. C., A. Lidgard, J. R. Simpson, N. A. Olsson. Erbium-doped fiber amplifier pumped in the 950–1000 nm region. IEEE Photon. Technol. Lett. 2:35 (1990). 130. Kimura, Y., K. Suzuki, M. Nakazawa. 46.5 dB gain in Er 3⫹-doped fibre amplifier pumped by 1.48µm GaInAsP laser diodes. Electron. Lett. 25:1656 (1989). 131. Agrawal, G. P. Amplifier-induced crosstalk in multichannel coherent lightwave systems. Electron. Lett. 23:1175 (1987). 132. Jopson, R. M., T. E. Darcie, K. T. Gayliard, R. T. Ku, R. E. Tench, T. C. Rics, N. A. Olsson. Measurement of carrier density-mediated intermodulation distortion in an optical amplifier. Electron. Lett. 23:1394 (1987). 133. Pettit, M. J., A. Hadjifotiou, R. A. Baker. Crosstalk in Er-doped fiber amplifiers. Electron. Lett. 25:416 (1989). 134. Laming, R. I., L. Reekie, P. R. Morkel, D. N. Payne. Multichannel crosstalk and pump noise characterization of Er 3⫹-doped fibre amplifier pumped at 980 nm. Electron. Lett. 25:455 (1989). 135. Giles, C. R., E. Desurvire, J. R. Simpson. Transient gain and crosstalk effects in erbiumdoped fiber-amplifiers. Opt. Lett. 14:880 (1989). 136. Desurvire, E., C. R. Giles, J. R. Simpson. Gain dynamics of erbium-doped fiber amplifiers. Proc. SPIE 1171:103 (1989). 137. Desurvire, E. Analysis of transient gain saturation and recovery in erbium-doped fiber amplifiers. IEEE Photon. Technol. Lett. 1:196 (1989). 138. Darcie, T. E., R. M. Jopson, A. A. M. Saleh. Electronic compensation of saturation-induced crosstalk in optical amplifiers. Electron. Lett. 34:2346 (1963). 139. Desurvire, E., M. Zirngibl, H. M. Presby, D. DiGiovanni. Dynamic gain compensation in saturated erbium-doped fiber amplifiers. IEEE Photon. Technol. Lett. 3:453 (1991). 140. Willner, A. E., E. Desurvire. Effect of gain saturation on receiver sensitivity in 1 Gb/s multichannel FSK direct-detection systems using erbium-doped fiber preamplifiers. IEEE Photon. Technol. Lett. 3:259 (1991).

11 Erbium-Doped Fiber Amplifiers: Advanced Topics PAUL F. WYSOCKI Leco Corporation, St. Joseph, Missouri

11.1 INTRODUCTION The erbium-doped fiber amplifier (EDFA) has become a key component in many optical networks because it provides efficient, low-noise amplification of light in the optical fiber low-loss telecommunications window near 1550 nm. As more systems using EDFAs have been built and tested, new issues and effects have emerged as critical to the development and expansion of this technology into the future. Single-channel amplification, as described in Chapter 12, is being supplanted by multiple channel wavelength–divisionmultiplexed (WDM) systems. EDFAs are being used in analog applications, not solely in digital systems. In most new applications, a high-output power and a low-noise figure (NF) are required. To achieve these goals, the emphasis has been placed on both fiber optimization and clever EDFA designs. High-power pump sources have made this task easier, while advances in fiber-grating technologies have facilitated more complex EDFA designs. This chapter assumes that the reader has a sound understanding of the basic physics and characteristics of EDFAs discussed in Chapter 10. Because the issues faced in EDFA design may evolve over time, the emphasis here is placed on developing intuition that can be applied in future situations. Simplified treatments and models are used wherever possible. The chapter is divided into four main sections. Section 11.2 deals with the EDFA gain spectrum and how it affects the use of these amplifiers in various applications. Section 11.3 discusses fiber design optimization issues for selected applications. Section 11.4 discusses effects that are small in a single EDFA, but can become significant in systems utilizing many EDFAs. Finally, Section 11.5 summarizes some of the novel EDFA designs used to meet NF, power, and spectral requirements for various applications. 583

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11.2 GAIN SPECTRUM CONTROL As erbium-doped fiber amplifiers are used in new applications, such as multiple-wavelength WDM systems and analog CATV systems, the shape of the gain spectrum is increasingly important [1]. This issue has led to three main areas of research. The first area involves modification of the erbium host composition to produce fibers with improved spectral characteristics. The second is the development of EDFA designs with integrated components that overcome the inherent spectral shortcomings of the fiber. The third area is the development of accurate spectral measurement techniques for the characterization of basic spectral properties and multiple wavelength gain. All of these efforts have benefited from the ability to model and predicts the behavior of different erbium-doped fibers (EDFs) operated in various configurations. These three areas of research are discussed in the following sections. 11.2.1 Modeling and the Homogeneous Gain Approximation An energy level diagram of the lowest states of the erbium ion is illustrated in Figure 1. It shows the center wavelength of the ground-state absorption (GSA) transitions, the standard excited-state absorption (ESA) transitions from the 4I13/2 state, referred to as ESA1, and the ESA transitions from the 4I11/2 state, referred to as ESA2. The decay rates (inverse lifetimes) of these levels are shown in Figure 1 of Chapter 10. When modeling EDFAs, it is important to note any ESA transition that is coincident with an absorption or emission band of either the pump or the signal, because these transitions may produce important loss mechanisms in practical devices. ESA1 transitions exist near 790 and 630 nm, making pumping of EDFAs near the GSA bands at 800 and 650 nm very inefficient. However, an ESA2 transition exists near 980 nm, where many EDFAs are pumped. In a silica-based host, most models have treated erbium as nearly ideal when pumped near 980 nm. The pump is absorbed to the 4I11/2 state and decays rapidly to the long-lived 4I13/2 state, which produces gain near 1550 nm. Hence, under normal conditions, only the ground state and 4 I13/2 state are appreciably occupied. When pumped near 1480 nm, this is guaranteed to be true because pumping occurs directly into the 4I13/2 state. Furthermore, 1480 nm pumping is free of both ESA1 and ESA2, and a high efficiency is expected. In fluoride glasses and some other hosts, the 4I11/2 state has a long lifetime and, therefore, can be appreciably occupied. Furthermore, 980-nm power can be absorbed by the ESA2 process mentioned earlier, thus wasting power. Even in silicates, the slight occupation of the 4I11/2 state can cause efficiency reduction at high pump power levels near 980 nm. This issue is further discussed in the following. The basic rate equations governing the performance of EDFAs were derived in Section 3 of Chapter 10. As EDFA use progresses into the future, more advanced and accurate modeling will be required. A complete model for an EDFA might include the following: 1. 2. 3. 4. 5. 6. 7.

Radial mode and dopant distributions ESA from all levels, even those slightly occupied Spectral or polarization hole-burning Ion–ion interaction processes known as cooperative upconversion Ion clustering or pairing and associated loss mechanisms Background losses and contaminant losses present in the material Time-dependent processes.


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Figure 1 Energy-level diagram of Er 3⫹ in a silicate host showing the three principal energy states of population density N1, N2, and N3, as well as the center wavelengths for the ground-state absorption (GSA) and excited-state absorption (ESA) transitions originating from these states.

An ideal model would include all of these effects because they are important under certain conditions. Unfortunately, parameters for many of these processes are difficult to measure and are not necessarily easy to incorporate in the model equations. For example, radial distributions are difficult to measure because in many EDFs the erbium is present in only trace amounts in small core areas. Measurements in the preform do not necessarily predict where the dopant will be located after the thermal processing required to draw it into fiber. Also, absolute concentration levels in the preform are often estimated only from processing data. Additionally, ion clustering, upconversion, and hole-burning all require knowledge about ion subsets and inhomogeneity that is not readily available. ESA loss coefficients and cross sections are not fully known for all levels and are difficult to measure except for ESA1 processes. The model for EDFA performance presented in Chapter 10 is based on fundamental physical quantities such as cross sections, lifetimes, and ion concentrations. Such physicsbased models are useful in understanding the properties of an EDF that affect its performance as an EDFA. They can be used to predict ideal ion distributions, to study the dependence of the EDFA performance on fiber numerical aperture (NA), or to compare the theoretical performance of different host compositions. In fact, even if physical parameters are poorly known, such a model can be used to predict trends in EDFA performance

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with changes in fiber design. However, to accurately model and predict measured EDFA gain spectra, power output, and NF as a function of operating conditions, it is more useful to base a model on physically measurable quantities. The model used here is based on work by Giles [2] that has been expanded to include the loss mechanisms of ion pairing and ESA2 at 980 nm. Parameters for these processes, including an ion pair fraction and an ESA2 loss coefficient, can be used to fit measured performance data. This model is accurate for low-concentration silica-based EDFs under the following approximations [3]: 1. 2. 3. 4.

Radial distributions are well approximated by overlap integrals. Hole-burning effects are small (mostly homogeneously broadened). ESA1 does not occur at the pump (980 or 1480 nm) or signal wavelengths. The glass phonon energy is low enough that the 4I13/2 level decays radiatively to the ground state. 5. The glass phonon energy is high enough that the 4I11/2 pump state is nearly unpopulated at steady state. 6. Homogeneous cooperative upconversion is weak at low concentrations. 7. The ion 4I13/2 lifetime is long so that a steady-state approximation is appropriate. Of particular importance is the assumption of homogeneous broadening. As shown in Chapter 10, inhomogeneous broadening has been observed and measured in EDFs. However, because the magnitude of the inhomogeneity is small, it can be neglected to first order. A correction can be added at the end of the process to account for residual inhomogeneous broadening, as discussed in Section 11.4.1. When erbium is considered to be mostly homogeneously broadened in a silicate host [4,5], many quantities can be computed without running a full computer model. In particular, predicting the shape of the gain spectrum produced by an EDFA is relatively simple if we assume homogeneity and occupation of only the 4I13/2 and 4I15/2 states. All possible spectra are then predictable by fractional combinations of the gain spectrum measured when all ions are pumped to the 4I13/2 state and the absorption spectrum measured when all ions occupy the 4I15/2 state. Neglecting background loss, the gain spectrum produced by a length of EDF with a given ion inversion (fraction in upper state) can be written as: G(λ, Inv) ⫽ {[g*(λ) ⫹ α(λ)]Inv ⫺ α(λ)}L

(1)

where g*(λ) is the measured gain per unit length produced by the EDF when all ions are in the 4I13/2 state, α(λ) is the measured loss per unit length produced by the EDF when all ions are in the4I15/2 state, Inv is the fraction of ions inverted (in 4I13/2 state) averaged along the fiber length, and L is the EDF length. Note that Eq. (1) is expressed in decibels (dB) if g*(λ) and α(λ) are expressed in decibels per meter (dB/m), and in nepers (np) if g*(λ) and α(λ) are expressed in nepers per meter (np/m). The inversion coefficient is a dimensionless number that can be written in terms of the level occupations (using the notation shown on Fig. 1) as: Inv ⫽

1 L

冮

L

z⫽0

冢冣

N2(z) dz N0(z)

(2)

where N0(z) ⫽ N1(z) ⫹ N2(z) is the total, radially averaged erbium-ion concentration, and N1(z) and N2(z) are the fractional populations of the ground state and first excited state at

587


position z, respectively. Assuming dopant longitudinal invariance, the coefficients g*(λ) and α(λ) can be written in terms of the physical quantities described in Chapter 10 as: ∞

冮 ψ(r)N (r)rdrdθ

g*(λ) ⫽ σ He (λ)N0 Γ(λ) ⫽ σ He (λ) α(λ) ⫽ σ Ha (λ)N0 Γ(λ) ⫽ σ Ha (λ)

0

(3a)

0

∞

冮 ψ(r)N (r)rdrdθ 0

(3b)

0

where σ He (λ) and σ Ha (λ) are the homogeneous emission and absorption cross sections, respectively, ψ(r) is the normalized transverse mode envelop assuming circular symmetry, N0(r) is the erbium-ion density assuming circular symmetry and longitudinal invariance, and Γ(λ) is the spatial overlap between the dopant profile N0(r) and the mode profile ψ(r). The computation of g*(λ) and α(λ) according to Eq. (3) is only as accurate as our knowledge of the cross section, mode distribution, dopant distribution, and absolute dopant concentration involved in the formula. The errors in these values are compounded when used in Eq. (3) and produce an unacceptable error in the spectra computed with Eq. (1). However, measured values for g*(λ) and α(λ) can be used in Eq. (1) without requiring such detailed fiber characterization. The advantage of this approach is in its ease of use and accuracy. Its main disadvantage is the loss of ability to fully explore EDF design. Measured normalized spectra g*(λ) and α(λ) are shown in Figure 2a for a silica-based EDF with a high aluminum concentration, and in Figure 2b for a fluoride-based EDF. The measurement of these parameters in fluoride-based fibers has been described [6]. Equation (1) is useful for predicting the spectrum of a fluoride-based EDF when the fiber is pumped near 1480 nm, but not near 980 nm, because pumping this host at this wavelength produces occupation of the 4I11/2 state. The absorption and gain spectra of Figure 2 have shapes similar to the cross section plots shown in Chapter 2, but differ in the fact that they include the wavelength-dependent overlap of the ions with the mode profile [see Eq. (3)]. The spectra of Figure 2 are for fibers that represent the state of the art for producing flat amplification. These spectra are used liberally in gain flatness calculations throughout this chapter. Equation (1) can be simplified by realizing that the gain and loss spectra are not independent. All of the 56 possible transitions have the same emission and absorption strengths, and each manifold is occupied according to Boltzmann statistics. Hence, the probability of emission on a given transition is not equal to the probability of absorption on the same transition, because these processes depend not only on the transition strength, but also on the probability that the initial level of each process is occupied. It has been shown by McCumber that the gain and absorption at a given wavelength for two Stark split manifolds are related simply by [7,8]:

冤冢

冣冥

1 g*(λ) hc 1 ⫽ exp ⫺ α(λ) kT λ λ 0

(4)

where h is Planck’s constant, c is the speed of light, k is Boltzmann’s constant, T is the temperature in degrees Kelvin, and λ0 is the crossover wavelength where the excited-state gain equals the ground-state loss. Equation (4) is expected to hold for all transitions in rare earth-doped fibers and its validity has been confirmed in EDFs [8]. Equations (1) and (3) are used together in results presented in this chapter to reduce the number of measurements required to assess spectral characteristics.

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Figure 2 Ground-state absorption and gain spectra (both normalized to the absorption peak near 1530 nm) of Er 3⫹ in (a) a silica-based fiber doped with 12 mol% aluminum, and (b) a fluoridebased fiber.


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11.2.2 Gain Peak, Gain Flatness, Gain Bandwidth, Gain Tilt, and Gain Slope The literature is filled with definitions and claims for gain peaking, gain flatness, gain bandwidth, gain tilt, and gain slope in EDFAs. These terms describe characteristics of the spectrum of an EDFA that are important in particular applications. However, different authors have used these terms differently. Furthermore, proper measurement of these quantities requires an understanding of what they represent. Measurements presented in the literature have sometimes misrepresented which spectral characteristic is being quantified. To avoid possible confusions, precise definitions of these spectral characteristics and measurement techniques for each are described in the following sections. Definitions and Importance Gain peaking is the simplest spectral concept discussed for EDFAs. A diagram depicting gain peaking is shown in Figure 3. The gain peak wavelength (GPW) is simply the wavelength within a certain wavelength range of interest that experiences the maximum gain. The GPW depends on the ion inversion, which is determined by the complete set of EDFAoperating conditions. The operating conditions that must be fixed include the pump wavelength(s), pump power(s), signal wavelength(s), signal power(s), fiber length, temperature, and spectral characteristics of the components in the EDFA. The wavelength range under question must be specified because some gain spectra have multiple GPWs, and operation occurs sometimes near a secondary GPW. In single-channel long-haul communications, EDFAs operate with a signal at a particular wavelength to produce the desired level of dispersion. In such systems, the gain spectrum of the ions is used to filter the accumulated amplified spontaneous emission [9]. To optimally utilize this autofiltering property, the GPW of the chain must correspond to the optimal dispersion wavelength and the selected operating wavelength. In many systems, EDFAs operate with substantial signal power to produce gain compression, high output power, and automatic gain control [9]. Under such conditions, the EDFA operating conditions must be precisely set to determine the GPW of the EDFA. The GPW of the EDFA and the spectral characteristics of the system components can then be used to determine the GPW of the entire system. A simple rule for determining the GPW of an EDFA is discussed in Section 11.2.3. Whereas gain peaking facilitates single-channel communications over long distances, it is detrimental to multiple-channel WDM systems. In such systems, the most important spectral characteristic is gain flatness (see Fig. 3). This quantity is critical whenever multiple channels propagate through multiple amplifiers because the channel with the most gain eventually dominates over the channels with less gain. The signal-to-noise ratio (SNR) of the weakest channel determine the maximum system length that can be achieved before significant transmission errors are produced. Several different definitions exist for gain flatness. Conceptually, gain flatness is achieved when the gain of an EDFA is constant across a specific wavelength range under a set of fixed operating conditions. Once again the operating conditions that must be fixed include the pump wavelength(s), pump power(s), signal wavelength(s), signal power(s), fiber length, temperature, and spectral characteristics of the components in the EDFA. Any measure of gain flatness must somehow quantify the gain variation across a wavelength range under fixed conditions. The gain flatness may be excellent in a given wavelength range, yet poor in another wavelength range. The more gain each EDFA produces, the fewer EDFAs are needed to cover

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Figure 3 Diagrams illustrating the definitions used in this chapter for the gain peak wavelength, gain flatness, gain slope, and gain tilt of an EDFA.

a given span. Hence, gain flatness must be normalized to the gain level achieved. Some figures of merit (FOMs) for flatness are described in the following. The bandwidth, which is related to gain flatness, is also used to describe EDFAs for WDM systems. The bandwidth indicates the spread of wavelengths over which the EDFA gain is constant to within some specified tolerance. It is normally used to quantify the total possible useful wavelength range of a gain medium, or as a means of characterizing the number of channels that may be supported by a given fiber. Often the specified tolerance is 3 dB, sometimes even 10 dB, which is a far greater variation than is normally acceptable for WDM systems. An EDFA with an excellent flatness FOM over a specified wavelength range is often characterized as having a bandwidth far greater than the flatgain wavelength range. In practice, a single FOM can be developed that includes both flatness and bandwidth, as discussed next. The gain slope, as depicted in Figure 3, is the first derivative of the gain versus wavelength at a given wavelength under the same set of fixed operating conditions as


591

mentioned for gain flatness. This concept is mostly used in analog applications, particularly when a signal has been modulated and broadened to a significant bandwidth. In this case, any difference in gain across the bandwidth leads to distortion of the analog signal. Curves of gain slope versus wavelength can represent two different quantities. If the slope is computed or measured without disturbing the EDFA operating point, it is truly just a derivative of a particular gain curve for fixed operating conditions. However, in real analog systems, the important value is the gain slope at the signal wavelength as the signal wavelength is varied across the band. This does not produce the same result except in the smallsignal regimen because tuning a large signal alters the operating point of the EDFA. This effect is further discussed later. The gain tilt (see Fig. 3) is more complex than other spectral characteristics because it involves a change in the operating point of the EDFA. As might be surmised from Eq. (1) and Figure 2, the shape of the gain spectrum of an EDFA varies as a function of ion inversion. A plot of the spectrum produced by a given EDF for different average ion inversion levels [see Eq. (2)] is shown in Figure 4. The change shown in Figure 4 can be characterized in any region as mostly a tilting of the spectrum. More formally, the gain tilt is a measure of the difference between the change in gain at one wavelength and the change in gain at another wavelength for a given change in the EDFA operating point. The gain tilt is important in many practical situations because the operating point of an

Figure 4

Achievable spectra of the gain per unit length for a high-Al (12 mol%) erbium-doped silica-based fiber with a peak absorption of 2.7 dB/m, computed for various population inversion levels. The horizontal line illustrates the spectrum for which four wavelengths can simultaneously achieve the same gain.

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EDFA often does vary. In particular, the pump power and wavelength, the number of signals present and their power levels, and the component losses all affect this operating point. For example, a digital WDM system may be reconfigured to handle the presence of different signals at different power levels. Pump sources age and degrade in power, whereas the loss of some components may increase over time. Also, in most analog systems the signal power level varies. In all of these cases, it is desirable for the gain shape not to vary with a change in operating point. Otherwise, the system must be designed to handle the resulting variations in output signal power levels. Methods to overcome gain tilt are discussed in Section 11.2.5. Figures of Merit Figures of merit are useful tools to compare the spectral characteristics of EDFs and EDFA designs. No FOMs are needed to represent GPW, gain slope, or bandwidth in an EDFA, for these are measured directly. The gain slope is often characterized by requiring that its value be within a certain range for a given analog application [10]. The level of harmonic distortion can then be used as an FOM for the gain slope. The gain flatness and the gain tilt do require FOMs, and they are the focus of the following discussion. Although an EDF with an ideally flat gain has not yet been identified, some fiber host compositions perform better than others. For an EDFA, the gain spectrum is typically only known at discrete wavelengths. For example, in a multiple channel measurement, the gain level of 8, 16, or 32 channels might be measured. On the other hand, spectra based on measured modeling parameters and computed using Eq. (1) might be known at wavelengths 1, 0.5, or 0.1 nm apart, depending on the resolution used in measuring the modeling parameters. One flatness FOM may be computed within a certain wavelength range using the mean µ G and σ G standard deviation of the gain measured or computed at n discrete wavelengths λn µG ⫽

1 n

n

冱 G(λ , Inv)

√

冱 G (λ , Inv) ⫺ 冤冱 G(λ , Inv)冥 n

n

σG ⫽

(5)

n

i⫽1

n

2

n

2

n

i⫽1

i⫽1

n2

(6)

Then a flatness FOM can be defined as the ratio FOM1a ⫽

µG σG

(7)

Note that this FOM is the inverse of the coefficient of variance of the gain spectrum across the band of interest. It increases with improved flatness. Another FOM that has also been used is based on the maximum gain variation ∆G max within a band FOM1b ⫽

∆G max µG

(8)

The worst case for flatness happens when channels are set at the maximum and minimum gain wavelengths within a given band. Values for FOM1b are often given in percentage variation, a smaller value indicating better flatness. The inverse of FOM1b might be a more

593


appropriate FOM because it would increase with improved flatness, such as FOM1a. All flatness FOMs depend on the operating point (ion inversion). Usually, the FOM obtained for the best case EDFA operating point produced by a given EDF has been presented in the literature. A flatness FOM that combines both bandwidth and flatness can be computed by simply multiplying the value of a given FOM1 (or its inverse when appropriate) by the bandwidth ∆λ over which it was achieved. For this sake we use the inverse of FOM1b and define a total FOM: FOM1T ⫽ ∆λ ⫻

冢

冣

1 FOM1b

(9)

This FOM is in units of nanometers and represents a flatness-bandwidth product. A chart of this quantity is provided later. It is important to note that both values of FOM1 can be misleading if misused. FOM1a is insensitive to a sharp spike in the gain spectrum, because such a spike would not greatly alter the standard deviation. On the other hand, FOM1b might capture narrow features that can be avoided when selecting channels in a real system. Furthermore, both figures of merit depend on the number of channels and the particular wavelengths of the channels. Clearly, for many of the spectra in Figure 4, four particular channels could easily be selected that exhibit exactly the same gain. However, a fifth channel at any wavelength would necessarily experience a different gain. The actual goal is to make an EDFA that has a flat gain regardless of channel selection so as to reduce the wavelength requirements on the system channels. The resolution of the gain spectrum used to compute FOM1 should be adequate to determine such channel expandability. An FOM for the gain tilt must indicate a relative change in gain at one wavelength versus another wavelength. Taking a derivative of Eq. (1), relative to the average inversion, yields dG(λ, Inv) ⫽ [g*(λ) ⫹ α(λ)]L dInv

(10)

To achieve zero gain tilt requires

冤

冥

d dG(λ, Inv) d [g*(λ) ⫹ α(λ)] ⫽ 0 ⫽L dλ dInv dλ This condition can be achieved if F(λ) ⫽ α(λ) ⫹ g*(λ) ⫽ constant

(11)

If we then compute the mean and standard deviation of this function as done earlier for G(λ, Inv) in Eqs. (5) and (6), we can define an FOM for the gain tilt as FOM2 ⫽

µF σF

(12)

This FOM is not independent of inversion. The gain of an EDFA tilts at a constant rate for a fixed change in inversion. A given gain change at one wavelength implies a linearly related gain change at another wavelength. Another way to characterize the gain tilt is to plot the function F(λ) [see Eq. (11)] normalized to its value at one wavelength of choice. The closer this normalized function is to a horizontal line, the lower the gain tilt is.

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Ideal Host Spectrum To simplify the search for ideal flatness, Eq. (3) can be inserted in Eq. (1) to eliminate the gain coefficient and compute an ideal absorption spectrum. The only difficulty is that the McCumber crossover wavelength is unknown. This is not a serious problem because a shift in the crossover wavelength results in a shift in the computed spectrum, but does not affect its shape. If we assume a constant λ 0 for ease of plotting, the ideal absorption spectrum for flatness for a given inversion can be written as 2Inv ⫺ 1 α(λ) ⫽ α(λ 0) [(1 ⫹ e [hc/kT(1/λ 0⫺1/λ)])Inv ⫺ 1]

(13)

The ideal spectra computed from Eq. (13) are plotted in Figure 5 for different average inversion levels, assuming a crossover wavelength of 1535 nm. The closer a normalized EDF absorption spectrum comes to following one of these curves (when normalized), the closer it is to achieving ideal flatness at some operating range. Equation (4) and the function F(λ) of Eq. (11) can be combined to solve for the ideal absorption spectrum that produces zero gain tilt α(λ) 2 ⫽ [hc/kT(1/λ 0⫺1/λ)] α(λ 0) [(1 ⫹ e )

(14)

The constant in Eq. (11) was required to equal 2 once the computed absorption was normalized to its value at λ0. This ideal spectrum, assuming again a 1535-nm crossover wave-

Figure 5 Theoretical ideal absorption spectra (normalized to α(λ0) at 1535 nm, see text) to achieve perfect gain flatness at various inversion levels, or to achieve zero gain tilt.


595

length, is shown in Figure 5 along with the ideal flat-gain spectra. Figure 5 shows that if a host produces a perfectly flat EDFA, it cannot also produce zero gain tilt. It is necessary to decide which of flatness and gain tilt is more important before setting out to achieve one or the other. An EDFA designer could achieve gain flatness, then force the inversion to be invariant (as discussed later) or seek a fiber with zero gain tilt, then filter the resultant wavelength dependence to achieve flatness. The shape of the filter required to flatten a zero-gain-tilt EDF can be deduced from Eq. (1). If the sum of the gain and loss was wavelength-independent, the only remaining wavelength dependence would arise from the loss spectrum alone. Hence, the filter would need to exactly compensate the ideal loss spectrum of Figure 5 (across the desired band) multiplied by the device length. A comparison of a typical absorption curve from a high aluminum silica-based EDF and for a fluoride-based EDF with some ideal spectra is presented in Figure 6. Over a limited wavelength range, both of these hosts are reasonably close to producing one of the ideal flat spectra when the average inversion is between 60 and 70%. The fluoride follows the detailed shape of the curves more exactly for a broader wavelength range, and it produces a flatter-gain EDFA. However, neither host is close to producing the spectrum for zero gain tilt. Later, these fibers will be compared using the FOMs defined in the previous section. Measurement of EDFA Characteristics One of the difficulties with comparing gain spectra from the literature is that many different measurement techniques have been used, and often, the measurement technique is

Figure 6 Comparison of the absorption spectra of a high-Al (12 mol%) silicate and erbiumdoped fluoride fiber to some of the ideal spectra of Figure 5.

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poorly described. For a measurement of the gain peaking or the gain flatness to be valid, it must meet the following criteria: 1. 2. 3. 4.

The average inversion must remain constant during the measurement. Adequate spectral resolution must be used. Spectral hole-burning must be understood and accounted for. The polarization dependence of the components must be controlled.

Gain peaking has been measured in EDFAs using an EDF laser ring with an adjustable intracavity loss [11]. In this method, the inversion is determined by the gain required to produce laser action, and the GPW is the laser wavelength. The polarization dependencies in the ring can be eliminated by scrambling the polarization at various locations along the loop [11]. Alternatively, gain peaking and gain flatness can be measured in a carefully controlled EDFA. In such a technique, four main methods exist to maintain a constant inversion: 1. Apply a constant saturating signal (also called a tone) and pump power while probing with a low-power tunable signal across the band. 2. Apply simultaneously multiple saturating tones across the band and measure all gain levels. 3. Apply a saturating tone and turn it off periodically at a fast rate so that a broadband ASE source can probe the gain without interference from the saturating tone. 4. Adjust the pump power to maintain a constant gain at one particular wavelength outside the measurement band while tuning a saturating tone across the band. In any event, tuning a large saturating tone across an EDFA to measure gain is not a legitimate technique unless adjustments are made to maintain constant inversion, as suggested in item 4. The gain slope can be obtained by carefully measuring the gain spectrum as described in the foregoing, then computing the first derivative of this curve. This is the gain slope for a fixed operating point. Alternatively, a saturating tone may be provided along with two small probe signals located on either side of the saturating tone. The gain can then be measured on either side and the derivative evaluated directly. Scanning all three tones together provides the gain slope for an EDFA with variable inversion, which is appropriate for an analog EDFA. The gain tilt can be computed by measuring multiple gain spectra as described previously and comparing the change in gain at one wavelength with the change in gain at another, fixed wavelength. Spectral characteristics can always be computed by measuring modeling parameters accurately, then computing spectra using Eq. (1). This is the approach used in the following treatment. 11.2.3 Gain Peaking and ASE Accumulation in Long Multiple-EDFA Systems Measurement of the GPW to the accuracy necessary for long, multiamplifier chains is difficult in a single EDFA. However, measurement in a long amplifier chain requires the construction and concatenation of many identical amplifiers. To simplify this measurement, the EDF can be placed in a fiber ring laser with a known loss, as depicted in Figure


597

Figure 7 Experimental setup to measure the gain peak wavelength using a depolarized fiber loop.

7. This loop consists of a single EDFA with a counterpropagating pump at 1.48 µm, 0.8 km of dispersion-shifted fiber with a small effective area, an optical isolator to force signal flow in one direction, a polarization controller, and a variable attenuator to vary the loop loss. As long as this ring laser operates above threshold, laser emission is guaranteed to occur at the wavelength with the maximum gain for the operating level of saturation. Furthermore, as in any laser, the gain of the EDF equals the loss in the rest of the loop. To eliminate polarization-induced instability and accurately measure the GPW, polarization must be incorporated in the fiber loop, as in Figure 7. A total of six scramblers were used, because each component is slightly polarization-dependent and slightly repolarizes the signal. Taps can be included on both sides of the EDFA to monitor the signal power levels and compute the gain. All components must be carefully selected to minimize the wavelength dependence of the loop loss. Under the assumption of homogeneous broadening, the GPW of an EDFA is always the same for a certain average inversion [12]. Because the average inversion and the gain per unit length are linearly related, as can be seen from Eq. (1), the GPW is also completely specified if the gain per unit length is known at a given wavelength. This is demonstrated in Figure 8, which shows the gain spectrum predicted, using measured modeling parameters, for various levels of average inversion in an aluminum-co-doped silica-based EDF. The circles in Figure 8 indicate the GPW for each curve other than the 1530-nm peak (which is assumed to be filtered). For a given peak gain per unit length and average inversion, the GPW is determined. The GPW was measured using this method for the EDF of Figure 8 for various lengths and 1.48-µm pump power levels as a function of the gain per unit length [12]. The result appears in Figure 9, superimposed on the predictions of the model. It demonstrates the excellent agreement between theory and experimental values. The nearly linear

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Figure 8 Demonstration of the shift in gain peak wavelength with increasing inversion level for a high-Al silica-based EDF. A postulated ASE filter near the 1530-nm peak is shown. The dots indicate the peak locations.

Figure 9

Measured gain peak wavelength versus gain per unit length for the high-Al EDF of Figure 4 pumped backward at 1480 nm. The fiber length and signal power were varied to generate the various values of gain per unit length. The solid curve is a fit generated by computer simulation.


599

relation over a short range is useful in predicting the sensitivity of the GPW to fiber length and operating gain. As long as the operating gain and fiber length are known, the GPW is independent of pump wavelength, pump power, signal power, compression level, and amplifier configuration. To generalize this concept to other EDFs, similar measurements were performed for four fibers [12] and were normalized to the peak absorption to compensate for differences in dopant level (see Fig. 10). Fibers 1 and 3 contained similar Ge and Al levels and produced good agreement with each other. Fibers 2 and 4 contained more Al and were both shifted in the same direction (i.e., toward longer wavelengths). This result shows that measurements for one fiber can only be generalized to fibers of very similar composition. However, the rule that GPW and gain per unit length are directly related applies independently to each fiber type. In EDFA chains, the GPW is determined not only by the EDFA performance, but also by the wavelength-dependent losses of the components in each span. Owing to the flatness of the EDFA gain, even slight wavelength-dependent losses can shift the GPW. This dependence can be used to the advantage of the system designer. If the ring laser of Figure 7 is configured to incorporate representative components of a single span in a real amplifier chain, the measured GPW is the peak of the actual system. The only complication is that the result cannot be plotted in terms of gain per unit length because the introduced losses do not all scale with amplifier length. Such a measurement is most useful for fine-tuning the EDFA design once the span loss, fiber length, signal power, and pump power have been finalized. This simple theory and measurement technique dramatically simplifies EDFA design for an amplifier chain. If the desired gain and GPW are computed from system considerations, a plot similar to Figure 9 measured for a single fiber length completely determines the required fiber length. This is shown in Figure 11, which plots the required fiber length to achieve both a given gain and GPW for the fiber of Figure 9. Once the length is fixed,

Figure 10

Dependence of the gain peak wavelength on the gain per unit length (normalized to the peak absorption per unit length) measured for four EDFs with different Al concentrations, in the range of 1–12 mol%.

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Figure 11 Required fiber length to achieve a given gain peak wavelength as a function of operating gain for the fiber of Figure 4.

the pump power and signal power can be adjusted separately to define the possible combinations that produce the desired gain. This is illustrated in Figure 12, which shows typical saturation curves for the EDF of Figure 9 and a length of 18 m. Crossings between the horizontal lines that produce a given GPW and the saturation curves define the signal and pump power levels that combine to yield the desired GPW. Based on other system considerations, limitations are placed on the acceptable amplifier NF, desired gain compression level, available pump power, and usable signal power level. These limitations can be used to choose the pump power and signal power combination (the particular curve on Fig. 12) that are optimal for system performance. 11.2.4 Gain Flatness in WDM Systems Wavelength-division multiplexing is an efficient way to increase the capacity of fiber systems. Consequently, approaches to flattening the gain of EDFAs are important, and they abound in the literature. A chart comparing some of these approaches appears in Table 1. It includes most publications that have reported sufficient data to compute a value for FOM1b in a broad bandwidth. It should be noted that these amplifiers range in bandwidth from about 9 to 70 nm, indicating that the required bandwidth depends dramatically on the application. The value of FOM1T, the total flatness-bandwidth product FOM, can be computed for most of the approaches in Table 1. The values of FOM1T for all experiments that produced bandwidths greater than 18 nm are plotted in Figure 13 versus the time the result was reported. This figure illustrates the general trend toward improved flatness and increasing bandwidth over the past 5 years. The demand for flatness and


601

Figure 12 Theoretical signal saturation curves for a signal at 1558 nm in an 18-m length of the fiber of Figure 4 pumped backward at 1480 nm. The horizontal lines identify the crossing points at which a particular gain peak wavelength is reached.

bandwidth is ever-increasing. The following subsections discuss host modifications and some of the other approaches to produce flat-gain EDFAs. Comparison of Host Materials The possible spectra produced by EDFs, without using filtering techniques, are limited by the possible co-dopants and by the magnitude and type of the splitting mechanisms involved. The 4I13/2 state consists of seven closely spaced broadened levels, and the 4I15/2 state of eight closely spaced broadened levels (multiply these values by 2 to include very small magnetic splitting). The locations of each level and the strength of all 56 possible transitions between them are controlled by the local environment of the ions (i.e., by the host composition) [4,5]. The energy levels of each manifold are occupied according to Boltzmann statistics. Certain co-dopants have been observed to dramatically alter the erbium spectrum. For example, Al co-doping in silica-based fibers has been generally used to broaden the spectrum [4]. All elements of the periodic table can be considered as potential co-dopants, and all glass-forming materials can be considered as hosts, but many can or must be eliminated. Some elements are difficult to incorporate in a host, or they create absorption or scattering within the 1550-nm erbium window. Most transition metals are eliminated for this reason. Some elements can be incorporated into a host, but are known to produce little change in the erbium spectrum. Many host media are unsuitable because of poor glass-forming characteristics. Some of the remaining elements and hosts have been explored in bulk glass [40] and in fibers, [4] whereas others are relatively unknown. Germanium, aluminum, and phosphorus have been studied in detail in silica because they are often used to alter the fiber index of refraction in standard fiber processing.

a

EDFA/raman

Dual band: SiF and Si

Al and Yb/P/Al Al Si and F

Fourier filter AOTF P/Al and Al

1545–57 (12) 1543–58 (15) 1540–60 (20) 1530–60 (30) 1547–56 (9)15.3 1532–60 (28) 1532–60 (28) 1570–1600 (30) 1570–1600 (30) 1572–1600 (28) 1542–60 (18) 1532.5–65 (32.5) 1550.4–61.8 (11.8) 1542–61 (19) 1528–62 (34) 1528–68 (40) 1526–61 (35) 1527–1560 (33) 1541–59 (18) Various (15) 1543–58 (15) 1535–1560 (25) 1544–61 (17) 1533–57 (24) 1531–60 (29) (70) 1530–60,76–00 (54) 1552–1613 (61)

All gain and gain variation values are on a per EDFA basis for system experiments.

Ultrabroad

Hybrids

Mach–Zehnder Blazed grating Periodic filters Long-period fiber grating

Filter

Tapered fiber

Low inversion EDFA

Long band

P/Al Fluorides

High-Al

Specifics

Band (nm) parentheses ⫽ width

Demonstrations of Gain-Flattened Broadband EDFAsa

Composition

Approach

Table 1

15 22–32 20 20 0.05 23 26 24 29.5 29 15 11.8 9.2 17.8 24 22 30 32 19 20 29.2 29 38 25 26.3 24 30 19

Gain (dB) (avg) 0.22 0.2 0.82 2.54 0.33 1.2 1.5 1 0.9 1.0 0.5 0.6 0.08 0.2 0.6 1 2.8 1.4 0.2 1 1.3 1.5 0.5 0.6 1.0 4 1.7 1.5

max ∆G (dB) Gmax ⫺ Gmin

5.2 5.8 4.2 3.0 3.4 3.3 5.1 0.8 1.1 2.5 4.5 9.3 4.4 1.0 5.0 4.4 5.2 1.3 2.4 3.8 16.6 5.6 7.9

1.5 0.6–0.9 4.1 12.7

Variation ∆G/gain (%)

5–7 ⬍7 8

4.5 5

4 (internal)

5.2

5 (internal) 6.3 6.2

16

3.9 5.3

Ext. NF (unless noted)

17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39

13 14 15 15

Ref.

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Figure 13

Summary of the evolution over time of the factor of merit FOM1T, which described achieved gain flatness over bandwidth. The solid curve shows the best fit to those approaches that use host material changes only.

Of all the hosts considered so far, the fluorides and silicates have shown the highest potential for gain flatness, as indicated by the approaches listed in Table 1. The gain and absorption spectra (normalized to the peak loss value) of representative fibers are shown in Figure 2. It is noted that these spectra do not differ dramatically in the usual 1530- to 1560-nm gain region. However, the details of their shape determine the flattest gain spectrum achievable. The difference between the fluorides and the high-Al silicates is not in the width of the gain pedestal (the region over which the gain parameter drops below a factor of 2 from the peak) but in the detailed shape near the top of the pedestal. Although the fluorides have a flatter pedestal top, it can be argued that the high-Al silicates actually have a broader pedestal. Fluoride hosts might be characterized as providing a flatness advantage, whereas silicate hosts produce a broader bandwidth when defined at 3 or 10 dB down in a standard EDFA. Table 2 summarizes, for two wavelength ranges, the best values for FOM1a, a value of ∆Gmax for an EDFA with an average gain of 20 dB, and the inversion required to produce the flattest gain spectrum. The first wavelength range includes most of the full pedestal, ranging from 1530 to 1560 nm. The second wavelength range is the naturally flatter region from 1540 to 1560 nm. For comparison with published data and with Table 1, the maximum gain difference in Table 2 has been converted to a value of FOM1b, shown in percent. Note that the conclusions drawn by using these different FOMs are not dramatically different. It is noted that in the 30-nm bandwidth, FOM1a for the fluoride fiber is higher than for any of the silica-based fibers. However, in the 20-nm bandwidth, the highest aluminum silicate outperforms the fluoride host. None of the fibers shown in Table 2 achieves an

b

a

12 M% Al 6 M% Al Al 3 M% Al P,Al,Yb

66.4% 65.4% 63.2% 63.2% 62.6% 68.0%

48.1 28.7 24.3 22.2 15.9 4.4

FOM1a 4.4 4.8 4.2 4.2 3.7 2.7

FOM2

Best Inv is the inversion that produces the highest FOM1a. Max ∆gain is the maximum gain variation for a 20-dB gain EDFA.

Fluoride Ge/Si Ge/Si La/Si Ge/Si Ge/Si

Best inv

a

1530–1560 nm

1.33 (6.6%) 2.54 (8.5%) 2.94 (14.7%) 3.44 (17.2%) 3.84 (19.2%) 18.6 (93%)

Max ∆gainb in 20-dB Amp

Flatness FOMs for Selected EDFs in Two Wavelength Rangesa

Core codopant

Table 2

65.4% 70.9% 70.6% 69.9% 74.8% 59.8%

Best inv

a

66.2 133.3 90.1 70.9 41.2 13.3

FOM1a

1540–1560 nm

6.9 10.8 10.4 9.7 11.5 4.4

FOM2

0.82 0.66 0.81 1.01 1.69 5.50

(4.1%) (3.3%) (4.0%) (5.0%) (8.4%) (27.5%)

Max ∆gainb in 20-dB Amp

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extremely high FOM1a for the 30-nm test range. However, most of them perform much better in the narrower 20-nm band. In fact, taking this argument one step farther, some compositions produce FOM1a exceeding 400 for bandwidths narrower than 15 nm. The worst fiber in all cases is the phosphorus/Yb-co-doped fiber. This type of fiber is typically used in power amplifiers in which flatness is not critical. This issue is further discussed later. Figure 14a and b shows the flatness FOM computed as a function of average inversion level for different fiber compositions; for Figure 14a in the 1530- to 1560-nm range, and (14b) in the 1540- to 1560-nm range. It shows that the gain of an EDFA made with a given fiber is flat only if the inversion is properly controlled. This, in turn, implies a certain fiber length to achieve both a desired gain and gain flatness. Over both ranges, all the silicate compositions tested reach a maximum FOM1a (i.e., the flattest gain or the broadest bandwidth, for an inversion between approximately 60 and 75%). Additionally, Figure 14 and Table 2 show that the inversion for the flattest spectrum depends on the band to be flattened. If only small bandwidths or particular channels are to produce equal gains, the optimum inversion is different. Regardless of the signal and pump power levels injected into the EDFA (and assuming homogeneous broadening), the spectrum is determined solely by the average inversion level of the erbium ions. Equation (1) shows that gain and average inversion are linearly related. Hence, for a properly chosen fiber length, as long as the design gain is reached (regardless of the operating conditions), the EDFA gain is flat. This is an important rule that greatly simplifies the design of filters for an EDFA, as discussed in the following. Approaches to Improve Gain Flatness Because alteration of the EDF host composition has not produced extremely wide and flat EDFAs, various approaches have been tested to flatten their gain, as summarized in Table 1. The overall FOM1T achieved by each approach is charted as circles in Figure 13. Of these approaches, filtering silica-based EDFAs and hybrid silica-based and fluoridebased EDFAs have been the most successful for a 30-nm flat region. Particular configurations of these approaches are shown in Figure 15. Clearly the pumping scheme, pump power, and interstage components can be configured in various ways. However, in the filtered EDFA the filter must be placed between two EDF stages to optimize its performance. A filter placed before the EDF increases the NF, whereas a filter placed after the EDF reduces the output power. In the hybrid design, not only do the two EDFs produce somewhat complementary spectra, but the silica-based EDF also produces a lower NF because it can be pumped at 980 nm, whereas the fluoride-based EDF can be efficiently pumped only near 1480 nm. These two designs are optimized for comparison in the following. Proper optimization of each flat-gain EDFA design under consideration here is complex. A single-stage unfiltered EDFA is optimized as follows: 1. Decide on optical gain for a given input power and available pump power. 2. Select a length such that the inversion produces the flattest gain spectrum. 3. Consider different pumping schemes to produce the lowest NF and highest power output with a flat gain. A multistage unfiltered EDFA is optimized as follows: 1. Decide on optical gain for a given input power and available pump power. This includes gain to overcome all interstage component losses.

