Mid-Infrared Coherent Sources and Applications (NATO Science for Peace and Security Series B: Physics and Biophysics)

MID-INFRARED COHERENT SOURCES AND APPLICATIONS NATO Science for Peace and Security Series This Series presents the re...

Author: Majid Ebrahim-Zadeh | Irina T. Sorokina

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MID-INFRARED COHERENT SOURCES AND APPLICATIONS

NATO Science for Peace and Security Series This Series presents the results of scientific meetings supported under the NATO Programme: Science for Peace and Security (SPS). The NATO SPS Programme supports meetings in the following Key Priority areas: (1) Defence Against Terrorism; (2) Countering other Threats to Security and (3) NATO, Partner and Mediterranean Dialogue Country Priorities. The types of meeting supported are generally "Advanced Study Institutes" and "Advanced Research Workshops". The NATO SPS Series collects together the results of these meetings. The meetings are coorganized by scientists from NATO countries and scientists from NATO's "Partner" or "Mediterranean Dialogue" countries. The observations and recommendations made at the meetings, as well as the contents of the volumes in the Series, reflect those of participants and contributors only; they should not necessarily be regarded as reflecting NATO views or policy. Advanced Study Institutes (ASI) are high-level tutorial courses intended to convey the latest developments in a subject to an advanced-level audience Advanced Research Workshops (ARW) are expert meetings where an intense but informal exchange of views at the frontiers of a subject aims at identifying directions for future action Following a transformation of the programme in 2006 the Series has been re-named and re-organised. Recent volumes on topics not related to security, which result from meetings supported under the programme earlier, may be found in the NATO Science Series. The Series is published by IOS Press, Amsterdam, and Springer, Dordrecht, in conjunction with the NATO Public Diplomacy Division. Sub-Series A. B. C. D. E.

Chemistry and Biology Physics and Biophysics Environmental Security Information and Communication Security Human and Societal Dynamics

http://www.nato.int/science http://www.springer.com http://www.iospress.nl

Series B: Physics and Biophysics

Springer Springer Springer IOS Press IOS Press

MID-INFRARED COHERENT SOURCES AND APPLICATIONS

edited by

Majid Ebrahim-Zadeh ICFO - Institut de Ciències Fotòniques, ICREA - Instituticio Catalana de Recerca i Estudis Avancats Barcelona, Spain and

Irina T. Sorokina Norwegian University of Science and Technology Department of Physics Trondheim, Norway

Published in cooperation with NATO Public Diplomacy Division

Results of the NATO Advanced Research Workshop on Middle Infrared Coherent Sources (MICS) 2005 Barcelona, Spain 6 – 11 November 2005

A C.I.P. Catalogue record for this book is available from the Library of Congress.

ISBN 978-1-4020-6462- 3 (PB) ISBN 978-1-4020-6439-5 (HB) ISBN 978-1-4020-6463-0 (e-book)

Published by Springer, P.O. Box 17, 3300 AA Dordrecht, The Netherlands.

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Printed on acid-free paper

All Rights Reserved © 2008 Springer Science + Business Media B.V. No part of this work may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission from the Publisher, with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work.

PREFACE

Coherent sources of mid-infrared (mid-IR) radiation are of great interest for a wide range of scientific and technological applications from spectroscopy and frequency metrology to information technology, industrial process control, photochemistry, photobiology and photomedicine. The mid-IR spectrum, which may be defined as wavelengths beyond ∼2 µm, covers important atmospheric windows, and numerous molecular gases, toxic agents, air, water, and soil pollutants, components of human breath, and several explosive agents have strong absorption fingerprints in this region. The development of practical coherent solid-state sources in the mid-IR can thus provide indispensable tools for a variety of applications in environmental monitoring and pollution control, detection of water and soil contaminants, food quality control, agriculture and life sciences, and noninvasive disease diagnosis and therapy through breath analysis. Coherent mid-IR sources also offer important technologies for atmospheric chemistry, free-space communication, imaging, rapid detection of explosives, chemical and biological agents, nuclear material and narcotics, as well as applications in air- and sea-born safety and security, amongst many. The timely advancement of coherent mid-IR sources is, therefore, vital to future progress in many application areas across a broad range of scientific, technological, and industrial disciplines. On the other hand, more than 40 years after the invention of laser, much of the mid-IR spectrum still remains inaccessible to conventional lasers due to fundamental limitations, most notably a lack of suitable crystalline laser gain materials. This has confined the spectral range of conventional solid-state lasers mainly to wavelengths below ∼3 µm, resulting in a severe shortage of coherent laser sources at longer wavelengths, and presenting a major obstacle to the widespread advancement of mid-IR science and technology. At the same time, alternative technologies for the generation of mid-IR radiation have been proposed, devised and developed, with the goal of overcoming this persistent barrier. In particular, over the past decade, there have been major new developments in mid-IR sources, driven by the emergence of a number of new technologies and continuing innovations and refinements in many of the more established techniques. Advances in material science, crystal growth, and semiconductor material processing have led to the realisation of a new generation of coherent mid-IR sources based on novel operating principles such as quantum cascade lasers, new types of semiconductor

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PREFACE

lasers, as well as novel diode-pumped crystalline and fiber lasers based on new solid-state laser gain materials and structures. At the same time, there has been unprecedented progress in some of the more traditional technologies for mid-IR generation, in particular nonlinear frequency conversion and parametric sources, brought about by breakthroughs in nonlinear materials, innovative device design concepts and ongoing advances in pump laser technology. The advent of a new generation of birefringent, quasi-phase-matched, doped, waveguide, fiber and semiconductor nonlinear materials together with novel solid-state, semiconductor, and fiber pump lasers have led to the development of new frequency conversion and parametric sources for the mid-IR with previously unattainable performance capabilities. The ongoing progress in related technologies including synchrotron, free-electron and gas lasers, as well as novel techniques for terahertz (THz) generation have also led to further improvements in such radiation sources with enhanced overall operating capabilities. The important advances in mid-IR science and technology have also had a major impact on new application areas, paving the way for the practical deployment of mid-IR sources in spectroscopy, environmental trace gas detection and sensing, life sciences, imaging, safety and security, and photomedicine. The wide range of mid-IR technologies have proved highly effective in advancing coherent sources in selected spectral regions from ∼1 to ∼100 µm, and beyond, into the THz region. The various techniques are often competitive, and in many cases complimentary. Some technologies can deliver mid-IR radiation in regions not accessible to others, while suffering from drawbacks of low power, temporal and spectral inflexibility, or high cost. There are important merits and limitations associated with each approach, making a particular technology more favorable for a given set of requirements and applications than others. However, the broad scope and multi-disciplinary nature of mid-IR technology across a wide range of disciplines (from semiconductor physics and laser engineering to nonlinear optics, material science, spectroscopy and biomedicine) has, at the same time, led to the confinement of each technology mainly to its own specialist community, resulting in a lack of connectivity among the different areas. This factor, in addition to the fundamental barriers, has contributed yet another important obstacle to a more timely advancement of mid-IR science and technology. The aim of this book is to bring into focus this important research area and provide a comprehensive review of the research topics most pertinent to the advancement of coherent mid-IR sources and their applications. The volume brings together contributions from the most eminent international researchers in the field, covering various aspects of mid-IR technology from fundamental principles to materials, systems and applications, and addresses the most important recent advances in the field since the publication of an earlier volume in 2003 (SolidState Mid-Infrared Laser Sources, I. T. Sorokina and K. L. Vodopyanov, Eds., Springer, 2003). A central theme of the present volume is the strong emphasis on