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Figure 14 Computed figure of merit FOM1a for the gain flatness as a function of population inversion for EDFs with different host compositions, in the wavelength range of (a) 1530–1560 nm, and (b) 1540–1560 nm.


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Figure 15

Diagrams of two possible configurations for a gain-flattened EDFA: (a) a dual-stage silica-based EDFA with an interstage filter (showing filter spectrum) and isolator; and (b) a hybrid EDFA with a silica-based first stage and a fluoride-based second stage.

2. Select the total EDF length to produce the flattest gain (as just summarized). 3. Consider all possible divisions of the total fiber length between the stages. As long as the EDF gain and total length are as chosen in steps 1 and 2, the spectrum will be flat. 4. Consider different pumping schemes to achieve the lowest NF and highest power output with a flat gain. Optimization of a filtered multistage EDFA is far more complex. The total fiber length is no longer constrained to be the one that produces natural gain flatness. A filter can be designed to flatten any spectrum. The steps required can be summarized as follows: 1. Decide on design gain for a given input power and available pump power. This includes gain to overcome all interstage component losses. 2. Select a particular total fiber length. 3. For the selected total fiber length, a certain minimum inversion is required to produce, for all wavelengths in the band to be flattened, at least the design gain of step 1. Using this inversion, the gain spectrum of the EDFA can be computed

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using Eq. (1). The required filter spectrum is the loss shape that will reduce the computed EDFA gain to the design gain within the bandwidth. For each length, a single filter design applies. 4. Consider all possible divisions of the total fiber length between the different stages. For each length division, consider different pumping schemes and power levels to identify which scheme produces the lowest NF and most efficient pump power usage when the EDFA produces the design gain. As long as the EDFA gain, length, and filter spectrum are as designed in steps 1–3, the EDFA gain spectrum will be flat. 5. Repeat steps 2–4 for a series of different total lengths. 6. Retain the best result. Optimization of the hybrid silica-based and fluoride-based EDFA is also complex. Because the total fiber length is not fixed and each stage produces different spectra, a wide parameter space must be explored. Combinations of different fiber lengths and different inversions can produce the desired total EDFA gain. One possible method to proceed is as follows: 1. Decide on expected gain for a given input power and available pump. This includes gain to overcome all interstage component losses. 2. Choose fiber length for stage 1. 3. For a known pump power, compute the average inversion for stage 1. 4. Explore all stage 2 length and inversion combinations that, along with the stage 1 length and inversion from steps 2 and 3, produce the expected total gain. Select the stage 2 length and inversion combination that yields the best total gain flatness. 5. Consider different pumping schemes to identify the best NF and power output with flat gain. 6. Repeat steps 2–5 for a series of different stage 1 lengths. 7. Choose best result. Performing any of these optimizations without a model is tedious and consumes large quantities of fiber. A few examples help to illustrate how flat-gain EDFAs are designed. The filter design requires utilizing the following variation of Eq. (1): G(λ, Inv) ⫽ G des ⫽ [(g*(λ) ⫹ α(λ))Inv ⫺ α(λ)]L tot ⫺ α com (λ) ⫺ α fil (λ)

(15)

where the model parameters are defined in Section 2.1 and G des is the wavelength-independent EDFA design gain after all filtering and component losses. L tot is the total EDF length in all stages. α com (λ) is the total loss of all passive components other than the filter, in dB. α fil (λ) is the loss of the filter, in dB. For a chosen fiber length the minimum population inversion required to produce adequate gain to exceed the design gain across the design band can be deduced from the inequality:


[(g*(λ) ⫹ α(λ))Inv ⫺ α(λ)]L tot ⱖ [G des ⫹ α com (λ)]

609

(16)

for all λ in the range. Equation (16) is based on the simple fact that the filter can only produce loss, so that the gain produced by the EDF must exceed the design gain and all component losses at all wavelengths. By using Eq. (16), once a total fiber length and design gain are selected, the required inversion is known. The spectrum produced by the EDF is then also known, and the filter is just the difference between the achieved gain and the final design gain. An example of the result of this process is shown in Figure 16. In this case, the gain was to be flattened from 1530 to 1560 nm. The filter required to achieve 28 dB of total gain (without any component losses) is plotted in Figure 16 for a series of lengths. A glance at Figure 4 is useful to understand these plots. For short fibers the inversion must be high to produce sufficient gain for all wavelengths from 1530 to 1560 nm, so the filter spectrum resembles one of the high inversion gain spectra of Figure 4. For long fibers, the required inversion is low, and the filter spectrum look like a low-inversion gain spectrum. An example of three plots used to optimize the design of the hybrid EDFA is shown in Figure 17. The achieved flatness FOM obtained from modeling is plotted in Figure 17a as a function of the silica-based EDF (stage 1) for different lengths of the fluoride-based EDF (stage 2). Also plotted are the power output (see Fig. 17b) and NF (see Fig. 17c).

Figure 16

Series of filters to flatten the gain of the hybrid EDFA design of Figure 15a, computed for different total EDF lengths and for a gain of 28 dB between 1530 and 1560 nm. The EDF is a high-Al silica-based fiber with 6.2 dB/m of peak absorption near 1530 nm.

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Figure 17

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Study of the performance of the hybrid EDFA of Figure 15a as the lengths of EDF in stage 1 and stage 2 are varied: (a) factor of merit FOM1a for the gain flatness between 1530 and 1560 nm; (b) achievable output power; and (c) noise figure at 1551 nm. The pump is 100 mW at 980 nm in stage 1, and 100 mW at 1480 nm in stage 2.

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The details of this study are described in the following paragraph. Clearly, optimization of the two fiber lengths in a hybrid design is a complex task most easily performed by a computer model. Figure 17a shows that a narrow range of lengths produces the flattest gain (1–3 m for stage 1). However, these lengths produce neither the lowest NF nor the highest output power (see Fig. 17b,c). The results of a comparative study of these approaches, including results from Figures 16 and 17, are summarized in Table 3 for a particular total signal level. In all cases, Table 3 Study of Silica and Fluoride EDFAs for WDM Design with a 30-nm Bandwidth (1530–1560 nm)

11 Channels at ⫺18 dBm (total ⫺7.6 dBM)

Number of stages

Stage 1 pumpa (nm)

Unfiltered fluoride1 Unfiltered Al/Si Unfiltered Al/Si Unfiltered fluoride Unfiltered Al/Si Ideal-filtered Al/Si 3-gaussian-filtered Al/Si Al/Si and fluoride hybrid

1 1 1 2 2 2 2 2

1480 980 1480 1480 980 980 980 980

a

Best FOM1a overall

11 channel FOM1a

Total output power (dBm)

NF (1551 nm) (db)

48.1 28.7 28.7 48.1 28.7 ∞ 400 76.9

43.8 28.6 28.6 43.8 28.6 — — —

17.3 17.0 17.3 20.1 20.1 19.2 19.2 18.5

4.32 3.34 4.31 4.29 3.19 3.25 3.25 3.56

The second stage is pumped in the counterpropagating direction at 1480 nm. Isolation between stages is 40 dB, and interstage loss is 1 dB.

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a 100-mW pump power was available in each EDFA stage, and the EDFA was configured as in Figure 15a,b. Eleven channels of equal power were used, evenly spaced from 1530 to 1560 nm. The first three rows of Table 3 are the results for co-pumped single-stage silica-based and fluoride-based EDFAs. Two different values of FOM1a are listed. The first one is the overall value for the broad bandwidth for many signals (which were computed directly from modeling parameters measured at 0.2-nm spacing). It represents the best possible value for closely packed channels. The second FOM1a is the particular value for the 11 channels modeled. This value can be higher or lower than the broadband value depending on how well these 11 channels happen to fall at wavelengths representative of the average EDFA flatness performance. Clearly, in a single unfiltered stage, the fluoridebased EDFA is flatter than the silica-based EDFA, but it produces a higher NF than the 980-nm pumped silica-based EDFA. Results for dual-stage silica-based (see Fig. 15a without an interstage filter) and fluoride-based EDFAs without filters are shown in rows four and five of Table 3. They differ from the single-stage results only in the total output power achieved in each case, solely because of the presence of a second pump in stage 2. Although an ideal filter could produce perfect gain flatness (see sixth row of Table 3), real filters do not exactly fit the required shape. To assess what can be expected from practical filters, the ideal filter shape was fit using three gaussian-shaped filters (see filter inset in Fig. 15a). Such filters of gaussian or near gaussian shape are available and can be used as building blocks to synthesize more complex filters. The performance of the foregoing design (see Fig. 15a) was assessed using this more realistic filter. The result appears in the seventh row of Table 3. FOM1a is still substantially better than that expected for an unfiltered EDFA using either fluoride-based or silica-based fiber. Furthermore, the three-gaussian filter could be improved by using four, five, or even more component filters. The remaining issue is the reproducibility of such a filter and its sensitivity to environmental changes. Such characteristics will determine the practicality of this approach. To summarize all the dual-stage designs, the optimum flattened gain and NF are plotted in Figure 18a,b, respectively, for the dual-stage amplifiers of Table 3. The overall best performance is predicted for the filtered EDFA design. The hybrid silica-based fluoride-based design has potentially the second-best performance and it offers the advantage of not requiring filters. The disadvantage comes from the use of fluoride fiber technology, which still poses significant challenges in handling, splicing, strength, and reliability. As EDFAs are used in systems with more channels, the demand for greater bandwidth grows. As Figures 4 and 5 show, neither the high-Al silicate nor the fluoride EDFs can easily produce a gain flatness over a bandwidth beyond 30 nm. Clearly, the further one tries to filter one of the spectra of Figure 4, the more filter loss is required at some wavelength, the higher the loss between stages is, and the more strongly affected are either the NF or the output power. Various combinations of total length and filter shape were evaluated for broadband filtering [27]. The use of longer fibers was ideal because more fiber could be allotted to stage 1 to provide a good NF while leaving enough fiber for stage 2 for efficient power conversion. One filter design that was found by modeling to produce good optical performance is shown in Figure 19 for a 45-nm bandwidth. The ideal filter and a more realistic three-gaussian filter are also shown. The resultant EDFA spectrum for the three-gaussian filter is also shown. The calculated FOM1a is 35. Note that most of the gain flatness discrepancy occurs near the edges of the filter. Thus, if this 45-nm filter were used over only a 43-nm width, the flatness FOM1a would exceed 50. The penalty for this filtering is degradation of the noise figure. The 45-nm filtered EDFA produces an NF near 4 dB, compared with 3.25 dB for the same EDFA filtered over only


Figure 18

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Theoretical study of (a) the flattest gain spectrum, and (b) the noise figure at flattest design point, for four of the dual-stage EDFA designs of Table 3 (the ideal design is not shown). Each EDFA utilizes two pump sources (100 mW at 980 nm for the first stage, and 100 mW at 1480 nm in the backward direction for the second stage), and 11 equally spaced signal wavelengths.

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Figure 19

Gain spectrum of the EDFA design of Figure 15a made of a high-Al silica-based EDF with a 6.2-dB/m maximum absorption. The extremely broadband and flat gain spectrum from 1528 to 1573 nm was achieved by using the interstage filter shown in the figure, which was composed of three gaussian filters.

a 30-nm bandwidth. To filter this EDFA to 50 nm would require almost 25 dB of filter loss at the peak, which would produce an even larger NF degradation. The possibility of achieving an even greater bandwidth using split-band designs has been explored [26], as illustrated conceptually in Figure 20. An EDF can produce gain from 1500 nm to approximately 1620 nm. However, for the long-band region, beyond

Figure 20

Dual-band EDFA architecture combining an independent conventional (C) band and long (L) band EDFA, each one using a different fiber length and pump architecture, to produce a flat gain across as much as 80 nm of bandwidth.


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1570 nm, an EDFA requires a far greater fiber length than an EDFA for the short-band region. Flat-gain versions of such long-band EDFAs (summarized in Table 1) have appeared in the literature [19–21]. Using standard WDM components it is possible to separate signals into the two bands, individually amplify each band with EDFAs utilizing different fiber lengths, and recombine the two amplified bands. A filter can be used in each band (not shown in Fig. 20) to flatten the gain in this band, and thus produce flat gain over the entire spectrum. Such designs have produced the ultrabroadband results listed in Table 1. One challenge to the use of such dual-band EDFAs is the need to avoid multiple paths with different time delays for the same signal wavelength, which produce noise in a real system. For this reason, spectrally sharp components are required to separate and recombine the two bands, and a guard band (an unused wavelength region between the two bands) is also typically incorporated in the design. 11.2.5 Gain Tilt in Multichannel Systems Gain tilt is a critical problem in many multichannel EDFAs, especially those required to produce gain flatness. Flattening an EDFA to a great accuracy at one operating point is not useful if the operating point changes regularly during use and the spectrum tilts in the process. FOM2, as defined earlier, is a good indication of this tilt. However, this FOM represents how much the spectrum changes for a given change in gain; but it does not indicate how much the gain changes for a given change in signal power or pump condition. This change depends on the EDFA design. In particular, pump wavelength, pump power, fiber length, signal power, and fiber NA are all important. For example, for the same signal change, the change in gain for an EDFA pumped at 1480 nm is typically lower than for a comparable EDFA pumped at 980 nm. An EDFA with considerable excess pump power is also less sensitive to changes in signal power. Some designs for low-gain tilt are described in the following. Comparison of Host Materials Values of FOM2 for various EDFs are shown in Table 2 for two wavelength ranges. Fluoride-based EDFs and high-aluminum-co-doped silica-based EDFs have similar gain tilt characteristics for the 30-nm–wide range considered (FOM2 between 4 and 5). In the 20-nm range, the silica-based EDFAs produce less gain tilt (FOM2 ⫽ 10.8) than the fluoride-based EDFA (FOM2 ⫽ 6.9). However, in both ranges and in other ranges considered, no EDF in Table 2 produces a particularly high value of FOM2. It is important to realize that gain tilt depends on inversion. No matter what operating point is chosen, a given change in gain at one wavelength (a given inversion change) usually implies a different change in gain at another wavelength. Another way to look at the gain tilt issue is to plot the value F(λ) ⫽ α(λ) ⫹ g*(λ) of Eq. (11) to see whether it is constant. Such a plot appears in Figure 21 for a series of Al-co-doped silica-based EDFs. Some of these curves are flatter in certain regions than in others, but none of them are particularly flat over a broad region. Searches have been made for fiber compositions that produce a low gain tilt, but this has been achieved only over narrow bandwidths. Clearly, more work to produce hosts with lower gain tilt is warranted. Approaches to Reduce the Effect of Gain Tilt in EDFAs The effect of gain tilt can be eliminated in an EDFA by forcing the population inversion, and thus the gain, not to change with signal or pump operating parameters. This goal has been accomplished by the following methods:

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Figure 21

Spectrum of the gain tilt characteristic F(λ) for silica-based EDFs with different Al concentrations.

1. Pump power control [41,42]: Any change in signal power or number of signals is compensated by adjusting the pump power. Any degradation of the pump power is compensated by increasing the pump current. The gain is held constant. 2. Independent laser operation [43–46]: The EDFA is made to function as a laser at some wavelength outside of the signal band by inclusion of wavelengthselective reflectors. Thus, the inversion is clamped at the level needed to produce a round-trip gain of unity at the laser wavelength. 3. Inclusion of a variable-power local signal [47,48]: An injected signal controls the inversion. The control signal is adjusted by an active feedback loop such that the saturation produced by all transmission and control signals remains constant. As the power of a transmission signal is reduced, the control signal power is increased. 4. Inclusion of a variable attenuator (sometimes in combination with the foregoing approaches): The EDF produces constant inversion and gain, but the EDFA gain is not constant. The difference is made up by the attenuator. As the power of any or all transmission signals is increased at the input of the EDFA, the attenuation (usually between EDFA stages) is increased by active control. The output power of the EDFA remains constant, as does the gain of the EDF alone, but the gain of the overall EDFA is different. None of these approaches comes without its costs. Pump power control requires excess pump power to compensate for the full range of signals and pump degradation. Laser operation is effective only if the system signals are weak enough not to saturate the gain of the EDFA, or a round-trip gain of unity will no longer be achieved and laser operation at the laser wavelength will cease. This limits the maximum signal output and


617

efficiency. A large variable signal uses pump power that is unavailable for the main EDFA signals. The inclusion of a variable attenuator clearly wastes signal power. All of these approaches tend to produce a higher NF as well. An additional problem is that these constant-gain approaches do not allow the EDFA to compensate for system changes and degradation. For example, as a system ages, the loss of a transmission fiber span increases. This causes a drop in the signal power entering each EDFA. An unstabilized EDFA operating in compression can then compensate by producing an increase in gain. Consequently, a chain of unstabilized EDFAs will establish a new operating condition such that the output power of each EDFA is only slightly lower than the output power at the beginning of the system life. If foregoing approach 1, 2, or 3 is used, the gain of each EDFA remains constant, and as the system ages, the output power of each successive EDFA drops by exactly the amount that the system span loss increases. After enough EDFAs, one of two system failure mechanisms may occur. The power output may become too low for good signal-to-noise performance, or the gain stabilization method may cease to maintain constant inversion (if the dynamic range of the scheme is exceeded). Approach 4 differs in that the gain is not constant. The EDFA can produce constant output power regardless of the input power. In some of the foregoing approaches, compression can be traded for less variant operation. In fact, because approaches 1, 3, and 4 require active monitoring of the signal gain or the output power, the active gain stabilization can be turned off (either completely or partially) to allow the gain to change whenever the output power is below a certain level. Approach 2, the resonant laser approach, is more difficult to turn off unless the resonant cavity can be eliminated by introduction of some loss. In fact, this approach tends to set a maximum gain and can operate only at gain levels below the design point set by laser operation. To avoid these complications, it is preferable to find a host with the lowest FOM2 so that gain compression and flatness can be maintained simultaneously. Another way to reduce gain tilt and achieve flatness simultaneously is to use inhomogeneous broadening. Spectral inhomogeneity has been used to this end at low temperatures [49] and even produces some flattening and reduced tilt at room temperature [50]. The use of twin-core fibers to produce spatial inhomogeneity has also been reported [51,52]. However, the difficulty of coupling to such fibers makes this approach impractical. One interesting technique for reducing the gain tilt is the use of variable tunable filters such as acousto-optic tunable filters [31] and tunable long-period gratings [53]. As long as an adjustable filter can match the spectral shape of an EDFA over a wide range of inversion levels, gain tilt can be compensated. However, available adjustable filters may have significant practical drawbacks, such as multipath interference, and they all require substantial development before becoming viable system alternatives. 11.2.6 Gain Slope in Analog Applications Gain slope is an important issue in EDFA applications with broadened signal sources and analog signal modulation. In analog systems, the signal source can be modulated either internally or externally. External modulation does not broaden the source bandwidth, so gain slope is unimportant. However, an internally modulated source, such as a laser diode, is broadened in proportion to the level of modulation. In such systems, the EDFA is usually highly saturated by a single signal, so that its gain is virtually independent of the wavelength of this saturating tone. However, for such a system to be economical, the wavelength of the saturating tone is usually allowed to vary considerably to use the entire

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Figure 22

Gain slope at the saturating wavelength for a 20-dB–gain EDFA made from a highAl EDF as the saturating tone is tuned across the band. This diagram shows that the fiber length may be chosen to minimize the slope across a particular signal tuning range.

range of available laser diodes. Hence, the gain slope must be low for every wavelength over the entire range of possible signal wavelengths. The simulated gain slope of a highAl silica-based EDFA is shown in Figure 22 for a series of lengths and a 20-dB gain level. It is clear that the gain slope of this fiber can be relatively constant and low in the wavelength range of 1545–1560 nm for an optimally selected fiber length of about 10 m. However, other parts of the spectrum have substantially higher and more variable gain slopes. Whether a given slope is acceptable in an analog system depends on the level of modulation and wavelength spread produced by the signal. 11.3 OPTIMIZATION OF EDFs FOR SPECIAL APPLICATIONS Since the late 1980s, substantial efforts have gone into the optimization of EDFs for specialized applications. Optimization has often been based on computer models. However, the results of such models can be misleading if important secondary processes are omitted. For example, a simplified model that ignores background loss, ESA processes, and ion interactions would predict that the higher the fiber NA is, the lower is the threshold of a device and the more efficiently it is. Yet, for very high power levels, lower NA fibers with low background loss prove to be the most efficient in practice. To properly represent the dependence of performance on design a model should include the following: 1. 2. 3. 4.

Radial ion distributions and mode profiles. Background loss for the pump, signals, and ASE. All ion–ion interactions as a function of concentration. All other processes that waste either pump or signal photons, such as ESA.


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The next discussions focus on a few particular cases for which optimization has proved essential to produce high performance. 11.3.1 Processes That Affect Efficiency As EDFAs move into higher-power applications, new processes that affect efficiency have been discovered. One of them is ion–ion interaction, depicted for Er 3⫹ in Figure 8a of Chapter 2. This process is most precisely known as homogeneous cooperative upconversion, because it is assumed to occur uniformly in all erbium ions [54]. Any two excited erbium ions that happen to be near each other are able to exchange energy, so that one ion is excited to the 4I9/2 state, while the other drops to the 4I15/2 (ground) state. The ion in the 4I9/2 state relaxes rapidly to the original 4I13/2 excited state. This process is undesirable because it leads to a loss of inversion without emission of a stimulated photon. It can be represented mathematically by the ion inversion rate equation [55]: N dN2 ⫽ ⫺ 2 ⫺ K up N 32 dt τ

(17)

where K up is the upconversion constant and τ is the lifetime of the 4I13/2 state for isolated ions. The form of the upconversion term in Eq. (17) has been a source of considerable debate. Some authors have used the cubic dependence on inverted ion concentration shown in Eq. (17) based on the assumption of a dipole–dipole interaction [55]. Others have used a square-law dependence based on fitting measured data [54]. Regardless of the form of Eq. (17), the effect is an observed nonexponential decay and an apparent reduction in lifetime for high-concentration erbium-doped fibers. A fluorescence decay curve of a typical high-concentration EDF is shown in Figure 23. The initial decay rate is 1/τ ⫹

Figure 23

Measured fluorescence decay for an EDF with a high erbium concentration, showing the reduced lifetime and the nonexponential decay owing to homogeneous cooperative upconversion.

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K up N 20 , where N0 is the total erbium-ion concentration. After a few tens of milliseconds, the inversion approaches zero and the final decay rate in Figure 23 approaches 1/τ. Hence, this measurement can be used to deduce the upconversion constant and the erbium lifetime, assuming that the total ion concentration is known. Because of its high-order dependence on concentration, homogeneous upconversion is negligible at low concentrations. Yet the measured efficiency of a low concentration EDF is poorly predicted by a model that includes background loss as the sole loss mechanism. Clearly, another loss mechanism must be present, even at low concentrations. The postulated additional loss mechanism is the presence of a subset of erbium ions that are paired or clustered with other erbium ions. Even at low to moderate concentrations, there is a finite probability that ions are grouped in clusters. The smallest such cluster is a pair (two ions in close proximity), but larger-sized clusters are also possible. When two or more clustered erbium ions are excited to the 4I13/2 state, the physical energy exchange that occurs under homogeneous cooperative upconversion (see Fig. 8 of Chap. 2) takes place within the cluster. Because the erbium ions are located in close proximity, the interaction is very fast. At usual pump power levels, multiple erbium ions in a given cluster cannot be simultaneously excited because rapid deexcitation of one ion occurs. For typical continuous wave (CW) power levels, erbium ion clusters act as unsaturable absorbers that waste both the pump and signal power. Saturation of the clusters might occur when many watts of pump power are present, although this effect has not been demonstrated. Clusters dramatically limit the possible power conversion efficiency from pump to signal photons. In a laser device, they strongly affect the slope efficiency but only slightly affect the threshold. In an EDF power amplifier they cause a direct reduction in power conversion efficiency. In contrast, homogeneous upconversion reduces the lifetime and a higher power is required to saturate the upconvertion process, but once it is saturated no additional power is wasted. Homogeneous upconversion can be characterized as affecting a laser device’s threshold but not its slope efficiency. The effect of both homogeneous upconversion and ion pairs (or clusters) on EDFAs has been modeled [54,56–60]. Detailed rate equations for paired ions have been derived [57,60]. The effects of the relative concentration of pairs β on the small-signal gain and NF of an EDFA are shown in Figures 24 and 25, respectively. Paired ions reduce the small-signal gain and increase the small-signal NF achievable in EDFAs. However, most practical applications of EDFAs require a low gain and a high output power, parameters that are more affected by the efficiency of conversion of pump power to signal power than the production of maximum gain. The power conversion efficiency is represented in Figure 26, which shows the maximum high-power quantum efficiency and the computed ion-pair fraction of an EDFA as a function of dopant concentration [61]. This figure was generated by considering various EDFs with different known ion concentrations. The measured efficiency for a high-pump–power case at the optimum length was fit using a pair fraction in a model that included paired ions, which allowed one to infer the pair fraction shown in Figure 26. Clearly, even at modest concentrations, even small fractions of paired ions reduce the power conversion efficiency in high-power EDFAs. Another important small effect in EDFAs is ESA from the 4I11/2 state when pumping at 980 nm (ESA2, see Fig. 1). This process has generally been neglected in the literature under the assumption of a very short 4I11/2 lifetime and a small cross section for the process. However, the ESA is centered near 980 nm and may very well be stronger than GSA near 980 nm. This process can be included in a model by writing the rate equations and solving for the occupation of levels 1, 2, and 3 of Figure 1. Such equations were derived in a


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Figure 24 Dependence of the gain of an EDFA on fiber length for different percentages of paired ions, a launched pump power of 70 mW, and a signal power of ⫺100 dBm. The dashed curve traces the locus of the gain maxima. (From Ref. 59.)

Figure 25 Noise figure of an EDFA versus absorbed pump power for increasing percentages of paired ions. For each curve the length is the optimum length at 70 mW. (From Ref. 59.)

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Figure 26 Dependence of the quantum efficiency (QE) of different EDFAs, measured at 1530 and 1550 nm, on the erbium concentration (left axis). The right axis shows the dependence on concentration of the percentage of pairs, inferred by fitting computer predictions to the gain saturation curves of these EDFAs. (From Ref. 61.)

general form in Section 10.3.1. Then, a pump absorption term proportional to N3 must be added to the pump propagation equation to represent this mechanism. The occupation of the 4I11/2 state depends heavily on the lifetime of this state. Additionally, the solution of the rate equations shows that more ions occupy this state in the presence of both highpump power near 980 nm and high-signal power near 1530 nm. The loss produced by such occupation depends on the absorption cross section of the ESA2 process. This cross section can be used to fit measured data, because its magnitude has yet to be verified by independent measurement. The advent of fluoride-based EDFAs has shown the importance of the ESA2 process, as these fibers have a long 4I11/2 lifetime. The predicted efficiency of an EDFA pumped at 980 nm as a function of this lifetime is shown in Figure 27. The ESA2 process was included by using the ESA2 absorption coefficient needed to fit measured data for a highaluminum silicate and assuming that this coefficient is independent of host composition. This is probably a reasonable assumption to within an estimated 25% for all hosts. Figure 27 illustrates the reason 980-nm pumping is not often used for fluoride-based EDFAs. Most of the pump power is wasted in absorption to higher levels and the efficiency is low. However, even in silicates the efficiency is slightly affected by this process. The lifetime would have to be less than about 1 µs for ESA2 to truly be negligible. This issue is further discussed later for high-power EDFAs. 11.3.2 Fiber for Remote Pumping Applications A typical configuration for a remotely pumped EDFA fiber link is shown in Figure 28. Such links are useful to connect points that are too far apart to be reached by fiber alone,


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Figure 27

Maximum theoretically achievable efficiency and small-signal gain for an EDFA pumped at 980 nm in the presence of ESA2, plotted as a function of the 980-nm pump state lifetime. The lifetime ranges for silicate and fluoride fibers are shown.

but close enough that a full optical repeater is unnecessary. In such a case, pump power propagating from the transmitter or receiver end of the link can provide amplification to increase the total span attainable. In Figure 28, two 1480-nm–pumped remote EDFAs are shown, although one may be sufficient in certain systems. Pumping near 1480 nm is required because the loss of the transmission fiber is intolerably high near 980 nm. These two EDFAs have substantially different performance requirements. Both the pump and signal begin at relatively high power levels at the transmitter and both experience loss while traveling through the transmission fiber. In fact, the pump experiences more loss

Figure 28 Diagram of a remotely pumped EDFA transmission link with two 1480-nm pumps launched in opposite directions to enhance the achievable span length between transmitter (TX) and receiver (RX).

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than the signal, so it is useful to convert the pump power into signal power as early as possible. However, nonlinear effects in the fiber limit the maximum signal power that can be injected or present at a given location. Hence, the signal is allowed to drop in power before being boosted using the remaining pump power in the remote transmitter postamplifier EDFA. This EDFA is a power amplifier and is required only to produce the best power conversion possible. In fact, the gain produced by this EDFA is typically no more than 6 dB, and its NF is inconsequential to the system performance. The optimization of such a fiber involves only reducing the loss mechanisms described in the foregoing. Lowconcentration fibers with moderate NAs are ideal. Optimization of the second remote EDFA, the receiver preamplifier, is more complex because it contributes to not only the gain, but also to the noise accumulation of the link. In this EDFA the signal is extremely small but the pump can be large or small, depending on whether the EDFA is near the receiver. However, because the receiver typically includes an EDFA preamplifier, the remote EDFA must be located far away from the receiver to increase the total span length. Ideally, it must provide a high gain and a low NF and use as little pump power as possible. However, the pump in this EDFA is counterpropagating relative to the signal, which tends to produce a higher NF than a copropagating pump. The optimization is best performed by treating the entire section from the front of the second remote EDFA to the receiver as a single extended receiver. This extended receiver contains not only two EDFAs for amplification, but also a long transmission fiber between the EDFAs with high pump power near 1480 nm. Such a fiber produces nonlinear Raman gain that further enhances the improvement produced by the injected pump. A repeaterless link as depicted in Figure 28 can be assigned a power budget B that may be written as B ⫽ PT ⫺ PR

(18)

where PT is the transmitter output power and PR the receiver sensitivity (i.e., the power required at the receiver to produce a given bit error rate, typically 10⫺9). The new extended receiver, including its remotely pumped EDFA, can be treated as a receiver with an input end located a distance from the actual receiver and with a sensitivity Pext. The power budget increase produced by the remote EDFA in the repeaterless span is ∆B ⫽ PR ⫺ Pext

(19)

The power budget increase directly translates into a greater total span length because the ability to overcome power loss directly allows the addition of transmission fiber in the link. The extended receiver sensitivity can be written as a function of the sensitivity of the actual receiver, the NF and gain of the remote EDFA, and the length and characteristics of the added transmission fiber. One conclusion drawn from such an analysis is that an EDFA that produces the same gain and NF for a lower pump power can be located farther from the receiver to produce the same increase in sensitivity. Hence, maximizing the gain efficiency is critical to a remote EDFA. Modeled gain and NF are plotted versus length (Fig. 29) for a series of EDFs with different NAs, for 2 and 10 mW of 1480-nm counterpropagating pump power. The model used to generate these curves included all loss mechanisms described earlier for these EDFs. The fibers were assumed to have dopant in the entire core, rather than confined to a narrower region and, based on the relative losses of the fibers modeled, all fiber lengths in Figure 29 were assumed to have the same absorption per unit length of 5 dB/m at the peak wavelength of 1530 nm. Figure 29 shows that, for


Figure 29

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Theoretical dependence on fiber length of (a) the small-signal gain, and (b) the noise figure, both at 1558 nm, of an EDFA pumped in the backward direction at 1480 nm for remotepumping applications: The EDF is a high-Al silicate fiber with 5-dB/m peak absorption at 1530 nm. These curves are plotted for two pump power levels available at the EDFA, and for a series of numerical apertures.

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remote preamplifier applications, high intensity in the doped region enhances the performance. The highest NA fiber has the highest intensity and the lowest saturation power, thus it produces the highest gain and the lowest NF at low pump power levels. Clearly, a stronger dopant confinement would further enhance the gain efficiency and improve these fibers as remote amplifiers. It is also noteworthy that the higher-NA fiber simulated in Figure 29 had a substantially higher background loss. Yet, this is fairly unimportant to the performance of fibers in remotely pumped applications because only short lengths are generally used. 11.3.3 Fiber for High-Power Applications: 1480 nm Versus 980 nm Pumping In high-concentration EDFAs, homogeneous cooperative upconversion is detrimental to the efficiency. Consequently, in EDFs designed for power amplification the erbium concentration is usually kept low. For low-concentration EDFs, four other characteristics influence the efficiency: 1. The fiber NA and dopant confinement determine the threshold power, which is the amount of power used in spontaneous emission to invert the ions to their required inversion level. 2. Fiber background loss due to scattering or absorbing contaminants in the fiber. 3. Pump ESA from any occupied state. The effect of any ESA1 is greater than the effect of ESA2 (see Fig. 1), but all such processes matter. 4. Erbium ion clusters, as described in the foregoing. These four processes are not independent, and for a given application they must be traded off. Table 4 summarizes the effect of some fiber design changes on each loss mechanism. The fiber background loss (effect 2) typically increases with increasing fiber NA, whereas the fiber threshold power (effect 1) decreases as the NA increases. This is illustrated in Figure 30, which shows the measured background loss for a typical series of Alco-doped silica-based EDFs as a function of NA. The measurements were performed at 1200 nm because this wavelength experiences little Er 3⫹ absorption. Figure 30 shows that the background loss increases rapidly and nearly linearly with fiber NA for high NA values. The loss at 1550 nm is typically 40% that at 1200 nm, whereas the loss at 980 nm is higher by about 80%. Figure 30 also shows the threshold power, quantified as the total spontaneous emission (SE) power near 1550 nm, for a 25-dB EDFA made from each fiber with the ions inverted to 65% inversion (flat gain spectrum). This power should be multiplied by the ratio of signal to pump wavelengths to compute the pump power wasted Table 4 Fiber Design Changes and Their Effects Fiber design change ⫺NA ⫺Dopant (⫽confinement) Confine dopant (⫽concentration)

Threshold power

Pairing loss

—

⫽

⫺Loss, ⫺effect

⫽(unless coop upconversion⫺) —

⫺

⫽Loss, (device ⫽Loss, (device

⫽

Background loss

effect shorter) ⫺effect longer)

ESA2 loss ⫺Effect (⫺intensity) ⫽ ⫺Effect (⫺intensity)


627

Figure 30

Dependence of two power-wasting mechanisms on the fiber NA: left axis, the measured total EDFA spontaneous emission for a 25-dB gain at 1550 nm; and right axis, the measured fiber background loss at 1200 nm.

to produce this SE. For a 980-nm pump, the lowest NA fiber considered wastes more that 12 mW of pump power as SE to produce 25 dB of gain. Pump ESA at 980 nm (effect 3) also changes with fiber NA, but it is difficult to quantify in the form of a figure. The ESA2 process is a two-photon stepwise loss mechanism, whereas the signal emission process utilizes only one pump photon. Hence, ESA2 increases rapidly with an increase in NA (as the latter produces an increase in optical intensity). Finally, ion clustering (effect 4) and background loss can be traded off using erbium ion concentration. A highconcentration fiber has more clusters, but suffers less from background loss because it can produce the same gain in a shorter device. In high-power 980-nm–pumped applications, ESA2 from the 980-nm–pump band affects performance. Assuming negligible ion clustering, the predicted efficiency for the same fibers as in Figure 29 are plotted as a function of 980-nm pump power in Figure 31. A first series of curves is shown assuming no ESA process, but typical background loss values. It predicts that the performance is relatively independent of pump power, and even improves a little with pump power for low NAs, but that it decreases at higher NA owing to the presence of background loss alone. Only the lowest NA fiber produces a significantly lower efficiency for 50 mW than for higher-power levels. This difference can be attributed to the high-threshold power shown in Figure 30 for these fibers. However, most of the remaining difference between the plots in Figure 31 is due to differences in background loss. The second series of curves in Figure 31 shows the same simulation when ESA2 is included. The lowest NA fiber then produces a dramatically greater efficiency at very high pump power than does the highest NA fiber. At lower pump powers, higher NA fibers begin to be more efficient than low NA fibers. Data measured at two power levels for two of these fibers shows that this model predicts the measured efficiencies accurately

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Figure 31

Theoretical efficiency at optimum length in a high-Al silica-based EDFA pumped with 100 mW at 980 nm in the direction of the signal (1550 nm): The curves were generated with and without pump ESA2 for a series of fiber NAs. The experimental data points provide evidence of the presence of ESA2 at 980 nm.

with the inclusion of ESA2. This study shows that both background loss and pump ESA in an EDFA model are essential to accurately predict power EDFA efficiency. 11.3.4 Er/Yb Co-doped Fibers Ytterbium co-doping of EDFs has been proposed as a method to produce high-power amplifiers and very short fiber lasers [62–65]. A diagram explaining the principle of this approach is shown in Figure 32. Yb3⫹ is a three-level medium that produces a very broad absorption and gain spectrum from 800 to 1100 nm. The measured Yb3⫹ spectra for a typical Yb-co-doped EDF are shown in Figure 33. The ytterbium can absorb a photon within this band and be excited to its upper state. From this state it can transfer its energy to the 4I11/2 state of an erbium ion, which can then decay to the 4I13/2 state and produce amplification. Hence, Yb co-doping broadens the effective pump band of erbium, making it possible to pump the fiber at wavelengths available from high-power lasers that cannot pump fibers doped with erbium alone. In particular, cladding-pumped Yb- and Nd-doped fiber lasers pumped by laser diode arrays or high-power emitters have produced many watts of output near 1064 nm [66]. The introduction of Yb to an EDF adds many potential loss mechanisms. Some of the processes that may be important are shown in Figures 32 and 34. They include the following: 1. 2. 3. 4.

ASE and SE from the erbium ions. ASE and SE from the ytterbium ions. Upconversion in the erbium ions (as described earlier). Backtransfer from the erbium to the ytterbium. This process occurs if the erbium ion 4I11/2 state remains partly occupied in steady state.


629

Figure 32

Diagram of the minimum processes to be modeled in an Er/Yb co-doped amplifier. The ideal pump absorption, transfer, rapid phonon decay, and signal gain processes are accompanied by the presence of backtransfer, spontaneous emission (SE), and amplified spontaneous emission (ASE).

5. 6. 7. 8.

Pump, ASE, and signal ESA from any excited erbium level. Transfer from ytterbium to erbium already excited to some excited level. Paired or clustered Er ions. Radial dependence of spectrum, transfer coefficient, ytterbium concentration, erbium concentration, pump power, and signal power.

Because the transfer process depends linearly on both the Yb and Er concentrations, radial distributions can be quite important. Assuming typical ion distributions (e.g., gaussian profiles), ions at the center of the core can transfer energy much more rapidly than ions near the core–cladding interface. The magnitudes of processes 3–7 are difficult to quantify, but all processes can play a role in the performance of these devices. Models Modeling of Er/Yb-co-doped fibers (EYDF) can be performed using simple measurable parameters, as in EDFs, as well as a few parameters more difficult to quantify. Evidence seems to show that transfer, backtransfer, ASE , SE, upconversion, and pump ESA from the erbium 4I13/2 state all may exist in certain fibers. For simplicity, we can first write equations assuming no radial dependencies. In the equations presented below, only one pump wave and one signal wave are considered. Clearly, multiple pump and signal waves can be added by summing these equations (as in EDF treatments), whereas ASE waves

630

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Figure 33

Measured ground-state absorption and excited-state gain parameters of Yb3⫹ in a typical high-phosphorus Er/Yb-co-doped fiber.

Figure 34 amplifier.

Possible loss mechanisms that may affect the performance of an Er/Yb-co-doped fiber

631


are equivalent to signals when computing saturation. The rate equations to solve can then be written as follows: YbSe Pump abs

Pump emis

Yb–Er transfer

Er–Yb backtransfer

N dN 2y ⫽ WpaN 1y ⫺ WpeN 2y ⫺ τ 2y ⫺ K Tr N 2y N 1e ⫹ K Tr N 1y N 3e y dt Er decay to sig band Yb–Er transfer

Er decay to sig band

N 3e τ3

Er Pump ESA1

N 3e τ3

1 K up N 32e ⫹ Wesa N 2e 2

⫹

(19b)

ErSe Er upconversion

dN 2e ⫽ dt

Er upconversion

Er–Yb backtransfer

dN 3e ⫽ K Tr N 2yN 1e ⫺ K Tr N 1y N 3e ⫺ dt

(19a)

Er Pump ESA1

Sig abs

Sig emis

N ⫺ τ 2e ⫺ K up N 32e ⫺ WesaN 2e ⫹ WsaN 1e ⫺ WseN 2e e

(19c)

N e ⫽ N 1e ⫹ N 2e ⫹ N 3e

(19d)

N y ⫽ N 2y ⫹ N 1y

(19e)

where N e, N y are the total Er and Yb concentrations, respectively. N 2y, N 1y are the occupation of the Yb excited and ground states, respectively. N 3e, N 2e, N 1e are the occupation of the Er pump, excited, and ground states, respectively. K Tr is the Yb–Er transfer coefficient. K up is the Er–Er homogeneous upconversion constant. τ y, τ e, τ 3 are the lifetime of Yb, the Er signal band, and the ER pump band, respectively. Wpa, Wpe are the pump absorption and emission rates of Yb. Wsa, Wse are the signal absorption and emission rates in Er. Wesa is the pump ESA rate in Er. The absorption and emission rates can be related to simple model parameters such as saturation parameters, gain parameters, absorption parameters, and lifetimes. For example, in erbium Wsa ⫽

Psα s , hνsξ eτ e

Wse ⫽

Ps g s* , hνsξ eτ e

Wesa ⫽

Ppα esa hνsξ eτ e

where Ps is the signal power at frequency νsPp is the signal power at frequency νp; and the parameters αs and g*s are erbium gain and loss parameters at the proper wavelengths, as defined by Eqs. (3). ξ e is a saturation parameter as ξ e ⫽ N e /τ e, where N e is the linear Er density i.e., the total erbium density integrated over the fiber cross section. Similar expressions can be written for Yb: Wpa ⫽

Ppα p , hνpξ yτ y

Wpe ⫽

Pp g*p hνpξ yτ y

with definitions parallel to the Er definitions. Then gain and loss evolution equations can be written for the pump, signal, and ASE waves, neglecting background loss:

冤

冥

N 2y dPp N ⫽ [g*p ⫹ α p ] ⫺ α p Pp ⫺ α esa Pp 1e dz Ny Ne

(Yb pump) (20a)

632

Wysocki

冤

冥

N dPs ⫽ [g*s ⫹ α s ] 2e Ps dz Ne

(Er signal) (20b)

冤

冥

(Yb ASE) (20c)

冤

冥

(Er ASE)

N 2y N 2y dPyASE ⫽ [g*yASE ⫹ α yASE ] ⫺ α yASE PyASE ⫹ Poy g*yASE dz Ny Ny dPeASE N N ⫽ [g*eASE ⫹ α eASE ] 2e ⫺ α eASE PeASE ⫹ Poe g*eASE 2e dz Ne Ne

(20d)

where all ASE parameters are gain- and loss-modeling parameters at a given ASE wavelength and Poe, Poy are the spontaneous input power in the ASE bandwidth represented by each ASE wave (one photon per mode per bandwidth is usually used). These equations can clearly be expanded by summing over all pump waves, signal waves, and a finite number of ASE waves, and by summing over a series of radial regions, each representing a certain pump intensity, signal intensity, erbium concentration, and ytterbium concentration. Alternately, the radial distributions can be represented by integrals over the radial dimension. Fundamentally, it is critical that all terms be considered before being neglected. ESA may not be important in a particular pump region, but it is expected to exist at some pump wavelengths. In some applications, ASE in either Er, Yb, or both might be negligible. Upconversion, transfer, and lifetimes all depend strongly on the host. All these effects must be included if these fibers are to be modeled correctly. This model was used to generate some of the following results. Spectrum and Gain Flatness As mentioned earlier, the gain flatness of an EDFA is important in many applications. Energy transfer between ytterbium and erbium ions is most effective in phosphorus codoped fibers [64–66]. Unfortunately, such fibers do not readily produce flat gain spectra [15,34]. The flatness FOM of a typical Er/Yb-doped fiber (EYDF) co-doped with phosphorus is listed in the last row of Table 2. They are all lower than for an EDF. The gain spectrum of this fiber at various inversion levels are plotted in Figure 35. Comparison with the corresponding spectra for an Al-co-doped silicate (see Fig. 4) shows that the phosphorus-co-doped fiber does not produce a region of flat broadband gain. Furthermore, its FOM for gain tilt is poor, as shown in Table 2. Fortunately, in many high-power applications for Er/Yb-doped fiber amplifiers (EYDFAs), gain flatness and gain tilt are not important issues. In the applications for which these parameters are important, better spectral characteristics can be achieved by combining an Al-co-doped EDFA with a Pco-doped EYDFA. Between 1544 and 1561 nm, a highly inverted EDF produces a decreasing gain with increasing wavelength (see Fig. 4), whereas a 45%-inverted EYDF produces an upward slope (see Fig. 35). By properly selecting their lengths, these two fibers can be combined to produce a flat gain spectrum. Figure 36 shows an example of two individual spectra and the flat gain spectrum obtained when combining them. Fortunately, the inversion levels required to produce this result are typical of a dual-stage power EDFA. A firststage highly pumped at 980 nm produces a high inversion and a low NF, whereas a saturated second stage with a reduced inversion allows for good power conversion. Using an EYDFA (of proper length) for the second stage allows for higher output power and a flat spectrum.


633

Figure 35

Series of theoretical gain spectra achievable in an Er/Yb-co-doped high-phosphorus silica fiber for increasing inversion levels. This figure illustrates that the gain spectrum of this host is not as flat as that of the high-Al host of Figure 4.

Figure 36

Theoretical gain spectra of a possible flat-gain hybrid EDFA using a typical high-Al EDF and a high-P Er/Yb-co-doped fiber.

634

Figure 37

Wysocki

Diagram of the hybrid fiber amplifier design modeled in Figure 36.

A diagram of an experimental flat-gain hybrid amplifier is shown in Figure 37. It used a 15-m length of the EDF of Figure 4 and a 9-m length of the EYDF of Figure 35. These lengths were chosen as a compromise between power output, spectrum, and NF. The first-stage EDF was pumped with 100 mW at 980 nm, and the second stage with up to 2 W at 1064 nm. An isolator was placed between stages to suppress backward-traveling ASE. To test the performance of this design, a saturating tone was provided at 1548 nm, and its power was adjusted to various levels. A small probe signal was added and swept across the spectrum to measure the gain. For each saturating tone level, the pump power of stage 2 was adjusted until the flattest spectrum was achieved. The flattest gain spectrum was achieved for a small saturating tone, but the output power was low, which is of little interest for most applications. For higher saturating powers, the spectrum was not as flat (the first-stage inversion was reduced) but the output power was enhanced. The resultant best spectra are shown in Figure 38 for some useful saturating tone levels. Fortunately, the flattest net gain spectrum was degraded only slowly by increasing the signal power. The solid curves in Figure 38 are theoretical fits using the known component losses and postulated inversion levels. The fits are good, although some discrepancy is observed near the dip near 1551 nm. It may be attributable to slight spectral hole-burning, described later, or errors in measured parameters. All four spectra of Figure 38 achieve a bandwidth of more than 17 nm with as little as 0.4-dB variation in the best case. The 1064-nm pump power levels were 307, 425, 645, and 1024 mW for ⫺15, ⫺11, ⫺7, and ⫺3 dBm signal inputs, respectively. The measured output powers at 1548 nm were 14.53, 18.01, 21.06, and 23.61 dBm for ⫺15, ⫺11, ⫺7, and ⫺3 dBm signals, respectively. The NF of this dual-stage EDFA is determined by the NF of the first stage. Including preamplifier loss, the NF at 1548 nm was measured to be less than 5 dB for all cases, with a minimum of about 4.2 dB for the smallest-signal case. This value corresponds to an internal NF of approximately 3.2 dB. It is shown in the following that the EYDFA itself could not produce an NF this low. Efficiency As shown earlier in Section 11.3.4 (under Models), erbium pumped by transfer from an ytterbium ion behaves differently from erbium pumped directly at 980 nm. Some of the additional processes that may be present were described. ASE and SE in the ions waste energy and limit the ytterbium inversion. Backtransfer reduces the apparent forward transfer rate and sets a maximum erbium inversion. A variety of ESA and transfer processes


635

Figure 38

Measured flattest gain spectra for the hybrid fiber amplifier of Figure 37, saturated with a single signal at 1551 nm. The pump power at 1064 nm in stage 2 was adjusted in each case to 307, 425, 645, and 1024 mW from the top to the bottom curve.

to higher levels are likely, and they have been observed in some hosts [5]. To build an accurate model one must decide which of these processes are present in a given host, then incorporate them accurately in the governing equations. Examples of exploratory measurements are shown in Figures 39 and 40. ESA1 from the 4I13/2 level can be measured (see Fig. 39) by observing the change in absorption between pumped and unpumped erbium-doped fibers with Al and P co-doping, similar to compositions used for Er/Ybdoped fibers. ESA1 bands exist near 780, 850, and 1130 nm, which may cause pump loss, depending on the pump wavelength. These bands are stronger and wider in Al-co-doped fibers. ESA2 from the 4I11/2 level is difficult to measure but is known near 980 nm (as in the foregoing) and is expected at other wavelengths (see Fig. 1). By using the process described in the following section, transfer rates and ion pairs can be estimated using fluorescence spectra measured in very short fibers pumped at 980 nm (with direct and indirect erbium pumping), 930 nm (strong indirect pumping), and 1064 nm (weak indirect pumping), such as the spectra shown in Figure 40. Ions not inverted at 930 nm but inverted at 980 nm are apparently not coupled with Yb ions. These may be Er–Er pairs. Ions not inverted at 1064 nm indicate inadequate transfer when the Yb ions are poorly inverted. By using the foregoing measurements and measured lifetimes, upconversion coefficients, spectra, radial distributions, and losses, a model was built of a typical Er/Yb-doped fiber using the treatment of Section 11.3.4 (under Models) and performing summations over wavelength and radial dimension within Eqs. (19) and (20). It included: 1. Radial ion distribution (the transfer depends on the product of Yb and Er concentrations).

636

Figure 39

Wysocki

Measured ESA1 spectra for silica-based EDFs co-doped with phosphorus or alu-

minum.

Figure 40

Fluorescence spectra measured from a 2-cm length of Er/Yb-co-doped fiber pumped at various pump wavelengths and powers, illustrating the inability of a 1064-nm pump to invert all the erbium ions in such a fiber.


637

2. Yb ASE, Er ASE, Yb SE, and Er SE. 3. Pairs, upconversion, ESA, scattering, and other loss mechanisms. An account of the utilization of pump power is shown in Figure 41 for 2 W of copropagating pump power at (1) 1064 and (2) 980 nm, for 1 mW of 1550-nm signal power. At 1064 nm, pump power is used mostly to generate signal and is lost in paired ions and other losses. However, substantial Yb and Er SE are also produced. The key to performance is achieving rapid Yb–Er energy transfer. At 980 nm, pump power is used almost exclusively to generate ASE and SE in the Yb ions. The pump power is used up in less than 1 m and little signal power is generated. Noise Performance In many potential EYDF applications such as CATV, LAN, and WDM systems, an excellent NF is required. In 980-nm–pumped EDFAs, a 3-dB NF can be achieved. This is not always true in EYDFAs pumped at 1064 nm. In EYDFAs, the best NF is achieved with a small signal, a high pump power, and without significant ASE power from either ion type. Then, the inversion of the ytterbium and erbium ions can be approximated from Eq. (19): N 2y ⫽ Inv y ⫽ Ny High Pp α y (ν p)Pp /hνpξ y α y (νp) → (21) [g*y (νp) ⫹ α y(νp)]Pp /hνpξ y ⫹ 1 ⫹ K trτ y N e (1 ⫺ Inv e) g*y (νp) ⫹ α y (νp) 1064 nm pump K tr τ eN y Inv y K trτ eN y Inv y ⫹ α e (νp)Pp /hνpξ e N 2e ⫽ Inv e ⫽ → Ne 1 ⫹ K trτ eN y Inv y ⫹ α e(νp)Pp /hνpξ e 1 ⫹ K tr τ e N y Inv y

(22)

where g*e , α e, ξ e, N e, and τ e are the gain, loss, saturation parameter, concentration, and lifetime for erbium, and the like-parameters with a y subscript the same quantities for ytterbium. Equation (22) includes terms for both indirect and direct (dropped for 1064 nm) pumping of erbium. The direct pump term was not shown in Eq. (19) under the assumption that the pump was not near 980 nm. For a typical efficient silica-based EYDFA co-doped with P and Al, the estimated Er and Yb concentrations are 2.15 ⫻ 1025 m⫺3 and 2.15 ⫻ 1026 m⫺3, respectively. The measured low-inversion lifetimes of Er and Yb are 10.3 ms and 940 µs, respectively. Upconversion in erbium [55] reduced the high-inversion lifetime to 4.4 ms (upconversion constant K up ⫽ 2.7 ⫻ 10⫺49 s⫺1m⫺6). A lifetime corrected for upconversion can be used when applying Eq. (22) so that the upconversion terms of Eq. (19) can be dropped here. The measured ytterbium gain and absorption coefficient spectra for this fiber near 980 nm appear in Figure 33. Because ytterbium is a two-level medium, only a small inversion takes place with 1064-nm pumping. Using the measured spectra and Eq. (21) yields a computed inversion of about 2.4%. The erbium inversion can be measured using fluorescence at 1530 nm for the same 2-cm fiber pumped at 980 and at 1064 nm. At 980 nm, both direct and indirect pumping occur [see (Eq. 22)], so complete inversion is expected, whereas at 1064 nm only indirect pumping occurs. The observed fluorescence is shown in Figure 40. The 500-mW, 1064nm pump produces only 86% as much fluorescence as the 110-mW, 980-nm pump, indicating 86% inversion. At this level, the lifetime of the erbium ions is 5.34 ms (owing to upconversion). The transfer coefficient computed from Eq. (22) is K tr ⫽ 2.25 ⫻ 10⫺22 s⫺1m⫺3. Using this value and Eqs. (21) and (22), it is possible to compute the maximum

638

Figure 41

Wysocki

Account of the use of the available pump photons by various processes, as a function of fiber length, in an Er/Yb-co-doped amplifier pumped in the direction of the signal with 2 W at (a) 1064 nm and (b) 980 nm. The signal is at 1550 nm, and its launched power is 1 mW.


639

Figure 42

Theoretical lowest achievable noise figure for a typical Er/Yb-co-doped fiber amplifier (large-pump, small-signal case) for a series of pump wavelengths and a single-signal wavelength. The crosses represent measured data points for 1064-nm pumping.

erbium inversion and the best possible NF as a function of signal wavelength. The NF is plotted in Figure 42. For a 1064-nm pump, it is limited to 3.8 dB at 1550 nm and 4.4 dB at 1530 nm. The best NFs measured, using a short (⬍ 2-m) 1064-nm co-pumped EYDFA and a polarization nulling technique, are also shown as crosses in Figure 42. These data points agree well with theory. The NF cannot be improved by pumping harder because it is limited by the ytterbium inversion [see Eq. (22)], which approaches a high-pump– power limit for a given pump wavelength [see Eq. (21)]. However, improvement is observed in Figure 42 for shorter pump wavelengths because the maximum ytterbium inversion increases. Clearly, an EDFA pumped at 980 nm cannot be replaced by an EYDFA highly pumped at 1064 nm without considering this noise issue. However, the hybrid twostage design of Figure 37 avoids this problem by utilizing the excellent NF of a 980-nm EDF in a first stage. 11.4 IMPORTANT SMALL MAGNITUDE EFFECTS IN EDFAs Simple models and diagrams of EDFA performance have usually neglected a variety of small-magnitude effects. Some of the approximations made were summarized in Section 11.2.1. Yet, in long systems and in high-precision applications, these effects often accumulate and become important. This is especially true when the effect occurs in successive EDFAs and tends to add, rather than cancel or be randomly oriented in some way. Some of these effects are described in this section.

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11.4.1 Spectral Inhomogeneity Chapter 10 described some of the issues involving spectral inhomogeneity in EDFAs. As described in Section 11.2.1, the homogeneous broadening approximation is used extensively in predicting the gain spectrum of an EDFA. Spectral hole-burning has typically been measured at low temperatures at which spectral thermal broadening is small. However, recent measurements have demonstrated that spectral hole-burning is important at room temperature [67,68]. In Chapter 10 a function f(ν) was used to define the inhomogeneous broadening. A gaussian of width ∆ν I was substituted for this function and a postulated homogeneous spectrum was derived from the total spectrum (see Fig. 13 of Chap. 10). One important assumption in this approach is that all erbium ions have the same spectral shape, with a distribution only in the center wavelength of each ion. Yet there is no fundamental reason why ions in a glass should occupy such a continuum of sites. Another possibility is that a finite number of different local environments exist and that each environment produces a different erbium ion spectrum. The summation of these spectra is the total spectrum observed. This view is supported by the result shown in Figure 43, which shows the spectral hole width measured as a function of saturating wavelength for an Al-co-doped silicate EDF. Neither the width nor the depth of these curves is independent of wavelength, as might have been expected for a continuum of sites. A model of spectral hole-burning consistent with these new results might postulate a finite number of ion subsets, each represented by the following parameters: g*i (λ s) and α i(λ s), the gain and absorption parameter for the ith ion subset at signal wavelength λ s. g*i (λ p) and α i(λ p), the same parameters at pump wavelength λ p. ξ i, the saturation parameter (linear density/lifetime) of the I-th subset.

Figure 43

Spectral hole spectra and widths measured for saturation at different wavelengths in a high-Al (12 mol%) silica-based EDF. (From Ref. 67.)


641

We know that the total gain and absorption parameters at each wavelength must be g*(λ) and α(λ), respectively. We can thus sum over all the ions (for either the signal or the pump wavelength): n

冱 g*(λ)

g*(λ) ⫽

i

(23a)

i⫽1

n

α(λ) ⫽

冱 α (λ) i

(23b)

i⫽1

However, the saturation parameter does not sum in this fashion because each ion set may have a different lifetime τi. If the saturation parameter of a homogeneous model represents the linear density of all ions divided by the average lifetime of all ions, we can write n

τξ ⫽

冱τξ

i i

(23c)

i⫽1

A model can then be built using the standard modeling procedure described in the foregoing, but summing the gain contribution of each subset of ions. The inversion of each ion subset can be computed using the parameters for that subset in the equations of Chapter 10. The difficulty of such a model is that it is nearly impossible to measure the number of ion subsets and their spectra. A model can easily be built with only two subsets, and postulating some method to distinguish their spectra. For example, a constant ratio of spectral values between subsets or a postulated form of wavelength dependence such as a slope across the band could be used as long as Eqs. (23a–c) are satisfied. Such a model can be used to fit data for the relative saturation between two particular wavelengths and can improve the theoretical fit to measured data for those two wavelengths. However, it would then not necessarily accurately predict results at a third wavelength, unless the fiber did contain only two ion subsets of exactly the form chosen. Because identification or postulation of ion subsets is difficult, it is useful to measure spectral hole-burning and deduce a rule for its inclusion in a model. In particular, it is useful to use a homogeneous model first to establish the homogeneous result, then to add spectral hole-burning as a small correction to this result. One type of experimental results that can be used for such a model is shown in Figure 44. In this plot, the hole width and hole magnitude is plotted for various EDFA compression levels at 1551 nm. The hole width remains constant with compression, but the depth of the hole increases linearly with compression. At 1551 nm the linear coefficient of proportionality was measured to be 0.27 dB/dB compression [67], but this coefficient depends on both the fiber host and signal wavelength [68]. Theoretically, this coefficient should also depend somewhat on the EDFA design. For a multiwavelength WDM EDFA, inclusion of the proper spectral holes for all signals is complex. Each signal at wavelength λ j creates a hole of different width ∆λ(λ j). If we define G t(λ j) as the gain at signal wavelength λ j when all signals are present, and G nj (λ j) as the gain at λ j when all signal except signal at λ j are present, then we can define the compression produced solely by signal j as C j (λ j) ⬅ G nj (λ j) ⫺ G t (λ j)

(24)

642

Wysocki

Figure 44

Dependence of the spectral hole-burning spectrum on the amplifier compression for saturation at 1551 nm in a high-Al (12 mol%) silica-based EDF. (From Ref. 67.)

The spectral hole depth ∆G j (λ j) at wavelength λ j generated by signal j is then related to this compression using a spectral hole-burning constant K HB in the equation ∆G j (λ j) ⫽ K HB (λ j)C j (λ j)

(25)

Assuming the hole has a gaussian shape, the hole generated at some wavelength other than λ j is given by

冤冤

∆G j (λ) ⫽ ∆G j (λ j) exp ⫺

(λ ⫺ λ j) ∆λ(λ j)

冥冥 2

(26)

Then, if the homogeneous gain is given by G(λ), the total gain in the presence of holeburning caused by all signals can be written: nsig

G tot (λ) ⫽ G(λ) ⫺

冱 j⫽1

冤冤

K HB (λ j) C j (λ j)exp ⫺

(λ ⫺ λ j) ∆λ(λ j)

冥冥 2

(27)

Equation (27) indicates that each wavelength experiences hole-burning produced by each signal in the EDFA in proportion to the compression caused solely by that signal and reduced in a gaussian fashion, by how far the wavelength is away from each saturating tone. At first, this might seem to imply that the hole-burning produced by many signals is greater than the hole-burning produced by a single saturating tone carrying the sum of the signal powers. This is not generally true. For example, compare the case of a single saturating tone with the case of eight channels of equal power, with the same total power and mean wavelength as the saturating tone. The total compression produced at a given wavelength by the sum of the eight signals is in general similar to that produced by the single saturating tone. Each channel produces roughly one-eighth as much compression


643

as the single saturating tone. Clearly, if all the signals were located at nearly the same wavelength, Eq. (27) would approach the case of a single signal with all the power located at that wavelength. The result of Eq. (27) represents signal-induced spectral hole-burning. In general, the more signals in a WDM system, the more the spectral hole is distributed across the band and the less the depth is expected to be at any given wavelength. This effect tends to equalize the gain in EDFAs because a signal of higher power produces more compression and thus a deeper hole. However, pump-induced spectral hole-burning, also known as site-dependent pumping, has also been observed in EDFAs [69]. This effect is present because the gain and absorption at the pump wavelength are also different for each ion subset. The gain and absorption spectra at the pump wavelength determine how effectively each ion set is pumped at a given pump wavelength. Yet the gain and absorption spectra in the signal band determine how well the signal can experience gain from a given ion subset. Ions that are easily pumped are not necessarily effectively utilized at the desired signal wavelength. Hence, the spectrum produced by an EDFA deviates from the predicted homogeneous spectrum and varies as a function of pump wavelength near 980 nm [69]. This effect makes it more difficult to design filters for EDFAs, or to predict resultant spectra in complex designs, because the result is pump–wavelength-dependent, even if the EDFA gain and fiber length are the same. The effect is relatively small, but is very difficult either to model precisely or to measure in a way such that a simple correction to the homogeneous approximation can be derived. This is one effect that is best measured for a particular EDFA design. 11.4.2 Polarization-Dependent Gain In long EDFA chains, ASE with a state of polarization (SOP) orthogonal to a saturating signal experiences substantially more accumulated gain than ASE with the same SOP as the saturating signal [70]. This effect has also been observed in single EDFAs by the use of differential measurement techniques [71,72]. Additionally, it has been noted that similar effects occur for the pump SOP, except that signals with the same SOP as the pump experience more gain [71]. In an EDFA operating with a 5-dB gain compression, the magnitude of the polarization-dependent gain (PDG) difference is typically about 100 mdB at 1558 nm [73]. When enough EDFAs are chained together in a long system, ASE orthogonal to the signal polarization can grow to substantial levels by the end of the chain and lead to degradation of the signal-to-noise ratio (SNR) and the Q of the system [74– 76]. The source of the PDG in EDFAs has been identified as polarization hole-burning (PHB) caused by anisotropy of the erbium ion’s absorption and emission properties. Signals with orthogonal SOPs can utilize different subsets of gain-producing ions. Even in an amorphous glass with no preferred ion orientations, PHB occurs if each ion possesses some level of spatial gain anisotropy. The model of PHB generally used postulates that the orientation of the local electric field determines an axis of symmetry for the Starksplitting of the ions energy levels. This sets an axis for an ellipsoidal surface representing the ion emission and absorption cross sections. We define g*p (λ) and α p(λ) as the gain and loss parameters of the ion along its major axis, respectively, and g*s (λ) and α s(λ) the corresponding parameters along the minor axis. The major axis is defined here as the unique axis, which has a 360-degree symmetry. The two minor axes are perpendicular to it and they both exhibit identical properties. We can then define an anisotropy parameter as

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A(λ) ⫽

g*s (λ) α (λ) ⫽ s g*p (λ) α p(λ)

(28)

Although not intuitively obvious, it can be shown that this ratio is the same for gain and loss. Generally, A(λ) is wavelength-dependent and can range from zero for completely anisotropic ions with response on a single axis, to 1 for an isotropic ion to infinity for completely anisotropic ions with equal response on two axes. For lack of adequate data, A(λ) is treated in the following as wavelength-independent. It is also assumed that there is no circular SOP, although this assumption has been challenged by measurements [77]. Adjustments for circular hole-burning are described later. A detailed model of PHB has been presented and is the basis of the results shown here [78]. Similar to SHB, PHB can be modeled by modifying a standard model and dividing the ions into subsets with different orientations. Measured PHB data can then be used to deduce A at a particular wavelength, which is then used to compute model parameters for the ion’s major and minor axes. Reference axes can be set and the ions subdivided based on orientation relative to these axes. The gain, loss, and saturation coefficients are computed for each ion subset for these axes. The evolution of the SOP of all waves along the fiber can be computed and projected locally onto the reference axes. The population inversion is then computed for each ion subset at each step along the fiber and the gain summed for each wave over all ion sets. The coordinate system for the angular subdivision of the ions may be chosen in any fashion, provided all ions are represented. A simple model might include only three ion groups, as illustrated in Figure 45. Such a model is quick and produces reasonably accurate results. Because ion group 3 of Figure 45 appears isotropic for propagating waves, a further simplified model might ignore this group and retain only the first two groups. Such a model can predict the PDG, but does not properly represent the saturation behavior of ion group 3. The greatest complication to the understanding and measurement of PHB arises from the polarization evolution of the waves along an EDFA in the presence of structural

Figure 45

Diagram showing a signal with an arbitrary state of polarization with major and minor axes, and the three basic groups of anisotropic erbium ions used to model the effects of polarization hole-burning in EDFs.


645

and externally induced birefringence [79]. Assuming either time invariance or time averaging, the spatial evolution of the SOP of all waves can be computed if the fiber birefringence is known. Wavelength-dependent birefringence produces different spatial evolution rates for the pump, signal, and ASE waves. To represent realistic cases, we assume birefringence caused by an internal structural anisotropy that induces fast and slow birefringence axes with a characteristic beat length L b. The axes of birefringence are assumed to rotate uniformly and to make a 2π angular rotation with a characteristic length L r. In a fiber with weak internal birefringence, external birefringence might dominate. Then both the magnitude and axis orientation of the birefringence might vary in an unpredictable fashion. This case could be treated using a random external birefringence; however, it is well approximated by rapid deterministic rotation. All-state polarization-maintaining fiber can be created if all birefringence is eliminated or if L r ⬇ L b ⬎⬎ L dev, where L dev is the device length. Linear polarization-maintaining (PM) fiber has a high internal birefringence and L b ⬍⬍ L r, so that polarization evolution is rapid, but predictable. A standard fiber produces rapid evolution of the SOP when L r ⬇ L b ⬍⬍ L dev, so that evolution of the SOP is rapid and unpredictable. This case applies to most EDFs. If the signal SOP evolves rapidly and randomly along an EDFA, all possible SOPs are reached somewhere. If the signal polarization is scrambled on a time scale that is short compared with the erbium lifetime, all states are produced at a given point within each lifetime and PDG is eliminated [80–82]. However, spatial scrambling does not eliminate PDG because, within the assumptions of this discussion, all noncircular SOPs produce selective saturation of certain ions and some PHB. Linearly polarized light produces the most PHB, whereas all elliptical SOPs produce a reduced level of PHB. Averaged over the entire Poincare sphere, signal-induced PHB is expected to be nonzero. In the presence of a polarized saturating signal or a polarized saturating pump, virtually any two orthogonal signals experience a different gain through an EDFA. Measurements have been performed by adjusting orthogonal probes and searching for the highest gain difference [72]. However, in long EDFA chains where PDG is a significant problem, the SOPs of interest are not arbitrary. The saturating signal establishes one SOP and the orthogonal ASE experiences the relevant increase in gain. Some published measurements [71,73] have successfully used PHB probes in these SOPs. The distinction between different PHB probes is illustrated in Figure 46. Two of the many possible probe sets are shown in Figure 46a for a fiber with no birefringence and a fully polarized saturating tone. The probes of set A are determined by the saturating signal SOP, whereas set B probes are aligned with, and are orthogonal to, the saturating signal major and minor axes, respectively. Computer simulations show that probe set B experiences a greater PDG than probe set A, as expected. Random probe searches might find set B, but the gain difference experienced by probe set A represents the pertinent PDG experienced by ASE in systems. Partially polarized saturating signals also create interesting probe issues. Such signals occur in systems in two main cases: 1. When a signal is deliberately time-scrambled and is either still partially polarized or is partially repolarized by polarization-dependent loss (PDL) in components. 2. When unpolarized accumulated ASE produces saturation near the system end. Two possible probe sets for a partially polarized PHB are shown in Figure 46b. Probe set A consists of partially polarized signals for which the polarized portions are orthogonal and set by the saturating signal-polarized portion. Probe set B consists of two polarized

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Figure 46

Illustration of some possible probes to measure the effect of polarization hole-burning in an EDFA: (a) probes used for a saturating tone that is polarized—set A is better than set B for capturing effect; (b) probes used if the signals are partially polarized.

probes set by the polarized portion of the saturating tone. The simulations that follow show that probe set B experiences a greater gain difference than probe set A. Probe set A is most useful for a time-scrambled signal when the relevant PDG is relative to the entire partially polarized saturating signal. However, probe set B is relevant when ASE provides the unpolarized part of the saturating signal. In this case, the relevant PDG is relative to the polarized signal. In the following presented results, probe sets A of Figure 46 were used uniformly, unless otherwise noted. PHB in EDFAs has been quantified by PDG gain difference measurements. We define G sig ⬅ gain (dB) experienced by a saturating tone that establishes the axis reference. G ort ⬅ gain (dB) experienced by a signal orthogonal to the saturating tone. P s, maj ⬅ signal power on the saturating tone SOP major axis.


647

P s ,min ⬅ signal power on the saturating signal SOP minor axis. ∆G ⫽ (G ort ⫺ G sig ) ⬅ gain difference between the orthogonal signal and the saturating tone. The degree of linearity (DOL) of the polarized saturating signal is DOL s ⫽

P s, maj ⫺ P s, min P s, maj ⫹ P s, min

(29)

The maximum gain difference produced by a linear SOP launched on axis in a PM fiber is defined as ∆G s,max ⫽ ∆G(DOL s ⫽ 1, nonevolving) ⬅ maximum value of ∆G(linear PM signal). For a partially polarized signal, further definitions are required. As illustrated in Figure 46b, the saturating signal can be broken into a polarized and unpolarized portion: Ps, pol ⫽ DOP s ⫻ Ps, tot

(30a)

P s ,npol ⫽ (1 ⫺ DOP s) ⫻ P s, tot

(30b)

By combining Eqs. (29) and (30), the apparent DOL of a partially polarized signal can be written in terms of the DOL of the polarized portion: DOL s,tot ⫽ DOP s ⫻ DOL s, pol

(31)

A partially polarized signal is treated by dividing the unpolarized portion equally between the reference axes of the model and treating the polarized portion as in the foregoing. The anisotropy parameter of Eq. (28) is used as a fitting parameter to measured data. Measurements for a polarized signal have shown a signal-induced gain difference of 120 mdB at 1558 nm for the 5-dB–compressed EDFA modeled here. This value can only be fit if the signal SOP evolution is known. The fiber used was a high-NA EDFA with moderate birefringence wrapped on a standard spool. This is expected to produce rapid evolution of the SOP along the fiber and an averaging of the SOP over all possible states. Because the measurements isolated the signal-induced PHB from the pump-induced PHB, the proper case to simulate includes rapid SOP evolution with an unpolarized (or time-scrambled) pump. The PDG predicted by the model for these conditions for a scrambled pump and rapid SOP evolution of a launched linear signal is shown in Figure 47 as a function of the anisotropy parameter. Two values of A, 0.535 and 2.17, produce the required 120 mdB of gain difference. With the limited data available, it is impossible to decide which value of A is correct. A ⫽ 0.535 is used in the following. The range of validity of this value was assessed by measuring and simulating the PDG as a function of signal level for this EDFA. The results are in good agreement with each other, as shown in Figure 48. The slight disagreement in certain regions is attributed partly to measurement errors, and partly to the inability of the model to exactly predict gain and saturation for this EDFA. For a simulated linear PM case, the simulation with A ⫽ 0.535 predicts ∆G s,max ⫽ 180 mdB. This quantity is difficult to measure in practice in most fibers with external birefringence. Some treatments of PHB in EDFAs have combined pump-induced and signalinduced PHB effects [72]. Such a treatment ignores the fundamental difference between these effects. Signal-induced PHB always produces a greater gain for the SOP orthogonal to the signal. On the other hand, pump-induced PHB can produce a greater gain or a smaller gain for the SOP orthogonal to the signal, depending on the signal SOP relative to the pump SOP. Assuming that the ion anisotropy is the same for the pump and the

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Figure 47 Computed signal-induced PHB (scrambled pump) as a function of the ion anisotropy parameter A for a rapidly evolving signal in a 16.7-m length of high-Al EDF with a ⫺13.8-dBm signal at 1558 nm and 14 mW of counterpropagating pump power. These conditions produced 5 dB of compression and a 1558-nm GPW (18.9-dB gain). Circles indicate fit to a measured value of signal-induced PHB.

signal, a pump aligned with a saturating tone along the entire fiber enhances the saturating signal gain relative to the orthogonal SOP, whereas a pump orthogonal to the saturating tone reduces the saturating signal gain relative to the orthogonal SOP. The pump-induced PDG always averages to zero over all possible pump SOPs. However, in any given EDFA, pump-induced PHB can be substantial. Because of its random orientation relative to the signal, pump-induced PHB acts similar to a polarization-dependent loss (PDL) element in a system. Additionally, if the pump and signal experience different birefringence and evolve at different rates, the pump-induced PHB is reduced or even eliminated. Because PHB is most noticeable when accumulated in long, compressed EDFA systems, the following work assumes an EDFA designed for transoceanic application. In such systems, the gain, compression, and gain peak wavelength (see Sec. 11.2.2 on gain) are often fixed. This analysis assumes a GPW of 1558 nm, which is achieved whenever the gain per unit length is 1.1 dB/m in the EDF considered here. The signal-induced gain difference was simulated as a function of signal power at 1558 nm for different scrambled pump powers and fiber lengths, assuming A ⫽ 0.535 and rapid SOP evolution. A compression value and gain difference were computed for points with the same GPW, and they were plotted against each other in Figure 49. In many instances the gain difference depends on only the EDFA compression level C. This is the same type of rule as for SHB. We may write: ∆G os (λ) ⬇ K PHB (λ)C(λ)

(32)

649


Figure 48

Measured gain compression and PHB gain difference versus signal input power in a 16.7-m length of EDF pumped in the counterpropagating direction with 14 mW at 1480 nm, and with a signal at 1558 nm: the solid curves are theoretical fits using A ⫽ 0.535.

The polarization hole-burning constant K PHB (λ) takes the value of 24 mdB/dB of compression at 1558 nm. Similar rules can be derived for other GPW, and the value of the slope is wavelength-dependent. For high-gain EDFAs, this rule no longer applies, and full computation is required. Detailed modeling has been able to derive the dependence of PDG on the degree of linearity of the signal [78]. In short, PDG depends on the integrated degree of linearity squared of a polarized signal (using the probe set A of Fig. 46): ∆G s (dB) ⫽

1 L

冮

L

0

d∆G s,max (z) [DOL s (z)]2dz dz

(general signal PDG)

(33)

This equation can be used to compute PDG in any general case or to derive simpler rules for different fiber types. A fiber without signal SOP evolution would simplify to: ∆G s (dB) ⫽ (DOL s )2∆G s,max (dB)

(nonevolving signal)

(34)

This is the easiest case to simulate, but it is difficult to measure in practice. In a typical linear PM fiber, the SOP evolves rapidly compared with the changes in PDG evolution along the fiber. In this case, the gain difference can be removed from the integral of Eq. (33) and ∆G s (dB) ⬇ ∆G s,max

冤冮 (DOL ) dz冥 1 L

L

s

0

2

(rapid SOP evolution)

(35)

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Figure 49 Simulated PHB gain difference versus gain compression for an EDFA pumped at 1480 nm and for a series of designs and operating points that all produce a gain peak at 1558 nm (which occurs in this particular EDF for a gain per unit length of 1.1 dB/mW). The solid line is a fit to the minimum data points.

In particular, when a linear signal is launched at 45 degrees relative to the birefringence axes of a PM fiber, it evolves periodically from a linear SOP, to a circular SOP, to the orthogonal linear SOP, and to the orthogonal circular SOP. The average squared DOL along this path is 0.5. Measurements confirm a reduction by a factor near this value for this [83]. The slight discrepancy is explained by circular PHB, as described later. Finally, when the signal evolution is rapid, but random (for many fibers in practice), the signalinduced PHB is independent of launching condition. Here, Eq. (35) implies an averaging of the squared DOL over all possible SOPs. This value is computed to be 2/3, which is surprisingly high but indicates that more SOPs are nearly linear than are nearly circular. Polarization scrambling is a standard method for eliminating PHB in long EDFA systems [80–82]. To apply Eq. (33) to a system with polarization scrambling—complete or partial—it is necessary to know the PDG as a function of the degree of polarization (DOP) of the saturating signal. Inserting Eq. (31) into Eq. (33) and assuming rapid SOP evolution, we obtain

冤∆GL 冮 (DOL ) dz冥 L

∆G A (dB) ⬇ DOP 2s

s,max

pol

2

0

(partially polarized, rapidly evolving)

(36)

This is the gain difference for probe type A in Figure 46. The quantity in the integral is the DOL of the polarized portion of the saturating signal. The better the scrambling is, the less polarized the signal is in a time-averaged sense, and the lower the PDG is.


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Pump-induced PHB is a different case. The maximum value of pump-induced PHB occurs when a linearly polarized pump remains aligned or orthogonal to a linearly polarized signal. The pump-induced PHB (in dB) when aligned with the linear signal is designated by ∆G p,max. In practice, this value can be observed only in a PM fiber by launching of the pump and the signal along the same birefringence axis. However, a model can predict its magnitude if the anisotropy parameter is postulated for the pump wavelength. Inadequate amplifier test data exists to indicate whether A is different at 1480 and at 1558 nm, although a published independent theory suggests that it is different [84]. To illustrate pump-signal interactions, A ⫽ 0.535 was assumed at both the pump and signal wavelengths. For this value, computer simulations predict that ∆G p,max ⫽ ⫺435 mdB. A sample plot of the gain difference for signal probe set A for aligned and orthogonal pump conditions is shown in Figure 50 as a function of signal power in rapid SOP evolution. When the pump is scrambled, PDG is zero at small signal power and increases with signal power. When the pump is aligned or orthogonal to the signal, the gain difference is reduced or enhanced, respectively. The pump-induced PDG varies with signal power, is nonzero for a small signal, and is of greater magnitude than the signal-induced effect (for equal A values). When rapid SOP evolution occurs and the signal-induced PDG is 120 mdB at 5 dB of compression, the pump effect is predicted to be 295 mdB. This value is conjectural, since A ⫽ 0.535 was assumed for the pump. Because pump-induced PHB depends on the relative orientations of the pump and signal and their evolution, it is best treated statistically. The expectation value of pump-induced PHB is always zero. The magnitude of the effect was simulated for different fiber types for about 12,000 pump SOPs distributed

Figure 50

Total PHB gain difference versus input signal power in a typical EDFA operated with a single saturating signal at 1558 nm and a 1480-nm pump. These curves show that the pump can either add to or subtract from the signal effect depending on the pump polarization.

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uniformly over the Poincare sphere. The distribution of the pump-induced PHB is shown in Figure 51 for various fiber parameters. Pump PDG at the signal wavelength can be written as ∆G pump ⫽

1 L

冮

L

0

冤

冥

∆G pump,max P pump, maj ⫺ P pump, min DOL sig dz dz P pump,maj ⫹ P pump ,min

(37)

where P pump,maj and P pump, min are the pump power projected onto the signal major and minor axes, respectively. This expression is analogous to Eq. (33) for the signal and illustrates clearly the difference between the pump and the signal effects. The pump-induced PHB varies linearly

Figure 51

Distribution of pump-induced PDG gain difference for 12,000 launched pump SOPs in an EDFA with 5 dB of gain compression and (a) a linear nonevolving signal in a zero-birefringence fiber; (b) a nonevolving signal with a DOL of 0.5; (c) a linearly polarized signal launched on the axis of a PM fiber; (d) a circularly polarized signal launched in a PM fiber; (e) a linearly polarized launched signal and rapid SOP evolution; (f) a circularly polarized launched signal and rapid SOP evolution; and (g) a linearly polarized launched signal and a pump and signal evolving rapidly at different rates.

653


with the DOL of the signal and is proportional to a term representing the projection of the pump onto the signal major and minor axes. Figure 51a shows that if the fiber produces no SOP evolution and the signal DOL is 1, the pump effect takes all values from ⫺435 mdB to 435 mdB with equal probability. The standard deviation is 250 mdB. If the signal is not linearly polarized (see Fig. 51b), the spread of values is reduced by the signal DOL, but the mean is still zero. For the case shown with a signal DOL of 0.5, the standard deviation is 125 mdB (a reduction by 1/2). When the fiber is PM and the signal SOP is linear and launched on a birefringence axis (see Fig. 51c), the pump PDG is distributed as in Figure 51a. When the launched signal is circular, the distribution is as in Figure 51b (reduction by average DOL of signal or 1/2 in this sample). For a standard EDFA with rapid SOP evolution, if the birefringence for the signal and pump is equal (see Figs. 51e and f ), the standard deviation is reduced to 96.6 mdB, independently of the launching condition of the signal. If the pump and signal evolve at different rates, the spread of the pump-induced PDG is further reduced and the standard deviation is 45.6 mdB for the case simulated. The lack of symmetry for cases of Figure 51e and f is due to the deterministic rotation used in the simulations, which has a particular direction. A truly random birefringence would produce a symmetrical distribution. Because no special fiber preparation was used, most pump PDG studies reported in the literature likely involve rapid SOP evolution with slightly different pump and signal evolution rates. This situation makes it difficult to use such data to infer a pump anisotropy parameter. An important distinction can now be made between 1480 and 980 nm pumping. For a 1480-nm pump, the pump and signal may evolve at similar rates and pump-induced PHB may be substantial (see Figs. 51e and f ). However, for a 980-nm pump, the pump and signal evolution rates should differ sufficiently that pump-induced PHB is likely to be reduced to an even greater extent, depending on the fiber parameters. In any event, at this time A is poorly known in either pump band and requires further investigation. In EDFAs, PDG is wavelength dependent for three reasons: 1. The gain and loss coefficients are wavelength-dependent. 2. The anisotropy parameter can be wavelength-dependent. 3. The wavelength differences in birefringence randomizes the relative SOPs at different wavelengths. Effect 2 cannot be quantified with available data. Effect 3 can be neglected in short fibers for similar signal and pump wavelengths. Effect 1 is fundamental and can be simulated or measured. Clearly, the PDG is a significant function of the probe wavelength. Although not shown here, it also depends on the saturating wavelength, and it is a complex function of the saturation power at the saturating wavelength and of the pump power level. No simple rule has been found to express these dependencies. The foregoing treatments can be combined to predict PHB for arbitrary signal and pump SOPs. By assuming rapid SOP evolution, which applies in many fibers, we approximate for a low-gain EDFA:

冤

∆G tot(dB) ⬇ DOP 2s

∆G s,max L

冮

L

DOL 2s, pol dx

0

冥

(38)

冤∆GL 冮 DOL 冢PP L

⫹ DOPsDOPp

p,max

p, pol, maj

s, pol

0

p, pol,maj

冣冥

⫺ P p, pol,min dx ⫹ P p,pol ,min

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In this equation, all values in the integrals refer to the polarized component of the signal or pump, and all quantities, including the pump quantities, are projected onto the major and minor axes of the polarized portion of the saturating signal. Equation (38) breaks down the prediction of PHB into three steps: 1. Measure or compute the maximum pump and signal PDG for the EDFA design. 2. Compute the degree of polarization of the pump and the saturating signal. 3. Compute the evolution of the polarized components of the pump and signal SOPs and project them onto the signal major and minor axes to compute the integrals. Equation (38) eliminates the need for a full model when polarization evolution is either rapid or nonexistent. Intermediate cases require a full model. PHB does not vanish in an EDFA for circularly polarized signals [77]. Equation (38) consists of a signal and a pump term (additional terms can be added for other saturating signals), both of which vanish for a circularly polarized signal. This result was built into the treatment by assuming ellipsoidal gain surfaces. To account for circular anisotropy, ions can be further divided into groups based on circular gain response. It is also easy to adapt the signal term of Eq. (38) to this case. The degree of circularity of a signal SOP is DOC 2s ⫽ 1 ⫺ DOL 2s

(39)

If the maximum circular PHB value is ∆Gcir,max, the signal term in Eq. (38) becomes

冤

∆G sig (dB) ⫽ DOP 2s ∆G cir,max ⫹

(∆G s,max⫺ ∆G cir,max ) L

冮

L

0

冥

DOL 2s, pol dx

(40)

Scrambling still eliminates all PDG, but a circular SOP does not eliminate all PDG; circular PDG remains. The pump term for this is more complex and is not treated here. The influence of PHB in long EDFA systems can be divided into two parts. The signal-induced PHB causes ASE orthogonal to the signal to experience a greater gain. If the ASE and the signal SOPs remained orthogonal between EDFAs, the small gain difference would accumulate and might become quite large after numerous EDFAs. However, as long as the polarization of the additional ASE remained orthogonal to the signal SOP, this would not add noise to the system, because orthogonal components do not interfere. The only effect would be a possible reduction in the gain of later EDFAs in the system. However, this is not true in real systems because polarization-dependent loss elements and fiber birefringence couple orthogonal ASE power into the signal polarization. This effect causes a direct degradation of the system SNR. Pump-induced PHB does not impair the SNR of the system, on average because it can either help or hinder the signal relative to the ASE. However, it does increase the spread of the possible resultant SNR of a system over time. The worst cases with many pumps orthogonal to the signal might happen randomly and must be guarded against. The treatment of PHB for multiple signals might be handled similarly to the treatment of multiple signals for SHB. Once again, each signals evolution is expected to create PHB in proportion to the compression that it produces alone. Each signal evolution can be projected onto each other signals major and minor axes (much like a randomly aligned pump) to compute its effect on that signal. Fortunately,


655

such a complex computation is rarely necessary because few WDM systems are expected to be so long that their SNR are severely hindered by the small, accumulated PDG. 11.4.3 Rayleigh Scattering and Double Rayleigh Scattering Rayleigh backscattering can hurt the performance of an EDFA [85]. A system study is therefore incomplete without considering scattered signals. Backscattering from an EDFA exceeds backscattering from an equivalent length of undoped fiber [85,86]. It is useful to know the return loss for a particular design when deciding whether to isolate an EDFA, choosing fiber lengths and components for a two-stage EDFA [87], or simulating system performance. Backscattering is incorporated in an EDFA model by coupling each forwardtraveling signal P⫹ at wavelength λ to a backward-traveling signal P⫺ at the same wavelength: dP⫹(z, λ) ⫽ [(g*(λ) ⫹ α(λ))Inv(z) ⫺ α(λ) ⫺ α s(λ) ⫺ α ns (λ)]P⫹(z, λ) dz ⫹ caps(λ)αs(λ)P⫺(z, λ) dP⫺(z, λ) ⫽ ⫺[(g*(λ) ⫹ α(λ))Inv(z) ⫺ α(λ) ⫺ α s(λ) ⫺ α ns (λ)]P⫺(z, λ) dz

(41a)

(41b)

⫺ caps(λ)αs(λ)P⫹(z, λ) where α s(λ) is the background loss caused by scattering (including Rayleigh), α ns (λ) represents other background loss (excluding scattering), and cap s (λ) is the backward scattering capture fraction. The total background loss includes a scattered portion and an otherwise lost portion. The scattered portion includes Rayleigh scattering and scattering from large scatterers or boundaries. Pump scattering in EDFAs can be neglected without changing the signal results, whereas ASE scattering is important only in small-signal, high-gain (⬎30 dB) devices. Because of the presence of erbium absorption, scattering parameters near 1550 nm are typically estimated using values measured at shorter wavelengths. The loss measured from 1050 to 1250 nm in a typical high-NA EDF is attributed solely to background loss. The loss values at 1100 and 1200 nm are 9.45 dB/km and 7.30 dB/km, respectively for a particular fiber (EDF1). The ratio of these losses is 0.77, whereas the expected ratio for Rayleigh scattering, assuming a λ⫺4 dependence [88], is 0.706. If we assume a λ⫺n dependence, we find n ⫽ 2.95. When using the Rayleigh–Gans–Debye (RGD) scattering theory [89], this value is consistent with spherical scatterers of radius slightly larger than 0.2 µm. When using n ⫽ 2.95, the scattering loss is projected to be 5.70 dB/km and 3.43 dB/km at 1305 and 1550 nm, respectively. To estimate a capture fraction, measurements were made at 1305 nm. For a long fiber, the total power reflected approaches R L,0 ⫽

caps(λ)αs(λ) P⫺(0) ⫽ P⫹(0) 2(αs(λ) ⫹ α ns (λ))

(42)

Ideally, this value should be measured where erbium is transparent (e.g., at 1200 nm) and scaled to other wavelengths. In this treatment, a commercially available return loss module at 1305 nm was used. The measured return loss of a 2-km length of EDF1 was ⫺33.4 dB. At 1305 nm, the total measured background loss was 14.15 dB/km. By using Eq.