PREFACE

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the applications of mid-IR sources to emerging areas of science and technology, with no less than 8 out of the 22 chapters dedicated to this topic. These include spectroscopic techniques for trace gas detection and sensing in environmental monitoring, life sciences, safety and security, applications of mid-IR sources in breath analysis and medicine, as well as potential applications in high-intensity and attosecond physics. It is hoped that this volume will also provide added stimulus for further progress in the field, where major challenges still remain and great potential exists for further new breakthroughs. The timely advancement of midIR coherent sources will undoubtedly have important implications across a broad range of scientific and technological disciplines and the field promises to remain a fertile ground for further innovation and exploitation in the future. In preparing the book, we have relied on the timely contribution of the authors, without whose expert insight, motivation and commitment the publication of this volume would not have been possible. We, thus, extend our appreciation to all the authors. We also convey our thanks to Springer for affording us the opportunity to publish this volume and to the editorial and publishing staff, in particular Wil Bruins, for their assistance, organization and efficiency in coordinating the timely preparation and production of the book. We are also grateful to the North Atlantic Treaty Organization for their valuable support of the Advanced Research Workshop on Mid-Infrared Coherent Sources (MICS) 2005, Barcelona, Spain, which served as the original impetus for the publication of this volume. Majid Ebrahim-Zadeh, Irina T. Sorokina Barcelona, Vienna, October 2006

CONTENTS

Preface

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I CRYSTALLINE LASER AND NONLINEAR OPTICAL MATERIALS FOR THE MID-IR 1. New Monocrystals with Low Phonon Energy for Mid-IR Lasers L. Isaenko, A. Yelisseyev, A. Tkachuk, and S. Ivanova 1 Introduction 2 Crystal growth and common properties of RE-doped MPb2 Hal5 (M = K, Rb; Hal = Cl, Br) crystals 2.1 Crystal growth 2.2 Phase transitions 2.3 Structural analysis 2.4 Optical properties of undoped MPb2 Hal5 crystals 2.5 Key physical properties 3 Spectroscopic characteristics of RE3+ ions in MPb2 Hal5 crystals 3.1 Optical spectra and spectroscopic parameters 3.2 Emission spectra in low concentrated crystals 4 Energy transfer and dynamics of RE3+ levels population 4.1 Upconversion processes in praseodymium doped KPC crystals 4.2 Upconversion and dynamics of neodymium levels population 4.3 Upconversion and dynamics of erbium levels population 5 Conclusion 2. Orthorhombic Crystals of Lithium Thioindate and Selenoindate for Nonlinear Optics in the Mid-IR J.-J. Zondy, V. Petrov, A. Yelisseyev, L. Isaenko, and S. Lobanov 1 Introduction 2 Development, growth, composition, and structure of LIS and LISe 3 Band-gap, transparency, and IR cut-off of LIS and LISe 4 Dispersion and birefringence of LIS and LISe 5 Nonlinear susceptibility of LIS and LISe

ix

3 3 6 6 8 9 11 19 20 22 38 46 48 49 55 59 67 67 69 73 75 77

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CONTENTS

6 7 8

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Thermo-mechanical properties and damage resistivity of LIS and LISe Phase-matching in LIS and LISe Nonlinear frequency conversion with LIS and LISe 8.1 Mid-IR femtosecond OPA 8.2 Continuous-wave DFG of mid-IR radiation 8.3 Nanosecond OPO Conclusion

3. Quaternary Nonlinear Optical Crystals for the Mid-Infrared Spectral Range from 5 to 12 µm V. Petrov, V. Badikov, and V. Panyutin 1 Introduction 2 Mixed defect chalcopyrites Cdx Hg1−x Ga2 S4 2.1 Growth and properties of CGS, HGS, and CHGS 2.2 Potential and frequency conversion schemes realized with quaternary CHGS crystals 3 Orthorhombic Agx Gax Ge1−x S2 crystals 3.1 Growth and properties of AGGS 3.2 Potential and frequency conversion schemes realized with quaternary AGGS crystals 4 Conclusion 4. Microstructured Semiconductors for Mid-Infrared Nonlinear Optics P. S. Kuo and M. M. Fejer 1 Introduction 2 Properties of zincblende semiconductors 2.1 Dispersion 2.2 Nonlinear susceptibilities 3 Fabrication of microstructured zincblende semiconductors 3.1 Stacked plate methods 3.2 Orientation-patterned growth 4 QPM in bulk microstructured zincblende semiconductors 4.1 Mid-IR SHG 4.2 Mid-IR DFG 4.3 Optical parametric oscillators 4.4 Ultrafast interactions 4.5 THz 5 Current research directions 5.1 Waveguides 5.2 Other QPM semiconductors

82 85 90 90 93 95 97 105 105 107 107 117 125 125 133 140 149 149 150 151 151 154 154 155 158 158 159 159 160 164 164 164 164

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II SOURCES IN THE MID-IR 1. Progress in Quantum Cascade Lasers J. Faist, T. Aellen, T. Gresch, M. Beck, and M. Giovannini 1 Introduction 2 Optimization of doping level 3 High power devices 4 Linewidth enhancement factor 5 Acknowledgements 2. High-Brightness 2.X µm Semiconductor Lasers M. Rattunde, M. T. Kelemen, N. Schulz, C. Pfahler, C. Manz, J. Schmitz, G. Kaufel, and J. Wagner 1 Introduction 2 III-Sb based material system 2.1 Material properties 2.2 Growth 3 High brightness GaSb-based diode lasers 3.1 Active region design 3.2 Vertical epitaxial structure 3.3 Broad-area lasers 3.4 Ridge-waveguide lasers 3.5 Tapered lasers 4 GaSb-based optically pumped semiconductor disk lasers 4.1 Introduction 4.2 Epitaxial layer structure and sample characterization 4.3 Thermal management 4.4 OPSDL device performance 4.5 In-well optical pumping 5 Outlook 3. Broadband Mid-Infrared Solid-State Lasers I. T. Sorokina 1 Introduction 1.1 Motivation 1.2 Applications 2 Bandwidth and wavelength scaling rules 3 TM2+ -based solid-state lasers 3.1 Historical perspective and state-of-the-art sources 3.2 Co:MgF2 laser 3.3 Cr2+ -doped II-VI lasers 4 Conclusion and outlook 5 Acknowledgements

171 171 174 179 184 189 193

193 195 195 196 197 198 200 203 207 208 211 211 212 213 214 215 218 225 225 225 226 228 230 230 232 234 252 253

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CONTENTS

4. New Regimes of Excitation and Mid-IR Lasing of Transition Metal Doped II–VI Crystals S. Mirov and V. Fedorov 1 Introduction 2 Non-traditional Cr-doped mid-IR lasers 2.1 Cr:ZnSe and Cr:ZnS microchip lasers 2.2 Hot pressed ceramic Cr:ZnSe lasers 2.3 Multi-line and ultrabroadband Cr:Znse laser 3 Fe-doped mid-IR lasers 3.1 Iron ions in II–VI materials 3.2 Sample preparation 3.3 Spectroscopic characterization 3.4 Fe2+ :ZnSe laser characteristics 4 En-route to electrically pumped TM doped II–VI mid-IR lasers 4.1 TM-doped II–VI thin films for mid-IR applications 4.2 Excitation mechanisms of TM dopant ions in II–VI bulk semiconductors 4.3 Experimental verification of photoionization transitions 4.4 Future directions 5 Conclusion remarks 6 Acknowledgements 5. Advances in Mid-Infrared Fiber Lasers M. Pollnau and S. D. Jackson 1 Introduction 2 Fiber materials 2.1 Silicates 2.2 Fluorides 2.3 Chalcogenides 2.4 Ceramics 3 Fiber, pump, and resonator geometries 3.1 Fiber designs for cladding pumping 3.2 Fiber-laser resonators 3.3 Thermal issues 4 Overview of mid-infrared fiber lasers 5 Thulium-doped fiber lasers at 1.9–2.5 µm 5.1 Three-level lasers at 1.9–2.0 µm 5.2 Four-level lasers at 2.3–2.5 µm 6 Holmium-doped fiber lasers at 2.1–2.9 µm 6.1 Three-level lasers at 2.1 µm 6.2 Four-level lasers at 2.9 µm