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(42) and the foregoing scattering loss, we find caps(1305 nm) ⫽ 2.27 ⫻ 10⫺3 ⫽ ⫺26.44 dB. For Rayleigh scattering, the theoretical backward capture fraction is [90] capR(λ) ⫽

λ 冤2πnw(λ) 冥

(43)

where w(λ) is the mode field radius. For an NA of 0.276 and a cutoff wavelength of 900 nm, the computed Rayleigh capture is ⫺22.10 dB at 1305 nm and ⫺22.27 dB (0.17 dB lower) at 1550 nm. The difference between the measured total capture at 1305 nm and the theoretical Rayleigh capture is 4.34 dB. Using RGD theory [89], this reduction (favoring forward scattering) suggests scatterers with a radius of about 0.25 µm, consistent with the foregoing value. Assuming the Rayleigh and total capture fractions scale the same way with wavelength (0.17 dB difference from 1305 to 1550 nm), an assumption that has been verified in an undoped high-NA fiber, we find caps(1550 nm) ⫽ 2.18 ⫻ 10⫺3 ⫽ ⫺26.61 dB. Solving Eq. (41) for the reflected power is not generally possible in closed form because the inversion varies with position. However, in short EDFAs the inversion is nearly longitudinally invariant. In this approximation, the return loss in the presence of accidental reflection R2 after the amplifier and fiber scattering is ⫺R L(λ) ⫺

冤冢

冣冥

冢

2G(λ) 2G(λ) caps(λ)αs(λ)L exp ⫺ 1 ⫹ R 2 exp 2G(λ) 10 log10 e 10 log10 e

冣

(44)

where G is the amplifier gain in dB and L is the EDF length. The first term is the power scattered by the fiber, and the second term the power reflected from spurious far-end reflections. Measurement of the return loss of an EDFA is hampered by reflections at the far end, which are enhanced by traveling twice through the amplifier medium. Such reflections arise when components are added to measure EDF performance or to provide additional pump power. Computation using Eq. (44) shows that for a 20-dB gain EDFA made from 20 m of EDF1, internal scattering is overwhelmed by far-end reflections when R 2 ⬎ ⫺54 dB. An isolator at the EDF output may not be used because the isolator itself produces a reflection. Careful measurements without such reflections have been performed [86]. Sample plots of the gain and return loss measured at 1556 nm for a typical EDFA are shown in Figure 52. The return loss was fit using Eq. (44) with measured gain values. The fit agrees with the experimental data within 0.3 dB for all signal power levels. Discrepancies between measurements and theory may arise from (1) inaccurate gain values, (2) component reflections, (3) inaccurate scattering coefficients used in Eq. (44), and (4) the approximation of uniform inversion embedded in Eq. (44). Note that, although the gain of this EDFA is under 20 dB, the return loss approaches 20 dB for a small signal. The predictions of Eq. (44) are not as accurate for cases that violate the approximation of uniform inversion. However, it provides a good first-order approximation that can be better improved by solving a complete model based on Eq. (41). Clearly, from Eq. (44) the return loss can be reduced by increasing the erbium concentration, by inverting more ions to achieve the same gain in a shorter length, or by reducing the scattering and capture coefficients. Configurations using copumping produce a lower NF, but they also have a lower return loss than configurations using counter-

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Figure 52

Measured gain (dashed curve is a guide) and measured and estimated return loss at 1556 nm for an 18.0-m length of high-Al EDF pumped in the same direction as the signal with 7.93 mW at 1480 nm.

pumping with the same gain. High inversion at the front end of the fiber favors backscattering, because more scattered light passes through the high-gain region. EDFAs with about 30 dB of gain have been observed to produce return losses of less than 0 dB (‘‘return gains’’). Isolation is not only recommended in such cases, but also the level of isolation required is high. As EDFAs are designed in the future to be more cost-effective, the elimination of isolators or reduction in the level of isolation may be considered. Equation (44) helps decide whether this is feasible. Double Rayleigh scattering is a problem in many EDFAs because it creates paths of different lengths for signals to travel. Some portion of a signal is reflected from a scatterer, travels some distance, reflects back from a second scatterer, and exits the EDFA along with the rest of the signal. The double-scattered power is delayed in time relative to the main signal, which leads to noise and distortion, especially in analog EDFAs. The total power double scattered in an EDFA can be derived assuming uniform gain distribution and integrating over all possible combinations of scattering points. The result is

冤

PDR (λ) caps(λ)αs(λ)L ⫽ Pout (λ) 2G(λ)

⫺ 2G(λ) ⫹ 1]冥冥冤exp冢102G(λ) log e冣 2

(45)

10

A graph of the expected total double-scattered power as a function of EDFA gain for a 20-m length of EDF1 is presented in Figure 53. The gain level at which this doublescattered power is a problem depends on the allowable noise level and the conversion of this power into noise. Figure 53 does not provide information about the relative time delay between the signal power and the double-scattered power. For a given time delay ∆t, it

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Figure 53

Total double-Rayleigh scattering for a 20-m length of high-Al EDFA with 3.5 dB/ km of background loss at 1550 nm and a Rayleigh capture fraction of 2.16 ⫻ 10⫺3, plotted as a function of EDFA gain. Plot assumes uniformly distributed gain.

is possible to solve for the double-scattered power at the output as a function of time delay. This can be written as PDR (λ, ∆t) ⫽ [caps(λ)αs(λ)]2 Pout (λ)

c∆t 冤冤L ⫺ c∆t2n 冥 exp冢102G(λ) log 冣冢 2n 冣冥

(46)

10e

The shape of this function for a 25-dB EDFA made with fiber EDF1 is shown in Figure 54. It is noteworthy that more double-scattered power experiences nearly the maximum time delay of 2nL/c than experiences near zero delay. This is clearly because double Rayleigh scattering from points far apart in an EDFA passes through substantially more gain than scattering from points close together. On the other hand, there are more points that are only a short distance apart. The net result is the form of Figure 54. 11.4.4 Temperature Dependence of the Gain In a typical WDM system, most components exhibit some temperature dependence in loss shape or magnitude, or both. Early fiber systems often had enough margin in performance that such changes could be tolerated. However, as systems evolve toward denser wavelengths, higher bit rates, and greater distances, such temperature dependencies are no longer acceptable. Rare earth ions such as Er 3⫹ in a silica host are generally considered to be insensitive to temperature. However, a typical EDFA provides between 15 and 45 dB of gain. The erbium-doped fiber gain compensates for the losses of components placed within the EDFA and also provides the net gain of the amplifier. In a typical 30-dB EDFA, a 1% change in the gain with temperature translates into a 0.3-dB gain difference. This


659

Figure 54

Time delay experienced by the power that has been scattered by double Rayleigh scattering in a 25-dB gain EDFA as described in the legend of Figure 53. The quantity plotted is a probability density of experiencing a certain delay given that double-Rayleigh scattering has occurred.

change is a significant part of the available margin in an EDFA required to achieve flatness within 1 dB. For the 1550-nm transition of Er 3⫹, the initial and terminal energy manifolds consist of seven and eight broadened energy levels, respectively. The location of these levels is not expected to be a function of temperature. The same is true of the location of the level in the 980-nm pump manifold. Furthermore, the modal properties of the fiber are very weak functions of temperature. The temperature dependence exhibited by an EDF is mainly attributable to the variation in the occupation probability density of each manifold with temperature. In particular, the relative occupation probabilities P of any two energy levels in thermal equilibrium is expected to follow Boltzmann’s law: P(E 2) ⫽ e⫺[E 2⫺E 1/kT] P(E 1)

(47)

where T is the temperature in degrees Kelvin and k is Boltzmann’s constant. Using this expression, it is possible to compute the occupation probability of each level of a manifold once the density of states ψ(E) is known as a function of energy. Because each manifold has a finite extent, we can apply the fundamental principle that the sum of all occupation probabilities for all states of the manifold must equal unity (under the assumption that the ion is excited to that manifold). By using this rule and defining the lowest and highest energy levels in the manifold as EB and ET, we can write:

冮

ET

EB

ψ(E)P(E)dE ⫽ 1

(48)

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The important point is that the probability of occupation of levels at the top of each manifold increases with increasing temperature, whereas the probability of occupation at the bottom of each manifold decreases with increasing temperature. At infinite temperature, all levels are equally occupied. The gain and absorption spectra of an erbium ion are determined by (1) the strengths of the 56 broad transitions possible between the levels of these manifolds, and (2) the probability that the levels are occupied. Only the probability of occupation is temperaturedependent, and it follows the rules described by Eqs. 47 and 48. Hence, the temperature dependence of an EDFA is determined by the temperature-dependence of g*(λ) and α(λ). The population inversion at any given location along the fiber is temperature-dependent for two reasons. First, the power present at each saturating signal or pump wavelength at that position is affected by the power evolution at other positions. Second, the saturation power changes in inverse proportion to the changes in the gain and absorption coefficients. This may be written as Psat ⫽

hνξ [g*(λ) ⫹ α(λ)]

(49)

where h is Planck’s constant, ν is the frequency of the wave, and ξ is the saturation parameter, which is equivalent to the linear ion density divided by the ion lifetime. This last quantity is temperature-dependent only through the temperature dependence of the gain and absorption parameters. Hence, to understand the temperature dependence of an EDF, only g*(λ) and α(λ) need to be known at various temperatures. It is possible to fit measured values of g*(λ) and α(λ) to a simple expression based on physical intuition and use the fitting parameters to generate modeling parameters at any temperature. The following fitting expression are useful [91]. α(λ, T ) ⫽ α(λ, ∞)e [β a(λ)/kT]

(50a)

g*(λ, T ) ⫽ g*(λ, ∞)e

(50b)

[β e(λ)/kT]

The fitting parameters g*(λ, ∞) and α(λ, ∞) are both temperature-independent and can be interpreted as the absorption and gain at infinite temperature when all energy levels are equally occupied. The parameters β a(λ) and β e(λ) are expected to model the thermal occupation probability of the initial energy level for the transition at a given wavelength. Figure 55a shows the measured absorption coefficient α(λ) of a typical high-Al silicabased EDF at several temperatures as a function of wavelength. Similarly, Figure 55b shows the measured gain coefficient g*(λ) for the same fiber at several temperatures. For clarity, only the end temperatures are labeled in Figure 55b. In all cases, the temperatures displayed are ⫺40°, 0°, 40°, and 80°C. The gain curves shown in Figure 55b were inferred from ASE spectra measured in a short section of EDF pumped with over 300 mW at 980 nm. As such, they show the existence of signalband ESA above 1600 nm and also include losses produced by fiber scattering and ground-state erbium ions. Both figures also show the best fit generated using Eqs. (50) to predict the value at each temperature from the measured value at T ⫽ 20°C. The fit is excellent for both the absorption and gain over this temperature range, which lends credence to the validity of Eq. (50). The wavelength dependence of the fitting parameters β a(λ) and β e(λ) inferred from these fits are plotted in Figure 56a. The parameters α(λ, ∞) and g*(λ, ∞) in Eq. (50) can be interpreted as the absorption and gain at infinite temperature. This is a somewhat misleading interpretation because the


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Figure 55 Spectra of (a) the absorption coefficient and (b) the gain of a high-Al EDF measured at several temperatures (solid curves). The dashed curves are theoretical fits using an exponential function.

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(a) Wavelength dependence of the fitting parameters βa (for the absorption) and βe (for the gain) used to generate Figures 55a and 55b, respectively; and (b) absorption and gain spectra at infinite temperature.

Figure 56


663

treatment of gain and loss as independent quantities was based on the assumption of longlived manifolds with independent occupation statistics. Yet, according to Boltzmann statistics, at infinite temperature, occupation of both manifolds would be equal. A more proper interpretation of α(λ, ∞) and g*(λ, ∞) is that they represent the absorption and gain coefficients when all levels of the relevant manifolds are uniformly occupied. The values for those parameters that best fit the gain and loss coefficients of Figure 55 are shown in Figure 56b. It illustrates the interesting point that the gain and absorption coefficient spectra approach the same form for equal occupation of all states in each manifold. The agreement is excellent except at wavelengths in the wings, where the data is expected to be inaccurate. Clearly, the summation of all upward transitions must equal the summation of all downward transitions, and that these two spectra are identical is an expected result. To complete the picture of the temperature dependence of an EDF, the temperature dependence of the ground-state absorption near 980 nm has also been measured [91]. It also fits the form of Eqs. (50a) and (50b). In most of the wavelength range typically used for EDFA pumping, the pump absorption drops as the temperature is increased. Operation at high temperatures, therefore, is expected to produce a penalty in noise figure for many EDFA designs. By using Eq. (50) and the measured values of its parameters, the temperature dependence of the spectrum of an EDFA can be explored without running a complete computer model. In particular, in many EDFAs the pump power is varied to set the gain to the desired level. In this case, the fact that the saturation power is temperature-dependent does not affect the gain spectrum. The pump power must be adequate to achieve the desired gain at all temperatures. The average inversion can be determined such that the required gain is achieved at each temperature. The only effect neglected by this approach is spectral hole-burning (SHB). However, assuming that an EDFA is filtered to provide the appropriate gain flatness at the design temperature, SHB is accounted for in the filter. An example of this approach is illustrated in Figure 57. Here, an ideal filter was assumed to perfectly flatten the gain spectrum of a 25-dB EDFA between 1528 and 1563 nm at 20°C. The EDFA was assumed to maintain the same constant output power (same average gain) by controlling the pump power for all temperatures. The result of Figure 57 is independent of EDFA design except for the relatively small effect of SHB. Figure 57 shows the calculated gain spectrum at different temperatures. It states that an EDFA cannot be expected to maintain flatness over a broad spectrum and over a wide temperature range. The error is greatest on the edge of the spectrum and is not linear. Reducing the temperature has a greater effect than raising the temperature (by the same amount). This result stems from the Boltzmann-like form observed for the coefficients, which has a smaller derivative at higher temperatures. 11.5 EDFA DESIGN CHOICES Erbium-doped fiber amplifier designs have advanced dramatically since the first singlestage amplifier demonstrations. Some of the advances have been the result of new fiber component development and improvement, wheras others have come from clever engineering. The possible design choices for an EDFA now include the following: 1. The number of stages 2. The signal wavelength range 3. The fiber types and lengths in each stage

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Figure 57

Theoretical evolution with temperature of the gain spectrum of an EDFA. The EDFA is assumed to be filtered to have a gain of 25 dB and an ideal gain flatness from 1528 to 1563 nm at 20°C. The curves at all other temperatures are computed assuming that the EDFA evolves in temperature according to the dependence shown in Figure 55.

4. The number, power, and wavelengths of each pump 5. The direction of pumping (and possible pump interactions that result) 6. Transmission of pump power from stage to stage around or through components 7. Pump reflectors to pass the pump twice through an EDF 8. The use and location of isolators to eliminate backward propagating waves 9. The use and location of filters for gain shaping or to reject unwanted wavelengths (a filter may be any wavelength selective element like a WDM) 10. The use of reflectors at a particular wavelength to make a laser and stabilize an EDFA 11. The use of pump power control or attenuator adjustment to actively adjust an EDFA The possibilities are endless. The choice made for a given application is always based on a cost/benefit analysis of each additional option. An EDFA model is essential to perform such comparisons. Some of these choices are discussed in the following sections. 11.5.1 Multistage Designs Multistage designs have become a standard approach in all but the simplest EDFAs. The advantages of multiple stages can be summarized as follows: 1. They allow the easy use of many pumps, because two pumps can easily be injected into each stage without complex combiners.


665

Figure 58

A single-stage EDFA pumped in opposite directions by two 980-nm–laser diodes. This design generally yields poor performance owing to optical interaction between the laser diodes, which cause pump power instability.

2. They allow the use of filters between EDF stages to shape the gain and reject the ASE. 3. They allow the use of isolators between EDF stages to reduce backward-traveling ASE and improve the NF. 4. They facilitate stable multiple pump operation without interactions and instability. Point (4) turns out to be a critical issue in many single-stage configurations. Figure 58 shows a dual-pumped single-stage EDFA that appears useful, but is often a poor performer in practice. This design produces unstable performance because of interactions between the two 980-nm pump diodes. This instability can be understood as follows: In a typical EDFA pumped at 980 nm, very little pump power is transmitted by the EDF owing to the high erbium absorption near 980 nm. However, spontaneous photons are produced by the laser diode near 1030 nm, outside the erbium absorption band, and are transmitted by the EDF with little loss. They are then reflected by the back face of the other laser diode and returned with a high reflection coefficient. The result is that the two laser diodes can collectively lase at 1030 nm and thus become nearly useless as pump sources for erbium. Even if they continue to lase at 980 nm, they are often destabilized by the 1030-nm reflections. One solution is to insert a dichroic loss element in the pump path that produces loss near 1030 nm but transmits 980-nm light. A general diagram of a multistage EDFA is shown in Figure 59. Such an EDFA can contain n stages with multiple pumps, and components located at the input, between stages, and at the output. The choice of adding another stage to a given EDFA substantially depends on the components added between stages. An interstage isolator suppresses backward-traveling ASE, which allows the forward signal to reach a higher power and reduces the overall NF. However, an isolator followed by an additional stage is beneficial only if the loss of the isolator wastes less power than is gained by suppressing the backward

Figure 59

Diagram of a general n-stage EDFA.

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ASE. The NF is substantially improved only if the backward-traveling ASE is large, which is expected only in a high-gain EDFA. Clearly, a isolator that perfectly transmits the pump and signal power (and does not produce reflections) cannot degrade the performance, but such a component does not exist. Some of these issues are illustrated by the simulations shown in Figure 60 for a single-pump EDFA. Figure 60 compares a single-stage EDFA pumped in the copropagating direction to a dual-stage EDFA in which excess pump from stage 1 is allowed to be transmitted to stage 2, bypassing an interstage isolator that produces 1 dB of loss and 50 dB of isolation. In the second example, the total fiber length was split equally between the two stages. In this design, the gain is increased by as much as 4 dB (see Fig. 60a) and the NF reduced by as much as 1 dB (see Fig. 60b) for fiber lengths near 30 m and a relatively small input signal (⫺30 dBm). As this signal level is increased, the enhancement due to the isolator reducing the backward ASE is overwhelmed by the additional loss introduced by the isolator. For a 10-dBm signal, the dual-stage, isolated design produces an NF that is 0.4 dB higher and an output power that is 0.7 dB lower than the single-stage design. Under this condition, the backward ASE is inconsequential, but power wasted in the isolator is unrecoverable. The use of two stages also facilitates the introduction of additional pump sources, although an isolator would always be useless for high-signal levels. The flexibility of adding a filter to an EDFA between gain stages is another reason for considering multistage designs. This advantage is shown in Figure 61a, which plots the NF and the pump power required to produce a certain gain in a two-stage filtered EDFA as a function of the fiber split between stages 1 and 2, for a total fiber length of 44 m. Figure 61b shows the penalty in gain and NF produced by the filter relative to an unfiltered EDFA of the same design. The case of a single-stage EDFA with a filter either before or after the stage is represented on these graphs by a first-stage length of zero and 44 m, respectively. Clearly, the overall penalty for filtering between stages is substantially lower than filtering either before or after a single stage. Filtering before a single stage would degrade the NF by 3.2 dB for the design used in Figure 60, whereas filtering after a single stage would reduce the power output and the gain by 2.25 dB. 11.5.2 Pumping Schemes and Redundancy Pumping schemes for EDFAs have evolved as designs have become more complex. The main limitations on pumping schemes come from the following issues: 1. The most practical pump sources are laser diodes at 980 and 1480 nm that are pigtailed to a single-mode fiber. 2. Pump sources of different wavelengths must be combined using a WDM before injection into an EDFA. 3. Pump sources of same wavelength can be combined using polarization combiners, although this approach tends to be inefficient. 4. Inexpensive, low-loss isolators are available at 1480 nm, but not at 980 nm. 5. Pump sources of similar wavelengths often become unstable when power from one source is allowed to be coupled into the other source without substantial loss. 6. Pump sources fail. The likelihood increases rapidly as the power is increased. To eliminate interaction between pump sources, some 1480-nm pump sources are optically isolated. To avoid the power loss introduced by isolation and to use 980-nm pumping,


Figure 60

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Comparison of a single-stage EDFA and a two-stage EDFA in which residual pump power from stage 1 is used as the input of stage 2, bypassing an interstage isolator with a 1-dB loss: the signal is at 1550 nm, the pump at 980 nm, and the pump power is 100 mW, copropagating with the signal in the single-stage EDFA. (a) Gain, and (b) noise figure, plotted versus total fiber length, which is identical for both designs.

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Figure 61

Wysocki

Illustration of the penalty introduced by filtering in a dual-stage high-Al EDF and its dependence on the filter location. (a) Pump power required and NF for the worst channel of a 30channel WDM EDFA with 100 mW of 980-nm pump power in stage 1 and 100 mW of 1480-nm pump power in stage 2. The filter spectrum, shown in the inset, was chosen for optimum gain flatness for a 44-m total fiber length; and (b) similar results plotted in terms of the penalty paid relative to an unfiltered EDFA.


669

many pump schemes avoid bidirectional pumping in a single stage. Mixing pump wavelengths on a stage is also quite useful, provided they do not interact. For example, a singlestage EDFA can be pumped at 980 nm in the copropagating direction to achieve a low NF, and at 1480 nm in the other direction for high-output power. Pump redundancy is one way to overcome the problem of pump source failure. A few of the pump redundancy schemes that have been used are illustrated in Figures 62a– c. The first scheme (see Fig. 62a) involves two pump sources connected to the same EDF through an optical switch. One pump source is used until it fails, at which time the second pump source is turned on and the switch is toggled to select that source. The control is provided by monitoring the pump power with a tap placed near the EDF output. Clearly, a wide variety of methods can be used to identify a pump failure. In the second scheme (see Fig. 62b), two pump sources are combined through a 3-dB coupler and fed into the two stages of an EDFA. The pump power in each stage is half of the total power. When one of the pump sources fails, both stages lose half of their pump power, but neither stage is left unpumped. The pump sources could be combined through an uneven coupler. The power would still be split equally between the two EDFs when both pump sources are on, but after a pump failure the split would depend on which pump failed. Usually, this is not a desirable feature, and a 3-dB split is selected. A third pump redundancy scheme is shown in Figure 62c. Two pump sources are combined and split as in Figure 62b except that they are used to pump EDFAs in two different directions of propagation. The benefits are the same as in Figure 62b. The designs of Figures 62b and c have the advantage of increased flexibility over that of Figure 62a. In both cases, the two pump sources could be operated at lower power levels to save diode life. After one pump source fails, the power from the remaining pump source could then be increased to provide the same power to the EDF. 11.5.3 Pump Reflectors The development of low-loss, highly reflective fiber gratings has made possible designs in which the residual pump power unabsorbed after a first pass through an EDF is reflected to pass through it a second time, thereby increasing the absorbed pump power. For such designs to be useful, additional losses introduced at both the pump and signal wavelengths must be minimized. Such pump reflectors have been demonstrated for use in typical undersea applications with low pump power levels and reasonably small signal powers [92]. In this case, EDFAs were pumped at 1480 nm in the counterpropagating direction, as shown in Figure 63a. A broadband grating pump reflector exhibiting the transmission spectrum of Figure 63b was added to improve performance. A comparison of the performance of a typical undersea EDFA with and without this reflector is shown in Figure 64. The gain and NF are plotted for different conditions. When the reflector peak wavelength does not match the pump wavelength, the sole effect of the grating is to add loss at the signal wavelength, which degrades both the gain (see Fig. 64a) and the NF (see Fig. 64b). If the reflector loss was not so low, this degradation would be greater. However, when the reflector and pump wavelengths are matched, the additional pump power available near the front end of the EDFA more than overcomes the degradation caused by the filter loss. The gain increases by over 2 dB whereas the NF decreases by about 0.5 dB. Pump reflectors can also be used to enhance the performance of power amplifiers. In an EDFA pumped with a high power, the signal power levels are often high and power conversion must occur rapidly to achieve the desired spectrum. In particular, in Section

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Figure 62

Wysocki

Three pump power redundancy schemes: (a) switching pump upon failure; (b) using two pumps for two stages, and (c) using two pumps for two EDFAs.


Figure 63

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Pump reflector concept: (a) configuration and (b) grating reflector shape.

11.2.4 we discussed the need to produce a given inversion to achieve the flattest gain spectrum. Yet, as the signal power increases, the length required for ideal gain flatness becomes too short for complete power conversion. One solution is to pass the pump power through the fiber twice to achieve the same results as those in a shorter fiber length. This is illustrated in Figure 65, which shows (1) the output power, and (2) the NF for a simulated EDFA pumped at 980 nm in the direction of the signal, with and without a pump reflector. The latter was assumed to be lossless and 100% reflective. This design achieved a higher power output with than without the pump reflector, and the fiber length is about 25% shorter. The EDFA was able to produce more power with the pump reflector because the shorter fiber produced a lower accumulated background loss and SE power. When using this shorter length, the NF was at least 0.1-dB lower (depending on the power level) than the same design without the reflector. The pump reflector was able to enhance the rate of power conversion in the EDFA and thereby improve its performance. The improvement would obviously be reduced by the loss present of the grating reflector, but this is typically quite small. 11.5.4 Bidirectional EDFAs As cost becomes a significant issue in EDFA design, new methods to use components and fibers more effectively are becoming important. One method is to use EDFAs in a

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Figure 64 Theoretical performance of the EDFA configuration using a pump reflector shown in Figure 63a: (a) gain, and (b) noise figure, both at 1558 nm. These curves show that the reflector increases the gain and reduces the NF, except when the pump wavelength misses the grating wavelength, in which case the reflector induces a penalty.

bidirectional fashion. A few approaches to bidirectional use are possible, depending on how many components are shared in the two propagation directions. From most integrated (potentially cheapest) to least integrated (least cost savings), these approaches can be categorized as follows: 1. Total bidirectional use of full EDFA and system fibers; the signals propagating in the two directions are separated only at each of the transmitter/receiver levels. 2. Bidirectional use of communication fibers, pump sources, and all EDFA components, except the EDF. 3. Bidirectional use of only the communication fibers. Option (1) is difficult because it necessarily eliminates the possibility of incorporating isolators in either direction. This limitation adds a host of problems. In particular, scattering in the fiber and components couples light from one direction to the other. ASE traveling through the system is able to accumulate in both directions and to affect noise accumulation. Additionally, bidirectional signals in a single EDF tend to hurt the NF of signals traveling in the opposite direction. Both ends of the EDF have high signal levels and, therefore, they are not highly inverted. Consequently, a totally bidirectional system is rarely attempted.


Figure 65

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Modeled improvement by a pump reflector in a power amplifier with a 0-dBm signal at 1550 nm and a 980-nm pump cotraveling with the signal: (a) gain, and (b) noise figure. The main advantage is the ability to reach the same output power in a shorter length of EDF.

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Options (2) and (3) offer many, but not all, of the advantages of option (1), without as many complications. The EDFA of Figure 62c is an example of a possible bidirectional design consistent with option (2). In this figure, isolators are present in both directions, but separate fibers are used so that ASE, scattering, and the saturation effects described earlier are eliminated. Pump redundancy is facilitated or, alternatively, a single pump source could be shared between two EDFAs. The added cost of such schemes is the need for some way to separate the signals from opposite directions. This can be accomplished with a three-port circulator placed at each end of the EDFA to combine signals in one communication link. This circulator also serves as a replacement for the isolator required in one direction. However, it does not serve this function perfectly in the other direction because reflections would end up coupling light from one direction to the other. Another possibility is to split these signals by wavelength with a certain amplification band in one direction and a different amplification band in the other. Then any component that separates different wavelengths, such as a WDM, can be used to combine the signals. The ability to combine pump sources and communication fibers must always be weighed against the need for these added components and the complication of additional coupling mechanisms between directions. Additionally, the use of different wavelengths in each direction reduces the available bandwidth for WDM signals in each direction. 11.5.5 L-Band and Dual-Band EDFAs The gain curves of Figure 2 clearly suggest the use of an EDF to provide gain between 1525 and 1565 nm. This wavelength range is commonly referred to as the conventional or C band. Most EDFAs to date have operated in this range. However, early on researchers recognized the potential for amplification in the wavelength range from 1565 to 1620 nm [19–21], which is commonly called the long or L band. Excellent gain flatness has been achieved in this range, as is noted in Table 1. Combined with a C-band EDFA, an L-band EDFA can be used in a very broadband dual-band EDFA, as depicted in Figure 20. The design of an L-band EDFA differs substantially from the design of a C-band EDFA. One main reason is illustrated in Figure 66, which shows the gain shape of the same EDF shown in Figure 4, but with lower inversion levels, which is achieved by using a longer fiber. To achieve gain flatness in the L band, this fiber may be operating at about 37% inversion, whereas gain flatness in the C band requires approximately 67% inversion (see Fig. 4). The gain in the L band with 37% inversion is only about 0.07 dB/m, or about one-tenth what it is in the C band. To achieve 25 dB of gain and flatness simultaneously, more than 350 m of fiber are required. Alternatively, it is possible to operate with higher inversion. With 100% inversion this fiber produces about 0.4 dB/m of gain at 1600 nm (see Fig. 4). Hence, 25 dB of gain could be reached with about 60 m of fiber. Unfortunately, this last design is difficult to use because a 100% inverted length of this fiber also produces 2.7 dB/m of gain near 1530 nm or about 160 dB of gain in 60 m. This does not occur in practice, however, because ASE near 1530 nm saturates the EDFA and reduces the inversion. The only way to eliminate this ASE would be to suppress the gain in the C band using either strong filters periodically located along the fiber or a distributed loss. The required filter would need to have a very strong peak attenuation. For practical reasons, Lband EDFAs are operated with longer EDFs and lower inversion levels. Several clever designs have been proposed for L-band EDFAs. The use of ASE suppression filters in the C band has produced excellent results [93,94]. Such a filter maintains a high inversion and produces a low noise figure, especially when it is placed near


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Figure 66

Modeled gain per unit length spectrum in the L band for the same fiber as Figure 4, but for lower levels of inversion.

the beginning of the EDFA. Additionally, a high gain can accumulate rapidly in the L band to overcome interstage component losses effectively. The use of out-of-band resonant laser operation can also be considered. In such designs, one or several stages of the EDFA operate as lasers in the wavelength range between 1480 and 1560 nm. This is accomplished with high reflectors at these wavelengths. This approach has the effect of reducing the inversion so that gain accumulation is avoided in the C band. An L-band signal can then utilize more of the available pump power at the expense of C-band ASE power. Unfortunately, this approach does not produce the desired low noise figure because inversion is low. The requirement for a long fiber in an L-band EDFA has prompted new designs of the fiber itself. Effects such as PMD, background loss, and nonlinear interactions would be significant in a very long (hundreds of meters) high-NA EDF with a high-signal–power level. The cost of an EDFA requiring this much EDF can also clearly be a significant issue. Fortunately, paired ion interactions are less significant in the L-band region because pairs have low absorption coefficients at longer wavelengths. Consequently, EDFs with a higher concentration or a higher absorption (by higher-overlap factors) have generally been used in the L band. Additionally, both macrobend and microbend losses may be an issue at long wavelengths. A well-designed L-band EDF must take into account all of these issues, and compromises are required to optimize its performance. 11.6 SUMMARY AND CONCLUSIONS This chapter has summarized many of the key new developments in EDFA technology that have taken place over the past seven years. New demands on these devices will con-

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tinue to stretch the imagination of EDFA designers to develop new solutions to new problems. Realistically, it is difficult to utilize existing EDFAs to amplify in bandwidths exceeding 80 nm because there is a limit to the possible gain bandwidth of these fibers. However, designs providing flatter gain spectra and clever methods to combine EDFAs will likely continue to expand the capacity of EDFA-based systems for years to come. REFERENCES 1.

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12 1.3-µm Fiber Amplifiers KAZUO FUJIURA NTT Photonics Laboratories, Tokai-mura, Ibaraki, Japan SHOICHI SUDO NTT Science & Core Technology Laboratory Group, Atsugi-shi, Kanagawa, Japan

12.1 INTRODUCTION Almost all optical telecommunication systems throughout the world still operate in the 1.3-µm band. This is because a large amount of standard 1.3-µm single-mode fiber has already been installed. Therefore, there is great demand for the development of practical optical amplifiers for use at this wavelength. There have been three main approaches to meet this need: the neodymium (Nd3⫹ )-doped fiber amplifier (NDFA), the praseodymium (Pr 3⫹ )-doped fiber amplifier (PDFA), and the Raman fiber amplifier. This chapter focuses mainly on the NDFA and PDFA. In 1988, it was predicted that amplification at 1.3 µm could be achieved by using a Nd3⫹-doped ZrF 4-based fluoride fiber amplifier [1]. This prediction was actually demonstrated the same year by Brierly et al. [2]. ZrF 4-based fluoride glass is used as a fiber host for Nd3⫹ to suppress the signal excited-state absorption (ESA) that prevails in Nd3⫹-doped silica-based fibers and thus to shift its useful gain spectrum from the 1.32- to 1.34-µm range to a shorter wavelength region [1,2], as required for existing 1.3-µm communication systems. However, experimental work to assess the performance of Nd3⫹-doped ZrF 4based fluoride fibers (NDF) has shown that it is difficult to achieve sufficient signal gain for the 1.3-µm transmission window. This is because of (1) the strong signal ESA located near 1.30 µm, which remains despite the use of a ZrF 4-based fluoride glass host, and (2) competition from amplified spontaneous emission (ASE) at 1.06 and 0.88 µm. These factors have limited the highest reported signal gain close to 1.3 µm in an Nd-doped fluoride fiber to just 10 dB [3,4]. All these properties are further discussed in Section 2, which 681

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Figure 1 Gain spectra of Pr 3⫹-doped and Nd3⫹-doped ZrF 4-based fluoride fiber amplifiers.

describes a theoretical model and the basic characteristics of the NDFA. Section 2 also presents research on material considerations with a view to reducing the strength of signal ESA and shifting the ESA spectrum to a shorter wavelength. It also describes several amplifier configurations designed to suppress ASE from the competing transitions. The Pr3⫹-doped ZrF 4-based fluoride fiber amplifier (PDFA) was proposed by Ohishi et al. in 1990 to overcome the problems of the NDFA and provide a new type of fiber amplifier at 1.3 µm [5]. Durteste et al. [6] and Carter et al. [7] also reported optical amplification using Pr 3⫹-doped ZrF 4-based fluoride fiber (PDF) at almost the same time. The PDFA is superior to the NDFA in that its gain spectrum covers the operational 1.29- to 1.33-µm wavelength region of the 1.3-µm communication window, as illustrated in Figure 1. Although the PDFA is problematic in terms of its low-gain coefficient resulting from the low quantum efficiency of the 1.3-µm transition [5], the possibility of realizing a PDFA with a signal gain in excess of 30 dB and an output power of 17.8 dBm was demonstrated by pumping with a Ti:sapphire laser [8]. Subsequent improvements have included an increase in the gain coefficient by using a fiber with a high numerical aperture (NA) and by decreasing the scattering loss of the PDF [9,10] and the experimental demonstration of a PDFA module pumped with high-power sources such as InGaAs laser diode modules, a master oscillator power amplifier (MOPA) laser diode, or a Nd:YLF laser [11– 13]. The performance of the PDFA has been gradually improved to the point that it is now attracting attention as a promising practical optical amplifier for 1.3-µm communication systems [14–17]. In Section 3, we discuss a theoretical model and the basic characteristics of the PDFA. We also describe a PDFA module fabricated recently and outline future prospects. Finally, Section 4 discusses fiber amplifiers operating in the 1.4- and 1.65-µm bands, based on Tm-doped fluoride fibers. 12.2 NEODYMIUM-DOPED FIBER AMPLIFIERS The development of 1.3-µm fiber amplifiers started with the neodymium-doped fiber amplifier (NDFA), which eventually involved extensive research efforts to attempt improving its performance. The reasons for this initial direction of research was that the optical

1.3-µm Fiber Amplifiers

683

properties of Nd3⫹ in various glasses were well known, and available data suggested that this ion had a reasonable potential for amplification near 1.3 µm, as discussed in Chapter 2. However, this work has had limited success because, (1) the NDFA cannot cover the operational band of 1.3-µm transmission systems, and (2) its maximum gain and gain coefficient are relatively low. These limitations are fundamental to Nd3⫹, and are due to signal ESA and to the fact that the transitions at 0.88 and 1.05 µm are stronger than at 1.3 µm. As a result, in spite of numerous tests of different materials and amplifier configurations, Nd3⫹-doped fibers have not yet produced a practical 1.3-µm amplifier. This section concentrates mainly on theoretical models, technical issues, and approaches for improvement. 12.2.1 Amplification Model Amplification models for the NDFA have been reported [18–22]. In this section, we use the formalism developed by Bjarklev [18]. The amplification model of the NDFA is based on the energy level diagram shown in Figure 2 [23]. The lower-lying levels are labeled 1 through 6. The following transitions: 4I 13/2 → 4I 11/2, 4I 13/2 → 4I 9/2, 4I 11/2 → 4I 9/2, 4F 5/2 → 4 F 3/2, and 4G 7/2 → 4I 9/2 are all taken to be fast, nonradiative transitions. It means that the lifetimes of τ 32, τ 31, τ 21, τ 54, and τ 61 are very short compared with other metastable lifetimes and are assumed to be equal to zero. The lifetime of the 4F 3/2 → 4I 13/2 transition (⬃880 nm), the 4F 3/2 → 4I 11/2 transition (⬃1050 nm) and the 4F 3/2 → 4I 9/2 transition (⬃1300 nm) are labeled τ 43, τ 42, and τ 41, respectively. Ground-state absorption (GSA) occurs from the 4 I 9/2 level to the 4F 5/2 level at close to 795 nm, and stimulated emission near 1.3 µm occurs from the 4F 3/2 metastable level to the 4I 13/2 ground state. The signal photons near 1.3 µm are also absorbed by signal ESA from the 4F 3/2 metastable level to the 4G 7/2 level (see Fig. 2).

Figure 2 Energy level diagram of Nd3⫹ ions in ZBLAN. (From Ref. 3.)

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The rate equations for the ion population density N 4 of the 4F 3/2 metastable level and N 1 of the 4I 13/2 ground state, taking the foregoing transitions into account and assuming N 6 ⫽ N 5 ⫽ N 3 ⫽ N 2 ⫽ 0, are given by Eqs. (1) and (2).

冢

冣

(1)

1 dN 1 ⫽ N 4 W 43, W 46 ⫹ W 41 ⫹ W 42 ⫹ ⫺ N 1 (W 15 ⫹ W 14) dt τ4

(2)

1 dN 4 ⫽ N 1 (W 15, W 14 ) ⫺ N 4 W 43 ⫹ W 46 ⫹ W 41 ⫹ W 42 ⫹ dt τ4

冢

冣

where τ 4 is the total lifetime of level 4: 1 1 1 1 ⫽ ⫹ ⫹ τ 4 τ 41 τ 42 τ 43 and W ij is the transition rate from the ith level to the jth level. The transition rates W 15, W 14, W 43, W 46, W 41, and W 42 are given by: W 15 ⫽

σ 15 (νp) hνp

Pp(z)ψ(r, θ, νp)

(3)

W 43 ⫽

σ 43 (νs) σ (ν) Ps(z)ψ(r, θ, νs) ⫹ ∫ 43 [P ⫹1300 (z, ν) ⫹ P ⫺1300 (z, ν)]ψ(r, θ, ν)dν hνs hν

(4)

W 46 ⫽

σ 46 (νs) σ (ν) Ps(z)ψ(r, θ, νs) ⫹ ∫ 46 [P ⫹1300 (z, ν) ⫹ P ⫺1300 (z, ν)]ψ(r, θ, ν)dν hνs hν

(5)

W 41 ⫽ ∫

σ 41 (ν) ⫹ [P 880 (z, ν) ⫹ P ⫺880 (z, ν)]ψ(r, θ, ν)dν hνs

(6)

W 42 ⫽ ∫

σ 42 (ν) ⫹ ⫺ [P 1050 (z, ν) ⫹ P 1050 (z, ν)]ψ(r, θ, ν)dν hν

(7)

W 14 ⫽ ∫

σ 14 (ν) ⫹ ⫺ (z, ν)]ψ(r, θ, ν)dν [P 880 (z, ν) ⫹ P 880 hν

(8)

In Eqs. (3) through (8), σ ij is the stimulated transition cross section from the i → j transition, ν S and ν P are the signal and pump frequencies, respectively, and h is Planck’s constant. P P (z) and P S (z) are the pump and signal powers, respectively, where z represents the fiber longitudinal coordinate, and ψ(r, θ, ν) is the normalized transverse mode envelope of the light at frequency ν, where (r, θ) represent cylindrical transverse coordinates. ⫾ ⫾ P ⫾880 (z), P 1050 (z), and P 1300 (z) are the spectrally dependent powers of the forward (⫹) and backward (⫺) propagating ASE in the 880-, 1050-, and 1300-nm bands, respectively. The total population density ρ(r, θ) satisfies ρ(r, θ) ⫽ N 1 ⫹ N 4. At steady state, the solution of Eqs. 1 and 2 provide the population densities N 1 and N 4 for the ground and the metastable state: N1 ⫽ ρ

W 43 ⫹ W 46 ⫹ W 41 ⫹ W 42 ⫹ (1/τ 4 ) W 15 ⫹ W 14 ⫹ W 43 ⫹ W 46 ⫹ W 41 ⫹ W 42 ⫹ (1/τ 4 )

(9)


N4 ⫽ ρ

W 15 ⫹ W 14 W 15 ⫹ W 14 ⫹ W 43 ⫹ W 46 ⫹ W 41 ⫹ W 42 ⫹ (1/τ 4 )

685

(10)

The set of coupled differential equations describing the spatial evolution of the pump ⫾ and signal power P ⫾P (z), P ⫾S (z), and the ASE powers P 880 (z), P ⫾1050 (z), and P ⫾1300 (z) along the fiber are given by: dP ⫾p ⫽ ⫾g P (z) ⋅ P ⫾p (z) dz

(11)

dP ⫾S ⫽ ⫾g S (z) ⋅ P ⫾S (z) dz

(12)

dP ⫾880,1050,1300 ⫽ ⫾g 880,1050,S (z) ⋅ P ⫾880,1050,1300 (z) ⫹ 2hν ⋅ α 880,1050,1300 (z, ν) dz

(13)

where g P (z) ⫽ σ 15 ∫∫N 1 (r, θ, z) ⋅ ψ(r, θ, ν)rdrdθ

(14)

g S (z) ⫽ (σ 43 ⫺ σ 46 )∫∫N 4 (r, θ, z) ⋅ ψ(r, θ, ν)rdrdθ

(15)

g 880 (z) ⫽ ∫∫[N 4 (r, θ, z) ⋅ σ 41 ⫺ N 1 (r, θ, z) ⋅ σ 14] ⋅ ψ(r, θ, ν)rdrdθ

(16)

g 1050 (z) ⫽ σ 42 ∫∫N 4 (r, θ, z) ⋅ ψ(r, θ, ν)rdrdθ

(17)

g 880 (z, ν) ⫽ σ 41 ∫∫N 4 (r, θ, z) ⋅ ψ(r, θ, ν)rdrdθ

(18)


(19)


(20)

In Eqs. (18) through (20), the coefficients a i (z, ν) represent the addition of new photons to the two bound orthogonal polarization modes owing to spontaneous emission. The amplification characteristics of Nd3⫹-doped ZrF 4-based fluoride fiber can be calculated by solving the foregoing differential equations [see Eqs. (11)–(13)] by using the values of the cross sections σ 15, σ 14, σ 41, σ 42, σ 43, σ 46 and the lifetime τ 4. Figure 3

Figure 3 Emission cross section spectra of σ 41, σ 42, and σ 43 of an Nd3⫹-doped ZrF 4-based fluoride fiber. (From Ref. 3.)

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shows the emission cross-sectional spectra of σ 41, σ 42, and σ 43, which were obtained by measuring the fluorescence spectrum from a short length of Nd3⫹-doped ZrF 4-based fluoride fiber pumped to full inversion and from the measured lifetime τ 4 ⫽ 720 µs [23]. The emission and absorption cross sections σ 14,41 for the 880-nm band, which are derived for the corresponding absorption coefficient of Nd3⫹-doped ZrF 4-based fluoride fiber, are reported as 20.5 ⫻ 10⫺25 m2 and 5.7 ⫻ 10⫺25 m2, respectively [23]. Another important cross section is that of signal ESA (σ 46 ). This spectrum is presented in the next section, along with the gain spectrum of Nd3⫹-doped ZrF 4-based fluoride fiber.

12.2.2 NDFA Amplification Characteristics NDFA Gain Spectrum Figure 4 shows the spectra of the gain, signal ESA, and emission cross section near 1.3µm measured in a Nd3⫹-doped ZrF 4-based fluoride fiber pumped at 795 nm [24]. The 3dB gain band is from 1318 to 1362 nm, although the emission cross section spectrum stretches are observed from 1280 to 1370 nm. The absence of the signal gain below approximately 1310 nm is the result of signal ESA. This is because the gain coefficient is proportional to σ 43 (v)–σ 46 (v), as shown in Eq. (15), and because below about 1300 nm the cross section of ESA exceeds that of stimulated emission (see Fig. 4). The performance of several potential Nd 3⫹-doped fiber glasses for 1.3-µm amplification has been studied [25–28] by using the figure of merit [20]:

Figure 4 Gain spectrum, ESA, and emission cross section associated with the 1.3-µm amplification band of an Nd3⫹-doped fluorozirconate fiber. (From Ref. 4.)


687

Table 1 Emission Characteristics of Phosphate, Fluoride, and Fluorophosphate Glasses SESA /Sem

Semτ (cm2ms; ⫻ 10⫺19)

m′ (ms; ⫻ 10⫺13)

λem (nm)

λESA (nm)

0.675 0.492 0.406

63.0 61.7 84.4

25.1 38.4 61.5

1324 1319 1323

1311 1316 1305

LHG8 (phosphate) ZBLA (fluoride) FPCO (fluorophosphate)

m⫽

冢

冣

4.34 σ σ τ 1 ⫺ 46 43 4 hν P σ 43 A eff

(21)

where m is expressed in units of decibels (dB) of gain per unit of absorbed pump power, and A eff is the mode effective area. Table 1 summarizes the emission characteristics near 1.3 µm of commercially available phosphate, ZrF 4-based fluoride, and fluorophosphate glass [27]. In this table, λ em and λ ESA are the peak wavelengths of the emission and ESA spectrum, respectively, and the modified figure of merit m′ ⫽ (1 ⫺ S ESA /S em ) (σ 43τ 4 /A eff ) is used instead of m, where S ESA and S em are the line strength of the ESA and the 1.3-µm stimulated emission transition, respectively. It has been confirmed that fluorophosphate glass has a better m′ value and a shorter signal ESA peak wavelength than phosphate and fluoride glass. (Fluoroberyllate glasses may have an even greater potential than fluorophosphate glasses [28]). On the basis of these spectroscopic predictions, an Nd3⫹-doped fluorophosphate glass single-mode fiber was fabricated [27]. As shown in Figure 5, it exhibited a slightly improved gain spectrum, with a gain peak wavelength of 1321 nm, which is shorter than that the fluoride fiber (see Fig. 4). However, there have been no reports of a glass host that offers either a gain spectrum covering the whole 1.29- to 1.33µm wavelength region, or a high gain (e.g., in excess of 20 dB).

Figure 5 Measured gain and fluorescence spectra of an Nd3⫹-doped fluorophosphate glass singlemode fiber. (From Ref. 27.)

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Table 2 Composition and Refractive Index of Fluoroaluminate Glasses Sample

Composition (mol%)

nD

AIF70 AIF117 AIF123 LG810 ZBLAN

37AIF3:12MgF2:15CaF2:9SrF2:6Baf2:14YF36NaPO3 39AIF3:7MgF2:30CaF2:7SrF2:7BaF2:9LiF 39AIF3:6MgF2:22CaF2:6SrF2:6BaF210LiF:10NaF Commercial fluorophosphate Commercial ZrF4-based fluoride

1.432 1.402 1.397 1.453 1.541

Recently, Taylor et al. proposed new host glasses designed to suppress ESA [29]. They pointed out that an ideal glass host must have a minimum Ω 2, Ω 4, and a maximum Ω 6 based on a Judd–Ofelt (JO) analysis. With these requirements, a novel family of nontoxic fluoroaluminate glasses was proposed as the most promising host for a neodymium-doped amplifier. Table 2 lists the compositions and refractive index n D of these glasses. Table 3 lists the ratio of their emission (A em ) and ESA (A e ) cross sections, their measured peak emission wavelength (λ peak ) and laser wavelength (λ laser ), and their JO parameters. For glass AlF123, they predicted an emission and ESA cross-section ratio almost 1.7 times that of ZBLAN. The implication of Table 3 is that because AlF glasses exhibit a larger A em /A e ratio than ZBLAN, they are potential candidates for amplification near 1300 nm. Figure 6 shows the measured gain and fluorescence spectra of a neodymium-doped fiber made of fluoroaluminate glass AlF70. The maximum gain was relatively low because the fiber was highly multimoded, but it was possible to shift the gain peak wavelength down to 1315 nm. Figure 7 shows the calculated gain spectra of different glass hosts, doped with either Nd3⫹ or Pr 3⫹ [29]. The conditions used in these calculations were a fiber NA of 0.4, a pump power of 100 mW, negligible fiber loss, and a pump wavelength of 1015 and 800 nm for the PDFA and NDFA, respectively. These simulations indicate that the gain spectra of the Nd-doped fluoroaluminate glass fiber still occurs at a longer wavelength than the telecommunication band, but that it can be expected to exhibit a high gain coefficient in the 1315- to 1360-nm range. If this glass system is thermally stable and low-loss, single-mode fiber can be fabricated, this amplifier might be a promising candidate to expand the usable communication windows beyond the 1300- and 1550-nm bands. Saturation and Noise Characteristics of NDFA Figure 8 shows typical saturation characteristics for an Nd-doped ZBLANP fiber amplifier [19]. The NDFA has good saturation characteristics, despite its relatively low gain performance. The measured gain was constant with varying signal power up to a launched signal Table 3 Characteristics of Fluoroaluminate Glasses Sample

Peak (nm)

Ω2

Ω4

Ω6

Aem /Ae

λlaser (nm)

AIF70 AIF117 AIF123 LG810 ZBLAN

1317 1317 1317 1320 1317

1.44 1.00 1.15 2.65 2.2

2.95 4.01 3.39 3.22 2.83

4.06 5.36 5.83 5.06 3.94

2.40 2.97 3.48 2.08 2.01

1317

1323 1330


689

Measured gain and fluorescence spectra of a Nd3⫹-doped fiber made of fluoroaluminate glass A1F70. (From Ref. 29.)

Figure 6

Figure 7 Comparison of the small-signal gain spectra of Nd3⫹ and Pr 3⫹ in different fluoride and sulfide glass hosts. (From Ref. 29.)

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Figure 8 Typical saturation characteristics of an Nd-doped ZrF 4-based fluoride fiber measured at two signal wavelengths. (From Ref. 19.)

power of approximately 0 dBm, beyond which the gain started rolling off. With the signal source available for these measurements, the maximum launched signal power was ⫹7 dBm, which was enough to observe gain saturation, but not enough to reach the 3-dB saturation point. These experimental results demonstrated that the saturation input power for both wavelengths was more than ⫹7 dBm. Extrapolating the experimental data points of Figure 8, using the theoretical fits, yields a 3-dB saturation output power of ⫹16.5 dBm at 1320 nm and ⫹18.5 dBm at 1337 nm. The saturation output power P OUT sat (ν S ) for a 3-dB gain compression is given by [18] P OUT sat (ν S ) ⬇

A eff hν S [σ 43 (ν S ) ⫹ σ 46 (ν S )]τ c

(22)

Therefore, an Nd-doped fiber with a low σ 43 ⫻ τ 4 product is expected to have good saturation characteristics. Also, Eq. (22) shows that the saturation output power decreases with decreasing signal wavelength because of the increase in signal ESA. It has been predicted that in the absence of ESA, the photon conversion efficiency, which is an important parameter when an NDFA is used as a booster amplifier, can reach 100% [22]. Furthermore, because the NDFA is a four-level system, in the absence of signal ESA and in the high-gain regime, its noise figure (NF) is expected to be close to the 3.0dB limit for an ideal optical amplifier. The NF is expressed as σ 43 (ν)∫∫N 4 (r, θ, z) ⋅ ψ(r, θ, ν)rdrdθ g S (ν) σ 43 ⫽2 σ 43 ⫺ σ 46

NF ⬇ 2N SP ⫽ 2

(23)


691

where N sp is a population inversion parameter. The measured gain and noise figure spectra reported for an Nd-doped fluorophosphate glass fiber are shown in Figure 9. The noise figure increases with decreasing signal wavelength, from 2.5 to 3.8 dB for wavelengths less than 1345 nm, owing to an increase in the signal ESA cross section. Although it has been predicted that NDFAs can have a good saturation and noise performance, a main difficulty is that the gain and efficiency of an NDFA are reduced by both signal ESA and ASE. There are three methods to suppress the ASE buildup: (1) designing the NDFA in a cascade configuration that incorporates optical isolators or filters, or both [4,23,30]; (2) optimizing the Nd ion distribution [31]; and (3) doping the fiber cladding with an ASE-absorbing ion such as Yb3⫹. The cascade configuration incorporating optical filters has been studied theoretically. Figure 10 shows the calculated signal gain as a function of total NDF length, for an increasing number of filters inserted along the NDF [23]. It shows that increasing the number of filters substantially improves the gain. A dielectric multilayer filter and a grating notch filter have been used to limit the ASE near 1050 nm, leading to the demonstration of signal gains of 10 [4] and 9.2 [30]. As an example, Figure 11a shows a cascade configuration of an Nd-doped ZBLANP fiber amplifier pumped at 0.82 µm in opposite directions, with a WDM fiber coupler acting as a 1.05/1.3-µm filter placed in the middle of the doped fiber. Its gain saturation characteristics, measured at three signal wavelengths, are shown in Figure 11b [4]. Another method to reduce unwanted ASE is to select a fiber with an Nd3⫹ ion distribution that overlaps more strongly with the 1.3-µm signal than with the 1050-nm ASE. It can be accomplished by placing the Nd3⫹ ions some distance from the fiber axis, where the signal mode intensity is larger at 1.3 µm than at 1050 nm, as illustrated in Figure 12a [31]. By using this distribution, the gain coefficient of the 1.05-µm band, expressed in Eq. (17), is reduced, and this reduction is larger than that of the 1.3-µm band. Figure 12b shows the expected improvement in the gain characteristics using this design. For a 100mW pump power, the signal gain increased by a factor of approximately two for the LP 01 signal mode, compared with a standard fiber design. The improvement was slightly greater for the LP 11 mode, which overlaps more strongly than the LP 01 mode with the offset Nd distribution. As for the third method to suppress ASE—namely, doping the cladding of the NDF with ASE-absorbing ions, such as Yb3⫹ —although it seems to be a comparatively easy approach, to our knowledge it has not yet been attempted. 12.3 PRASEODYMIUM-DOPED FIBER AMPLIFIERS The praseodymium-doped fiber amplifier (PDFA) was proposed in 1990 to overcome the problems posed by the NDFA. Recently, the PDFA has been greatly improved to satisfy practical system requirements. This section describes a theoretical model, amplification characteristics, and the performance of PDFA modules. 12.3.1 Amplification Model Amplification models of the PDFA have been described [32–35]. In this section, we use the description provided by Ohishi et al. [33]. The amplification model of the four-level 1 G 4 – 3H 5 transition of the PDFA is based on the simplified energy diagram of Figure 13. The spontaneous lifetimes of the 1G 4, 1D 2, and 3P 0 levels are indicated by τ i with i ⫽ 4– 6. The measured values for τ 4, τ 5, and τ 6 are 110, 350, and 58 µs, respectively, for a Pr 3⫹-

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Figure 9 Measured gain and noise figure spectra of an Nd-doped fluorophosphate glass singlemode fiber. (From Ref. 27.)

Figure 10

Calculated increase in the gain of an Nd-doped fiber amplifier versus total fiber length, as a function of the number of filters inserted into the fiber, as shown in the inset. (From Ref. 23.)


693

(a)

(b)

Figure 11

A 1.3-µm cascade Nd-doped ZBLAN fiber amplifier utilizing a WDM fiber coupler as a filter: (a) configuration and (b) gain saturation characteristics measured at three different signal wavelengths. (From Ref. 4.)

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(a)

(b)

Figure 12

Reducing the ASE around 1050 nm in an Nd-doped fluoride fiber amplifier by tailoring the Nd3⫹-ion distribution: (a) Nd3⫹ ion distribution that achieves this goal, as well as the fiber index profile, the pump mode, and the signal modes at 1050 and 1300 nm; (b) calculated signal gain versus pump power for a standard fiber with the Nd3⫹ ions near the center of the core, and for the improved design of (a), for both the LP 01 and LP 11 signal mode. (From Ref. 31.)


Figure 13

695

Simplified energy-level diagram and transitions of Pr 3⫹ ions in ZBLAN. (From

Ref. 33.)

doped ZrF 4-based fluoride fiber [32–34]. Pump-photon ground-state absorption (GSA) occurs between the 3H 4 level and the 1G 4 level. Pump photons are also absorbed by pump ESA between the 1G 4 level and the 3P 0 level, and by stimulated emission between the 1G 4 metastable level and the 3H 4 level. Signal photons are absorbed by the 3H 4 → 3F 4 GSA as well as the 1G 4 → 1D 2 ESA. In addition, the population of the 1G 4 metastable level can be reduced by cooperative upconversion caused by the (1G 4 → 1D 2 ) to (1G 4 → 3H 5 ) transition. Upconversion arises because the energy difference between the 1G 4 and the 1D 2 levels matches that between the 1G 4 and the 3H 5 levels. This process degrades the gain characteristics and must be included in any realistic model of PDFA. The 1G 4 level is populated by decay from the 3P 0 and 1D 2 levels. The branching ratios for the 3P 0 → 1G 4 and 1D 2 → 1G 4 transitions obtained by Judd–Ofelt analysis are B 64 ⫽ 2% and B 54 ⫽ 9% for a Pr 3⫹-doped ZrF 4-based fluoride fiber, respectively [32–34]. Excited Pr 3⫹ ions in the 1G 4 level can decay very easily to the 3F 4 level by multiphonon relaxation. Efficient amplification, therefore, requires the suppression of the 1G 4 → 3 F 4 nonradiative transition by choosing a glass host with a phonon energy as low as possible. Figure 14 shows the relation between the multiphonon relaxation rate and the energy gap for various glasses. The relaxation rate is lowest for fluoride, and of the order of 103 s for the 3000-cm⫺1 energy gap of the 1G 4 → 3F 4 transition. In view of this low relaxation rate, and of the fact that a fabrication technique exists to produce low-loss fluoride fiber, ZrF 4-based fluoride glass has been the preferred glass host for PDFAs. When we take these transitions into account, the rate equations for the ion population density N i (see Fig. 13) are given by

冢

冣

1 B N B N dN 4 ⫽ W 14 N 1 ⫺ W 46 ⫹ W 45 ⫹ W 42 ⫹ W 41 ⫹ ⫹ cN 4 N 4 ⫹ 54 5 ⫹ 64 6 dt τ4 τ5 τ6

(24)

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Figure 14

Dependence of the multiphonon relaxation rate on energy gap between levels for various glasses.

冢

冣

cN N dN 5 ⫽ W 46 ⫹ 4 N 4 ⫺ 5 dt 2 τ5

(25)

N dN 6 ⫽ W 46 N 4 ⫺ 6 dt τ6

(26)

where c is the cooperative upconversion coefficient. By assuming a uniform Pr 3⫹ density distribution ρ(r, θ) ⫽ ρ 0 for r ⱕ a and ρ(r, θ) ⫽ 0 for r ⬎ a, where a is the fiber core radius, and by using a gaussian approximation of the normalized transverse mode envelopes ψ S,P (r, θ) of the pump and signal, respectively—that is ψ S,P (r, θ) ⫽ [ exp (⫺r 2 / ω S,P2 )]/πω 2S,P, where ω S,P is the mode power radius for the signal and pump lights, the transition rates W 14, W 41, W 42, W 45, and W 46 are given by W 14,41 ⫽

Γ Pσ 14,41 (ν P ) ⋅ P p (νp, z) Ahν S

W 42,45,46 ⫽ ∫

Γ S σ 42,45,46 (ν) ⋅ P ⫹S (ν, z) ⫹ P ⫺S (ν, z)) Ahν S

(27) (28)

where P P (ν P ) is the pump power at the pump frequency ν P, P ⫾S (ν, z) are the forward (⫹) and backward (⫺) propagating signal and spontaneous emission power in the 1.3-µm band at frequency ν, Γ S ,P ⫽ 1 ⫺ exp(⫺a 2 /ω 2S,P ) is a filling factor, A ⫽ πa 2 is the core area, and h is Planck’s constant. Figure 15 shows the cross-section spectra of σ 14, σ 41, σ 13, σ 45, and σ 42 [35]. The peak value of σ 46 [33,34], is 0.6 ⫻ 10⫺22 cm2. The value of the cooperative upconversion coefficient c is discussed in Section 3.3.1. The total population density ρ satisfies ρ ⫽ N 1 ⫹ N 4 ⫹ N 5 ⫹ N 6. Because it was assumed that the Pr 3⫹ ions in the 3H 5 and 3F 4 levels relax instantaneously to the 3H 4 ground level, the populations N 2 and N 3 are taken to be zero. At steady state, the population


697

Figure 15

Measured cross-section spectra of various transitions in Pr-doped fluoride glass. (From Ref. 35.)

densities N 1, N 4, N 5, and N 6 for the 3H 4, 1G 4, 1D 2, and 3P 0 levels, respectively, are solution of Eqs. (24) to (26) and given by

冤

冢

N 1 ⫽ ρ ⫺ 1 ⫹ τ 4 W 46 ⫹

N4 ⫽

冣冥

cN 4 τ 6 W 35 N 4 2

⫺β ⫹ √β2 ⫹ 4α 1ρ 2α 1

冢

N 5 ⫽ τ 5 W 46 ⫹

(29)

(30)

冣

cN 2 N4 2

(31)

N 6 ⫽ τ 6 W 46 N 4

(32)

where α1 ⫽

c[τ 5 ⫹ (2 ⫺ B 54 /W 14 )] 2

β ⫽ 1 ⫹ W 45 τ 5 ⫹ W 46 τ 6 ⫹

W 46 ⫹ W 45 ⫹ W 42 ⫹ W 41 ⫺ B 54W 45 ⫺ B 64 W 46 ⫹ 1/τ 4 W 14

(33)

(34)

The set of coupled differential equations describing the spatial evolution of the pump and signal powers P p and P s, and of the ASE along the fiber are dP P (ν P, z) ⫽ [γ Pe (ν P, z) ⫺ γ P (ν P, z) ⫺ γ P⫺ESA (ν P, z) ⫺ α(ν P, z)] ⋅ P P (ν P, z) dz

(35)

698

Fujiura and Sudo ⫾ dP s (ν, z) ⫽ ⫾g S (z, ν)P ⫾S (ν, z) ⫾ P 0 γ e (z, ν) dz

(36)

g S (ν, z) ⫽ γ Se (ν, z) ⫺ γ S⫺ESA (ν, z) ⫺ γ GSA (ν, z) ⫺ α(ν, z)

(37)

where P 0 ⫽ 2hν s∆ν is the spontaneous emission power per mode per unit bandwidth, and γ Se, γ P, and γ P⫺ESA are the stimulated emission coefficient, absorption coefficient, and ESA coefficient for the pump, respectively. The factors g S, γ Se, γ S⫺ES, and γ GSA are the gain coefficient, stimulated emission coefficient, ESA coefficient, and GSA coefficient for the signal, and α is the scattering loss of the PDF. These coefficients are given by γ Pe ⫽ σ 41N 4 A

(38)

γ p ⫽ σ 14N 1 A

(39)

γ P⫺GSA ⫽ σ 46N 4A

(40)

γ Se ⫽ σ 42 N 4 A

(41)

γ GSA ⫽ σ 13 N 1 A

(42)

γ S⫺ESA ⫽ σ 45N 4 A

(43)

Although Eqs. (29) through (32) are useful to precisely calculate the local population density N i and the amplification characteristics, they are difficult to use for a qualitative discussion. Omission of the contribution of pump ESA and cooperative upconversion yields the following simplified expressions [33,36]: N1 ⫽ ρ

[W 41 ⫹ W 42 ⫹ W 45 ⫹ (1/τ 4 )] W 14 ⫹ W 41 ⫹ W 42 ⫹ W 45 ⫹ (1/τ 4 )

(44)

N4 ⫽ ρ

W 14 W 14 ⫹ W 41 ⫹ W 42 ⫹ W 45 ⫹ (1/τ 4 )

(45)

N4 ⫽ ρ

W 14 W 45τ 4 W 14 ⫹ W 41 ⫹ W 42 ⫹ W 45 ⫹ (1/τ 4 )

(46)

Hence, the gain coefficient g S and population inversion parameter N sp are expressed as g S ⫽ (σ 42 ⫺ σ 45 )Γ S N 4 ⫺ σ 14Γ S N 1 ⫺ α N sp ⫽ ⫽

(47)

σ 42Γ S N 4 gs

(48)

1 1 ⫺ (σ 45 /σ 42 ) ⫺ (σ 41 N 1 /σ 42 /N 4 ) ⫺ (σ/σ 42Γ S N 4 )

The saturation output power for a 3-dB gain compression, P OUT sat , which can be approximated by the signal power for which the density of ions in the 1G 4 level, in the absence of signal input, has fallen to half the original number, is given by P OUT sat ⫽ ⬇

冤

冥

Ahν S 1 P P (σ 14 ⫹ σ 41 ) ⫹ (σ 42 ⫹ σ 45 )Γ S Ahν S τ4 Ahν S (σ 42 ⫹ σ 45 )Γ Sτ 4

(49)


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The simplified expressions given by Eqs. (44) through (49) are helpful to provide an intuitive understanding of the PDFA characteristics. 12.3.2 Basic Amplification Characteristics This section describes the basic PDFA amplification characteristics such as gain spectrum, saturation characteristics, and noise characteristics. Gain Spectrum Unlike the gain spectrum of the EDFA, the PDFA gain spectrum has no structure. Figure 16a shows typical gain spectra measured in a Pr 3⫹-doped ZrF 4-based fluoride fiber for various launched pump powers, and Figure 16b shows gain spectra in the same fiber measured for various input signal powers [37]. The signal gain spectrum has a peak at about 1.30 µm, and provides good coverage of the 1.29- to 1.33-µm communication window, irrespective of pump and signal power conditions. The 3-dB spectral bandwidth decreases with increasing pump power and decreasing input signal power, as expected. Figure 17 shows the strong dependence of the measured signal gain spectrum on the PDF length [37]. The measured 3-dB gain bandwidth decreases with increasing fiber length, because the signal gain at signal wavelengths higher than 1.30 µm decreases with increasing length owing to signal GSA. Therefore, it is important to optimize the PDF length to achieve a high-gain and a wide-amplification bandwidth. Figure 18 shows the relation between the signal gain and the 3-dB gain bandwidth [37]. The signal gain increases with increasing length until an optimum length is reached. The signal gain then decreases slightly with further increases in length owing to the scattering loss of the PDF. In contrast, the gain bandwidth decreases monotonously with increasing length. The conclusion is that the Pr 3⫹-doped fiber used in a PDFA amplifier module must be adjusted to some optimum length that depends on the parameter that needs to be maximized. The relations between the signal gain, the internal gain, and the signal GSA spectrum in a Pr 3⫹-doped ZrF 4-based fluoride fiber can be better understood from Figure 19 [36]. The wavelength dependence of fiber loss, which consists of both scattering loss and signal GSA, is due to the wavelength dependence of the GSA, shown as σ 13 in Figure 15. Although the peak wavelength of the signal gain is near 1.30 µm, the peak of the internal gain spectrum is at 1.31 µm. This wavelength shift is due to the influence of the GSA spectrum. Gain Saturation Figure 20 shows a typical gain saturation characteristics for a Pr 3⫹-doped ZrF 4-based fiber. The solid curves are calculated dependencies [33]. The gain saturation power for 3-dB– gain compression decreases from 12 to 10 and 9.5 dBm as the signal wavelength increases from 1.29 to 1.31 and 1.33 µm, respectively. This is due to signal ESA, as can be seen in Eq. (49). However, the signal ESA cross section in the 1.29- to 1.33-µm region is more than ten times smaller than the stimulated cross section. The effect of signal ESA on signal gain, therefore, is not thought to be a serious concern. Furthermore, the power conversion efficiency and slope efficiency are important parameters that characterize the saturation performance of a PDFA. It has been reported that the former is about 36% for a pump wavelength of 1010 nm, and 21% for 1047 nm [38]. The maximum power conversion efficiency is about 80%. The slope efficiency is discussed later in relation to its use for evaluating various pump source.

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(b)

Figure 16 Typical calculated gain spectra of a Pr-doped ZBLAN fiber: (a) for a fixed input signal power (⫺45 dBm) and various pump powers; (b) for a fixed pump power (230 mW) and various input signal powers. (From Ref. 37.)


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Figure 17 Effect of the fiber length on the small-signal gain spectrum of a Pr-doped ZBLAN fiber. (From Ref. 37.)

Figure 18

Effect of the fiber length on the small-signal gain (calculated) and on the 3-dB gain bandwidth (measured) in a Pr-doped ZBLAN fiber. (From Ref. 37.)

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Figure 19

Measured spectra of the small-signal gain, internal small-signal gain, and GSA in a Pr 3⫹-doped ZrF 4-based fluoride fiber amplifier. (From Ref. 36.)

Figure 20

Typical measured and modeled gain saturation characteristics of a Pr 3⫹-doped ZBLAN fiber amplifier at three signal wavelengths. (From Ref. 33.)


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Noise Figure Characteristics If there were no signal ESA and no GSA in the PDFA, the optimum NF of this amplifier would be close to the value of 3.0 dB of an ideal optical amplifier based on stimulated transition [33,36,38,39]. However, because Pr 3⫹-doped fluoride fiber is severely influenced by signal ESA and GSA, its noise characteristics are somewhat worse than ideal. From Eq. (48), and ignoring the PDF scattering loss, the NF can be written as follows [33,36]: NF ⫽ 2N SP ⬇3(dB)

(λ S ⬍ 1.31 µm)

冤

2

10 log

1⫺

冥

σ 45 σ N ⫺ 41 1 σ 42 σ 42 N 4

(dB)

(λ S ⬎ 1.31 µm)

(50)

Figure 21 shows the measured NF spectrum of a Pr 3⫹-doped ZrF 4-based fluoride fiber amplifier [36]. The NF is 3.4 dB at wavelengths less than 1.31 µm. The 0.4-dB difference between the measured NF and the quantum limit value of 3.0 dB is thought to be due to the scattering loss of the PDF. In contrast, at wavelengths larger than 1.31 µm, the NF worsens with increasing signal wavelength owing to the signal ESA cross section σ 45 and the GSA cross section σ 14, as expressed by the second and third terms of the denominator in Eq. (50). Figure 22 shows the measured dependence of the gain and NF on the signal output power [38]. With a pump power of 780 mW, the small-signal gain at 1.3 µm was as high as approximately 18.5 dB. The noise figure was about 5 dB, and it did not change for signal wavelengths less than 1.31 µm because of the four-level nature of the amplification process. These and the foregoing results show that PDFAs can amplify signals with a noise figure close to the quantum limit of 3 dB, except in the wavelength region higher than 1.31 µm.

Figure 21 Measured noise figure spectrum of a Pr 3⫹-doped ZBLAN fiber amplifier. (From Ref. 36.)

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Dependence of the signal gain and noise figure on the signal output power in a Pr 3⫹doped ZBLAN fiber amplifier. (From Ref. 38.)

Figure 22

Temperature Dependence The temperature-dependent characteristics of Pr 3⫹-doped fluoride fiber are important in practical applications and have been investigated both theoretically and experimentally [36,40]. Figures 23a and b show the temperature dependence of the signal gain and NF, respectively, of a Pr 3⫹-doped ZrF 4-based fluoride fiber 15 m in length, measured for various signal wavelengths between 1.28 and 1.33 µm [36]. The fiber temperature was varied from ⫺40 to 80°C. Regardless of the signal wavelength, the gain decreases monotonically as the fiber temperature is increased. In contrast, the NF increases with increasing fiber temperature for signal wavelengths higher than 1.31 µm, whereas it changes negligibly at wavelengths less than 1.31 µm. As shown in Figure 23c, the saturation output power of the same fiber at a 3-dB–gain compression increased with increasing temperature [36]. Note that the temperature dependencies of the signal gain and output power can be compensated by using automatic gain control (AGC) and automatic power control (APC) techniques over the temperature range of ⫺40° to 80°C. To understand the origin of these temperature variations, it is useful to return to the simplified expressions that describe the gain, noise figure, and saturation power of a PDFA [see Eqs. (44) through (50)]. In these equations, the parameters that exhibit a temperature dependence are the cross sections σ 14, σ 41, σ 42, and σ 45, and the lifetime τ 4. The changes in τ 4 and σ 42 are of particular importance when considering the temperature dependence of a PDFA [36,40]. Figure 24 shows the temperature dependence of the lifetime τ 4 of Pr 3⫹ in a ZrF 4-based fluoride glass. The lifetime decreases monotonically with increasing temperature, from 77 µs at 335 K to 155 µs at 9 K [40]. This dependence is caused by a variation in the nonradiative relaxation probability as a result of multiphonon relaxation from the 1G 4 level to the 3F 4 level, which increases with temperature [41]. In EDFAs, the temperature-dependent gain characteristics result only from the stimulated-emission crosssection temperature dependence, because the energy interval between the 4I 13/2 metastable level and the 4I 15/2 ground level is sufficiently large that multiphonon relaxation does not affect the metastable lifetime. In Pr 3⫹, the change in τ 4 affects the population densities


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(b)

Figure 23

Measured dependence on temperature of a Pr-doped ZBLAN fiber amplifier: (a) smallsignal gain at various signal wavelengths; (b) noise figure at various signal wavelengths; and (c) saturation output power. (From Ref. 36.)

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Figure 23

Continued

Measured temperature dependence of the lifetime τ 4 of the 1G 4 level of Pr 3⫹ in a ZrF 4based fluoride glass. (From Ref. 40.)

Figure 24


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N 4 and N 1, as described by Eqs. (44) and (45), and as the fiber temperature is increased, N 4 decreases while N 1 increases. Figure 25 shows the measured evolution of the 1G 4 → 3H 5 fluorescence spectrum 3⫹ of Pr in a ZrF 4-based fluoride glass in the 9- to 320-K temperature range [40]. The emission intensity in the 1.28- to 1.33-µm region increases with decreasing temperature up to ⬃250 K, whereas the emission peak wavelength shifts toward longer wavelengths. Because of this red shift, the emission intensity near 1.30 µm is noticeably reduced for temperatures lower than approximately 100 K. These changes in fluorescence spectrum reflect a change in the spectrum of the cross section σ 42 with temperature, which is itself due to a change in the Boltzmann distribution of the sublevel populations. By taking into account both the changes in τ 4 and in σ 41, the temperature dependence of the PDFA characteristics on fiber temperature described in Figure 23a–c can be understood as follows: 1. As the temperature is reduced, the signal gain increases owing to the increase in N 4, the decrease in N 1, and the increase in σ 42, according to Eq. (44). 2. At signal wavelengths less than 1.31 µm, the NF is constant, which σ 42 is larger than σ 45 and σ 41, and the second and third terms in the denominator of Eq. (48) can be neglected. But for signal wavelengths longer than 1.31 µm, as the fiber temperature is increased the NF increases because of the increase in the third term in the denominator of Eq. (48), owing to the decrease in N 4, the increase in N 1, and the decrease in σ 42. 3. As the temperature is increased from ⫺40° to ⫹40°C, the lifetime τ 4 and σ 41 both decrease, and Eq. (39) predicts that the saturation output power should increase, as observed in Fig. 23c. Figure 26 shows the measured and calculated temperature dependence of the smallsignal gain of a PDFA at several wavelengths from 1.29 to 1.33 µm, including the temperature region below ⫺40°C [40]. The gain does not increase monotonically below-40°C. Instead, it exhibits a maximum that depends on the signal wavelength. This is due to the rather complex behavior of the stimulated emission cross section σ 42 versus temperature shown in Figure 25. At low temperatures, the gain is degraded in spite of the improvement in quantum efficiency. 12.3.3 PDFA Module The first PDFA module was reported in 1991 [11]. This amplifier was pumped at 1017 nm with strained quantum-well semiconductor laser diodes. Other pump sources have been used since then in other PDFA modules. A laser-diode module with a fiber pigtail was used to produce a high-gain and a high-output power [42]. The pump power was maximized by optimizing the laser structure [43,44] and by employing an MOPA design [45,46]. A compact laser–diode-pumped Nd:YLF laser with a fiber pigtail was also employed as a pump source with a low-noise and high-power laser [47]. A key development to the construction of practical PDFAs was splicing between a Pr 3⫹-doped ZrF 4-based fluoride fiber with a high ∆n and a silica fiber with a conventional ∆n (⬃0.3%). This problem was overcome by using the thermally expanded core (TEC) connection technique [47–49] or the tilted V-groove connection technique, or by the angled-polishing and active-alignment technique [47]. Excellent fiber connections with low loss and low reflection were thus realized [42,47,50]. By using these connection techniques and high-power pump

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Figure 25 Fluorescence spectrum of the 1G 4 → 3H 5 transition in Pr-doped ZrF 4-based fluoride glass, measured at various temperatures in the 9 to 320-K range. (From Ref. 40.)

Figure 26

Measured and calculated temperature dependence of the small-signal gain at various signal wavelengths from 1.29 to 1.33 µm. (From Ref. 40.)


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sources, high-performance PDFA modules have been fabricated with gains exceeding 30 dB and signal output powers of over 18 dBm. In this section, we discuss issues of fiber design, pumping scheme, fiber fabrication, fiber connection technique, and pump sources relevant to PDFAs. We then report the performance of recent PDFA modules, including PDFA configurations designed to achieve a high-gain and high-output power. Finally, we describe the performance of a few PDFAs that have recently become commercially available. Amplifier Design Optimum Design of the Pr-Doped Fiber The main problem with the Pr 3⫹-doped ZrF 4-based fluoride fiber amplifier is its low gain coefficient caused by the low quantum efficiency of the 1G 4 → 3G 5 transition, as mentioned earlier [5]. Excited Pr 3⫹ ions in the 1G 4 level decay rapidly to the 3F 4 level owing to multiphonon relaxation. For a particular Pr 3⫹-doped ZrF 4-based fluoride fiber (49ZrF 4 – 25BaF 2 –3.5LaF 3 –2Yf 3 –2.5AlF 3 –18LiF), the measured decay time constant is τ Measured ⫽ 110 µs, and the radiative lifetime is τ Radiative ⫽ 3.24 ms [5]. The quantum efficiency, defined as τ Measured /τ Radiative, is only 3.4%. As a consequence, the first reported Pr 3⫹-doped ZrF 4based fluoride fiber amplifier required a launched pump power of 180 mW to achieve a gain of 5.2 dB, corresponding to a gain coefficient of only 0.05 dB/mW [5]. To improve this performance, the best approach is to use a host glass with a lower phonon energy. Several candidates, in particular chalcogenide glass, InF 3-based fluoride glass, and mixed halide glasses, have been reported to achieve efficient amplification. Another practical approach is to optimize the parameters of the Pr-doped fiber. Several investigations have shown that optimizing the Pr 3⫹ concentration, increasing the fiber NA, and reducing the scattering loss of the fiber, all are critical improvements for increasing the gain coefficient. The dependence of the gain on the Pr 3⫹ concentration has been studied experimentally and theoretically [32]. Figure 27 shows the internal gain measured in two Pr 3⫹-doped ZrF 4-based fluoride fibers with Pr 3⫹ concentrations of 500 and 1000 ppm. (Note that the internal gain is measured as the ratio of the pumped to unpumped signal level at the output end of the PDF. Therefore, it excludes the fiber loss, in particular, scattering loss. Internal gain was commonly used to characterize the gain in the early years of PDFA research because there was no low-loss PDF and no satisfactory low-loss technique for connecting a PDF to a silica fiber to inject the signal and the pump.) The fibers were pumped at 1017 nm in the forward direction. Their lengths were 14 and 7 m, respectively, so that the product of PDF length by the Pr 3⫹ concentration was the same for both fibers. All other parameters were the same for both PDFs. As shown in Figure 27, the internal gain of both fibers started to increase with almost the same slope. However, the gain of the 1000-ppm fiber saturated much more strongly than that of the 500-ppm fiber. This comparison shows that a concentration of 1000 ppm is too high to produce a Pr 3⫹-doped ZrF 4-based fluoride fiber with an optimum gain coefficient. This difference in behavior was attributed to upconversion. By fitting calculated gain curves (solid curves in Fig. 27) to the measured data, this study inferred upconversion coefficients c of 0.2 ⫻ 10⫺22 cm3 /s and 1.1 ⫻ 10⫺22 cm3 /s for Pr 3⫹ concentrations of 500 and 1000 ppm, respectively [32]. The upconversion coefficient is reduced by a factor of nearly five even though the Pr concentration was reduced by only a factor of two. Further modeling, in fact, showed that the gain curve of Figure 27 for the 500-ppm fiber was very close to the theoretical gain curve in the limit of no upconversion. This study concluded that a Pr 3⫹ concentration of 500 ppm is suitable for fabrication of an efficient PDFA [32].

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Measured dependence of the internal gain on the pump power for Pr 3⫹-doped ZrF 4based fluoride fiber amplifiers with Pr 3⫹ concentrations of 500 and 1000 ppm. (From Ref. 32.)

Figure 27

Other key PDF parameters that influence the gain coefficient are the NA and the scattering loss [5,9,10]. The calculated relation between the gain coefficient and the core radius of a Pr 3⫹-doped ZrF 4-based fluoride fiber, for various relative reflective-index differences ∆n between the core and cladding, are shown in Figure 28 [5]. This calculation models a forward-pumped fiber with no scattering loss and a step-index core profile, a uniform distribution of Pr 3⫹ ions in the core, and a pump wavelength of 1017 nm. For a given core radius, the gain coefficient increases with increasing ∆n owing to an increasing confinement of the pump and signal modes. As the fiber ∆n increases, the core radius that produces the highest gain coefficient decreases slightly. This dependence of the optimum core radius on ∆n is consistent with the result of other theoretical investigations, which showed that in a PDF, the cutoff wavelength that maximizes the gain is approximately 0.8 µm, independently of the fiber ∆n [9,51]. From Figure 28, it is expected that a gain coefficient greater than 0.2 dB/mW can be achieved when ∆n is larger than 3%. However, to fabricate an actual amplifier, a PDF with a high ∆n must be connected to a silica fiber with a low splicing loss. For this connection to be possible, the ∆n of the PDF must be about 3.7%, which is about the highest NA of practical silica fibers. In Figure 29 the measured gain coefficient is shown as a function of the scattering loss for Pr 3⫹-doped ZrF 4-based fluoride fibers with an ∆n of 3.7 or 3.3% and a core radius of 1.8 µm [9]. To achieve an efficient fiber amplifier with a gain coefficient higher than 0.2 dB/mW requires a low scattering loss of less than 0.05 dB/m for a ∆n of 3.7%. Recently, by improving the fiber fabrication technique and optimizing the composition of the fluoride glass to suppress crystallization, the scattering loss of a PDF with a ∆n of 3.7% and a Pr 3⫹ concentration of 500 ppm was reduced to 0.1 dB/m at 1.3 µm, as illustrated in Figure 30a. A high gain coefficient of 0.21 dB/mW was achieved in this fiber (see Fig. 30b) [9].


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Figure 28 Calculated dependence on the core radius of the gain coefficient of a Pr 3⫹-doped ZrF 4based fluoride fiber amplifier, for various ∆n values. (From Ref. 5.)

The gain coefficient can also be improved by carefully selecting the pump and amplification configurations. The efficiency was indeed increased to 0.24 dB/mW with a bidirectional pump configuration, and it was doubled with a double-pass amplification configuration, leading to a gain coefficient of 0.4 dB/mW [52]. These two configurations are described in the following section. Conventional amplifier configurations employ singlepass amplification. With a double-pass configuration, the signal is amplified twice in the rare earth doped fiber under the same pumping conditions. This configuration, therefore, is very effective for a low-efficiency gain medium such as a PDF. Optimum Pump Wavelength and Pumping Scheme Considerations To achieve efficient pumping, it is useful to study the dependence of the gain on the pump wavelength [16,17,33,53] and on the pumping scheme [33,34] under both weak and strong input signals. In the following, we present calculated and measured characteristics obtained with a view to maximizing the efficiency of the PDFA. Figure 31 shows the measured pump wavelength dependence of the small-signal gain at 1.30 µm in a 15-m length of 500-ppm Pr-doped ZBLAN fiber [33]. The internal gain is maximum at the peak in the excitation spectrum near 1017 nm, and it decreases very slowly with pump wavelength on either side of this maximum. The gain remains within 3 dB of this maximum for pump wavelengths between 988 and 1033 nm, corresponding to a tolerance in pump wavelength of 45 nm.

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Figure 29

Gain coefficient of a Pr 3⫹-doped ZrF 4-based fluoride fiber measured as a function of scattering loss for two fibers with different ∆n values. (From Ref. 9.)

Figure 32 shows the calculated slope efficiency, normalized to the maximum efficiency (which occurs at a pump wavelength of 1017 nm), as a function of pump wavelength for an input signal of 0 dBm [17]. In this calculation, the PDF length is optimized for each pump wavelength. To obtain a normalized slope efficiency of 70% or more, the pump wavelength must fall within the range of 980 to 1051 nm. This region is wide enough that an Nd:YLF solid-state laser, operating at 1047 nm, a Yb:YAG solid-state laser, or a Yb-doped fiber laser, all can be used as a pump source for PDFAs, in addition to semiconductor lasers operating at the optimum pump wavelength of approximately 1017 nm. The effect of the pumping scheme on the PDFA performance can be seen in Figure 33, in which the measured and calculated internal small-signal gain at 1.30 µm are plotted versus pump power for a forward-pumped and a bidirectionally pumped PDFA [33,34]. In the bidirectionally pumped device, the same pump power is launched in both ends. Both devices are pumped with the same total pump power. The gain of the bidirectionally pumped PFDA is larger than that of the forward-pumped device (0.24 versus 0.21 dB/ mW). Figure 34 compares the pump power dependence of the output signal power of these two amplifiers [33,34]. It is seen that for pump powers higher than 100 mW, the output signal power is approximately twice as large for the bidirectionally pumped PFDA. The bidirectional pump scheme, therefore, is also advantageous by providing a substantially higher output signal power. This improvement can be explained as follows. Two processes—pump ESA and cooperative upconversion—reduce the population of the 1G 4 metastable level without contributing to the stimulated transition at 1.3 µm. Both processes depend on the square of the pump intensity. Because pump ESA is a two-step excitation


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(a)

(b) Measured characteristics of a highly efficient Pr 3⫹-doped ZrF 4-based fluoride fiber amplifier: (a) loss spectrum; (b) gain coefficient dependence on pump power. (From Ref. 9.)

Figure 30

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Figure 31 Measured pump wavelength dependence of the small-signal internal gain in a Prdoped ZBLAN fiber amplifier, illustrating the broad range of usable pump wavelengths. (From Ref. 33.)

Figure 32

Calculated gain slope efficiency of a Pr-doped ZBLAN fiber amplifier, normalized to its maximum value at a pump wavelength of 1017 nm, as a function of pump wavelength. The solid horizontal lines identify the pump-wavelength bandwidth for 90, 80, and 70% efficiency, and the dashed lines point to the wavelengths of potential pump lasers. (From Ref. 17.)


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Figure 33

Measured and calculated pump power dependence of the internal gain of a forwardpumped and a bidirectionally pumped 1.30-µm Pr-doped ZBLAN fiber amplifier. (From Ref. 33,34.)

process, the population of the 3P 0 level is proportional to the square of the pump power. As a result, the 1G 4 population does not increase linearly with pump intensity owing to the pump ESA. Pump cooperative upconversion (see Fig. 13) also prevents the 1G 4 population from increasing in proportion to the pump power, because the number of ions per unit time excited from the 1G 4 level to other levels is proportional to the square of the

Figure 34

Measured pump power dependence of the output signal power in a forward-pumped and a bidirectionally pumped 1.30-µm Pr-doped ZBLAN fiber amplifier. (From Refs. 33, 34.)