261 261 263 263 266 268 272 272 274 275 279 285 285 291 294 300 302 303 315 315 316 317 318 318 319 319 320 321 322 323 324 324 326 326 327 328

CONTENTS

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8 9 10

Erbium-doped fiber lasers at 2.7–2.8 µm 7.1 Excited-state absorption and cascade lasing 7.2 Lifetime quenching by co-doping 7.3 Energy recycling by energy-transfer upconversion Dysprosium-doped fiber lasers at 2.9 µm Outlook Conclusions

6. Mid-Infrared Optical Parametric Oscillators and Applications M. Ebrahim-Zadeh 1 Introduction 2 Mid-infrared optical parametric oscillators 3 Continuous-wave parametric oscillators 3.1 Singly-resonant oscillators 3.2 Multiply-resonant oscillators 4 Pulsed parametric oscillators 5 Applications 6 Summary 7. Mid-Infrared Integrated Optical Parametric Generators and Oscillators with Periodically Poled Ti:LiNbO3 Waveguides S. Orlov, W. Grundkötter, D. Hofmann, V. Quiring, R. Ricken, H. Suche, and W. Sohler 1 Introduction 2 Waveguide and resonator fabrication and characterization 3 Experimental setup 4 Optical parametric generators (OPG) 5 Optical parametric oscillators (OPOs) 5.1 Singly resonant oscillators 5.2 Doubly resonant oscillators 6 Conclusions 8. Optical Parametric Generators and Amplifiers V. Pasiskevicius and F. Laurell 1 Introduction 2 Parametric generation and amplification 2.1 Theoretical basis 2.2 Phase matching considerations 3 Broadband optical parametric generation and amplification 3.1 Collinear interaction 3.2 Noncollinear parametric interaction 4 Conclusions and future outlook

xiii 329 330 331 333 335 335 337 347 347 348 350 352 356 357 366 371 377

377 378 380 381 384 385 387 390 393 393 394 394 398 404 404 409 412

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9. Tunable THz Sources Based on Quasi-Phase-Matched Gallium Arsenide K. Vodopyanov 1 Introduction 2 Theory of optical THz generation in QPM media 2.1 Plane wave analysis, femtosecond pulses 2.2 Plane-wave analysis, picosecond pulses 3 Comparison of nonlinear optical crystals for THz generation 4 THz generation with fs-pulses from OPA/DFG (λ = 2– 4.4 µm) 5 THz generation using OP-GaAs pumped by a fiber laser 6 THz generation with a near-degenerate synchronously-pumped ps OPO 6.1 Extracavity THz generation 6.2 Intracavity THz generation 7 Conclusion 10. Semiconductor Waveguides for Nonlinear Frequency Conversion L. Lanco, M. Ravaro, J. P. Likforman, P. Filloux, X. Marcadet, S. Ducci, G. Leo, and V. Berger 1 Introduction 2 Form birefringence phase matching 3 Modal phase matching 4 Counterpropagating phase matching

III

419 419 421 421 424 427 428 432 434 436 437 439 443

443 444 448 453

APPLICATIONS

1. Semiconductor Laser Based Trace Gas Sensor Technology: Recent Advances and Applications F. K. Tittel, G. Wysocki, A. Kosterev, and Y. Bakhirkin 1 Introduction 2 Trace gas detection based on photoacoustic spectroscopy using QC and IC lasers 2.1 Photoacoustic spectroscopic techniques 2.2 Quartz enhanced photoacoustic spectroscopic techniques 2.3 QEPAS based chemical sensor architecture 3 Chemical sensing based on tunable thermoelectrically cooled CW quantum cascade lasers. Gas sensing with a cw DFB QC laser was first reported in Ref. [54]. 3.1 Detection of trace gases with widely tunable QC lasers 3.2 EC-QCL system configuration 4 Trace gas sensors using a high-finesse optical cavity 4.1 Cavity ringdown spectroscopy

467 467 470 470 471 478

481 481 482 484 485

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4.2 Cavity enhanced absorption spectroscopy Conclusions

486 487

2. Trace Gas Analysis with Isotopic Selectivity Using DFG-Sources H. Waechter and M. Sigrist 1 Introduction 2 Mid-infrared laser sources 3 Detection schemes 4 Applications in trace gas sensing 5 Studies on isotopic compositions of trace gases 6 DFG-studies on CO, CO2 and N2 O isotopomers 6.1 DFG-source 6.2 Isotopomer abundances and line strengths 6.3 Measurements and results 7 Conclusions and outlook

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3. Photoacoustic Spectroscopy Using Continuous Wave Optical Parametric Oscillators A. K. Y. Ngai, S. T. Persijn, M. M. J. W. van Herpen, S. M. Cristescu, and F. J. M. Harren 1 Introduction 2 Physical basics of optical parametric oscillators 2.1 QUASI phase matching in periodically poled crystals 2.2 Periodically poled lithium niobate 3 OPO cavity design 3.1 Oscillation threshold for singly resonant OPO 4 Frequency tuning with OPO’s 4.1 Tuning by changing the poling period and temperature 4.2 Tuning with intracavity elements 4.3 Pump tuning 4.4 Tuning by changing the cavity length 4.5 Frequency tuning by using a combination of tuning techniques 4.6 Wavelength coverage 5 High-resolution spectroscopy with cw OPO’s 6 Trace gas detection with OPO’s 6.1 Photoacoustic spectroscopy 6.2 Photoacoustics with CW OPO’s 6.3 CO2 monitoring from insect breath 6.4 Detection of methane and ethane using OPO cavity ring-down spectroscopy

495 496 498 498 499 501 501 502 503 506 511

511 514 514 515 516 518 518 519 520 521 522 522 523 524 524 525 526 527 527

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CONTENTS

4. Online Monitoring of Exhaled Breath Using Mid-Infrared Laser Spectroscopy M. Mürtz and P. Hering 1 Introduction 2 The role of trace gases in medicine and biology 2.1 Trace constituents of exhaled human breath 2.2 Other biological sources of volatile markers 3 Suitable laser spectroscopic approaches for online analysis 3.1 Multi-pass absorption 3.2 Cavity-enhanced techniques 3.3 Photoacoustics 3.4 Magnetic resonance 4 Monitoring of exhaled diseasemarkers 4.1 Nitric Oxide (NO) 4.2 Carbon monoxide (CO) 4.3 Ethane 5 Perspectives for laser spectroscopic breath monitoring 6 Acknowledgements 5. Ultrabroadband Solid-State Lasers in Trace Gas Sensing E. Sorokin 1 Introduction 2 Cr2+ -based mid-IR lasers 3 Trace gas analysis in the atmosphere 4 Intracavity laser spectroscopy 5 Conclusions 6. Medical Applications of Mid-IR Solid-State Lasers R. Steiner 1 Introduction 2 Laser-tissue-interaction 3 Transmission systems 4 Medical applications 4.1 Holmium and thulium laser 4.2 Er:YAG laser 5 Conclusions and future aspects 7. Opportunities for Mid-IR Sources in Intense-Field and Attosecond Physics M. Ivanov, V. Yakovlev, and F. Krausz

535 535 537 537 539 540 542 542 543 544 545 545 546 547 549 549 557 557 558 560 563 571 575 575 576 580 583 583 583 587 589

CONTENTS

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8. Ultrawideband Mid-Infrared Spectroscopy of Semiconductor Nanostructures T. Müller and K. Unterrainer 1 Introduction 2 Generation and detection of ultrawideband mid-infrared pulses 2.1 Sources of ultrawideband mid-infrared pulses 2.2 Time-domain detection of mid-infrared pulses 3 Intersubband carrier dynamics in quantum wells 3.1 Intersubband electron relaxation in quantum wells 3.2 Quantum interference of intersubband transitions 4 Intraband carrier dynamics in quantum dots 4.1 Electronic states and optical intraband transitions 4.2 Electron capture and relaxation in quantum dots