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G 4 population, that is, the square of pump intensity. Hence, there is a greater population reduction, due to both pump ESA and upconversion, in regions of the fiber where the pump power is strong than in regions where it is weak. For a constant total pump power launched in the fiber, the total number of Pr 3⫹ ions excited to the 1G 4 level is thus larger in a bidirectionally pumped fiber than that in a unidirectionally pumped PDFA. In addition, the increase in the population of the 1G 4 level in a bidirectionally pumped amplifier is mainly due to the suppression of cooperative upconversion, because to achieve a high gain coefficient the Pr 3⫹ concentration must be usually less than 500 ppm. These results show that the bidirectional pump scheme is effective in extracting the full potential of a PDFA and is an appropriate configuration to construct an efficient PDFA module. Key Technologies for PDFA Module Fiber Fabrication Glass Melting. The key requirements when melting glass to fabricate low-loss fluorozirconate fibers are as follows: 1. Avoid contamination of the starting materials and of the glass melt by impurities such as water, transition metals, and organic compounds. 2. Eliminate any resultant water, hydroxyl ions, and oxides in the starting materials and reduced zirconium ions in the glass melt. To meet these requirements, the glasses are processed in glove boxes, and fluorinating agents are used when the glass is melted. To avoid contact with the environment, a dry clean inert gas atmosphere is used when storing the raw materials, weighing and batching the fluoride powders, and melting and casting the glasses [54,55]. Figure 35 is a schematic of a typical glass synthesis apparatus, consisting of a melting furnace, two glove boxes, and an exhaust box. During glass preparation, the furnace and boxes are purged with a dry gas, generally nitrogen or argon vaporized from the liquid phase. This dry and clean atmosphere processing is effective in reducing OH⫺ absorption losses in the fiber. Ammonium bifluoride (NH 4 ⋅ HF 2 ) is used as a fluorinating agent to eliminate residual oxides present in the starting materials and OH⫺ adsorbed at their surface. Oxygen gas can be introduced to suppress the formation of reduced Zr.

Figure 35

Typical apparatus for melting fluoride glass.


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Thermodynamic calculations have shown that the fluorination process using NH 4 ⋅ HF 2 corresponds to a wet HF atmosphere in which the hydrated system is stable [56]. This indicates that it is difficult to achieve complete deoxygenation using NH 4 ⋅ HF 2. To suppress oxide formation in glasses, dry fluorination is desirable. The use of HF gas can produce such a dry atmosphere. Fluorination with HF gas, however, is not sufficient because it is less active than NH 4 ⋅ HF 2. One of the best ways to overcome this is to use both HF and NH 4 ⋅ HF 2 [56]. The presence of reduced Zr, which is indicated when the glass is gray or contains a black phase, causes optical absorption loss in the short-wavelength region that can extend to the 2-µm region [57]. Reduced Zr is probably produced by one of two mechanisms. One is the elimination of fluorine by the following reaction [57]: ZrF 4 → ZrF 2 ⫹ F2

(51)

The other mechanism is the elimination of oxygen, which often occurs during dehydration involving NH 4 ⋅ HF 2 [58]. Therefore, NH 4 ⋅ HF 2 can reduce the oxide content, but it also produces a lot of reduced Zr. Photoluminescence observations and loss measurements have shown that reduced Zr can be successfully eliminated by introducing O 2 gas into the glass-melting atmosphere. This process results in a reduction in the absorption loss in the short-wavelength region, as shown in Figure 36. In practice, fluoride glasses for optical fibers are ordinarily prepared under an oxygen gas flow to oxidize the reduced Zr.

Figure 36 Measured transmission loss spectra of ZrF 4-based fluoride fibers prepared in a glassmelting atmosphere of N 2 and N 2 ⫹ O 2. (From Ref. 57.)

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Reactive atmosphere processing (RAP) using an active gas, such as CF 4, NF 3, or SF 6 effectively reduces the presence of OH⫺ and oxides in glasses [59,60]. In the melting process using RAP, carbon crucibles must be used because noble metal crucibles react with these gases. These reagents are good fluorinating agents because of their high activity, but the use of carbon crucibles often leads to the glass becoming contaminated with carbon particles. A typical melting process with ZrF 4-based glass using noble-metal crucibles and NH 4 ⋅ HF 2 as a fluorinating agent is the following. Batches of starting materials with small amounts of NH 4 ⋅ HF 2 are placed in gold or platinum crucibles in a weighing glove box. The crucibles are transferred into a melting glove box to exclude the fine powders generated during the weighing and batching processes from the melting environment. The crucibles are then placed in the melting furnace located in the second glove box and held at 300–400°C. At this stage, the starting materials are fluorinated by NH 4 ⋅ HF 2 (and HF gas). The furnace temperature is then raised to 800–900°C to fuse and melt the materials, and is held at this temperature for a period to homogenize the melt. At this stage, the remaining NH 4 ⋅ HF 2 has been vaporized out of the crucibles. Finally, the melt is cooled down to near the liquidus temperature (650–700°C) to enhance the cooling rate during the final casting and quenching by reducing the heat of the melt. Oxygen is introduced at this stage. Preform Fabrication. Fluoride glass fiber preforms are prepared by a glass-melting process using crucibles followed by a mold-casting process that enables the melt to be rapidly quenched. The casting process in a metal mold makes use of the very low viscosity of fluoride glass melts that correspond to its fairly low glass-forming tendency and is necessary to form high-quality fluoride glass for optical fiber. Built-in casting [61], modified built-in casting [62], suction casting [63], rotational casting [64], and extrusion methods [65] are established preform fabrication techniques for preparing multimode fibers with low losses of 1–10 dB/km. With all these methods, except extrusion, preforms with a waveguide structure are directly formed inside molds. Of these techniques, built-in casting, suction casting, and rotational casting are used mainly for PDF fabrication. 1. Built-in casting: This was the first technique used to prepare a fiber preform with a fluoride glass waveguide structure in both the core and cladding. Figure 37 illustrates the built-in casting process [66]. The cladding glass melt is cast into a cylindrical mold preheated near the glass transition temperature, and the mold is then immediately inverted.

Figure 37

Built-in casting process used to fabricate ZrF 4-based fluoride fibers. (From Ref. 66.)


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The melt in the central part of the mold flows out and the solidified skin of glass formed on the inside walls is left behind as a cladding glass tube. The core glass melt is then cast into the cladding tube to form the core part, and the assembly is cooled and annealed. Although preforms fabricated by this technique typically have a core diameter that tapers along its length, they have a smooth core-cladding interface because of surface tension at the liquid–liquid interface. It is, therefore, possible to obtain fibers with a good optical quality. 2. Suction casting: This casting method (Figure 38), involves the rapid quenching of the core and cladding melt and allows the preparation of a preform with a fairly small core/cladding diameter ratio, although the preform also has a tapered core [63]. The suction casting technique uses a specially designed cylindrical mold with a reservoir at the bottom. The cladding glass melt is poured into the mold first. The core glass melt is then poured onto the cladding glass before the latter has completely solidified. Significant volume reduction occurs during cooling. When this cladding glass volume reduction occurs in the reservoir, a cylindrical cladding tube is formed in the mold, which produces a suction effect on the core melt. The core/cladding diameter ratio and preform length can be controlled by selecting an appropriate reservoir volume and mold diameter. 3. Rotational casting: Rotational casting, which is based on an old established method used to form glass tubes, makes it easy to prepare a preform with excellent radial and longitudinal uniformity. The technique is illustrated in Fig. 39 [64]. The cladding glass melt is poured into a preheated mold, and the mold is swung into a horizontal position and rotated at speeds of more than 3000 rpm until the melt has cooled to form a glass tube. The resulting tube is highly concentric and its inner diameter can be precisely controlled by the initial volume of the injected glass. The core melt is then cast into this tube and the assembly is cooled and annealed. These fabrication techniques cannot be directly applied to single-mode fiber (SMF) preparation, because the core diameter is not small enough for single-mode waveguides. Jacketing methods are necessary to prepare a small and uniform core structure. Rotational casting is ordinarily used to form jacketing tubes for fabricating single-mode fluoride glass fibers.

Figure 38

Suction-casting process used to fabricate ZrF 4-based fluoride fibers.

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Figure 39

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Rotational-casting process used to fabricate ZrF 4-based fluoride fibers.

Technique for Connecting a Pr 3⫹-Doped Fluoride Fiber and a Silica Fiber Figure 40 shows a schematic PDFA module configuration using a high-NA silica fiber at the input and output ends. To achieve a low-loss butt joint between the silica and the fluoride fibers, the two fibers are selected to have essentially the same parameters, including ∆n, core diameter, and cutoff wavelength. The tilted V-groove connection, which is illustrated in Fig. 41a, is used when the PDF (and thus the silica fiber) has a high ∆n, as required for high-gain performance [44,47]. Both fibers are first mounted in a V-groove and their end faces are polished at an angle. The fibers are then carefully aligned and bonded with a UV-curable adhesive. The alignment accuracy for both fibers must typically be better than 0.1 µm to ensure a connection loss under 0.2 dB. Figure 41b shows the measured relation between the connection angle and the power reflection. To achieve a low reflection, for example less than ⫺60 dB, the angle must be at least 25 degrees. Figure 42 illustrates a variation of this technique, which involves angle-polishing of the two fiber ends and active alignment of the fibers [50]. A 0.2-dB loss and a reflection less than ⫺80 dB were demonstrated.

Figure 40

Configuration of a Pr-doped ZrF 4-based fluoride fiber amplifier module, showing connections to high-NA silica fibers and fiber components.


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(a)

(b)

Figure 41

Tilted V-groove connection technique: (a) connection between a fluoride and a silica fiber; (b) measured dependence of the connection Fresnel reflection on the fiber angle. (From Refs. 44,47.)

Furthermore, a low-loss connection can be obtained between the other end of the high-NA silica fiber and a conventional SMF (∆n ⫽ 0.3%), for example, as required to couple it to a fiber coupler or an optical isolator. This connection can be accomplished by fusion splicing using the thermally diffused expanded core technique [47–49]. The two silica fibers are first fused by a conventional fusion-splicing method. The splice region is then heated with either an electric arc or a propane–oxygen microburner to a temperature

Figure 42

Angled-polish and active-alignment technique used to connect a silica fiber and a doped fluoride fiber. (From Ref. 50.)

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of about 1700°C. This thermal treatment causes ion migration and local expansion of the mode fields of the fibers without deformation of the cladding, as illustrated in the inset of Fig. 43. For example, the mode-field diameter can broaden by 20 µm after 5–10 min of heating. Figure 43 shows the measured connection loss as a function of heating time [47]. After heating for several minutes, the connection loss decreases to less than 0.1 dB at both the pump and the signal wavelengths. This process yields low-loss and inexpensive fibre-to-fibre connections. It has resulted in a low-splicing loss (⬍ 0.3 dB) and a low reflection loss (⬍ ⫺60 dB) between a high-NA Pr 3⫹-doped fluoride fiber and a conventional silica fiber (∆n ⬇ 0.3%) [47]. Reliability of Fluoride Fiber Modules for PDFA Reliability is a serious issue in PDFAs because a fluoride fiber is relatively sensitive to environmental conditions. Static fatigue tests and lifetime estimates of fluoride fibers, taking into account zero-stress aging and the stress corrosion effect, have been carried out [66]. Figure 44 shows the estimated lifetime dependence on applied stress at 80°C and 50% relative humidity. In this figure, the dashed line indicates the lifetime estimated only from stress corrosion. The solid curve indicates the lifetime estimated from stress corrosion and zero-stress aging. The estimated lifetime in a practical stress region of about 100 MPa exceeds 25 years, which means that a fluoride fiber can be expected to withstand a practical environment [66,67]. A fiber module consisting of a fluoride fiber, a fiber spool, V-grooves, a silica fiber, and an aluminum case was tested according to Bellcore Technical Advisory TA-NWT-001221 [68]. Reliability test results, including those for mechanical tests based on Bellcore requirements, are summarized in Table 4 [69]. In these tests, the loss changes were small and the conditions more severe than the technical advisory TANWT-001312, which specifies the reliability requirements for optical fiber amplifiers [70]. These tests indicate that the fluoride fiber module designed for PDFAs has a good longterm reliability and sufficient mechanical strength for practical use in optical fiber amplifiers.

Figure 43

Thermally expanded core technique: dependence on heating time of the loss of a fusion splice between a standard silica fiber and a high-NA silica fiber. (From Ref. 47.)


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Figure 44

Estimated mean lifetime of a fluoride fiber as a function of applied stress, at 80°C and 50% relative humidity (RH). (From Ref. 67.)

Pump Sources As described in Section 12.3.3 on optimum pump wave lengths, because of the broad pump band of Pr-doped ZrF 4-based fluoride pump, source candidates for this material include laser diodes operating near 1017 nm, a 1047-nm–Nd:YLF solid-state laser, a 1029nm Yb:YAG solid-state laser, and a Yb3⫹-doped fiber laser operating between 1010 and 1030 nm, have been developed. Figure 45 shows the calculated output signal power of a PDFA as a function of launched pump power for these various pump wavelengths and for a 1064-nm Nd:YAG laser [16]. In this calculation, the PDF has a ∆n of 2.5% and its length is optimized for each pump wavelength. To achieve an output signal power in excess of 16 dBm, the launched pump power must be 440 mW for a 1017-nm–laser diode and a 1017-nm Yb-doped fiber laser, 470 mW for a Yb:YAG laser, 520 mW for a Nd: YLF laser, and 720 mW for a Nd:YAG laser. In addition, laser–diode-pumped Yb-doped and Nd/Yb-doped fiber lasers, which are now being developed, are interesting potential future pump sources because of their optimum wavelength. Nd:YAG is not a candidate for a pump source because the pump efficiency at 1064 nm is not sufficient to produce a practical amplifier module.

Table 4

Reliability Test Results of Fluoride Modules for PDFA

Test Temperature–humidity cycling Temperature cycling Damp Low Temperature Vibration Heat shock

Requirements

Samples

Trouble

⫺40°C–75°C/90%RH, 5 cycles

40

0

⫺40°C–75°C, 500 cycles 75°C/90% RH, 5000 h ⫺40°C, 500 h 10–2000 Hz, 3 directions, 12 cycles ⫺40°C–70°C, 20 cycles

11 11 11 11 11

0 0 0 0 0

Duration

300 cycles 2000 h 1200 h

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Figure 45

Calculated output signal power of a Pr-doped fiber amplifier as a function of launched pump power for the pump wavelengths available from various pump light sources. The dashed lines indicate the pump power required for each pump laser to produce a signal output of 16 dBm. (From Ref. 16.)

Table 5 provides a more detailed comparison of the performance of PDFA modules pumped with some of these sources. A 1017-nm semiconductor laser is a good candidate because its wavelength is optimum and it allows packaging of the amplifier in a compact module. However, the pump power that is required from it, although lower than for the other pump lasers, is high for this laser diode, and there is a reliability issue. In contrast, the MOPA laser diode is very powerful and can exceed the required pump power at the optimum pump wavelength, although reliability is again a potential problem. A laser– diode-pumped Nd:YLF laser can provide a high pump power, but it is larger than either a standard or MOPA laser diode module. The next developmental targets for this laser, therefore, are to reduce its size to approximately that of a microchip solid-state laser. Replacing the laser material by a Yb:YAG crystal would also advantageously move its wavelength closer to the optimum value of 1017 nm. Among the pump sources listed in Table 5, the laser diode module, the MOPA laser diode module, and the Nd:YLF laser are the most appealing, and they are already commercially available. In addition, it is generally considered that the laser diode module is suitable for use in a preamplifier, which must be small and exhibit a high signal gain. Similarly,the laser–diode-pumped Nd:YLF laser is deemed suitable to pump a booster amplifier, which requires a high output power. It may also be possible to use the MOPA in both these amplifiers. PDFA Module Configurations In the first stage of PDFA module development, various configurations pumped with a laser diode [11,12,16,42,47,52,71] or a laser–diode-pumped Nd:YLF laser [14,15,50] were investigated. Figures 46a through 46d show typical configurations: a single-pass configuration [12,42,71]; a double-pass configuration [52]; a cascade configuration using our laser

a

470

⬃700(?) 470 (Pump 0.98 µm, 800 mW)

1.03 1.00–1.15

460 (1.017 µm)

520

⬃800

1.047

400

⬃600

Encircled source indicates commercially available light source.

Yb laser Fiber laser (LD pump) Yb, Yb–Nd

MOPA-LD (fiber-coupled) Solid-state laser (LD pump) Nd:YLF laser

Required power (mW) 440

Maximum output power (into PDF) (mW)

1(?)

1(?)

1

1

3⬃4

Required number

PDFA (18 dBm)

1 ⬃ 200

1.017 (Optimum pump wavelength)

Lasing wavelength (µm)

Comparison of Pump Sources for PDFA Modules

Semiconductor-LD Standard LD module

Sourcea

Table 5

Large (?)

Large

Small

Small

Size

Size reduction (microchip solid laser structure)

Reliability

High power reliability

Problem

Future

Future

Now in use

Now in use

Now in use

Time scale

1.3-µm Fiber Amplifiers 725

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(a)

(b)

Figure 46

Typical configurations for 1.3-µm Pr-doped fluoride fiber amplifiers: (a) Single-pass configuration with four laser diode modules; (b) double-pass configuration with a single laser diode module; (c) cascade amplifier with four laser diode modules; (d) amplifier pumped bidirectionally with a Nd:YLF laser. (From Refs. a: 12, 42, 71, b: 52; c: 47; d: 14, 15 50.)


727

(c)

(d)

diodes [47]; and a PDFA that is pumped bidirectionally with an Nd:YLF laser [14,15,50], respectively. The single-pass configuration (see Fig. 46a) is the standard configuration used in current PDFAs. It has produced a signal gain of about 30 dB by using four InGaAs laser diodes delivering a pump power of about 100 mW each, and a polarization multiplexing module to combine their powers [12]. Recently, the pump power of the laser diode module has been increased to over 200 mW, and a PDFA module pumped by two laser diodes has achieved a signal gain of over 30 dB with this configuration, without a polarization multiplexing module [17]. The double-pass configuration using an optical circulator and a reflector (see Fig. 46b) is more practical for obtaining a higher gain at a lower pump power. The basic design idea is the same as that previously reported for the EDFA. Both the signal and pump are reflected by the reflector. The signal light is amplified in both the forward and backward directions. Hence, its small-signal gain coefficient is twice that of the single-pass configuration. The double-pass configuration has produced a gain coefficient of 0.4 dB/mW, which is the highest reported value, and a PDFA pumped with a single laser diode has been constructed with a 23-dB signal gain at a pump power of about 100 mW [52]. The cascade configuration (see Fig. 46c), which incorporates an isolator or an optical filter between the two PDFs, yields stable amplification characteristics and a higher maximum gain by suppressing the ASE in the PDF. This configuration has also been proposed for the EDFA to realize high-gain and low-noise characteristics. The optical isolator is used to eliminate ASE that backpropagates from the second stage toward the first stage. An optical bandpass filter is used to reduce the ASE traveling from

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one stage to the other. Therefore, the cascade configuration results in a significant improvement in the signal gain characteristics. It was used to construct the PDFA with the highest reported signal gain of 42 dB [47]. Furthermore, a bidirectional pump injected with a 3dB splitter is interesting to achieve efficient pumping with a single Nd:YLF laser. A PDFA module of this type has been demonstrated with a signal gain of over 30 dB and an output signal power of 18 dBm [50]. In spite of their high-gain performance, the afore-described configurations may induce additional noise owing to optical interaction between the laser diode modules, or by reflected pump light coupled back into the pump laser. When light is coupled with a pump laser source, either from itself or from another source operating at almost the same wavelength, the pump light becomes unstable and noise is induced in the radio frequency region [72]. This noise degrades the picture quality in video signal transmission systems that use a subcarrier multiplexed multichannel amplitude-modulated vestigial-sideband (AM–VSB), which is an important application of the PDFA module [72,73]. This problem can be solved by placing an optical isolator at the output of the pump source. In fact, an optical isolator that exhibits a low loss (less than 0.5 dB) in the PDF pump light wavelength region has recently been demonstrated [74]. However, a pump source using such an isolator has yet to be fabricated. To avoid these feedback-related difficulties, and although bidirectional pumping greatly improves the efficiency, recent PDFA modules basically employ unidirectional pumping [16,17,44,75,76]. Figure 47a illustrates the configurations of a recent, commercially available PDFA module pumped with two Nd:YLF lasers in a cascade configuration [44]. The optical isolator prevents interaction between the two Nd:YLF lasers. The gain characteristics of this amplifier are shown in Fig. 47b. Its maximum signal gain is 40.6 dB at 1.30 µm, its maximum output signal power is 20.1 dB for an input signal power of 0 dBm, and its noise figure is about 5 dB. A second commercially available PDFA module is shown in Fig. 48a. It is pumped in the backward direction with an MOPA laser diode [76]. As shown in Fig. 48b, this amplifier produces a maximum signal gain of 30.5 dB at 1.30 µm, and a noise figure of 5.5 dB. The signal output power is 18.5 and 15 dBm for signal input powers of 10 and 0 dBm, respectively. Recent Progress in PDFAs One general approach to improve the PDFA performance is to increase the quantum efficiency of 1.3-µm transition, which would significantly reduce the load that the pump source has to bear. As discussed earlier, multiphonon relaxation from the 1G 4 level reduces the gain coefficient. The most effective approach to reduce the multiphonon relaxation rate is to use host materials with a phonon energy as low as possible. Table 6 compares the spectroscopy parameters of the 1G 4 → 3H 5 transition of Pr 3⫹ ions in a variety of glasses [5,33,77–83]. The quantum efficiency has been investigated in InF 3-based fluoride glasses, mixed halide glasses with halide ions other than fluoride, and chalcogenide glasses. The lifetime of the 1G 4 level (τ 4 ) in chlorine-doped ZBLAN and InF 3-based fluoride glasses is increased to 150–180 µs, compared with 110 µs in ZBLAN. Therefore, the radiative quantum efficiency of the 1.3-µm emission transition, which is given by η ⫻ B, is roughly doubled compared to ZBLAN. The quantum efficiency in chalcogenide glasses is considerably larger, almost 20 times as large as in ZBLAN, so that a noticeable improvement in the quantum efficiency is expected in these glasses. Figure 49 shows the theoretical gain coefficient, plotted versus core diameter, for a Pr-doped InF 3-based fluoride fiber (IBSPZ), a Pr-doped chalcogenide glass fiber (La-Ga-S), and Pr-doped ZBLAN fiber [33]. A ∆n


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(a)

(b)

Figure 47 Dual-stage Nd:YLF-pumped 1.3-µm Pr-doped fluoride fiber amplifier module: (a) configuration, and (b) output signal power and noise figure dependence on input signal power. (From Ref. 44.)

of 3.7% was assumed in these calculations. In the InF 3-based fluoride fiber, a gain coefficient of more than 0.5 dB/mW can be expected, whereas in a chalcogenide fiber it reaches 2.3 dB/mW. These values are two and ten times higher, respectively, than the highest gain coefficient reported in a ZBLAN fiber (0.24 dB/mW). Consequently, the development of these new hosts in a reliable single-mode fiber form is a target of great significance in current PDFA research. Recently, a Pr-doped InF 3-based single-mode fluoride fiber was successfully fabricated using InF 3 –BaF 2 –SrF 2 –PbF 2 –CaF 2 (IBSPC), InF 3 /GaF 3, and PbF 2 /InF 3 glasses. Both the InF 3 /GaF 3 and PbF 2 /InF 3-based fluoride fibers had a particularly high ∆n value

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(a)

(b)

Figure 48 1.3-µm Pr-doped fluoride fiber amplifier module pumped with a MOPA laser diode: (a) configuration; (b) output signal power and noise figure dependence on input signal power. (From Ref. 76.) of 6%, and they produced a high-signal gain coefficient in excess of 0.3 dB/mW, although their scattering losses need to be further reduced [80–82]. These efficient gain fibers make it possible to use laser diodes as a pump source. As a result, the PDFA module can be small, as shown in the plug-in module of Figure 50, which used a PbF 2 /InF 3-based fluoride fiber. However, because of their high ∆n these fibers may be difficult to splice to a silica


Table 6

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Spectroscopy Parameters of the 1G4 → 3H5 Transition of Pr ⫹3 Ions in a Variety of

Glasses

ZrF4-based fluoride ZBLAN Mixed halide ZBLAN-Cl InF3-based fluoride IZBSC IBSPZ InF3 /GaF3 PbF2 /InF3 Chalcogenide La-Ga-S As-S Ge-Ga-S

τ4a (µs)

σ42 (10⫺21 cm2)

ηb(%)

Bc

η⫻B

Ref.

110 180

3.48 3.75

3.4 6.5

0.64 0.61

2.18 1.98

5, 33, 77 33, 77

150 180 186 172

3.79 3.90 4.40 3.89

5.1 6.2 8.6 6.1

0.65 0.65 0.64 0.67

3.96 3.32 5.50 4.08

33, 77 33, 77 80 81, 82

300 250 354

10.5

60

0.6

36

13.3

71.7

0.57

40.87

78 83 83

τ4, life time. η, radiative quantum efficiency. B, branching ratio.

fiber. Similarly, a Pr-doped AsS-based chalcogenide fiber has achieved fluorescence at 1.3 µm [83]. The emission lifetime was about 250 µs for a 500-ppm Pr concentration, but gain could not be achieved because the loss was too high. Assuming that an attenuation loss of 0.48 dB/m at 1.02 µm and 0.17 dB/m at 1.3 µm can be achieved (which are the lowest losses observed for AsS fibers), it can be calculated that a gain coefficient of more than 1 dB/mW could be obtained. If the problem of scattering loss is successfully resolved, Pr 3⫹-doped AsS fibers can be expected to lead to efficient fiber amplifiers.

Figure 49 Calculated gain coefficient versus core diameter for Pr 3⫹-doped amplifiers made of an InF 3-based fluoride fiber (IBSPZ), a chalcogenide glass fiber (La–Ga–S), and a ZrF 4-based fluoride fiber. (From Ref. 33.)

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Figure 50

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Photograph of a plug-in Pr 3⫹-doped fluoride fiber amplifier module.

12.3.4 Applications in Telecommunication Systems Multichannel AM–VSB Video Signal Transmission PDFAs can be employed in CATV systems operating in the 1.3-µm band. Several CATV transmission experiments have been undertaken using PDFAs [72,73,84,85]. Figure 51 shows an experimental setup for an AM–VSB analog transmission system [16]. The signal source was a DFB laser operating at 1302 nm with an output power of 6.5 dBm. Forty channel carriers ranging from 91.25 to 403.25 MHz directly modulated the DFB laser with a modulation depth of 5.6%/channel. The laser output was amplified by the PDFA and attenuated with a variable optical attenuator. The carrier/noise ratio (CNR) and the composite second-order (CSO), composite triple-beat (CTB), and cross-modulation (XM) distortion characteristics, were measured for three carrier frequencies (91.25, 211.25, and

Figure 51

Experimental setup of an AM-VSB (amplitude-modulated vestigial-sideband) video analog transmission system.


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Figure 52

Carrier-to-noise ratio (CNR) measured against loss budget for the transmission system of Figure 51, tested with and without the PDFA. (From Ref. 85.)

403.25 MHz) using an RF spectrum analyzer. Figure 52 shows the CNR at 403.25 MHz as a function of the average received power (or loss budget) with and without a PDFA. The CNR was the same in the three measured channels. The loss budget improvement for a 52-dB CNR was 10 dB. The noise figure (NF), estimated from the CNR degradation, was 9.8 dB. The worst measured distortion values are summarized in Table 7. These values almost met the CATV trunk line specifications, and the difference in picture quality before and after PDFA amplification was imperceptible in subjective tests. This experiment indicates that a PDFA can improve the loss budget by 10 dB for a 52-dB CNR. 10-Gbit/s Digital Transmission A PDFA has been used in an experimental 10-Gbit/s digital transmission [44,73,86]. The 10-Gbit/s signal was successfully transmitted over 110.8 km of standard single-mode fiber Table 7 Worst Measured Distortions Values of an AM–VSB Analog Transmission Systema Carrier frequency (MHz) 403.25

CNR (dB) CSO (dB) CTB (dB) XM (dB) a

91.25 With PDFA

211.25 With PDFA

Without PDFA

With PDFA

51.6 71.7 70.2 71.5

51.3 69.2 68.4 65.6

55.9 63.5 69.9 63.7

52.1 66.5 67.8 60.2

Optical modoulation depth: 7.1%.

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with a PDFA used as a booster amplifier [44,86]. The transmitter was a strained MQW DFB laser operating at 1.315 µm. The laser was directly modulated using a nonreturn to zero (NRZ) pseudorandom signal with a pattern length of 223 ⫺ 1, and the output power was ⫺1 dBm. The transmitted signal was received by an APD with an average received power of ⫺25.4 dBm. Figure 53 shows the bit error rate (BER) performance for the test system and for a 2-m fiber. This result indicates that 10-Gbit/s signal transmission over 100 km can be achieved without an increase in the average receiver power penalty. WDM Transmission A 1300-nm WDM system transmission experiment employing a PDFA has been demonstrated [87]. The 1300-nm band, or second window, is a promising option to widen the signal wavelength region for WDM transmission. Although the fiber has a relatively high loss (⬃0.35 dB/km) in this band,dispersion is almost zero in the widely installed standard 1.3-µm SMF, as shown in Fig. 54. Therefore, optical transmission using this region has the merit that high-speed signals of about 10 Gbit/s can be transmitted without dispersion compensation over middle-distance or short-distance optical networks. One of the advantages of PDFAs over semiconductor or Raman amplifiers is that WDM channels can be amplified without interchannel cross talk, and the amplification characteristics have little polarization dependence. Figure 55a shows the schematic of a dual-stage PDFA comprising two PDFs separated by a fiber Bragg grating acting as a gain equalizer [87]. Each fiber was pumped with a laser–diode-pumped Nd:YLF laser, in the forward and backward direction, respectively. The gain and noise figure spectra of this PDFA are shown in Fig. 55b. A flat gain of 28 dB was achieved from 1290 to 1310 nm (20 nm) with a gain

Figure 53

Bit error-rate performance of a 10-Gbit/s digital signal transmission system using a PDFA module as a booster amplifier. (From Ref. 44.)


735

Figure 54

Loss and dispersion of a typical single-mode fiber, and amplification bands of the Prdoped, Tm-doped, and Er-doped fiber amplifiers. (From Ref. 87.)

variation of 1 dB. The output power was near ⫹16 dBm for a signal input of ⫺12 dBm. The NF was less than 7 dB at wavelengths shorter than 1306 nm (see Fig. 55b), which means that the usable wavelength range stretches from 1290 to 1306 nm (16 nm). The NF increase above 1290 nm is due to GSA of the Pr ions. The NF of the dual-stage amplifier was almost the same as that of the first-stage amplifier, and the gain equalizer (GEQ) caused no NF increase. Using this amplifier, an eight-channel WDM transmission experiment in an SMF was performed. A schematic diagram of the experimental setup is shown in Fig. 56. Because the dispersion of the fiber near 1300 nm is close to zero, four-wave mixing (FWM) might occur and degrade the signals by inducing cross talk between the channels. To avoid this problem, unequal channel spacings were employed (see Fig. 56). The frequency slot and the minimum channel separation were set at 40 and 200 GHz, respectively. The eight signals were multiplexed using a 1 ⫻ 8 fiber coupler, then modulated together with a 10Gbit/s pseudorandom bit stream (PRBS) with a length of 223 ⫺ 1. They were then boosted by the PDFA and input to the transmission fiber. The transmission line consisted of three 80-km spans of SMF separated by two in-line PDFAs. The signal power launched into each SMF span was set at ⫹6 dBm/channel. The loss of the 80-km SMF was 27–28 dB, and the zero-dispersion wavelength ranged from 1308 to 1311 nm. The transmitted signals were selected with a tunable optical filter and input into a preamplifier. The ASE was eliminated using a tunable filter with a full width at half maximum of 72 GHz, and input into a PIN-photodetector and BER testing equipment. Figure 57 shows the optical spectra at the input (top graph) and output (bottom graph) of the 240-km SMF transmission line. The power deviation between channels after transmission was close to 2.5 dB. This deviation was not only due to the gain deviation of 1 dB of the in-line amplifiers, but also to the fiber loss variation of ⫺0.05 dB/nm km⫺1 across the signal band. No new components due to FWM were observed, even though the signal input power was as high as ⫹6 dBm/channel. Figure 58 shows the BER perfor-

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(a)

(b)

Figure 55 (a) Diagram of a dual-stage Pr-doped fiber amplifier used for a WDM transmission system, in which the stages are separated by a fiber Bragg grating (GEQ); (b) gain and noise figure spectra of the gain-flattened PDFA of diagram (a). (From Ref. 87.)

Figure 56

Experimental schematic of a 10 Gbit/s eight-channel 1.3-µm WDM transmission system using a booster PDFA and two in-line PDFAs. (From Ref. 87.)


737

Figure 57

Optical power spectra of the eight channels of the 1.3-µm transmission system of Figure 56, measured before and after transmission. (From Ref. 87.)

Figure 58

Bit error rate of performance of the 1.3-µm WDM transmission system of Figure 56. (From Ref. 87.)

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Figure 59 Eye diagram of the 1.3-µm WDM transmission system of Figure 56. (From Ref. 87.) mance. All eight signals were successfully transmitted with power penalties of less than 2 dB. These penalties, which led to optical signal-to-noise ratio degradation, were caused by the in-line amplifiers. The eye diagrams of three representative channels are reproduced in Figure 59. The upper portion of the diagrams are thick owing to signal–ASE beat noise. The eye diagrams were open in spite of the absence of dispersion compensation, and even though the waveform was slightly degraded by either SPM or XPM. 12.4 THULIUM-DOPED FIBER AMPLIFIERS Fiber amplifiers operating in the 1.4- and 1.65-µm band must be developed to make better use of the vast bandwidth of optical fibers. Specifically, the 1.65-µm–band amplifier may be used for an optical transmission line-monitoring system [88,89]. A thulium-doped fiber amplifier (TDFA) has been investigated with a view to amplifying 1.4- and 1.65-µm signals. Efficient amplification in both bands has been demonstrated by using ZrF 4-based fluoride glass as the host for Tm3⫹. In this section, we describe the principle of amplification in TDFAs and the basic characteristics of these amplifiers in both the 1.4- and 1.65µm bands. 12.4.1 1.4-␮m and 1.65-␮m TDFA Amplification Principle Figure 60 shows the Tm3⫹ energy level diagram, including the lifetime of the metastable levels. Amplification in the 1.4-µm band is based on the four-level transition from the 3 H 4 level to the 3F 4 level, whereas amplification in the 1.6-µm band is based on the three-


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Figure 60

Energy level diagram of Tm3⫹ showing pump bands, amplification bands, and lifetimes in a fluoride glass.

level transition from the 3F 4 level to the 3H 6 level [90–92]. ZrF 4-based fluoride glasses are used as fiber materials to obtain efficient amplification. This is achieved by suppressing the nonradiative transition from the 3H 4 level to the 3H 5 for 1.4-µm amplification, and by increasing the fluorescence lifetime of the 3F 4 level from approximately 0.5 ms in silica glass to about 10 ms in ZBLAN for 1.6-µm amplification. However, other problems must be overcome to achieve practical TDFAs for both amplification bands. In the following, we describe these issues and the solutions that have been investigated. The main difficulty with the 1.4-µm Tm3⫹-doped fiber amplifier is that amplification is generally limited because the lifetime of the 3H 4 level (1.7 ms) is shorter than that of the 3F 4 lower level (11 ms), which makes it a self-terminating laser system. Therefore, it is difficult to create a population inversion between the 3H 4 and 3F 4 levels. To achieve a high gain, the lower level must be depopulated. Three approaches have been proposed to solve this problem. One is co-lasing on the 3 F 4 – 3H 6 transition, which corresponds to an emission at 1.8 µm [90,93,94]. The population density of the 3F 4 level is then reduced by stimulated emission of the laser oscillation close to 1.8 µm. The second approach utilizes 1.06-µm upconversion pumping [95]. An Nd:YAG laser operated at 1.06 µm excites ions in the ground state 3H 6 to the 3H 5 level, from which they decay rapidly to the 3F 4 level. A second 1.06-µm pump photon then excites the Tm3⫹ ions in the 3F 4 level to the 3F 2 level, from which they decay through nonradiative relaxation to the 3H 4 level. As a result, the 3F 4 level is depopulated and the 3 H 4 level is populated, the latter being obviously beneficial. In this upconversion-pumping method, the 1.4-µm signal is amplified as in a three-level system that uses the 3F 4 level as the virtual ground state. The third approach is to co-dope the fiber with acceptor ions [96–100] as illustrated in Fig. 61 with Ho3⫹. The 3F 4 level is depopulated as a result of energy transfer to the acceptor ions, have to the 5I 7 level of Ho3⫹ ions. The Ho3⫹ ion is one of the most efficient acceptor ions, because it shortens the lifetime of the 3F 4 level of Tm3⫹, but does not shorten

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Schematics of two methods to reduce the population of the 3F 4 level of Tm3⫹ in ZBLAN: (a) 1.06-µm upconversion pumping; (b) energy transfer to Ho3⫹ ions in the co-doping method. (From Refs. a: 93; b: 94.)

Figure 61

the lifetime of the 3H 4 level [96]. For example, by adding 1 wt% of Ho to a ZrF 4-based fluoride glass doped with 0.05 wt% of Tm, the lifetime of the 3F 4 level was greatly reduced, from 11 to 1.2 ms, whereas the lifetime of the 3H 4 level was only slightly reduced, from 1.71 to 1.48 ms [96]. Tb3⫹ is also used as an acceptor ion. Tm3⫹ ions excited in the 3F 4 level transfer their energy to the 7F 0 level of Tb3⫹ ions. It has been reported that the lifetimes of the 3H 4 and 3F 4 levels of Tm3⫹ are 0.5 and 0.43 ms, respectively, with 0.1 wt% Tm3⫹ and 1 wt% Tb3⫹ [97]. The advantage of this co-doping method is that a highpower commercial 0.8-µm laser diode can be used as a pump source. Of the three foregoing approaches, 1.06-µm upconversion pumping and co-doping with Ho3⫹ both have already been applied to TDFAs to obtain efficient 1.4-µm amplification. In contrast, the main problem with the 1.65-µm Tm3⫹-doped fiber amplifier, which is pumped in the 1.2-µm pump band (3H 6 → 3H 5 ), is that amplification is limited by the large ASE or laser oscillation close to 1.8 µm [101,102]. Figure 62 shows the absorption and emission cross sections of the 3F 4 → 3H 6 transition of Tm3⫹ in ZrF 4-based fluoride glass [103]. The emission cross-section spectrum is very wide, stretching from 1.6 to 2.0 µm. The high-gain region is from 1.75 to 2.0 µm, at which the emission cross section is larger than the absorption cross section. Therefore, 1.65-µm amplification is always accompanied by a large ASE power and often by laser oscillation close to 1.8 µm, which greatly reduces the gain in the 1.6-µm band. Doping of the cladding with terbium ions has been proposed as a way of overcoming these problems [103]. The energy level diagram and absorption spectrum of Tb3⫹ ions are shown in Figs. 63a and b, respectively. Tb3⫹ exhibits a large absorption from 1.75 to over 2.0 µm, which is related the 7F 6 → 7F 0 transition, and a small absorption near 1.6 µm. Therefore, the large ASE or laser power near 1.8 µm are absorbed by the Tb3⫹ ions and efficient amplification becomes possible. The cladding is doped instead of the core to avoid cross-relaxation between Tm3⫹ ions in the 3F 4 level and Tb3⫹ ions. The effectiveness


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Absorption and emission cross-section spectra of the 3F 4 → 3H 6 transition of Tm3⫹doped ZrF 4-based fluoride glass. (From Ref. 101.)

Figure 62

of this method is illustrated in Fig. 64, which compares the ASE spectrum of a standard Tm-doped ZBLAN fiber with that of a Tm-doped ZBLAN fiber with a Tb3⫹-doped cladding [103]. The peak of the ASE from the Tm–Tb-doped fiber is shifted to shorter wavelengths owing to effective absorption of the unwanted ASE close to 1.8 µm in the cladding. For reference, readers interested in theoretical models of the TDFA can consult Ref. [95] for 1.4-µm amplification and Ref. [103] for 1.65-µm amplification. 12.4.2 Basic Amplification Characteristics of 1.4 ␮m-band TDFA In this section, we describe and compare the basic characteristics of 1.4-µm Tm3⫹-doped fluoride fiber amplifiers using either the 1.06-µm upconversion pumping method or codoping with Ho3⫹. Figure 65 shows the measured gain spectra of a Tm3⫹-doped fluoride fiber amplifier with upconversion pumping and 2000 ppm of Tm3⫹ in the core, and a Tm3⫹ –Ho3⫹-doped fluoride fiber amplifier with 500 ppm of Tm3⫹ and 10,000 ppm of Ho3⫹ in the core [104]. Both devices have wide gain spectra that cover the entire 1.4-µm band. These spectra are much wider than the gain spectrum of the Tm3⫹-doped fluoride fiber amplifier pumped at 0.79 µm. As explained earlier, this is because in the upconversion and the Tm3⫹ –Ho3⫹-doped amplifiers the 3F 4 level is effectively depopulated and 1.4-µm absorption from the 3F 4 level to the 3H 4 is much smaller than in the 0.79-µm–pumped amplifier. Figure 66a shows the noise figure and small-signal gain spectra of a 1.4-µm TDFA using the 1.06-µm–band upconversion pumping method, and Figure 66b the noise figure spectrum of a 1.4-µm TDFA co-doped with Ho3⫹ [95,96]. In both amplifiers the NF exhibits a minimum near 1.48 µm, and it is only 3.5 dB in the upconversion amplifier. The increase in NF for signal wavelengths below 1.48 µm is due to the signal absorption from the 3F 4 to the 3H 4 level, whereas the increase in the region above 1.48 µm is due to the

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(b) (a) Energy-level diagram and (b) absorption spectrum near 1.8–2 µm of Tb3⫹ ions in ZBLAN glass. (From Ref. 101.)

Figure 63

GSA to the 3F 4 level. Comparison between Fig. 66a and 66b indicates that the NF of the Tm3⫹ –Ho3⫹-doped amplifier is higher than that of the upconversion amplifier. This is because of signal absorption from the 3F 4 level in the Tm3⫹ –Ho3⫹-doped amplifier. In contrast, in the upconversion amplifier there is almost no signal absorption from that level because almost all the Tm3⫹ ions in the 3F 4 level are excited to the 3H 4 level.

Measured ASE spectrum of a Tm3⫹-doped ZrF 4-based fluoride fiber with and without present in the cladding. (From Ref. 101.)

Figure 64 Tb

3⫹

Figure 65 Measured gain spectra of three different types of Tm3⫹-doped fluoride fiber amplifiers; namely, a standard TDFA, a TDFA using upconversion pumping, and a TDFA co-doped with Ho3⫹. (From Ref. 102.) 743

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(b)

Figure 66 (a) Measured noise spectrum and small-signal gain of 1.4-µm TDFA using 1.06-µm upconversion pumping; (b) measured noise spectrum of a 1.4-µm TDFA co-doped with Ho3⫹. (From Refs. a: 93; b: 94.)

Figure 67 shows the small-signal gain dependence on pump power of 1.4-µm TDFAs using either upconversion pumping or Ho co-doping [105]. The small-signal gain efficiencies are almost the same for both amplifiers. The crucial difference between them is that the gain does not saturate as strongly in the upconversion amplifier. The increased saturation of the Tm3⫹ –Ho3⫹-doped amplifier is due to the large ASE in the 0.8-µm band


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Figure 67

Measured small-signal gain versus pump power of a 1.4-µm TDFAs based on 1.06µm upconversion pumping or co-doped with Ho3⫹. (From Ref. 102.)