599 600 600 603 605 605 609 614 614 615

Index

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Part I

Crystalline Laser and Nonlinear Optical Materials for the Mid-IR

NEW MONOCRYSTALS WITH LOW PHONON ENERGY FOR MID-IR LASERS New Monocrystals LUDMILA ISAENKO, ALEXANDER YELISSEYEV Institute of Geology & Mineralogy, Russian Academy of Sciences, Siberian branch, 3, ac. Koptyug avenue, Novosibirsk 630090 Russian Federation ALEXANDRA TKACHUK∗ , SVETLANA IVANOVA S.I. Vavilov State Optical Institute, 12, Birzhevaja line, St. Petersburg 199034 Russian Federation

Abstract. Various aspects of crystal growth, structure, physical and optical properties of new low phonon energy crystals, namely the rare earth doped alkali-lead halide crystals RE3+ : MPb2 Hal5 (M = Rb, K and Hal = Cl, Br), are described. The crystals were grown using the Bridgman technique, most of crystals were grown for the first time. The results of spectroscopic study of the RE3+ -doped double chloride crystals, RE3+ :KPb2 Cl5 (RE3+ = Pr3+ , Nd3+ , Tb3+ , Dy3+ , Ho3+ , Er3+ , Yb3+ ), and new double bromide KPb2 Br5 and RbPb2 Br5 crystals doped with Nd3+ and Tb3+ are presented, including multiphonon non-radiative relaxation rates, and absorption and emission spectra. Judd-Ofelt intensity parameters, as well as radiative transition probabilities, lifetimes, and branching ratios are summarized. The efficiency of up-conversion is demonstrated in Nd and Er doped KPb2 Cl5 crystals. The luminescence dynamics and energy transfer processes responsible for population of excited RE3+ levels and laser action are discussed. The possibility of laser action in the mid-infrared is considered. Keywords: Double alkali-lead halides, crystal growth, phase transitions, crystal structure, optical properties, rare earth ions, optical spectra, phonon spectrum, absorption cross section, energy transfer, upconversion, multiphonon relaxation, population dynamics, laser action.

1. Introduction Mid-infrared (mid-IR) solid state lasers operating in the 3–10 µm spectral range are of great importance because of the overwhelming variety of fundamental and practical applications such as next-generation imaging devices, near-IR quantum ∗ Alexandra Tkachuk, P.O. box 37, St. Petersburg 195197, RUSSIA. Fax +7(812)328 58 91;

e-mail: [email protected] 3 M. Ebrahim-Zadeh and I. T. Sorokina (eds.), Mid-Infrared Coherent Sources and Applications, 3–65. c 2008 Springer.

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LUDMILA ISAENKO ET AL.

counting devices, remote sensing, molecular and solid state spectroscopy, clinical and diagnostic analysis, atmospheric sensing, optical metrology, and medicine. Currently, optical parametric oscillator systems are typically used to cover these wavelengths. These systems incorporate both nonlinear media and pump laser sources, leading to some complexity of the optical system. Another simpler approach to solve these problems is direct mid-IR laser operation in solid-state media. In this case, direct pumping of the working laser level is of specific interest for the development of mid-IR lasers with high efficiency. To achieve an acceptable quantum efficiency from a given energy level it is necessary to avoid luminescence quenching via multiphonon relaxation depending on energy gap and maximal phonon energy in given host material. Therefore, the host material must have low phonon frequency, which will ensure low non-radiative losses. Multiphonon quenching of closely-spaced energy levels limits laser operation to wavelengths near and shorter than 3 µm in host-matrices based on the oxygen-containing compounds (e.g. YAG, YSGG, GGG, YAlO3 , YVO4 , CaWO4 ) doped with Rare Earth (RE) ions [1]. More success has been achieved with laser operation in the range shorter than 4 µm with rare-earth-doped fluoride hosts, having effective phonon frequency of 400–560 cm−1 , about two times lower then in the oxygen containing compounds. Under direct pumping, laser action with double fluoride crystals has been achieved at 2.8–2.9 µm on Er3+ laser transition 4 I11/2 → 4 I13/2 in LiYF4 [2–15], BaY2 F8 [16–19], Na0.4 Y0.6 F2.2 [20], on Ho3+ laser transition 5 I6 → 5 I7 in BaYb2 F8 [21, 22], LiYbF4 [23], and at 3.0–3.4 µm on Dy3+ laser transition 6 H13/2 → 6 H15/2 in Ba(Y, Yb)2 F8 [24, 25] and LaF3 [26]. Laser action at 3.4–4.4 µm has been achieved on Dy3+ laser transition 6 H11/2 → 6 H13/2 in YLF [27]; on Ho3+ laser transitions 5 S2 → 5 F5 [28] and 5 I5 → 5 I6 [29] in LiYF4 , and on Pr3+ laser transition 1 G4 → 3 F4 in BaYb2 F8 [30]. Currently, the RE-doped sulfide and chloride hosts attract particular attention due to the possibility of laser action beyond the 4-µm limit owing to their lower vibrational frequencies and higher quantum yields. These low phonon energy hosts have extremely low non-radiative rates and have been demonstrated to be very advantageous for direct diode-pumped solid-state lasers operating in the 3–9 µm region [31–40]. Room temperature laser action in Dy3+ -doped CaGa2 S4 crystal at 4.31 µm was first reported in [37]. Tunable room-temperature laser action near 4.3–4.4 µm has been demonstrated in low-phonon-energy nonhygroscopic sulfide host (calcium thiogallate CaGa2 S4 ) doped with Dy3+ , and it was noted that the 4.3 µm laser emission is in accordance with the five-times-maximal phonon energy rule of thumb, suggesting that laser emission up to 5.7 µm is possible. Some advantages in output laser efficiency of Dy3+ -doped lead thiogallate (PbGa2 S4 :Dy3+ ) over CaGa2 S4 was demonstrated in [41]. The longest laser wavelength of 7.2 µm has been achieved with the low-phonon-energy host lanthanum trichloride (LaCl3 ) doped with Pr3+ [42].

NEW MONOCRYSTALS WITH LOW PHONON ENERGY

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However, Pr:LaCl3 crystal has the disadvantage of being highly hygroscopic and lasing at low temperatures (T < 200 K). An important step towards practicality was made when the rare-earth-doped alkali-lead halide crystals MPb2 Hal5 (M = Rb, K and Hal = Cl, Br) were identified as promising new low-phonon-energy host materials for mid-IR applications. First, potassium-lead double chloride crystals KPb2 Cl5 (KPC) were synthesized and studied in 1993 [43]. They show high chemical resistance, satisfactory mechanical properties, and have low hygroscopicity, unlike the known simple tri-chloride crystals (RE:LnCl3 ). The KPC material was assigned a promising new laser host material for rareearth ion doping, and having narrow phonon spectrum (h¯ ω0 ∼203 cm−1 ) [44]. The KPC crystal was found to exhibit superior spectroscopic and mechanical properties desirable for practical solid-state mid-IR lasers. Direct pump laser action in Er3+ :KPC at both 1.7 and 4.5 µm from the erbium 4 I9/2 manifold has been demonstrated [45]. In Nd3+ :KPC, laser operation was obtained on the 4 F3/2 → 4 I11/2 transition at 1.06 µm with a slope efficiency of 7.7 % [38] and in Dy3+ :KPC laser action was demonstrated on the (6 H9/2 + 6 F11/2 ) → 6 H13/2 transition at 2.43 µm [37]. New IR emission in Dydoped KPC single crystals around 1.55 µm on the promising 6 F5/2 → 6 H11/2 laser transition is also reported [46]. Narrower phonon spectra are exhibited by bromide crystals. The alkali-lead bromide crystals (RbPb2 Br5 and CsPbBr3 ) were grown first in 1995 and the results of the study of crystal growth and luminescence properties were reported [47]. An efficient purification procedure of starting bromides was proposed and single crystals without cracks, 20 mm in diameter and 30–50 mm in length, have been prepared. Luminescence of undoped RbPb2 Br5 crystal was measured for the first time [47]. The rare-earth-doped potassium-lead bromide (KPb2 Br5 or KPB) and rubidium-lead bromide (RbPb2 Br5 or RPB) crystals have properties similar to that of KPC crystals, but lower phonon cut-off energy (∼140 cm−1 ) [48]. They may be considered as the best matrix for minimizing the primary cause of the passive losses in laser rod arising from nonradiative multiphonon relaxation, therefore, these hosts permit lasing at longer wavelengths with extremely low thermal losses. Laser action in near-IR was demonstrated in Nd3+ -doped KPB and RPB crystals [48]. Spectroscopic study of the Tb3+ :KPB crystals gave evidence that room-temperature laser action should be possible in the mid-IR up to 9 µm [48]. Thus, the rare-earth-doped potassium- and rubidium-lead double halogenides MPb2 Hal5 (M = K, Rb; Hal = Cl, Br) can be considered as promising new materials emitting in a wide spectral range from the UV to mid IR. Interest in these crystals continues to increase each year. Having low hygroscopicity, high chemical resistance, good mechanical properties, and low maximal-phonon

6


frequency, they are readily manufactured and available in a large size of high optical quality for applications in solid-state lasers. The low phonon frequency of chloride and bromide crystals allows rare-earth ions to serve as favorable luminescent centers for laser action over a wide range in the IR and UV-visible spectral regions, where the luminescence of fluoride and oxide crystals is quenched by fast multiphonon relaxation. In the present work we considered the crystal growth, physical and optical properties of new laser crystals based on RE3+ -doped alkali-lead halide matrices, which are suitable for diode-pumped IR, visible and UV lasers. The RE3+ -doped double chloride crystals, RE3+ :KPb2 Cl5 (RE3+ = Pr3+ , Nd3+ , Tb3+ , Dy3+ , Ho3+ , Er3+ , Tm3+ , Yb3+ ), and new double bromides KPb2 Br5 and RbPb2 Br5 doped with Nd3+ and Tb3+ , were grown using the Bridgman technique. Most crystals were grown for the first time. Multiphonon non-radiative relaxation rates were estimated for the studied hosts. The absorption and luminescence spectra, Judd-Ofelt intensity parameters, calculated radiative transition probabilities, lifetimes and branching ratios are summarized. The intense luminescent bands in the UV, visible, and near-IR spectral regions show that all excited levels of RE3+ ions separated by energy gap of E > 1400 cm−1 in chlorides and of E > 1000 cm−1 in bromides are radiative, including 4 I9/2 (Er), 5 I5 (Ho), and 4 F5/2 (Nd) levels, which are considerably quenched in oxides and fluorides. The combination of the high intensity of luminescent transitions and long lifetime of rare-earth radiative levels, together with efficient up-conversion processes, permit us to conclude that MPb2 Hal5 :RE3+ crystals may be considered as promising new luminescent materials for UV, mid-IR, and visible laser-diode-pumped lasers. 2. Crystal growth and common properties of RE-doped MPb2 Hal5 (M = K, Rb; Hal = Cl, Br) crystals 2.1. CRYSTAL GROWTH

Synthesis of MPb2 Hal5 compounds with M = K, Rb, Hal = Cl, Br was performed from high purity chloride salts. The starting high purity (99.999%) reagents, PbCl5 , PbBr2 , KCl, KBr, RbCl and RbBr, were additionally purified by repeated directed crystallization by preliminarily removing of dirty parts. REHal3 was synthesized from RE oxides, 99.99%, with further distillation. The MPb2 Hal5 (M = K, Rb, Hal = Cl, Br) single crystals were grown using Bridgman technique in soldered ampoules with halogen atmosphere [32, 40, 43, 49–51]. To prevent compound decomposition, the internal ampoule pressure exceeded the atmospheric pressure. As follows from phase diagrams (Figure 1), KPC, KPB and RPB melt congruently at 434, 382 and 404◦ C, respectively [49, 52]. Linear temperature gradient in a growth zone of the furnace was ∼20 ◦ /cm and the rate


7

Figure 1. Phase diagrams for KCl-PbCl2 (a), KBr-PbBr2 (b) and RbBr-PbBr2 (c) [49, 52].

of ampoule translation into cold zone was 2 to 4 mm/day. We found regimes for obtaining single crystals of both undoped and RE-doped MPb2 Hal5 compounds with M = K, Rb, Hal = Cl, and Br, of optical quality and with sizes ∼15 mm in diameter and up to 40 mm long. Generally, halides such as chlorides and bromides hydrolyse and therefore crystals contain some products of hydrolysis. The most frequent radicals in MHal are anions like (OH)− , (O2 )− , and (CO2 )2− [51]. When heated, PbHal2 not only hydrolyses but also decomposes. Moreover, if the material contains water molecules or other impurities, decomposition increases. Because RE-doped halides as well as the halide components of MPb2 Hal5 are sensitive to oxygen and moisture, it is imperative that both O2 and H2 O be strictly excluded from the system. The best results are obtained when both PbHal2 and MHal were dried in a vacuum and treated afterwards in Ar-CHal4 atmosphere. It is important also to prevent any contact between purified material and air (i.e. oxygen and water) in both the handling operations of starting materials and the single-crystal growth process. Segregation coefficient, K, for halide crystals (where K is the ratio of RE concentration in crystal to RE concentration in melt for specific RE dopant), was determined by both crystal type and RE ion type: it varies from 0.1 to 1 (Figure 2). The segregation coefficient depends considerably on the difference between sizes of RE and Pb ions. It is minimal for small Yb ions and reaches unity for large Nd ions. Growth conditions for obtaining high quality crystals depend strongly on existence of phase transitions in the solid below melting temperature. Such

8


Figure 2. Segregation coefficients for RE ions in KPC. The Pb radii are given for cubic and octahedral coordination.

transitions are often a reason for twin structure formation and sharply worsen the optical quality of the crystal. 2.2. PHASE TRANSITIONS

Using a set of optical techniques such as differential scanning microcalorimetry, temperature dependence of birefringence and turning angle of optical indicatrix, the phase transitions were studied in MPb2 Hal5 (M = K, Rb, Hal = Cl, Br) crystals in the 270 to 620 K temperature range [53, 54]. Depending on the ratios of ionic radii, M/Hal and Pb/Hal, these compounds can be related to two structural types: monoclinic P21 /c and tetragonal I4/mcm [55]. Examinations showed phase transitions at 530 K/528 K in KPC and at 519.5/518.5 K in KPB in the heating/cooling regimes, respectively. The obtained data are in good agreement with previous data [52]. Phase transition is accompanied by a birefringence jump and a temperature hysteresis, which are typical of first type transitions. Geometry of twinning and turning of optical indicatrix shows that the phase is monoclinic with second-order axis along [010] at room temperature, which is in agreement with the P21 /c symmetry. As follows from observations in polarized light a high temperature phase has rhombic symmetry. This phase transition is related to ferroelastic ones of first type, with ∆H = 1000 ± 200 J/mol and 1300 ± 200 J/mol enthalpy changes for KPC and KPB, respectively. The transition is accompanied by twinning and mmm ←→ P21 /c symmetry changes. As a result of such transition, a component of shear spontaneous deformation appears and crystal is broken into twins with a ±ϕ turning around [010] for optical indicatrix. One can see in Figure 3 that temperature dependence ϕ = ϕ(T) is very unusual for KPC: at room temperature ϕ angle is small (only ∼1 to 2◦ as follows from points 1). This value remains constant with heating and it increases to only 5◦ near phase transition, but