(3H 4 → 3H 6 transition) produced by 0.79-µm pumping to the 3H 4 level. With 1.06-µm upconversion pumping, it is difficult to create a population inversion between the 3H 4 level and the ground state, and the problematic ASE in the 0.8-µm region does not occur. Similarly, the signal output power of the upconversion amplifier is much larger than that of the Tm3⫹ –Ho3⫹-doped fiber amplifier. For a pump power of 150 mW and a signal input power of 0 dBm, the output power of the upconversion amplifier is 15 dBm versus only 4.5 dBm for the Ho-co-doped amplifier. The reason is again the large ASE at about 0.8 µm in the latter, which consumes pump energy and reduces the signal output power [105]. The forgoing results demonstrate that the upconversion amplifier achieves a large gain, a wide-gain spectrum, a high-signal output power, and a low noise figure. The laser– diode-pumped Nd:YLF laser operated at 1.06 µm makes it possible to construct practical 1.4-µm–band TDFA modules. In contrast, the Ho-co-doped amplifier is advantageous in that it can be pumped with a commercial high-power GaAlAs laser diode, but it has the high ASE near 0.8 µm that must be suppressed to make it efficient. Recently, a 1.5-µm-band TDFA was proposed that employs a dual-wavelength pumping scheme [106]. Figure 68 describes its basic concept. The amplifier is pumped at 1.05 µm to benefit from upconversion pumping, but it is also pumped at 1.56 µm. As discussed earlier, upconversion pumping efficiently reduces the population of the 3H 4 level and increases that of the 3F 4 level. In homogeneously broadened materials, the gain coefficient per unit length is expressed as g(λ) ⫽ N U σ em (λ)-N Lσ abs (λ), where N U and N L are the population of the upper and lower laser levels, and σ em (λ) and σ abs (λ) are the emission and absorption cross-section spectra, respectively. Because N L is considered to be very small in a TDFA pumped by upconversion, the gain spectrum is essentially the same as

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Figure 68

Principle of dual-wavelength pumping in Tm3⫹-doped fluoride glass. (From Ref. 106.)

σ em (λ). This means that some additional method to control the gain spectrum of upconversion-pumped TDFAs is required. This is the role of the additional 1.56-µm pump, which can be understood as follows: 1. Gain shift: 1.56-µm pumping can increase the population of the lower laser level. Because σ abs (λ) is larger than σ em (λ) at shorter wavelengths, the result is a shift in the gain to longer wavelengths. Note that a longer fiber is necessary for efficient gain-shifted operation because of the small gain per unit length. 2. Gain enhancement: the 1.56-µm pump radiation assists the first step of the upconversion process and creates a population inversion more efficiently because its absorption cross section is one order of magnitude higher than at 1.05 µm. 3. Reduction in GSA loss at wavelengths longer than ⬃1500 nm: 1.56-µm pumping decreases the population of the ground-state manifold, which leads to a decrease in absorption at wavelengths longer than 1500 nm. A gain-shifted TDFA based on the foregoing principle was demonstrated using the experimental setup of Figure 69. This setup employed a three-stage configuration. The first stage was pumped in the forward direction by both a Yb-doped fiber laser at 1047 nm (330 mW) and an EDFA at 1555 nm (42 mW). The second and third stages were pumped together in a forward direction with a Yb:YAG laser at 1050 nm (395 mW) and 29 mW at 1547 nm. Figure 70 shows the small-signal gain spectrum of this and other

Figure 69

Schematic diagram of a three-stage gain-shifted TDFA based on the principle of Figure 68. (From Ref. 106.)


Figure 70

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Small-signal gain and noise figure of the gain-shifted TDFA of Figure 69. (From

Ref. 106.)

Figure 71

Calculated signal gain and noise figure of a 1.65-µm Tm-doped ZrF 4-based fluoride fiber at a signal wavelength of 1.65 µm, as a function of the Tb3⫹ concentration in the cladding. (From Refs. 101,102.)

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amplifiers. In the 1470- to 1510-nm band, the gain-shifted TDFA achieved a small-signal gain larger than 25 dB and a NF of about 5 dB, As expected, this wavelength region is greatly shifted compared with a conventional TDFA. This result also demonstrates that the power conversion efficiency can be improved 2.3 times at 1495 nm [106]. 12.4.3. Basic Amplification Characteristics of 1.65 ␮m-Band TDFA In this section, we describe the gain characteristics of a 1.65-µm-band TDFA with a Tb3⫹doped cladding. Figure 71 shows the calculated signal gain and NF of this amplifier at a signal wavelength of 1.65 µm, as function of the Tb3⫹ concentration [103–105]. In this calculation, the Tm3⫹ concentration is taken to be 0.2 wt%, and the fiber lengths are optimized for each Tb3⫹ concentration. As the Tb3⫹ concentration is increased, the gain increases up to a certain level, then decreases. This result confirms that efficient amplification

(a)

(b)

Figure 72

Two-stage 1.65-µm TDFA: (a) configuration; (b) measured small-signal gain versus pump power. (From Refs. 101,102.)


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is possible by doping Tb3⫹ ions in the cladding to suppress the ASE in the 1.75- to 2.0µm region, but that excessive doping reduces the gain because of the signal loss caused by the Tb3⫹ ions. The optimum Tb3⫹ concentration for achieving the highest small-signal gain is 0.4 wt%. Figure 71 also shows that the NF increases with increasing Tb3⫹ concentration, which is due to the increased signal loss caused by the Tb3⫹ ions. These predictions were implemented in the two-stage fiber amplifier configuration of Figure 72a, which used two lengths of a ZrF 4-based fluoride fiber with a Tb3⫹ concentration of 0.2 wt% in the core and a Tb3⫹ concentration of 0.4 wt% in the cladding. The small-signal–gain dependence on pump power of this amplifier is shown in Figure 72b. It produced a signal gain of 35 dB at a 1.65 µm, which is the highest reported value [103– 105]. However, the NF of this amplifier module is 8 dB. The difference between this value and the value of 5.9 dB predicted in Figure 71 is due to insertion loss. This noise figure is high because the Tb3⫹ concentration was optimized for only the signal gain. To achieve a practical high-gain and low-noise TDFA in the 1.65-µm band, the Tb3⫹ concentration must be optimized for both the signal gain and noise characteristics. 12.5 CONCLUSIONS This chapter reviews optical fluoride fiber amplifiers operating at 1.3, 1.4, and 1.65 µm. The development of 1.3-µm Nd-doped fiber amplifiers proved unsuccessful because of strong ESA and ASE buildup, in spite of clever optical improvements and extensive material studies. The Pr-doped fiber amplifier emerged as a promising alternative in 1991 and has been improved rapidly since then, even though its stimulated emission has a relatively low quantum efficiency. This disadvantage was overcome by identifying glass materials with low phonon energies and developing high-NA fiber fabrication technologies. As a result of this research and development, PDFAs with a high gain, low noise, high saturation output power, and high reliability are now on the verge of becoming practical commercial devices. This amplifier makes it possible to realize WDM transmission systems in the 1300-nm band. In addition, the PDFA could be used in CATV systems and metropolitan area networks employing standard single-mode fibers. Moreover, to meet the increasing demand for expanded transmission bandwidths, amplification in other wavelength regions, including the 1.4- and 1.65-µm bands, can be provided by the Tm-doped fluoride fiber amplifier, which could be a key device in the near future. As described in this chapter, the basic technologies for both PDFAs and TDFAs have matured to the point of being practical. REFERENCES 1. W. J. Miniscalco, L. J. Andrews, B. A. Thompson. 1.3 µm Fluoride fiber laser. Electron. Lett. 24:28–29 (1988). 2. M. C. Brierley, C. A. Millar. Amplification and lasing at 1350 nm in a neodymium doped fluorozirconate fibre. Electron. Lett. 24:438–439 (1988). 3. Y. Miyajima, T. Komukai, T. Sugawa. 1.31–1.36 µm Optical amplification in a Nd3⫹-doped fluorozirconate fibre. Electron. Lett. 26:194–195 (1990). 4. T. Sugawa, Y. Miyajima, T. Komukai. 10 dB Gain and high saturation power in a Nd3⫹doped fluorozirconate fibre amplifier. Electron. Lett. 26:2042–2044 (1990). 5. Y. Ohishi, T. Kanamori, T. Kitagawa, S. Takahashi, E. Snitzer, G. H. Sigel, Jr. Pr 3⫹-doped fluoride fiber amplifier operating at 1.31 µm. Proc. Opt. Fiber Commun. 1991: postdeadline paper PDP2.

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6. Y. Durteste, M. Monerie, J. Y. Allain, H. Poignant. Amplification and lasing at 1.3 µm in praseodymium-doped fluorozirconate fibres. Electron. Lett. 27:626–628 (1991). 7. S. F. Carter, D. Szebesta, S. T. Davey, R. Wyatt, M. C. Brierley, P. W. France. Amplification at 1.3 µm in a Pr 3⫹-doped single-mode fluorozirconate fibre. Electron. Lett. 27:628–629 (1991). 8. Y. Ohishi, T. Kanamori, T. Nishi, S. Takahashi. A high gain, high output saturation power Pr 3⫹-doped fluoride fiber amplifier operating at 1.3 µm. IEEE Photon. Technol. Lett. 3:715– 717 (1991). 9. T. Kanamori, Y. Terunuma, K. Fujiura, Y. Ohishi, S. Sudo. Fabrication of low-loss high∆n, Pr 3⫹-doped fluoride single-mode fibers for 1.3 µm optical amplifiers. Proceedings of 9th International Symposium on Non-oxide Glasses, 1994:74–79. 10. Y. Miyajima, T. Sugawa, Y. Fukasaku. 38.2 dB Amplification at 1.3 µm and possibility of 0.98 µm pumping in Pr 3⫹-doped fluoride fiber. Technical Digest of Optical Amplifiers and Their Applications, 1991: postdeadline paper PDP1. 11. Y. Ohishi, T. Kanamori, T. Temmyo, M. Wada, M. Yamada, M. Shimizu, K. Yashino, H. Hanafusa, M. Horiguchi, S. Takahashi. Laser diode pumped Pr 3⫹-doped and Pr 3⫹ –Yb3⫹-codoped fluoride fibre amplifiers operating at 1.3 µm. Electron. Lett. 27:1995–1996 (1991). 12. M. Shimizu, T. Kanamori, J. Temmyo, M. Wada, M. Yamada, Y. Terunuma, Y. Ohishi, S. Sudo. 28.3 dB gain 1.3 µm-band Pr-doped fluoride fiber amplifier module pumped by 1.017 µm InGaAs-LD’s. IEEE Photon. Technol. Lett. 5:654–657 (1993). 13. T. Whitley, R. Wyatt, D. Szebesta, S. Davey, J. R. Williams. Quarter watt output at 1.3 µm from a praseodymium doped fluoride fibre amplifier pumped with a diode-pumped Nd:YLF laser. Technical Digest of Optical Amplifiers and Their Applications, 1992: postdeadline paper PDP4. 14. T. Whitley, R. Lobbett, R. Wyatt, D. Szebesta. 5 Gbps transmission over 100 km of optical fiber using a directly modulated DFB laser and an engineered 1.3 micron Pr 3⫹-doped fluoride fiber power amplifier. Tech. Dig. Opt. Amplifiers Appl. 14:4–6, 1994; Paper WB1. 15. T. Whitley. A review of recent system demonstrations incorporating 1.3-µm praseodymiumdoped fluoride fiber amplifiers. IEEE J. Lightwave Technol. 13:744–760 (1995). 16. M. Yamada, M. Shimizu. Progress toward the telecommunication application of 1.3-µm praseodymium-doped fiber amplifiers. Tech. Dig. Opt. Amplifiers Appl. 14:18–21, 1994; WC1. 17. Y. Ohishi, T. Kanamori, K. Fujiura, Y. Nishida, M. Yamada, S. Sudo Recent progress in 1.3-µm fiber amplifiers. Proc. Opt. Fiber Commun. 2: 27, 1996; TuG1. 18. A. Bjarklev. Optical Fiber Amplifiers: Design and System Applications. Artech House, Boston, 1993. 19. J. E. Pedersen, M. C. Brierley. High saturation output power from a neodymium-doped fluoride fiber amplifier operating in the 1300 nm telecommunications window. Electron. Lett. 26:819–820 (1990). 20. M. L. Dakss, W. J. Miniscalco. Fundamental limits on Nd3⫹-doped fiber amplifier performance at 1.3 µm. IEEE Photon. Technol. Lett. 2:650–652 (1990). 21. J. E. Pedersen, M. Brierley, R. A. Lobbett. Noise characterization of a neodymium-doped fluoride fiber amplifier and its performance in a 2.4 Gb/s system. IEEE Photon. Technol. Lett. 2:750–752 (1990). 22. M. L. Dakss, W. J. Miniscalco. A large signal model and signal/noise ratio analysis for Nd3⫹doped fiber amplifiers at 1.3 µm. Conf. on Fiber Laser Sources and Amplifiers II. Proc. of SPIE 1373:111–124, (1990). 23. M. Øbro, B. Pedersen, A. Bjarklev, J. H. Povlsen, J. E. Pedersen. Highly improved fibre amplifier for operation around 1300 nm. Electron. Lett. 27:470–472 (1991). 24. M. C. Brierley, S. F. Carter, P. W. France, J. E. Pedersen. Amplification in the 1300 nm telecommunications window in a Nd-doped fluoride fibre. Electron. Lett. 26:329–330 (1990).


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25. S. A. Zemon, B. Pedersen, G. Lambert, W. J. Miniscalco, B. T. Hall, R. C. Folwefiler, B. A. Thompson, L. J. Andrews. Excited-state-absorption cross sections and amplifier modeling in the 1300-nm region for Nd-doped glasses. IEEE Photon. Technol. Lett. 4:224–227 (1992). 26. W. J. Miniscalco, B. A. Thompson, M. L. Dakss, S. A. Zemon, L. J. Andrews. The measurement and analysis of cross sections for rare earth doped glasses. Conference on Fiber Laser Sources and Amplifiers III. Proc. of SPIE 1581:80–90 (1991). 27. E. Ishikawa, H. Aoki, T. Yamashita, Y. Asahara. Laser emission and amplification at 1.3 µm in neodymium-doped fluorophosphate fiber. Electron. Lett. 28:1497–1499 (1992). 28. S. Zemon, W. J. Miniscalco, B. A. Thompson. Nd3⫹-doped fluoroberyllate glasses for fiber amplifiers at 1300 nm. Technical Digest of Optical Amplifiers and Their Applications 1992; WB3, 12–15. 29. E. R. M. Taylor, B. N. Samson, M. Naftaly, A. Jha, D. N. Payne, A 1300 nm Nd3⫹-doped glass amplifier. Proceeding of European Conference on Optical Communication, 1998; 45– 46. 30. M. Øbro, J. E. Pedersen, M. C. Brierley. Gain enhancement in Nd3⫹ doped ZBLAN fibre amplifier using mode coupling filter. Electron. Lett. 28:99–100 (1992). 31. A. Bjarklev, T. Rasmussen, H. Povlsen, O. Lumholt, K. Rottwitt, S. Dahl–Petersen, C. C. Larsen. 9 dB gain improvement of 1300 nm optical amplifier by amplified spontaneous emission suppressing fibre design. Electron. Lett. 27:1701–1702 (1991). 32. Y. Ohishi, T. Kanamori, T. Nishi, S. Takahashi E. Snitzer. Concentration effect on gain of Pr 3⫹-doped fluoride fiber for 1.3 µm amplification. IEEE Photon. Technol. Lett. 4:1338– 1341 (1992). 33. Y. Ohishi, T. Kanamori, M. Shimizu, M. Yamada, Y. Terunuma, J. Temmyo, M. Wada, S. Sudo, Praseodymium-doped fiber amplifier at 1.3 µm. Inst. Electron Information and Communication Engineers (IEICE) Trans. Commun. E77-B:421–440 (1994). 34. Y. Ohishi, T. Kanamori, Y. Terunuma, M. Shimizu, M. Yamada, S. Sudo. Investigation of efficient pump scheme for Pr 3⫹-doped fluoride fiber amplifier. IEEE Photon. Technol. Lett. 6:195–198 (1994). 35. B. Pedersen, W. J. Miniscalco, R. S. Quimby. Optimization of Pr 3⫹:ZBLAN fiber amplifiers. IEEE Photon. Technol. Lett. 4:446–448 (1992). 36. M. Yamada, M. Shimizu, Y. Ohishi, T. Kanamori, S. Sudo. Gain characteristics of Pr 3⫹doped fluoride fiber amplifier. Electron. Commun. Japan 77 (Part 2):75–87 (1994). 37. M. Yamada, M. Shimizu, Y. Ohishi, T. Kanamori, S. Sudo. Gain vs wavelength of 1.3 µmband fluoride fiber amplifier. Institute of Electron., Inform. Commun. Eng., general spring conference (IEICE), 1994; c-395. 38. T. Whitley, R. Wyatt, S. Fleming, D. Szebesta, J. R. Williams, S. T. Davey. Noise and crosstalk characteristics of a praseodymium doped fluoride fiber amplifier. Technical Digest of Optical Amplifiers and Their Applications, 1993: TuA2, 244–247. 39. T. Sugawa, Y. Miyajima. Noise characteristics of Pr 3⫹-doped fluoride fiber amplifier. Electron. Lett. 28:246–247 (1992). 40. Y. Ohishi, M. Yamada, A. Mori, T. Kanamori, M. Shimizu, S. Sudo. Effect of temperature on amplification characteristics of Pr 3⫹-doped fluoride fiber amplifiers. Opt. Lett. 20:383– 385 (1995). 41. C. B. Layne, W. H. Lowdermilk, M. J. Weber. Multiphonon relaxation of rare earth ions in oxide glass. Phys. Rev. B. 16:10–20 (1997). 42. M. Yamada, M. Shimizu, Y. Ohishi, T. Kanamori, M. Horiguchi, S. Takahashi, J. Temmyo, M. Wada. 15.1-dB-gain Pr 3⫹-doped fluoride fiber amplifier pumped by high power laser diode modules. Proc. Eur. Conf. Opt. Commun. 1:49–52, 1992: Mo A2.2. 43. M. Sugo, J. Temmyo, T. Nishiya, E. Kuramochi, T. Tamamura. 1.02-µm pump laser diodes with high power above 300 mW into single-mode fiber. Technical Digest of Optical Amplifiers and Their Applications, 1995: ThC3, 28–30.

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Index

Absorption anisotropy, 643–645, 647 Absorption cross section spectra Fluoride glasses Ce, 462 Dy, 468 Er, 65, 89, 470, 588, 595 Eu, 466 Ho, 469 Nd, 44, 197, 464, 483 Pr, 463, 697, 702 Sm, 465 Tb, 467, 742 Tm, 91, 471, 741 Yb, 472 Fluorophosphate glasses Er, 80, 89 Phosphate glasses Er, 65, 80, 89 Silicate glasses Er, 62, 65, 80, 82, 86, 89, 535, 560, 588, 595 Nd, 80 Yb, 145, 630 Temperature dependence, 660–663 Absorption spectra (See Absorption cross section spectra) Acousto-optic modulators (See Modulators) Additive pulse compression (See Modelocked fiber lasers) Amplifiers (See Fiber amplifiers)

Applications of fiber lasers and amplifiers (See also Communication systems) Applications of Fiber amplifiers, 459, 461 Fluoride fiber lasers, 171–172, 459, 500 Long-wavelength lasers, 459 Mode-locked fiber lasers, 430–438 Praseodymium-doped fiber amplifiers, 732–738 Silica fiber lasers, 51, 113, 134, 135, 149–150, 157, 126, 243, 261–262, 302–304 Data storage, 157 Fiber-optic gyroscope, 313–315, 335 Laser radar, 395, 488 LIDAR, 150 Medicine, 61, 149–150, 154, 315, 420, 459, 500 Optical clock recovery, 430–431 Optical communications, 134, 135, 488, 510 OTDR, 315, 505 Parametric wavelength conversion, 435– 438 Scanning delay lines, 433–434 Second-harmonic generation, 435–436 Sensing with fiber lasers Atmospheric, 150 Distributed, 243, 293 Magnetic field, 243, 302–303

755

756 [Applications of fiber lasers and amplifiers] Gas, 261–262, 500 Remote, 302, 488 Strain, 302–304 Temperature, 304 Signal regeneration, 430–432 Solitons, 243 Spectroscopy, 304 Terahertz generation, 395 Tests and measurements, 440 Wavelength division multiplexing, 432– 433 WDM systems, 315 ASE sources (See Superfluorescent fiber sources) ASE spectra (See Superfluorescent fiber sources; Erbium-doped fiber amplifiers) Auger processes, 39 Automatic gain control, 570, 589, 704 Background fiber loss (See Fiber loss) Boltzmann distribution, 538, 554 Borate glasses Branching ratios of Tm, 99, 100 Emission bandwidth of Er, 70 Neodymium-doped Branching ratios, 48, 53 Emission bandwidths, 49 Emission cross sections, 49 Peak emission wavelengths, 48 Nonradiative lifetimes in, 31–32 Radiative lifetimes in (See Radiative lifetime) Borosilicate glasses Neodymium-doped Branching ratios, 48, 53 Emission bandwidths, 49 Emission cross sections, 49 Peak emission wavelengths, 48 Radiative lifetime, 46 Transition linewidths in, 35 Branching ratios Definition, 26 Er-doped fluorides, 72–74 Nd in various glasses, 48, 52–53 Pr-doped chalcogenides, 515, 731 Pr-doped fluorides, 695, 731 Tb-doped chalcogenides, 518, 519 Tm-doped fluorides, 95–97, 99, 100 Tm in various glasses, 95, 99, 100 Broadband fiber laser, 315, 327, 336

Index Broadband fiber sources, 313–337 Broadband Nd-doped fiber laser, 315, 327 Superfluorescent fiber sources, 315–337 (See also Superfluorescent fiber sources) Superluminescent laser diode-EDFA, 318 Wavelength-swept fiber lasers, 318 Broadband light sources Broadband fiber sources (See Broadband fiber sources) Superluminescent laser diodes, 314, 318, 328, 333 Broadening (See Line broadening) Cerium-doped fluorides, 477 Absorption spectrum, 462 Absorption transitions, 473 Emission spectrum, 477 Chalcogenide fiber amplifiers Dy-doped (⬃1.3 µm), 516–517 Nd-doped (⬃1.08 µm), 487 Pr-doped (⬃1.34 µm), 514, 689, 729, 731 Chalcogenide fiber lasers Dy-doped (⬃1.3 µm), 517 Nd-doped (⬃1.08 µm), 487 Chalcogenide fibers (See also Chalcogenide glasses) Fabrication techniques, 457–458 Fiber loss, 450, 487, 514, 517, 731 Mechanical strength, 458 Chalcogenide glasses (See also Chalcogenide fibers) Compositions, 450, 451–452, 514 Glass-melting techniques, 452–453 Nonradiative lifetimes in, 32–33 Phonon energies, 462, 517 Radiative lifetimes (See Radiative lifetime) Solubility of rare earths, 462 Spectroscopy Dy, 516–518, 520 Er, 497–498, 520 Ho, 510 Nd, 487 Pr, 513–516, 520 Tb, 517–519 Tm, 506 Transmission spectra, 450 Cladding-pumped fibers (See Double-clad fibers) Clustering, 3–4 Co-dopants to reduce, 41–43 Mechanism, 41–43

Index [Clustering] In Er-doped glasses, 41–43, 620–622, 626 In Nd-doped glasses, 41–42 Co-doping Dy/Tm, 517 Er/Yb, 37, 62, 63, 138–141, 268–269, 272–274, 300, 636 Er/Yb/Sn, 273 Ho/Tm, 154–156, 510–511 Ho/Yb, 506 Pr/Nd, 184 Pr/Yb, 178, 179, 181–189 Tm/Eu, 231 Tm/Ho, 505, 739–740 Tm/Tb, 505, 740–743 Tm/Yb/Er, 100 Communication systems Accumulation of ASE, 596–597 Analog systems, 617, 732–733 Bit error rate, 570–571, 734, 737 CATV systems, 732–733 Digital systems, 733, 734 EDFA chains, 596–600 Four-wave mixing, 735 Noise accumulation, 550–551 Remotely pumped, 622–626 Repeaterless link, 624 Transmission AM-VSB video signal, 732–733, 728 Digital, 733–734 WDM, 600, 615, 734–738 Complex susceptibility, 553–557 Concentration quenching (See also Clustering; Solubility of rare earths in glasses) Effect of co-dopants, 3–4, 41–43, 132 Erbium, 3, 135–137 Neodymium, 4, 40–41, 130, 132 Mechanism, 37, 40–41 Ytterbium, 146, 178, 179 Continuous-wave fiber lasers (See Fiber lasers) Cooperative upconversion (See Upconversion) Cross relaxation, 37–38, 127–130, 151, 504 (See also Energy transfer; Upconversion) Cross sections Absorption (See Absorption cross section spectra) Emission (See Emission cross sections; Emission cross section spectra) Relation between, 28–29

757 Diode lasers (See Laser diodes) Dispersion of doped fibers, 400–401 Distributed EDFA (See Erbium-doped fiber amplifiers) Dopant profile, 11, 585 Double-clad fibers Lasers Er/Yb-doped, 140, 399, 401, 420, 427, 428, 429 Ho-doped, 156 Nd-doped, 129, 133, 399 Pr-doped, 173, 189 Tm-doped, 152, 153 Yb-doped, 147–149, 389 Principle, 2, 121–123, 328–329, 398– 399 Pump-coupling techniques, 123–124, 399 Shape optimization, 122–123 Side-pumping, 123–124, 399 Superfluorescent fiber sources, 328–329, 330 Yb-doped fiber amplifiers, 389 Dye fiber amplifiers, 2 Dysprosium-doped chalcogenide fiber lasers, 517 Dysprosium-doped glasses Fluoride glasses Absorption spectrum, 468 Absorption transitions, 473 Emission spectrum, 475 Radiative lifetime in chalcogenides, 517, 518 Tellurite glasses spectroscopy, 520 Effective mode area, 50 Einstein coefficients, 25,28 Electro-optic modulators (See Modulators) Emission cross sections (See also Emission cross section spectra) Chalcogenide glasses Dy, 517, 518 Er, 497 Ho, 510 Nd, 487 Pr, 514, 515, 731 Tb, 518 Fluorophosphate glasses (Nd), 51 Fluoride glasses Nd, 49, 51, 54, 686 Pr, 731 Phosphate glasses Er, 68

758 [Emission cross sections] Nd, 49, 51, 54 Silicate glasses Er, 51, 67 Nd, 49, 51, 54, 132 Emission cross section spectra (See also Emission cross sections) Chalcogenide glasses Er, 498 Pr, 515 Tb, 519 Determining, 6, 28–29, 535–536, 555 Fluoroberyllate glasses (Nd), 53 Fluorophosphate glasses (Nd), 46, 53 Fluoride glasses Dy, 475 Er, 65, 476, 498 Eu, 475 Nd, 46, 47, 53, 198, 199, 474, 486, 685, 686 Ho, 476 Pr, 474, 697 Sm, 474 Tb, 475 Tm, 93, 96, 97, 476, 741 Phosphate glasses Er, 69 Nd, 46, 47, 53 Silicate glasses Er, 64, 65, 69, 86, 498, 535, 560 Er/Yb, 636 Nd, 46, 47, 53 Yb, 145 Tellurite glasses (Er), 498 Emission spectra (See Emission cross section spectra) Emission transitions In fluorides (table), 478 Energy-level diagrams All rare earths (table), 460 Chalcogenide glasses Dy, 516 Tb, 518 Fluorophosphate glasses (Tm), 92 Fluoride glasses Er, 221, 488 Eu, 231 Ho, 202, 211, 507 Nd, 45, 190, 200, 201, 480, 683 Pr, 180, 511, 695 Tb, 742 Tm, 227–232, 499, 739

Index [Energy-level diagrams] Silicate glasses Er, 63, 77, 533, 534, 585 Ho, 154 Nd, 52 Tm, 150 Yb, 145 Energy transfer, 36–37, 38–40, 151, 156, 177–179, 181–184, 510–511, 630– 631, 739–740 (See also Cross relaxation; Upconversion) Erbium-doped fiber amplifiers, 531–576, 583–676 (See also Fiber amplifiers) Automatic gain control, 570, 589 Bidirectional amplifiers, 671–672, 674 Bidirectional pumping, 665, 669 C-band (definition), 674 Chalcogenide EDFAs, 497 Configurations, 607, 614, 623, 634, 670, 671 Design considerations, 663–676 Distributed amplifier, 4, 10–11 Double Rayleigh scattering, 657–659 Dual-band amplifiers, 602, 614–615, 674– 675 Fluoride EDFAs, 495–497, 540, 595, 602, 603, 604, 605, 607, 611, 613, 615, 622–623 Gain Bandwidth, 590, 602, 603 Bit error rate, 570–571 Cross talk, 567–570 Dependence on background loss, 618, 626–628 Dependence on pump power, 562–563 Dependence on pump wavelength, 563– 564, 626–628 Dual-stage, 607, 608, 634 Dynamics, 567–571 Effect of background loss, 4 Effect of clustering, 626 Gain coefficient, 135, 563 Gain inhomogeneity, 558–559, 640– 643 Gain peak wavelength, 596–599 Measurement techniques, 595–596 Polarization dependence, 157–158, 643–655 (See also Polarizationdependent gain) Pumped at 800 nm, 562 Pump wavelengths, 562 Saturation, 564–567, 657, 672

Index [Erbium-doped fiber amplifiers] Spectral hole burning, 558–559, 640–643 Spectra (experimental), 550, 588, 614, 635, 661 Temperature dependence, 660–664 Transparency, 562 Gain-clamped amplifiers, 616 Gain flatness Definition, 589–590 Effect of host composition, 601, 603– 605 Experimental results, 601–605 Figures of merit, 590, 592–593, 600, 603–606, 619–612, 615 Gain-flattening techniques, 600–602, 605–615 Gain peak wavelength, 589–590, 595– 600 Gain slope, 590–591, 617–618 Gain tilt, 591–592, 615–617 Ideal absorption spectrum, 594–595 Measurement, 595–596 Optimizing, 605–615 Yb co-doped, 635 High-power amplifier designs, 626–628 Hybrid amplifiers, 602, 607, 608, 609– 613, 633, 634 L-band amplifiers, 602, 674–675 Modeling Amplified spontaneous emission spectra, 557–558, 561 Distributed amplifiers, 537 Gain, 536–543, 553–561, 584–588 Gain bandwidth, 589–590 Gain coefficient, 50, 540–542, 553–557 Gain dependence on background loss, 655–659 Gain dependence on dopant profile, 542, 584–587 Gain dependence on fiber length, 621, 625, 666 Gain dependence on mode, 542 Gain dependence on numerical aperture, 618, 626–628 Gain dependence on pump wavelength, 78–79, 86–87 Gain dependence on temperature, 658– 664 Gain dynamics, 567–571 Gain efficiency, 623, 628, 634–637 Gain flatness, 589–593, 596–601, 605– 606, 611–612, 615–618

759 [Erbium-doped fiber amplifiers] Gain inhomogeneity, 557–558, 559–561 Gain saturation, 566, 601 Gain spectra, 550–552, 555–557, 591, 598, 613, 616, 633, 664, 675 Noise, 543–553, 621, 625 Polarization-dependent gain, 158, 645– 654 Pump absorption coefficient, 541–542 Pump excited-state absorption, 540, 620, 622–623, 626–628 Quasi-two-level system, 536, 549, 550, 562 Rate equations, 537–542, 572–574 Rayleigh scattering, 655–659 Remotely pumped amplifiers, 622–626 Spectral hole burning, 640–643 Transparency, 556 Upconversion effects, 619–622 Ytterbium co-doped, 629–633 Multi-stage amplifiers, 607, 608, 611–613, 634, 664–668 (See also Hybrid amplifiers, above) Noise Beat noise, 545 Bidirectionally pumped, 542–543 Distributed amplifiers, 551–552 Effect of background loss, 551–552 Effect of broadening, 544 Effect of saturation, 552–553 Excess noise, 545 Experimental, 546–547, 550, 613 Forward-pumped, 543 Measurement techniques, 550 Noise figure, 86–88, 547–550, 611, 620–621, 624–626, 639, 666–668, 669, 671–673 Saturated, 552–553 Shot noise, 545 Signal-to-noise ratio, 545–547, 589 Spontaneous emission factor, 548–551 Temperature dependence, 663 Optimization of EDFAs, 618–639 Preamplifiers, 624–626 Pump recycling, 669, 670–673 Pump redundancy, 666, 670 Rayleigh scattering, 655–659 Remotely pumped amplifiers, 622–626 Split-band amplifiers, 602, 614–615, 674– 675 Tellurite fiber amplifiers, 499 Twin-core fiber amplifiers, 617

760 [Erbium-doped fiber amplifiers] Upconversion effects in, 619–622 Ytterbium-co-doped (See Erbium/ytterbium-co-doped fiber amplifiers) Erbium-doped fiber lasers Fluoride glasses (See also Infrared fluoride fiber lasers; Ultraviolet fiber lasers; Visible fluoride fiber lasers) ⬃0.54 µm, 221–226 ⬃0.85 µm, 489, 494–495 ⬃1 µm, 489, 493–494 ⬃1.55 µm, 489, 492 ⬃1.65 µm, 489, 493 ⬃2.7 µm, 489, 490–492 ⬃3.45 µm, 489, 490 Mode-locked, 397, 412–413, 415–416, 418–419, 432, 438–440 Phosphate glasses (⬃1.55 µm), 64, 273– 274 Q-switched (⬃1.55 µm), 382, 384, 385, 389, 494 Silica glasses (⬃1.55 µm) (See Silica fiber lasers) Tellurite glasses (⬃1.55 µm), 498–499 Erbium-doped fibers (See also Erbiumdoped fiber amplifiers; Erbium-doped fiber lasers) Connecting to a communication fiber, 707 Fabrication, 3, 4, 7–9, 10–11 Low concentration, 10–11 Spectroscopy, 532–536 Erbium-doped fluoride fiber amplifiers (See Erbium-doped fiber amplifiers) Erbium-doped glasses Absorption in various glasses Bandwidths, 81, 89 Cross section spectra (See Absorption cross section spectra) Peak cross section, 81, 89 Peak wavelengths, 81, 89 Transitions in fluorides, 473 Branching ratios in fluorides, 72–74 Clustering, 41–43 Concentration quenching, 3, 40–41, 135– 137 Emission bandwidths in various glasses, 68–71 Emission cross sections in various glasses, 67, 72, 74, 497 Emission spectrum in chalcogenides, 498 Emission spectrum in fluorides, 476 Emission transition properties

Index [Erbium-doped glasses] 550-nm band, 73 660-nm band, 74 1550-nm band, 63–71 1660-nm band, 73–74 2700-nm band, 71–72 Emission spectra (See Emission cross section spectra) Energy-level diagrams (See Energy-level diagrams) Excited-state absorption around 800 nm, 75–76 General characteristics, 61–63 Ground-state absorption transitions, 45, 473 Homogeneous linewidth, 35, 559 Inhomogeneous linewidth, 35, 559 Pump transition properties, 75–90 800-nm band, 79–85 980-nm band, 88–90 1480-nm band, 84–88 Radiative lifetime (See Radiative lifetime) Spectroscopy in various glasses, 61–90, 498–499, 520 Ytterbium-co-doped (See Co-doping) Erbium/ytterbium-co-doped fiber amplifiers Experimental, 634–635 Gain efficiency, 634–638 Gain flatness, 604, 632–633 Hybrid, 633, 634 Modeling, 629–633 Noise, 637, 639 Principle, 628–629 Erbium/ytterbium-co-doped silica fiber lasers (See also Silica fiber lasers) Continuous-wave, 63, 138–141, 268– 269, 272–274, 300 Mode-locked, 397, 406–407, 416–417, 427 Q-switched, 389 Europium-doped glasses Fluorides Absorption spectrum, 466 Absorption transitions, 473 Emission spectrum, 475 Other glasses, 24 Evanescent-field fiber amplifiers, 2 Excitation migration, 37 Excitation spectra Holmium, 208–210 Neodymium, 193–195

Index Excited-state absorption, 176–179 Effect of composition on, 4, 55–57, 81– 84, 134 In Er-doped glasses, 4, 75–76, 77, 80–84, 85, 135, 137, 138, 488, 491, 495, 584–585, 634–636 Er/Yb-doped silica, 630 Eu-doped fluorides, 473 Ho-doped fluorides, 507 Nd-doped glasses, 45, 51–52, 54–57, 57–61, 134, 190, 480, 482, 683 Pr-doped fluorides, 180, 695 Tm-doped glasses, 97–98, 101, 150, 153, 499, 505 Upconversion lasers, 176–179, 505 Modeling in amplifiers, 57–61, 540, 620, 622–623, 626–628, 695–699 Spectra Er-doped glasses, 82, 83, 636 Nd-doped fluorides, 57, 486, 686 Fabrication of rare-earth-doped fibers Cerium doping, 7 Dopant profile, 585 Fluoride glasses, 453–458, 716–720 Casting techniques, 453–455, 718–720 Double-crucible technique, 454–456 Extrusion technique, 718 Silicate glasses Aerosol doping, 6,7 MCVD, 4–9, 10–11 OH content, 6, 7, 9 OVD, 4–8 PCVD, 4 Rod and tube, 9–11, 132 Sol-gel dip-coating, 9–10 Solution doping, 8–9 VAD, 4–8 Vapor pressure of rare-earth halides, 5 Faraday rotator (See Fiber laser resonators) Faraday rotator mirrors (See Fiber laser resonators) Fiber amplifier modeling Four-level system (See Neodymium-doped fiber amplifiers; Praseodymium-doped fluoride fiber amplifiers) Three-level system (See Erbium-doped fiber amplifiers) Fiber amplifiers ASE suppression, 691–694 At ⬃1.06 µm, 130, 487

761 [Fiber amplifiers] At ⬃1.3 µm, 681–738 Dy-doped chalcogenide, 517 Nd-doped (See Neodymium-doped fiber amplifiers) Pr-doped fluoride (See Praseodymiumdoped fluoride fiber amplifiers) At ⬃1.4 µm, 738–747 (See also Thuliumdoped fluoride fiber amplifiers) At ⬃1.5 µm, 745–747 (See also Thuliumdoped fluoride fiber amplifiers) At ⬃1.55 µm (See Erbium-doped fiber amplifiers, and Erbium/ytterbiumco-doped fiber amplifiers) At ⬃1.65 µm (See Thulium-doped fluoride fiber amplifiers) Chirped-pulse amplifiers, 429–430, 439– 440 Connecting to a communication fiber, 707, 720–722 Distributed amplifiers, 3, 4 Double-clad (Yb), 389 Evanescent-field amplifiers, 2 Femtosecond, 395 Flashlamp-pumped, 43 Halide glasses, 519 Modeling (See Erbium-doped fiber amplifiers; Neodymium-doped fiber amplifiers; Praseodymium-doped fluoride fiber amplifiers) Parametric chirped-pulse amplification, 397 Pulse amplification, 387–388, 428–430 Pulse amplification-compression, 428– 430 Tapered-fiber amplifier, 2 Wavelengths (table), 521 Fiber-amplifier sources, 316, 317–318, 335, 336 Fiber components (See Fiber laser resonators) Fiber dispersion spectrum, 400, 735 Fiber gratings (See Fiber laser resonators) Fiber laser modeling Continuous-wave lasers Approximate expressions, 118–121 Four-level system, 117–121 Frequency stability, 265–266 Slope efficiency, 120–121 Three-level system, 117–121 Threshold, 119–120 Effect of optical confinement, 173

762 [Fiber laser modeling] Mode-locked lasers Pulse width, 412–413 Timing jitter, 422–423 Q-switched lasers, 341–386 (See also Qswitched fiber lasers) Fiber laser resonators Configurations Continuous-wave, 114–117 Mode-locked, 399, 405, 407, 411, 412, 414, 416, 417, 419, 421, 427, 428, 432 Narrow-linewidth, 254, 257 Single-frequency, 260–263, 267, 269, 271, 274, 276, 277, 279, 281, 284, 286, 288, 289, 292, 297, 299, 301,302 Etalons, 260, 262, 278–279, 282, 283, 285–286, 288, 291, 293, 296, 433 Faraday rotator mirrors, 258–259, 298, 403, 407, 413, 414 Faraday rotators, 278, 295, 399, 411, 413, 414, 427, 430 Fiber Fabry-Perot resonators, 114–116, 254, 257, 260, 261, 269, 271, 274, 276, 277, 284, 297, 403, 414, 417 Fiber filters, 257–258 (See also Gratings, below) Fiber ring resonators, 115, 116, 128, 132, 136, 151, 256–259, 281–284, 286, 288–292, 294, 295, 296, 298–302, 403, 405, 414–415 Figure-8 laser, 412–413 Fox-Smith interferometers, 115–117, 262– 263 Gratings Bulk, 132, 142, 254, 255–256, 257, 260–263, 265–266, 294, 401, 411 Fiber, 116, 141, 148, 151, 161, 253– 255, 260, 262–264, 265, 268–276, 300, 387, 401, 418–419, 421, 429 Mach-Zehnder filter, 275 Master oscillator power amplifier, 268– 269, 271–272 Modulators (See Modulators) Prisms, 146, 185, 223, 401, 413 Sagnac loop reflectors, 115–116, 274– 277, 299 Saturable absorbers, 277–278, 415–418, 420, 427, 433 Switches (See Modulators) Tunable output coupler, 116

Index Fiber lasers Applications (See Applications) Broadband fiber laser, 315, 327, 336 Chalcogenide fiber lasers (See Chalcogenide fiber lasers) Cladding-pumped (See Double-clad fibers) Continuous-wave fiber lasers (See Chalcogenide fiber lasers; Infrared fluoride fiber lasers; Phosphate fiber lasers; Silica fiber lasers; Tellurite fiber lasers; Ultraviolet fiber lasers; Visible fiber lasers) Distributed-feedback, 270–273 Double-clad (See Double-clad fibers) Dual-wavelength pumping of, 197–201 Dysprosium-doped fiber lasers, 517 Flashlamp-pumped, 43 Fluoride fiber lasers (See Infrared fluoride fiber lasers; Ultraviolet fiber lasers; Visible fluoride fiber lasers) Gain-switched, 151 High-power, 121–127, 153 (See also Double-clad fibers) Infrared fiber lasers, Chalcogenide fiber lasers, 487, 517 Infrared fluoride fiber lasers (See Infrared fluoride fiber lasers) Phosphate fiber lasers, 64, 134, 273– 274 Silica fiber lasers (See Silica fiber lasers) Tellurite fiber lasers, 498–499, 520 Intensity noise, 267–268, 283–285, 287 Laser wavelengths (table), 114, 174, 175 Master oscillator power amplifier, 268– 269, 271–272, 388–389, 398 Modeling (See Fiber laser modeling) Mode-locked (See Mode-locked fiber lasers) Multiple-wavelength operation (See Multiple-wavelength fiber lasers) Narrow-linewidth (See Narrow-linewidth fiber lasers) Nonlinear effects (See Nonlinear effects in fibers) Phosphate fiber lasers (See Phosphate fiber lasers) Polarization properties, 157–160 Q-switched (See Q-switched fiber lasers) Resonators (See Fiber laser resonators) Self-terminating (See Self-terminating transitions)

Index [Fiber lasers] Self-pulsing in, 195–196, 264 Short-cavity, 132–133, 134, 140, 147, 148, 152, 155, 262, 264–274, 300 Silica fiber lasers (See Silica fiber lasers) Single-frequency (See Single-frequency fiber lasers) Single-polarization, 160–161 Table of output characteristics Er-doped fluoride, 225, 489 Er-doped silica, 136 Er/Yb-co-doped silica, 140 Ho-doped fluoride, 205, 508 Ho-doped silica, 155 Nd-doped fluoride, 479 Nd-doped silica, 128–129 Pr-doped fluoride, 186–187, 512 Pr-doped silica, 155 Sm-doped silica, 155 Tm-doped fluoride, 233, 501 Tm-doped silica, 152 Yb-doped silica, 147 Tellurite fiber lasers (See Tellurite fiber lasers) Temporal behavior, 195–197, 215–218, 224–226 Thermal issues, 126–127 Tunable (See Tunable fiber lasers) Twin-core fibers, 298–299 Ultraviolet fiber lasers (See Ultraviolet fiber lasers) Upconversion (See Upconversion) Visible (See Visible fiber lasers) Violet fiber lasers, 190–201 Wavelength-swept fiber laser, 318 Fiber loop reflectors (See Fiber laser resonators) Fiber loss Chalcogenide, 450, 487, 514, 517, 731 Fluoride, 450, 454, 472, 482, 500, 710, 713, 717 Silica, 7, 8, 11, 655, 735 Tellurite, 499 Fiber-optic gyroscope, 313–315, 335 Fiber strength and reliability, 11–12, 722– 723 Fiber polarizers, 160 Fiber-to-fiber connections, 707, 720–722 Figure-8 laser (See Fiber laser resonators) Flashlamp pumping, 43 Fluorescence spectra (See Emission cross section spectra)