Angle ϕ, deg


9

4 1 2 2

0 300

400

500

600

Temperature, K

Figure 3. Temperature dependence for a turning angle of the optical indicatrix ϕ(T) for KPC (1) and RPC (2) [54].

falls to zero afterwards. With further heating, extinction in the sample does not change. For RPC (points 2 in Figure 3) a value of off-orientation angle between adjacent areas does not change up to the melting temperature. There is no phase transition here and as a result we see no twin structure. The same situation (no twins, no phase transitions) also takes place in RPB, which crystallizes in tetragonal structure. Thus change of halogen ion and passing from chlorides to bromides in an MPb2 Hal5 family slightly decreases a boundary for rhombic phase stability, whereas a cation change with passing from potassium to rubidium increases this temperature, shifting the phase transition to the liquid state of the compound. Thus, RPB structure has tetragonal I4/mcm symmetry and this structure is stable up to the melting temperature. 2.3. STRUCTURAL ANALYSIS

Previously crystal structure of double chlorides was studied [56–58]. The single crystal structural analysis was carried out for all crystals of MPb2 Hal5 family using a STOE STADI4 diffractometer with a Mo Kα radiation. The refined lattice parameters for MPb2 Hal5 crystals are given in TABLE 1. In MPb2 Hal5 structure one can distinguish the layers from polyhedrons KHal9 and Pb(1)Hal9 , bound together by joint triangular faces: these layers are alternating along direction perpendicular to x axis (Figure 4). The Pb(2) ions are in asymmetric anionic cavities (Figure 4). The K and Pb(1) polyhedrons are tri-cap trigonal prisms, whereas Pb(2)Hal8 polyhedron is close to a tetragonal antiprism. Asymmetry in Pb(2) position in a Hal6 cycle brings to an umbrella character of cations location in polyhedrons. Cavities for Pb in chloride matrix and even to a larger extent in bromide matrix are too large for a Pb2+ cation: as a result Pb ions are shifted outside cavity center in both positions and pressed to one of the

10

LUDMILA ISAENKO ET AL. TABLE 1. Crystal

KPb2 Cl5 KPb2 Br5 RbPb2 Cl5 RbPb2 Br5

Symmetry

P21 /c P21 /c P21 /c I 4/mcm

Results of structural analysis for MPb2 Hal5 [59]. Lattice parameters, Z = 4 3

˚ a(A)

˚ b(A)

˚ c(A)

β, degrees

˚ ) V(A

8.854(2) 9.256(2) 8.959(2) 8.43(1)

7.927(2) 8.365(2) 7.973(2) 8.43(1)

12.485(3) 13.025(3) 12.492(5) 14.54(1)

90.05(3) 90.00(3) 90.12(2) 90

876.3(4) 1008.4(4) 892.3(4) 1033(4)

Figure 4. The KPB structure presented as combination of K and Pb(1) polyhedrons.

cavity walls. Imperfection of single crystal KPB samples depends strongly on a microtwin structure. Study of samples with different microtwinning brought one to the following conclusion: microtwinning results in increase of the sample volume and a decrease of monoclinic angle to 90◦ ; in other words microtwinning results in pseudorhombic unit cell. Optical measurements in polarized light showed that twin sizes are of about several microns, whereas the twinning pattern depends on thermal prehistory of the sample. In Figure 5 two KPC crystallographic unit cells are shown. One can see that YZ plane is close to a mirror plane. After twinning operation relative to the X (-x,y,z) axis, one obtains K , Pb and Cl positions, which are close to positions of these atoms in the initial cells. Maximal distances between atom ˚ positions in the initial cell and in the twin cell are 0.11, 0.16, 0.64 and 1.03 A for Pb(1)-Pb(1) , K-K , Cl(2)-Cl(2) and Pb(2)-Pb(2) , respectively. For other Cl ˚ Thus distances between atom positions atoms these distances are less than 0.1 A. of corresponding atoms in initial and twin cells are less than a half of the bond


11

Figure 5. Superposition of two crystallographic unit cells in the KPC structure. One type of unit cell is shown at left from the central vertical line and the other one, obtained after twinning operation (1-x, y, z), is shown at right.

length. Maximal shift is observed for Pb(2), which corresponds to atom jump from one half of the elongated Cl6 cycle in YZ plane to another half of the cycle. This allows one to suppose that twinning happens by hopping mechanism at crystal cooling and depends considerably on a set of point and extended defects, which are formed during crystal growth. The β angle is close to 90◦ for crystals under consideration, which promotes twinning relative to Y and Z axes. The RE ions incorporation into crystal lattice is supposed to go with Pb ions substitution, whereas formation of K vacancy provides local charge compensation. 2.4. OPTICAL PROPERTIES OF UNDOPED MPB2 HAL5 CRYSTALS

Since low frequency crystal dynamics is important both from fundamental and applications point of view, the study of optical properties of new low phonon energy crystals included refractive indices with their dispersion curves and temperature dependence, Raman, absorption, reflection and emission spectra of undoped MPb2 Hal5 crystals, including the nature of UV host absorption bands. 2.4.1. Refractive indices and thermo-optic coefficients Refractive indices were measured using a conventional technique of minimum deviation angle with two prisms of different orientation: n values were found to

12

LUDMILA ISAENKO ET AL. 2,20

a

Refractive indices

Refractive indices

3 1,95 2 1 1,90

2,15

2

8 4 6 Wavelength, µm

1 2

2,10 2,05

0

b

3

10

0

2

4 6 8 Wavelength, µm

10

Figure 6. Refractive indices nx (1), ny (2) and nz (3) versus wavelength in the 1 to 10 micron range for KPC (a) and KPB (b) at 300 K.

−7

−11

a bx

−12 bx

−8

i

−13 −14 by

i

−9

bz

−15 bz

−10 −11

b

bi=dn/dT, 10-5*C-1

bi=dn/dT, 10-5*C-1

−6

by 0

2

4

6 8 10 Wavelength, microns

−16

0

2

4

6 8 10 Wavelength, microns

Figure 7. Thermooptic coefficients βi = dni /dT with i = x, y, z for KPC (a) and KPB (b).

grow in the set KPC → RPC → KPB → RPB. Dispersion characteristics for KPC and KPB are given in Figure 6. In accordance with lattice parameters, nx and ny values are close, whereas nz values are considerably larger. Temperature dependence at 6 wavelengths (1, 2, 3, 5, 7 and 10 µm) was studied using a specially controlled heating device, which was mounted on the optical goniometer, and thermo-optic coefficients βi = dn i /dT were calculated: they are given in Figure 7 for KPC and KPB. One can see that refractive indices n i and βi values become larger in bromides as ion sizes and lattice parameters increase and crystal lattice becomes more friable. These parameters are considerably anisotropic: βx values are about 30 % higher than β y , βz . 2.4.2. Vibrational (Raman) spectra Since low frequency crystal dynamics is important both from fundamental and applications point of view, the Raman spectra were studied. For interpretation of vibrational spectra and establishment of lattice vibration frequency-to-structure correlations, we used the recently developed first-principles approach [60–62]. It is necessary to note that empirical techniques traditionally used ([63, 64], for example) bring in a large number of adjusting parameters in the case of low symmetry structures with many atoms in the unit cell, and it is impossible to


Figure 8.

13

Raman spectra for KPC (1) and KPB (2) crystals.

determine these parameters using a limited amount of experimental data. Thus, the use of parameter-free techniques becomes fundamentally important. Raman spectra were recorded in polarized light at room temperature for MPb2 Hal5 samples with edges oriented along crystallographic axes. For KPb2 Cl5 and KPb2 Br5 , the vibrational representation is reduced to the following irreducible representations in the center of Brillouin zone: = 24Ag (x x, yy, zz, x y, yx) + 24Bg (x z, zx, yz, zy) + 24Au + 24Bu ,

(1)

where the parentheses contain the Raman tensor components for which the corresponding lattice vibrations are active. The experimental spectra are shown in Figure 8. As expected, the spectra are restricted to frequencies hωmax < 250 cm−1 and hωmax < 150 cm−1 , with high frequency peaks located at 203 and 138 cm−1 , respectively; the spectra are strongly anisotropic, and the spectral lines are highly polarized. The number of well-resolved peaks is slightly smaller than the number of modes determined from Eq. (1); therefore, their interpretation requires comparison of the peaks with the results of model calculations. Taking these distortions into account is especially important for low-symmetry structures, since the interactions of multiple moments of ions in these structures contribute substantially to the total lattice energy and the crystal vibration frequency. The short-range part of inter-ionic interactions is calculated in terms of density functional theory, whereas for far-ranging part we used a multipole expansion (up to quadrupoles); multipole moments were found by minimizing the total crystal energy with respect to the corresponding moment. The eigenvectors were obtained by diagonalizing the dynamical matrix and subjected to symmetry analysis. The complete vibrational representation P(g) of the crystal space group was constructed and it was used further to calculate the

14


TABLE 2. Experimental and calculated frequencies of Raman-active lattice vibrational modes in KPC crystals [66]. Ag , ω(cm−1 ) Calculation 33.4 i 16.5 i 7.7 i 16.7 35.0 39.6 43.7 43.7 51.9 56.5 57.7 61.8 70.1 73.9 77.6 86.7 88.7 93.1 101.7 103.2 112.7 124.5 127.1 132.6 158.3

Experiment

18 27 35 43 50 56 62 73

85

108 120 124 127 132 200

Bg , ω(cm−1 ) Calculation 37.7i 28.3i 6.2 28.0 38.3 43.9 46.1 46.1 57.0 65.0 68.6 72.2 74.1 81.9 84.7 89.1 95.7 100.7 102.7 105.0 115.0 120.7 128.4 137.9 161.7

Experiment

33 40 42 48 57

75 85 88 95 108 119 132 144 158 173 202

projection operators [65]. The experimental and calculated frequencies of the Raman spectrum are given in TABLE 2. Note that these experimental and calculated frequencies agree well in the middle portion of the spectrum. For the lowest frequencies (below 20 cm−1 ), the calculated frequencies depend strongly on small changes in the atomic coordinates; their variation within the experimental error can result in significant (up to 100 %) changes in the vibration frequencies. A large number of vibrations in this portion show weak lattice stability: it is likely a result of a near phase transition.

15


A larger discrepancy at high frequencies (the understated calculated values) may be due to an incomplete consideration of the shape of electronic cloud of weakly polarized Cl ions in frames of multipole approximation (a partial covalence of M-Cl bonds). One can see that position of the peak with maximal frequency depends considerably on the halogen type (Figure 8): thus halogen ions take part in this vibration. 2.4.3. Absorption and reflection spectra Absorption spectra for MPb2 Hal5 crystals are shown in Figure 9, both in the IR (Figure 9a) and UV-visible region (Figure 9b). Position of the long-wave edge of the transparency range is determined by masses of the participating ions and vibration frequencies. It is 20 µm(500 cm−1 ) for KPC and 32 µm (312 cm−1 ) for KPB, as estimated on the 1 cm−1 absorption level. Taking into account that hωmax < 250 cm−1 and < 150 cm−1 from Raman spectroscopy, one can conclude that long-wave transparency edge is determined by two-phonon absorption. The short-wave edge of the transparency range was determined as a result of approximation of the fragments with maximal inclination angle relative to the abscissa in Figure 9 b until crossing with this axis (TABLE 3). Chlorides demonstrate maximum of transparency at short waves (RPC is transparent up to 306 nm), whereas for bromides the edge is shifted to longer waves (∼400 nm). The absorption edge shifts to lower energies when temperature increases. Analysis of the reflection spectra reveals several dips at shorter wavelengths, which are better pronounced at temperatures as low as 8 K (Figure 10). These dips are related to exciton absorption and their position depends on M and Hal components and on temperature. The average temperature coefficient for the main peak E1 in the 8 to 290 K range is ∂ E 1 /∂ T = −(2.8–3.0) × 10−4 eV/K. These values as well as specific form of the reflection spectra are typical of large radius excitons. Analysis of exciton peak positions carried out in frames of hydrogen-like Wannier-Mott model [67] allowed one to determine the band gap value Eg and exciton bonding energy R a

b 1

Optical density, D

2,0

2

3

4

1,5 1,0 1a

2 5

6

7

5a

8 1

0,5 0,0

40

60 80 100 Photon energy, meV

2

3 Photon energy, eV

4

0

Figure 9. Absorption spectra for undoped crystals KPB (1, 1a, 2), RPB (3, 4), KPC (5, 5a, 7) and RPC (6, 8), recorded at 290 K (1, 1a, 3, 5, 5a, 6) and 8 K (2, 4, 7, 8).

16


TABLE 3. Position of the short-wave absorption edge at 300 K and 8 K, band gap Eg from reflection spectra (8 K) and exciton parameters E1 , R (8 K) for different halide crystals. Parameter

Short-wave absorption edge

Temperature

KPb2 Cl5 KPb2 Br5 RbPb2 Cl5 RbPb2 Br5

300 K

Eg , eV

E1 , eV

R, eV

4.79 4.12 4.83 4.22

4.45 3.87 4.51 4.0

0.34 0.25 0.34 0.22

8K

E, eV

λ, nm

E, eV

λ, nm

3.77 3.10 3.89 3.36

329 400 318 370

3.99 3.23 4.06 3.56

310 383 306 348

Figure 10. Fragments of reflection spectra for RPC (1), KPC (2), RPB (3) and KPB (4), recorded at 8 K. Arrows show position of the first exciton peak E1 and band gap Eg .

(TABLE 3). Crystal RPC has maximal band gap and the Eg value decreases when Cl is replaced with Br. As follows from TABLE 3, the real short-wave absorption edge is located in MPb2 Hal5 crystals at longer wavelengths relative to Eg position: thus it is due to excitonic absorption. 2.4.4. Photoluminescence and luminescence excitation spectra In the photoluminescence (PL) spectra of MPb2 Hal5 crystals one can see broad non-elementary bands in 1.6–2.9 eV region, with their shape and maximal position depending on M and Hal components as well as on excitation wavelength. In Figure 11, PL spectra for RPC (a) and RPB (b) at different excitations are


17

Figure 11. Low temperature photoluminescence spectra (a, b) and luminescence excitation spectra (c). Photoluminescence spectra recorded at 8 K for RPC (a) and RPB (b) at different excitation: in the transparency region (1), in exciton absorption range (2) and in the range of band-to-band electronic transitions (3). c) Luminescence excitation spectra for RPC (1–4) for 2.4 eV (1) and 2.0 eV PL(2–4) in comparison with the reflection spectrum (5). Spectra (1, 2, and 5) were recorded at 8 K whereas (3, 4) were obtained at 80 and 300 K, respectively.

given. In the general case, one can see that different PL bands are excited in the transparency region, in exciton absorption range and in the range of bandto-band electronic transitions (Figure 11 a), although their position is sometimes close (for example, for bromides (Figure 11 b)). For RPC, the short-wave PL with maxima at 2.0 and 2.4 eV takes place only at band-to-band or excitonic excitations as well as in the region of inter-band transitions whereas a long-wave PL component (∼1.75 eV) corresponds to intra-center transitions in the defects. Intensity of 2.0–2.4 eV PL is maximal at low temperatures of 8–50 K and decreases as temperature increases: PL becomes completely quenched at ∼200 K. The luminescence excitation spectra (LES) demonstrate a set of bands depending on the crystal type: those for RPC are given in Figure 11 c. In all cases, PL intensity decreases in region of inter-band transitions, at excitation energies hν > E g, and the antibate behaviour of details takes place between