763 Fluoride fiber amplifiers Erbium (⬃1.55 µm) (See Erbium-doped fiber amplifiers) Erbium (⬃2.7 µm), 495, 496–497 Neodymium (⬃1.3 µm) (See Neodymiumdoped fiber amplifiers) Praseodymium (⬃1.3 µm) (See Praseodymium-doped fluoride fiber amplifiers) Thulium (⬃1.45, ⬃1.5, and ⬃1.65 µm), 505–506, 738–749 (See also Thulium-doped fluoride fiber amplifiers) Fluoride fiber lasers (See Infrared fluoride fiber lasers; Ultraviolet fluoride fiber lasers; Visible fluoride fiber lasers) Fluoride fibers (See also Fluoride glasses) Fabrication (See Fabrication of rare-earthdoped fibers) Mechanical strength, 458 Single-mode fibers, 454–456 Fiber loss, 450, 454, 472, 482, 500, 710, 713, 717 Fluoride glasses (See also Fluoride fibers) Absorption spectra, 462–472 Absorption transitions of rare earths (table), 473 Cerium-doped Absorption cross section spectra, 462 Compositions, 173–174, 451 Dysprosium-doped Absorption cross section spectra, 468 Emission cross section spectra, 475 Emission spectra of rare earths (See Emission cross section spectra) Emission transitions, 478 Emission wavelengths, 478 Energy-level diagram (See Energy-level diagrams) Erbium-doped Absorption bandwidths, 81, 89 Absorption cross section spectra, 65, 89, 470, 588, 595 Absorption cross section values, 67, 81, 89 Absorption transitions, 473, 488 Branching ratios, 72, 73, 74 Emission bandwidths, 71 Emission cross section spectra, 65, 476, 498 Emission cross section values, 67, 72 Emission transitions, 478, 488 Excited-state absorption transitions, 488 Peak absorption wavelengths, 67, 81, 89 Peak emission wavelengths, 67

764 [Fluoride glasses] Europium-doped Absorption cross section spectra, 466 Emission cross section spectra, 475 Glass-melting techniques, 452, 716–718 History, 450, 461–462, 477 Holmium-doped Absorption cross section spectra, 469 Absorption transitions, 473, 507 Emission cross section spectra, 476 Emission transitions, 478, 507 Excited-state absorption, 507 Homogeneous linewidths in, 35 Inhomogeneous linewidths in, 35 Neodymium-doped Absorption cross section spectra, 44, 197, 464, 483 Absorption cross section values, 686 Absorption transitions, 473, 480, 683 Branching ratios, 48, 53 Concentration quenching, 40 Emission bandwidths, 49, 54 Emission cross section spectra, 46, 47, 53, 198, 199, 474, 486, 685, 686 Emission cross section values, 49, 51, 54, 686 Emission transitions, 478, 480, 683 Excited-state absorption, 56–57, 480, 683 Excited-state absorption spectra, 57, 486, 686 Peak emission wavelengths, 48, 54, 687 Nonradiative lifetimes, 31, 32, 695–696 Oscillator strengths (See Oscillator strengths) Phonon energy, 174, 462, 494 Praseodymium-doped Absorption cross section spectra, 463, 697, 702 Absorption transitions, 473, 511 Branching ratios, 695, 731 Emission cross section spectra, 474, 697 Emission cross section values, 731 Emission spectrum temperature dependence, 707–708 Emission transitions, 511 Excited-state absorption, 180, 695 Lifetime temperature dependence, 704, 706 Quantum efficiency, 512, 513 Upconversion pumping, 181–184 Radiative lifetimes (See Radiative lifetime) Refractive index, 688

Index [Fluoride glasses] Samarium-doped Absorption cross section spectra, 465 Emission cross section spectra, 474 Solubility of rare earths in, 462 Terbium-doped Absorption cross section spectra, 467, 742 Emission cross section spectra, 475 Thulium-doped Absorption cross section spectra, 91, 471, 741 Absorption cross section values, 502 Absorption transitions, 473, 499 Branching ratios, 95, 99, 100 Co-doping, 505 Cross relaxation, 504 Emission cross section spectra, 93, 96, 97, 476, 741 Emission cross section values, 96 Emission transitions, 499 Excited-state absorption, 97–98, 499 Transmission range, 174, 450 Upconversion (See Upconversion) Ytterbium-doped, absorption cross section spectra, 472 Fluoroaluminate glasses Compositions, 451, 688 Fibers, 687–688, 689 Judd-Ofelt parameters, 688 Refractive index, 688 Fluoroberyllate glasses, 24 Neodymium-doped Branching ratios, 48, 53 Concentration quenching, 40 Emission bandwidths, 49 Emission cross section spectra, 53 Emission cross section values, 49 Peak emission wavelengths, 48 Radiative lifetime, 46 Fluorohafnate glasses, 69, 70 Fluorophosphate glasses (See also Phosphate glasses) Erbium-doped Absorption bandwidths, 81, 89 Absorption cross section spectra, 80, 89 Absorption cross section values, 67, 81, 89 Emission bandwidths, 70–71 Emission cross section spectra, 69 Emission cross section values, 67 Excited-state absorption spectra, 82 Peak absorption wavelengths, 67, 81, 89

765

Index [Fluorophosphate glasses] Peak emission wavelengths, 67 Radiative lifetime, 67 Homogeneous linewidths in, 35 Inhomogeneous linewidths in, 35 Neodymium-doped Branching ratios, 48, 53 Concentration quenching, 40 Emission bandwidths, 49, 54 Emission cross section spectra, 53 Emission cross section values, 46, 47, 49, 51 Peak emission wavelengths, 48, 687 Radiative lifetime, 46, 51, 54 Thulium-doped Absorption cross section spectra, 90–91 Excited-state absorption transitions, 98 Laser transitions in, 92 Fluorozirconate (Search under Fluoride) Four-wave mixing, 735 Fox-Smith fiber interferometers, 115–117, 262–263 Fuchtbauer-Ladenburg relationship, 28, 535–536, 549, 555, 560 Gadolinium, 472, 477 Gain coefficient (See individual amplifiers) Gain flatness Erbium-doped fiber amplifiers (See Erbium-doped fiber amplifiers) Erbium/ytterbium-co-doped fiber amplifiers, 604, 632–633 Praseodymium-doped fluoride fiber amplifiers, 734–737 Gain modeling (See Erbium-doped fiber amplifiers; Neodymium-doped fiber amplifiers; Praseodymium-doped fluoride fiber amplifiers) Gain-switched fiber lasers, 151 Germanate glasses Erbium-doped, 66 Homogeneous linewidths in, 35 Inhomogeneous linewidths in, 35 Neodymium-doped Branching ratios, 48, 53 Emission bandwidths, 49 Emission cross sections, 49 Peak emission wavelengths, 48 Radiative lifetime, 46 Nonradiative lifetimes in, 31, 32 Thulium-doped Branching ratios, 99, 100 Radiative lifetime, 99, 100

Gratings (See Fiber laser resonators) Ground-state absorption transitions Dysprosium, 473 Erbium, 63, 221, 473, 488, 533, 584– 585 Europium, 473 Holmium, 154, 211, 473, 507 Neodymium, 45, 190, 473, 480, 683 Praseodymium, 180, 473, 511, 695 Samarium, 473 Terbium, 473, 742 Thulium, 92, 100–102, 149–150, 202, 227–232, 473, 499, 739 Ground-state absorption spectra (See Absorption cross section spectra) Halide glasses, 519 History of rare-earth-doped fibers Chalcogenide fibers, 450–4511 Erbium-doped fiber amplifiers, 531–532 Fluoride fiber amplifiers (1.3 µm), 681– 682 Fluoride fibers, 450 Rare earth doped fibers, 531–532 Holmium-doped fiber lasers Fluoride glasses (See also Infrared fluoride fiber lasers; Visible fluoride fiber lasers) ⬃0.55 µm, 201–220 ⬃1.2 µm, 508 ⬃1.38 µm, 508, 510 ⬃2.08 µm, 508, 509–510 ⬃2.9 µm, 507, 508, 509 ⬃3.9 µm, 506, 508 Silica glasses (⬃2.04 µm), 114, 154–156 (See also Silica fiber lasers) Holmium-doped glasses Absorption spectrum in fluorides, 469 Absorption transitions in fluorides, 473 Emission spectrum in fluorides, 476, 509 Radiative lifetime (See Radiative lifetime) Spectroscopy in silica, 154–156 Thulium sensitization, 154–156, 510–511 Homogeneous linewidth (See Line broadening) Hydroxyls, effects of (See OH⫺) Index modifiers, 5, 8, 11, 57, 451, 452 Infrared fluoride fiber lasers Erbium, 488–495 At ⬃0.85 µm, 489, 494–495 At ⬃1 µm, 489, 493–494 At ⬃1.55 µm, 489, 493

766 [Infrared fluoride fiber lasers] At ⬃1.65 µm, 489, 492 At ⬃2.7 µm, 489, 490–492 At ⬃3.45 µm, 489, 490 Effect of length, 494 Excited-state absorption, 491, 495 Output power, 489 Q-switched, 494 Self-terminating, 490, 491, 492, 494, 495 Table of output characteristics, 489 Tuning, 492, 494 Upconversion, 492 Holmium, 506–511 At ⬃1.2 µm, 508 At ⬃1.38 µm, 508, 510 At ⬃2.08 µm, 508, 509–510 At ⬃2.9 µm, 507, 508, 509 At ⬃3.9 µm, 506, 508 Co-doped with Yb, 506 Excited-state absorption, 507 Linewidth, 509 Output power, 508 Self-terminating, 507 Table of output characteristics, 508 Tuning, 509 Neodymium, 51–52, 477–483 At ⬃1.05 µm, 477, 479, 480–481 At ⬃1.3 µm, 51–52, 479, 480, 481– 483 Excited-state absorption, 482 Laser-diode-pumped, 480, 482–483 Linewidth, 481 Output power, 479, 481 Pump wavelengths, 480 Table of output characteristics, 479 Tuning, 481, 483 Praseodymium, 511–512 At 0.885 µm, 511–512 At 0.910 µm, 511–512 Table of output characteristics, 512 Tuning, 512 Table of tuning ranges, 175 Thulium, 499–505 At ⬃0.82 µm, 501, 505 At ⬃1.48 µm, 501, 505 At ⬃1.51 µm, 501, 504 At ⬃1.9 µm, 501, 503–504 At ⬃2.3 µm, 500–503 Cross relaxation, 504 Excited-state absorption, 505 Laser-diode-pumped, 502, 503, 504 Linewidth, 503

Index [Infrared fluoride fiber lasers] Output power, 501, 502 Table of output characteristics, 501 Tb-doped cladding, 505 Tuning, 503, 505 Inhomogeneous linewidth (See Line broadening) Integrated-optic modulators (See Modulators) Ion pairs (See Clustering) Judd-Ofelt analysis, 27, 28, 43, 51, 54, 55, 56, 535, 688, 695 Lanthanides, 19 Laser diodes Array, used as pump sources, 129, 133, 136, 147, 148–149, 152 Coupling into fibers, 148 Laser rate equations Basic equations, 342–345, 377, 631, 684– 685, 695–696 Four-level system, 344–345, 683–685 Point model, 377–382, 385 Three-level system, 342–345, 537–542, 572–574 Laser transitions Dysprosium, 516 Erbium, 63, 221, 488, 533, 534 General table of, 18 Holmium, 154, 202, 211, 507 Neodymium, 45, 190, 200, 480, 683 Praseodymium, 180, 511, 695 Terbium, 518 Thulium, 92, 150, 227–232, 499, 739 Laser wavelengths (tables) (See also Laser transitions) in chalcogenides, 521 in fluorides, 18, 174, 175, 521 in silica glasses, 18, 114, 174, 175 Lifetime Nonradiative (See Nonradiative lifetime) Radiative (See Radiative lifetime) Line broadening (See also Spectral hole burning; Stark splitting) Homogeneous Er linewidth, 35, 265, 295, 559 Mechanisms, 33–36 Nd linewidth, 35 Temperature dependence, 295 Inhomogeneous Er broadening, 553–561

Index [Line broadening] Er linewidth, 35, 559 Mechanisms, 33, 35–36 Nd broadening, 315 Nd linewidth, 35 Temperature dependence, 35 Linewidth measurement techniques, 249– 253, 558 LS coupling, 21–22, 91 Lutecium, 472, 477 Master oscillator power amplifiers (See Fiber lasers) Measurement techniques Gain flatness in EDFAs, 595–596 Linewidth, 249–253, 558 Noise, 550 Timing jitter in mode-locked fiber lasers, 423–424 Mechanical strength of fibers, 458 McCumber analysis, 29–30, 536, 554, 555, 587 Microsphere laser, 520 Migration (See Excitation migration) Mode hopping (See Single-frequency fiber lasers) Mode-locked fiber lasers Active, 395–396, 403–408, 438–439 Active mode-locking Active-passive, 406–408 Amplitude modulation, 404–406, 425 Frequency modulation, 404–405 Principle, 404–406 Theoretical model, 405–406 Active-passive, 406–408, 439 Active-passive mode-locking, 406–408, 439 Additive pulse compression, 411, 413, 421–422 Advantages, 395–396 Cladding-pumped, 399, 420, 427, 429 Commercial, 435, 440 Dispersion, 400–402 Doped with Er, 397, 412–413, 415–416, 418–419, 432, 438–440 Er/Yb, 397, 406–407, 416–417, 427 Nd, 397, 401, 404, 411, 413, 416– 418 Pr, 156, 397 Sm, 157 Tm, 151, 397 Yb, 397

767 [Mode-locked fiber lasers] Frequency-doubling of, 429–430, 439–440 High-power, 418–419 In mode-locked fiber lasers, 396, 420 Measurement, 423–424 Multimode, 395–396, 425–427 Multiple wavelength, 432–433 Noise bursts, 420–421, 439 Nonlinear amplifying loop mirror, 408– 414 Nonlinear optical loop mirror, 409–411, 431 Optical FM, 421 Passive, 395–396, 408–421 Passive harmonic, 419–420 Passive mode-locking, 395–396, 408–421 All-optical switches, 408–411 Passive harmonic mode-locking, 419– 420, 438–439 Principle, 408 Self-starting ring resonators, 414–415 With saturable absorbers, 415–418, 420 Performance summary (table), 438–440 Physical origin, 422–423 Polarization in, 402–403 Principle, 404–406 Pulse amplification-compression, 428–430, 435 Pump sources, 397–399 Q-switched mode-locked, 389 Q-switching instabilities, 418 Regenerative technique, 425 Sliding-frequency soliton, 422 Soliton lasers, 401–402, 406, 407, 411– 412, 418, 420–423, 427, 439 Stabilization methods, 424–425, 431 Stretched pulse, 411–412, 422–423, 439 Time-bandwidth product, 405 Timing jitter Type of mode-locking Modulators Acousto-optic, 258–259, 278–279, 283, 294–295, 318, 386, 389, 411, 425 Fiber filters, 408–411 Lithium niobate Bulk, 389 Integrated optic, 387, 405 Liquid-crystal cell, 259 Phase, 404, 405 Piezoelectric, 260, 266, 280, 424–425 Saturable absorbers, 277–278, 376, 386– 387, 415–418, 420 MOPA (See Fiber lasers)

768 M-profile fibers Nd-doped fiber lasers (table), 129 Principle, 125 Multicomponent silicate glasses, 3 Multiphonon relaxation (See Nonradiative relaxation) Multiple-wavelength fiber lasers, 295–302 Erbium, 223, 295–296, 298–302, 432– 433 Holmium, 156, 218–220 Neodymium, 135, 296–298 Praseodymium, 189 Narrow-linewidth fiber lasers, 243–305 (See also Single-frequency fiber lasers) Basic concepts, 245–248 Erbium, 254–259, 278–279 Line-narrowed fiber lasers, 253–259 Linewidth measurement techniques, 249– 253, 558 Neodymium, 254–257, 259 Neodymium-doped fiber amplifiers At ⬃1.06 µm Silica, 130 Chalcogenide, 487 At ⬃1.3 µm (fluoride), 483–486 Figure of merit for various glasses, 55 Gain dependence on signal mode, 694 Gain dependence on pump power, 694 Gain spectrum, 483, 485, 486, 682, 686, 687, 689 Saturation, 688, 689, 693 Summary table, 484 Theoretical gain efficiency, 59 Theoretical quantum efficiency, 60 At ⬃1.3 µm Fluoroaluminate, 687–688, 689 Fluorophosphate, 687, 691, 692 Other glasses, 51–61 Modeling ASE suppression schemes, 691–694 Basic model, 50–51, 57–58, 683–686 Effect of dopant profile, 50 Effect of excited-state absorption, 57– 61 Effect of fiber length, 692 Effect of mode confinement, 50 Figure of merit (definition), 687 Figures of merit in various glasses, 55, 57–58, 687 Gain in various glasses, 50–51, 57–61

Index [Neodymium-doped fiber amplifiers] Gain efficiency in various glasses, 50, 59 Noise, 690–691 Saturation, 688–690 Neodymium-doped fiber lasers Chalcogenide glasses, 487 Fluoride glasses (See also Infrared fluoride fiber lasers; Visible fluoride fiber lasers) ⬃1.05, 477, 479, 480–481 ⬃1.3 µm, 51–52, 479, 480, 481–483 ⬃0.38–0.41 µm, 174, 190–201 Mode-locked fiber lasers (⬃1.06 µm), 397, 401, 404, 411, 413, 416–418 Phosphate glasses (1.36 µm), 58–59, 134 Q-switched fiber lasers (⬃1.06 µm), 380– 383, 389 Silica glasses (⬃0.94, ⬃1.06, ⬃1.36 µm), 114, 127–135, 160–161 (See also Silica fiber lasers) Tellurite glasses (⬃1.06 µm), 520 Neodymium-doped glasses Absorption properties, 127 Absorption cross section spectra (See Absorption cross section spectra) Absorption transitions in fluorides, 473 Branching ratios in various glasses, 47– 48, 52–53 Emission bandwidths in various glasses, 49, 54 Emission cross sections in various glasses, 49, 51, 54, 520 Emission properties 1060-nm band, 45–51 1300-nm band, 51–61 Emission spectra 880-nm band, 46 1060-nm band, 47 1300-nm band, 53 Energy-level diagrams (See Energy-level diagrams) Excited-state absorption around 1.3 µm, 54–57 Excited-state absorption around 0.6 µm, 190 Clustering, 41–43 Concentration quenching, 40–41, 127– 130 General characteristics, 43–45 Homogeneous linewidth for various glasses, 35

769

Index [Neodymium-doped glasses] Inhomogeneous linewidth for various glasses, 35 Peak emission wavelengths in various glasses, 48, 54 Pump bands, 190, 201 Radiative lifetimes (See Radiative lifetime) Spectroscopy, 43–61, 127–130, 190–191, 520 Nephelauxetic effect, 24, 47, 472, 514 Network modifiers, 3–4 Noise In fiber amplifiers Er-doped (See Erbium-doped fiber amplifiers) Er/Yb-co-doped, 637, 639 Nd-doped, 690–692 Pr-doped (See Praseodymium-doped fluoride fiber amplifiers) Tm-doped, 741, 742, 744, 747, 749 In mode-locked fiber lasers, 420–421, 439 In superfluorescent fiber sources, 333–334 Intensity noise in fiber lasers, 267–268, 283–285, 287 Measurement techniques, 550 Modeling (See Erbium-doped fiber amplifiers) Noise accumulation in systems, 550–551 Nonlinear amplifying loop mirror, 408–414 Nonlinear effects in fibers Self-phase modulation, 388, 390, 401– 402, 406 Stimulated Brillouin scattering, 300–302, 390–391 Stimulated Raman scattering, 390–391 Nonlinear optical loop mirror, 409–411, 431 Nonradiative lifetime Erbium, 533 Formula, 31 Holmium, 202, 203 In various glasses, 31–33, 695–696 Temperature dependence, 31, 704, 706 Thulium, 149 Nonradiative relaxation, 29–31, 696 Nonradiative transitions, 29–33, 90–92 (See also Nonradiative lifetime) OHⴚ Content in fibers, 6, 7, 9 Quenching due to OH⫺, 41 Reducing OH⫺ in fluoride fibers, 716

Optical damage, 388 Oscillator strength, 50, 55 Definition, 25–26 Er-doped fluorides, 28, 67, 81, 89 Er-doped fluorophosphates, 67, 81, 89 Er-doped phosphates, 28, 81, 89 Er-doped silicates, 28, 67, 81, 89 Parameteric chirped-pulse amplification, 397 Phonon energies, 174, 462, 494, 517 Phosphate fiber lasers Er-doped (⬃1.55 µm), 64, 273–274 Nd-doped (⬃1.36 µm), 58–59, 134 Phosphate glasses (See also Fluorophosphate glasses) Erbium-doped, 61 Absorption bandwidths, 81, 89 Absorption cross section spectra, 65, 80, 89 Absorption cross section values, 81, 89 Emission bandwidths, 70 Emission cross section spectra, 69 Emission cross section values, 68 Peak absorption wavelengths, 81, 89 Radiative lifetime, 68 Neodymium-doped Branching ratios, 48, 53 Concentration quenching, 40–41 Emission bandwidths, 49, 54 Emission cross section spectra, 46, 47, 53 Emission cross section values, 49, 51, 54 Excited-state absorption around 1.3 µm, 134 Gain modeling around 1.3 µm, 58–59 Peak emission wavelengths, 48, 54, 687 Radiative lifetime, 46, 51, 54, 56 Nonradiative lifetimes in, 31, 32, 696 Thulium-doped Branching ratios, 95, 99, 100 Radiative lifetime, 93, 94, 95, 99, 100 Photochromic effects (See Photo-darkening) Photo-darkening Er-doped fluorides, 224 Tm-doped fluorides, 234–237 Tm-doped silicates, 150, 154 Photon statistics master equation, 544 Polarization-dependent gain In EDFAs (experimental), 643–655

770 [Polarization-dependent gain] In fiber lasers, 158 Physical origin, 157–158, 643–644 Theoretical model, 158, 645–654 Polarization hole burning In EDFAs, 643–655 In fiber lasers, 298 Physical origin, 643–644 Pump-induced, 647–648, 651–654 Theoretical model, 645–654 Signal-induced, 645, 647 Polarization properties EDFAs (See Polarization-dependent gain) Fiber lasers, 157–161 Experimental, 158–160 Modeling, 158–160 Principles, 157–158 Single-polarization, 160–161, 402–403 Praseodymium, 472 Praseodymium-doped fiber lasers Fluoride glasses ⬃0.49–0.63 µm, 178–189 (See also Visible fluoride fiber lasers) ⬃0.9 µm, 511–512 Mode-locked fiber lasers, 156–397 Q-switched fiber lasers (⬃1.05 µm), 151, 389 Silica glasses (See Silica fiber lasers) Praseodymium-doped fluoride fiber amplifiers, 512–513, 691–738 Amplifier module, 707–732 Key technologies, 716–725 Recent progress, 728–732 Applications to communications, 732–738 Automatic gain control, 704 Bidirectional pumping, 712, 715–716, 727 Configurations, 720, 724–730 Design considerations, 709–716 Double-pass amplifiers, 711, 726–727 Dual-stage amplifiers, 727–729, 734–736 Gain (experimental), 699–715 Bandwidth, 735–736 Dependence on background loss, 710, 712 Dependence on pump power, 710, 713, 715 Dependence on pump wavelength, 711, 714 Gain, 513, 734–736 Gain coefficient, 513, 709, 727, 729, 730, 731 Gain flatness, 734–737 Gain peak wavelength, 699

Index [Praseodymium-doped fluoride fiber amplifiers] Saturation, 700, 702, 713, 715, 729, 730 Saturation power, 513, 698 Spectra (experimental), 682, 689, 699– 701, 736 Temperature dependencies, 704–708 Modeling, 691–699 Gain bandwidth, 701 Gain coefficient, 710–711 Gain dependence on core diameter, 731 Gain dependence on fiber length, 699, 700 Gain expression, 698 Gain saturation, 698–702, 704, 724 Noise figure expression, 703 Rate equations, 695–696 Temperature dependencies, 704, 706, 707–708 Noise figure, 513, 703–704, 728, 729, 730, 735, 736 Saturation, 704, 729, 730 Spectrum, 703, 736 Temperature dependence, 704–705 Pump sources, 707, 712, 714, 723–725 Pump wavelengths, 513 Temperature dependence, 704–706 Upconversion effects in, 709, 715–716 Praseodymium-doped glasses Fluorides Absorption cross sections, 181 Absorption transitions, 473, 695 Absorption spectrum, 463 Branching ratios, 695 Emission spectrum, 474 Emission transitions, 695 Excited-state absorption, 695 Spectroscopy, 180–184 Radiative lifetimes (See Radiative lifetime) Silica Lifetimes, 156 Spectroscopy, 156 Tellurite glasses spectroscopy, 520 Pump bands (See Ground-state absorption transitions) Quantum efficiency, 32, 40, 60, 84 Dy-doped chalcogenides, 517 Ho-doped silica, 156, 157 Nd-doped fluorides, 480, 482 Pr-doped chalcogenides, 513, 514, 515, 728, 731

Index [Quantum efficiency] Pr-doped fluorides, 512, 513, 709, 728, 731 Tb-doped chalcogenides, 518 Tm-doped silica, 93–94, 149 Quenching (See Clustering; Concentration quenching) Q-switched fiber lasers, 341–391 Active Q-switching, 376, 386 Experimental lasers Nd (⬃1.06 µm), 380–383, 389 Er (⬃1.55 µm), 382, 384, 385, 389, 494 Er/Yb (⬃1.55 µm), 389 Tm (⬃1.9 µm), 151, 389 Pr (⬃1.05 µm), 151, 389 Sm (⬃0.65 µm), 157, 387 Yb (⬃1 µm), 389 Experimental Q-switching methods, 386– 388 Passive Q-switching, 376, 386–387 Power limitations, 388–391 Principle, 375–376 Pulse amplification, 387–388 Theoretical model, 341–386 Effect of amplified spontaneous emission, 354–357 Excitation efficiency, 351–354 Extraction efficiency, 365–368 Laser rate equations, 342–345 Pulse amplification, 362–375 Pulse distortion, 362–365 Pump dynamics, 349–351 Q-switched oscillation, 375–386 Repetitive amplification, 368–371 Storage capacity, 357–358 Waveguiding effects, 345–349, 358– 362, 371–375, 384–385 Timing jitter, 387 Using saturable absorbers, 376, 386–387 Radiative lifetime Borate glasses Nd, 46 Tm, 99, 100 Borosilicate glasses (Nd), 46 Chalcogenide glasses Dy, 517, 518 Er, 497 Pr, 514, 515, 731 Tb, 518, 519 Effect of glass composition, 93–94, 149, 497

771 [Radiative lifetime] Fluoride glasses Er, 67, 72–74, 222, 490, 492, 494, 533, 534 Ho, 507, 510 Nd, 46, 51, 54, 686 Pr, 181, 512, 691, 731 Tm, 94, 95, 99, 100, 226, 227, 228, 500, 502, 739 Fluoroberyllate glasses (Nd), 46 Fluorophosphate glasses Er, 67 Nd, 46, 51, 54 General formula, 25–26 Germanate glasses Nd, 46 Tm, 99, 100 Halide glasses (Pr), 519 Phosphate glasses Er, 68 Nd, 46, 51, 54, 56 Tm, 93, 94, 95, 99, 100 Silicate glasses Er, 51, 67, 533, 637 Ho, 154 Nd, 46, 51, 54 Pr, 156 Tm, 94, 95, 99, 149 Yb, 637 Table for various glasses, 46 Tellurite glasses Nd, 46 Tm, 93, 94, 95, 99, 100 Radiative transitions, 24–29 (See also Radiative lifetime) Rate equations (See Laser rate equations) Refractive-index profile, 11 (See also Index modifiers) Relaxation oscillations in fiber lasers, 132 Resonators (See Fiber laser resonators) Ring fiber lasers (See Fiber laser resonators) Russell-Saunders coupling, 21–22, 91 Sagnac loop reflectors (See Fiber laser resonators) Samarium-doped fluoride glasses Absorption spectrum, 465 Absorption transitions, 473 Emission spectrum, 474 Samarium-doped silica fiber lasers Continuous-wave (0.65 µm), 114, 155, 157, 174

772 [Samarium-doped silica fiber lasers] Mode-locked, 157 Q-switched, 157, 387 Saturable absorbers, 277–278, 415–418, 420 Self-phase modulation, 388, 390, 401–402, 406 Self-pulsing in fiber lasers, 195–196 Self-terminating transitions, 71–72, 96, 100, 195–197, 490, 491, 492, 494, 495, 505, 507 Sensitizers (See Co-doping) Sensors (See Applications of fiber lasers and amplifiers) Silica fiber lasers Erbium (⬃1.55 µm), 135–144 Effect of length, 142–143 Excited-state absorption, 135, 137, 138 Output power, 136, 140 Polarization behavior, 158–160 Pump wavelengths, 135 Pumped around 530 nm, 137–138 Pumped at 810 nm, 138 Pumped at 980 nm, 141–142 Pumped at 1480 nm, 142–144 Ring laser, 136 Single-polarization, 158–160 Table of output characteristics, 136 Tuning, 114, 142–143 Erbium/Ytterbium (⬃1.55 µm), 138–141 Double-clad fibers, 140, 399, 427, 428, 429 Output power, 140 Pumped at 810 nm, 140 Pumped at 1060 nm, 63, 140 Single-frequency, 268–269, 272–274, 300 Table of output characteristics, 140 Holmium (⬃2.04 µm), 154–156 Double-clad fibers, 156 Effect of length, 156 Multiple wavelength, 156 Output power, 156 Table of output characteristics, 155 Tm3⫹ co-doping, 154–156 Tuning range, 114 Neodymium, 127–135 ⬃0.9 µm, 128, 134–135 ⬃1.06 µm, 128–129, 131–133 ⬃1.35 µm, 128, 134 Double-clad fibers, 129, 133, 399 Excited-state absorption at 1.3 µm, 134

Index [Silica fiber lasers] M-profile fibers, 133 Multiple-wavelength operation, 134– 135 Output power, 128–129 Relaxation oscillations, 132 Ring laser, 128, 132 Single-polarization, 160–161 Table of output characteristics, 128–129 Tuning, 114, 132 Wavelength dependence on composition, 132 Praseodymium (0.89, 1.05 µm), 155–157 Double-clad, 173, 189 Output power, 155 Pump wavelengths, 156 Table of output characteristics, 155 Tuning range, 114, 157 Samarium (0.65 µm), 114, 174 Output power, 155, 157 Table of output characteristics, 155 Thulium (⬃2 µm), 149–154 Double-clad, 152, 153 High-power lasers, 153 Laser transitions, 150–151 Output power, 152 Pump wavelengths, 150–151 Ring laser, 151 Table of output characteristics, 152 Tuning, 114, 151–153 Upconversion lasers, 153–154 Ytterbium (⬃1 µm), 144–149 Core-pumped fiber lasers, 146–148 Double-clad fibers, 147–149, 389 Effect of fiber length, 146 Output power, 146–149 Table of output characteristics, 147 Tuning, 146 Table of transitions, 18 Table of laser wavelengths, 18, 114, 174, 175 Tuning ranges, 114, 174, 175 Silica fibers (See also Silicate glasses) Dispersion of doped fibers, 400–401 Dispersion spectrum, 400, 735 Fiber amplifiers (See Fiber amplifiers) Fiber lasers (See Silica fiber lasers) Mechanical strength, 458 Fiber loss, 7, 8, 11, 655, 735 Silicate glasses, 647–648, 654 Erbium-doped Absorption bandwidths, 81, 89

Index [Silicate glasses] Absorption cross section spectra, 62, 65, 80, 82, 86, 89, 535, 560, 588, 595 Absorption cross section values, 67, 81, 89 Branching ratios, 72–74 Concentration quenching, 3, 135–137 Emission bandwidths, 70 Emission cross section spectra, 64, 65, 69, 86, 498, 535, 560 Emission cross section values, 51, 67 Excited-state absorption spectra, 82, 636 Peak absorption wavelengths, 67, 81, 89 Peak emission wavelengths, 67 Holmium-doped, 154 Homogeneous linewidths, 35 Inhomogeneous linewidths, 35 Neodymium-doped Absorption cross section spectra, 80 Branching ratios, 48, 53 Concentration quenching, 40, 132 Emission bandwidths, 49, 54 Emission cross section spectra, 46, 47, 53 Emission cross section values, 49, 51, 54, 132 Excited-state absorption around 1.3 µm, 54–57 Peak emission wavelengths, 48, 54 Nonradiative lifetimes in, 31, 32, 696 Phonon energy, 174 Praseodymium-doped, 156 Transparency range, 450 Radiative lifetimes in (See Radiative lifetime) Thulium-doped, 99–102, 149–151 Branching ratios, 95, 99, 100 Excited-state absorption, 150, 153 Photo-darkening, 150, 154 Upconversion, 153–154 Ytterbium-doped, 144–146 Absorption bandwidth, 144–145 Absorption cross section spectra, 145, 630 Concentration quenching, 146, 178, 179 Emission bandwidth, 145 Emission cross section spectra, 145 Pump lasers for, 145 Single-frequency fiber lasers (See also Narrow-linewidth fiber lasers) Er-doped, 260, 262–264, 266–278, 281– 293, 295

773 [Single-frequency fiber lasers] Frequency jitter, 260, 283, 291, 293 Nd-doped, 260, 278–280, 285, 294–295 Mode hopping, 261, 264, 266, 275, 277, 278, 279, 285, 286, 290, 291, 294, 295 Pr-doped, 282 Standing-wave lasers, 259–280 Tm-doped, 261–262 Traveling-wave lasers, 281–295 Yb-doped, 271, 278 Single-longitudinal-mode fiber lasers (See Single-frequency fiber lasers) Sol-gels, 9–10 Solitons Applications, 243 In mode-locked fiber lasers, 401–402, 406, 407, 411–412, 418, 420, 421, 422 Propagation, 401–402 Raman solitons, 428–429 Solubility of rare earths in glasses, 41–43 Erbium, 3, 41, 42, 135–137 In chalcogenide glasses, 462 In fluoride glasses, 462 Neodymium, 4, 41–43, 130 Spatial hole burning Eliminating, 259–260, 262, 274–278, 280, 294, 296 Principle, 246–247 Specialty fibers Double-clad fibers (See Double-clad fibers) M-profile fibers, 125, 129 Other designs, 125–126 Spectra Absorption (See Absorption cross section spectra) Emission (See Emission cross section spectra) Spectral hole burning (Er), 558–559, 640– 643 Spectroscopy of rare-earth ions, 17–102 (See also individual ions) Absorption anisotropy, 643–645, 647 Branching ratio (See Branching ratios) Complex susceptibility, 553–557 Concentration quenching (See Concentration quenching) Cooperative upconversion (See Upconversion) Cross relaxation, 37–38, 127–130, 151, 504 Electronic properties, 19–21

774 [Spectroscopy of rare-earth ions] Energy-level diagrams (See Energy-level diagrams) Energy transfer (See Energy transfer) Electronic structures, 20–24, 458–459 Line broadening (See Line broadening) Nonradiative lifetime (See Nonradiative lifetime) Nonradiative transitions, 29–33, 90–92 Optical properties, 19–21 Oscillator strength, 25–26, 28 Photo-darkening (See Photo-darkening) Radiative lifetime (See Radiative lifetime) Radiative transitions, 24–29 Rare-earth-doped glasses (See individual rare earth) Stark splitting (See Stark splitting) Transition parity, 26–27 Upconversion (See Upconversion) Spontaneous emission factor (See Erbiumdoped fiber amplifiers) Stark splitting In Er, 533–535, 558, 559, 560 General physics of, 23, 24, 33–36, 50 In Tm, 93 Stimulated Brillouin scattering, 300–302, 390–391 Stimulated emission cross sections (See Emission cross sections) Stimulated Raman scattering, 390–391 Strength and reliability, fiber, 11–12, 722– 723 Sulfide glasses Nonradiative lifetime, 31, 32 Superfluorescent fiber sources, 315–337 (See also Broadband light sources) Bandwidth Spectral narrowing, 330 Values, 313, 325, 327–328, 330 Configurations Backward SFS, 316, 317, 322, 332 Double-pass SFS, 316, 317 Fiber amplifier-source, 316, 317 Forward SFS, 316–317 Polarized, 332 Double-clad SFS, 328–329, 330 Effects of reflections, 316–318 Fiber-amplifier sources, 316, 317–318, 335, 336 Er-doped SFS (⬃1.55 µm), Modeling, 322–324 Polarized, 332–333

Index [Superfluorescent fiber sources] Power output, 324–326 Spectra, 326 Table of output characteristics, 325 Thermal stability, 334, 336 Wavelength stability, 334–336 Modeling, 318–324 Four-level system (Nd), 321–322 Three-level system (Er), 318–321 Noise characteristics, 333–334 Nd-doped SFS (⬃1.06 µm), 327–329 Amplified, 329 Double-clad, 328–329 Noise characteristics, 333–334 Phosphate fiber, 328 Power output, 327 Spectra (fluoride), 483 Table of output characteristics, 328 Thermal stability, 328, 334 Wavelength stability, 336 Polarized SFS, 331–332 Pr-doped SFS ⬃1.05 µm (silica), 156–157, 330, 331 ⬃1.3 µm (fluoride), 330, 331 Principle, 313, 315–317 Table of output characteristics, 330 Er-doped silica, 325 Nd-doped silica, 328 Pr-doped silica, 330 Tm-doped silica, 330 Yb-doped silica, 330 Tm-doped SFS (⬃1.8 µm), 330, 331, 743 Wavelength stability, 334–336 Against feedback, 335 Against polarization, 335, 336 Against pump mode, 336 Against pump power, 334 Against pump wavelength, 334–335 Against temperature, 328, 334 Improving, 335–336 Yb-doped SFS (⬃1.04 µm), 329–330 Double-clad, 330 Effect of length, 329 Table of output characteristics, 330 Tapered fiber amplifiers, 2 Tellurite fiber amplifiers Er-doped (⬃1.55 µm), 499 Tellurite fiber lasers Er-doped (⬃1.55 µm), 498–499 Nd-doped (⬃1.06 µm), 520

Index Tellurite glasses Dysprosium spectroscopy, 520 Erbium-doped Emission cross section spectra, 498 Spectroscopy, 498–499, 520 Neodymium-doped Branching ratios, 48, 53 Emission bandwidths, 49 Emission cross sections, 49, 520 Peak emission wavelengths, 48 Spectroscopy, 520 Radiative lifetime, 46 Nonradiative lifetimes in, 31, 32, 696 Praseodymium spectroscopy, 520 Thulium-doped Branching ratios, 95, 99, 100 Radiative lifetime, 93, 94, 95, 99, 100 Terbium-doped fluoride fibers Absorption spectrum, 467 Absorption transitions, 473 Emission spectrum, 475 Theoretical models Fiber amplifiers, Four-level system (See Neodymiumdoped fiber amplifiers; Praseodymium-doped fluoride fiber amplifiers) Three-level system (See Erbium-doped fiber amplifiers) Fiber lasers (See Fiber laser modeling) Pulse amplification, 362–375 Pump dynamics, 349–351 Q-switched fiber lasers, 341–391 Thermal issues In fiber lasers, 126–127, 149 In superfluorescent fiber sources, 328, 334, 335, 336 Thulium-doped fiber lasers Fluoride glasses (See also Infrared fluoride fiber lasers; Visible fluoride fiber lasers) ⬃0.48 µm, 226–237 ⬃0.82 µm, 501, 505 ⬃1.48 µm, 501, 505 ⬃1.51 µm, 501, 504 ⬃1.9 µm, 501, 503–504 ⬃2.3 µm, 500–503 Gain-switched, 151 Mode-locked, 151, 397 Q-switched, 151, 389 Silica glasses (⬃2 µm), 149–154 (See also Silica fiber lasers)

775 Thulium-doped fluoride fiber amplifiers, 505–506, 738–749 At ⬃1.4 µm, 738–747 Gain dependence on pump power, 744– 745 Gain spectrum, 743, 744, 747 Ho-co-doped, 739–740, 741–745 Noise figure, 741, 742 Noise figure spectrum, 744, 747 Principle, 738–741 Saturation, 745 Upconversion pumping, 739–740, 741– 745 At ⬃1.5 µm Configuration, 746 Principle, 745–746 Gain spectrum, 747 Noise figure spectrum, 747 At ⬃1.65 µm Configuration, 748 Gain, 747, 748 Noise figure, 747, 749 Principle, 738, 740–743 Tb-doped cladding, 506, 740–743 Thulium-doped glasses Absorption spectra in fluorides, 91, 471, 741 Absorption transitions in fluorides, 473 Branching ratios, 95, 99, 100 Emission bandwidths, 90 Emission transition properties 810-nm band, 95–96 1480-nm band, 96–98 1850-nm band, 93–95 2300-nm band, 96–98 Blue and UV, 150 Other bands, 99–100 Emission spectra in fluorides 1480-nm band, 97 1850-nm band, 93, 741 2300-nm band, 96 All bands, 476 Energy-level diagrams (See Energy-level diagrams) Excited-state absorption transitions, 98, 150 General characteristics, 90–92 Holmium sensitization, 505, 739–740 Quantum efficiency, 93–94, 149 Photo-darkening in silica, 150, 154 Pump band properties, 100–102, 150– 151

776 [Thulium-doped glasses] Radiative lifetimes (See Radiative lifetime) Spectroscopy, 90–102, 149–151 Upconversion (See Upconversion) Timing jitter, In Mode-locked fiber lasers (See Modelocked fiber lasers) In Q-switched fiber lasers, 387 Transmission spectrum of various glasses, 450 Tunable fiber lasers Fluoride glasses Ho, 156 Table of tuning ranges, 174, 175 Tm, 261–262 Mode hopping (See Single-frequency fiber lasers) Silica glasses Er, 254–259, 260, 266–267, 273–275, 278, 282–284, 294 Ho, 156, 157 Nd, 255–257, 259, 262–263, 279–280, 295 Table of tuning ranges, 114, 174, 175 Tm, 151–153, 257, 261–262 Yb, 146, 278

Ultraviolet fiber lasers Nd-doped fluoride (0.38 µm), 174, 190– 201 Upconversion In erbium, 38–40, 75, 619–622 Fluorides, 172–173, 175–180 Nd, 190–191 Pr, 181–184 Mechanism, 38–40, 175–180, 181–182 Modeling, 619–622 In neodymium, 37–38, 127–130 In praseodymium, 695, 709 Silica glasses Er, 637 Tm, 153–154 Yb/Tm, 153–154 In thulium, 101–102 Upconversion pumping In Er, 221–223 In Ho, 202–203, 209–211 In Nd, 190–191, 197–201 In Pr, 181–184 In Tm, 226–232, 739–740, 741–746 Uranium-doped fluoride glasses, 520

Index Violet fiber lasers, 190–201 Visible fiber lasers Fluoride (See Visible fluoride fiber lasers) Silica (See Samarium-doped silica fiber lasers) Visible fluoride fiber lasers, 171–237 Erbium (⬃0.54 µm), 221–226 Multiple-wavelength operation, 222–223 Output power performance, 223–224 Pump wavelengths, 221 Spectroscopy, 221–223 Table of output characteristics, 225 Temporal behavior, 224–226 Upconversion pumping, 221–223 Holmium (⬃0.55 µm), 201–220 Diode-pumped, 213–215 Excitation spectra, 208–210 Multiple-wavelength operation, 218– 220 Output power performance, 203–208 Pump wavelengths, 208–211 Spectra, 208, 210, 211–214, 219–220 Spectroscopy, 202–203 Table of output characteristics, 205 Temporal behavior, 215–218 Tuning range, 211–213 Upconversion pumping, 202–203, 209– 211 Wavelength competition, 218–220 Neodymium (⬃0.38, ⬃0.41 µm), 190–201 Dual-wavelength pumping, 197–201 Excitation spectra, 193–195 Laser transitions, 190 Output power performance, 191–195 Pumping schemes, 190–191 Spectroscopy, 190–191 Temporal behavior, 195–197 Upconversion pumping, 190–191, 197– 201 Praseodymium (⬃0.63, ⬃0.61, ⬃0.52, ⬃0.49 µm), 178–189 Cladding-pumped, 189 Laser transitions, 180–181 Multiple wavelength, 189 Output power, 186–187 Output power performance, 181, 184– 189 Pumping schemes, 180–184 Spectroscopy, 180–184 Table of output characteristics, 186–187 Upconversion pumping, 181–184 Ytterbium co-doped, 178, 179, 181–189

777

Index [Visible fluoride fiber lasers] Table of tuning ranges, 174 Thulium (⬃0.48 µm), 226–237 Dual-wavelength pumping, 226–232 Europium co-doping, 231 Laser transitions, 227–231 Output power performance, 226, 232– 234 Photo-darkening, 234–237 Pumping schemes, 226–232 Spectroscopy, 226–232, 234–237 Table of output characteristics, 233 Wavelength-swept fiber laser, 318 Ytterbium co-doping (See Co-doping) Ytterbium-doped glasses Absorption bandwidths in silica, 144–145

[Ytterbium-doped glasses] Absorption cross section spectra, 145, 472, 630 Concentration quenching, 146 Emission bandwidths in silica, 145 Emission cross section spectra, 145 General characteristics, 144–146 Pump lasers for, 145 Radiative lifetime in silica, 637 Spectroscopy, 144–146 Ytterbium-doped silica fiber lasers Continuous-wave, 144–149, 174, 175 (See also Silica fiber lasers) Mode-locked, 397 Q-switched, 389

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