18


reflection and luminescence excitation spectra (Figure 11 c). Specific features are considered in the region of Eg and excitonic absorption maxima. The LES longwave edge for 2.0–2.4 eV PL coincides with a long-wave edge of the transparency spectrum (Figure 9 b). In the case of excitation in the transparency range, excitation efficiency increases as temperature increases to 80 and 300 K (Figure 11 c, spectra 2–4), which can testify to thermally activated processes with participation of native or impurity defects. 2.4.5. Electronic excitations and energy transfer Comparison of the obtained experimental results on spectroscopy of MPb2 Hal5 crystals with known data concerning PbHal2 testifies to similarity of these crystal families from the point of view of physics of low-energy electronic excitations and dominating input of lead cations into formation of electronic structure of the states, which determine electronic transitions with minimum energies. In PbHal2 the valence band top is formed by hybridizated orbitals of 6s states of Pb2+ and np-states of Hal− ions (n = 4 for Hal = Br and n = 3 for Hal = Cl). Below, there are orbitals formed by np-states of Hal− ions [68]. Since bottom of the PbHal2 conduction band is formed mainly by 6 p orbitals of Pb2+ ion, electronic transitions with minimum energy take place between Pb ion states and correspond to 6s → 6 p electric dipole transition, bringing to excitation the cation exciton [69–71]. Thus, features in low-temperature reflection spectra of MPb2 Hal5 crystals may be related to electric dipole transitions 6s → 6 p between Pb2+ states, bringing about cation exciton excitation. Analysis of exciton parameters (TABLE 3) [69–72], calculated in frames of hydrogen-like model, allows one to suppose that observed excitonic-related features in reflection spectra (Figure 10) correspond to first (E1 ) and second excited states of free large-radius exciton. Typical dissociation channels for such exciton may be vibrational relaxation with further radiative annihilation, energy transfer to impurity or native defects with further PL in such center, non-radiative recombination in surface states and, finally, dissociation into individual charge carriers or partly bonded electron and hole pairs. Radiative exciton dissociation usually results in a set of specific narrow PL bands near the fundamental absorption edge. Such near-edge PL was not found for MPb2 Hal5 crystals but several bands in low-temperature PL spectra are obviously of excitonic origin. Among them are a short-wave 3.65 eV band in KPC and a weak 2.9 eV band in KPB, which are observed only at low temperatures and are not associated with any defect. There are exponential components in decay kinetics and these bands are excited only near the fundamental absorption edge. Considerable Stokes shift (0.4–0.5 eV) and large width of PL bands mean that excitonic emission appears after vibrational relaxation and therefore the exciton undergoes self-trapping. At 8 K, the mentioned PL bands appear only at excitation


19

in low-energy excitonic absorption band, which corresponds to 6s 2 → 6s6 p transition in Pb2+ ion. Further increase of photon energy results in a fast decline of PL excitation efficiency because of increasing input of non-radiative losses. It is an evidence of high mobility of excitons photo-excited in the excitonic band. Excitation of short-wave PL in the range of interband transitions (hν > E g ) is of low enough efficiency and it shows a low efficiency of recombination channel for these PL bands. Indeed the 3.65 eV band was not found in either X-ray excited or thermo-activated luminescence. Incorporation of the RE ions such as Pr, Er, Nd, Ho, Tb, and Tm results in the appearance of typical PL emission with a well-pronounced fine structure: a set of lines and relative intensity depend considerably on the RE type [72]. Impurity emission appears both at a selective direct excitation of the impurity (RE) center by photons with Eexc < Eg energy and at indirect excitation by high energy photons with Eexc ≥ Eg . In the first case, the lines in LES spectra characterize position of the excited states in energy diagram of the impurity center. Concerning high energy excitation, the analysis of spectra shows an effective energy transfer both by excitonic mechanism and as a result of migration of free electrons and holes with their further recombination in the RE ion. The energy transfer efficiency depends on temperature: it is higher at low temperatures. On the other hand, at Eexc > Eg the efficiency decreases as photon energy increases, which is due to growth of kinetic energy of created charge carriers and their non-radiative annihilation on crystal surface. A multiplication effect is absent for electronic excitations for energies, Eexc > (2 − 3)Eg , and this fact confirms efficiency of the surface losses channel. At T = 8 K there is low probability of exciton thermal dissociation in KPC crystals: thus excitonic mechanisms of energy transfer are effective. Analysis of optical spectroscopy data for KPC with Ho or Er as dopants shows that one of the possible mechanisms of RE excitation at low temperatures is a non-radiative resonant transfer of self-trapped exciton (STE) to impurity center as a result of the dipole-dipole interaction. In fact, there are several broad overlapping PL bands centered at 2.4 and 1.9 eV with microsecond decay and a fast emission at 3.75 eV with τ1 = 0.8 nsec, τ2 = 3.5 nsec. The 1.9 eV emission is due to crystal lattice defects in KPC, whereas 2.4 and 3.75 eV bands correspond to radiative annihilation of triplet and singlet self-trapped excitons, respectively. At room temperature, the STE emission is thermally quenched. Moreover, a thermal dissociation of non-relaxed excitons is possible. In such conditions, an electron-hole mechanism of energy transfer is dominating and recombination luminescence of the impurity (RE) center is observed. 2.5. KEY PHYSICAL PROPERTIES

The MPb2 Hal5 crystal-hosts are of high transparency in the UV to mid-IR spectral range (from 0.3 to 30 µm), have satisfactory mechanical properties, high

20

LUDMILA ISAENKO ET AL. TABLE 4.

The main physical properties of MPb2 Hal5 crystals.

Property

KPC

RPC

KPB

RPB

Transparency range, µm Space group Melting temperature, ◦ C Density, g/cm3 Refraction index at 300 K

0,33–20

0,32–20

0,4 −30

0,37 −30

5 P21 /c − C2h 434

5 P21 /c − C2h 423

5 P21 /c − C2h 382

18 I 4/mcm − D4h 382

4,629 nx = 1.9406 ny = 1.9466 nz = 1.9724 (at 1 µ m) −7.0 −10.0 −10.5 (at 1 µm)

5.041 n = 2, 019 (at 0.63 µm)

5,619 nx = 2, 191 ny = 2, 189 nz = 2, 247 (at 0.63 µm) −13.0 −14.1 −14.9 (at 1 µm)

5.83 no = 2, 2410 ne = 1, 9654 (at 0.63 µm)

4

4

2,5 203

2,5 203

2,5 138

2,5 138

stable

stable

stable

stable

Thermo-optic coefficient β∗ (10−5 ), ◦ C−1 (near 300 K) Thermal conductivity, W/m∗ K Mohs hardness Maximal phonon energy, h¯ ω0 , cm−1 Chemical stability

chemical resistance, low hygroscopicity, extremely low maximal phonon energy (∼200 cm−1 in chlorides and ∼150 cm−1 in bromides), and incorporate RE3+ ions with concentration up to 3%. The main physical properties of MPb2 Hal5 crystals are summarized in TABLE 4. 3. Spectroscopic characteristics of RE3+ ions in MPb2 Hal5 crystals Up to now, the strategy used to search for new laser channels of RE3+ activated crystals involves the problem of determining their spectroscopic characteristics. The feasibility of exciting stimulated emission on f-f transitions of RE3+ ions is most often reduced to the estimate of luminescence quantum yield for steadystate excitation. From the 1970’s until now comparatively simple semi-empirical methods for determination of the most important intensity characteristics of


21

intermanifold j → i radiative transitions of RE3+ ions in laser crystals have been developed and tested. The most important of these characteristics are the probability of spontaneous emission A ji and the probability of nonradiative transition W ji . These parameters affect both real luminescence efficiency of a given j-manifold, quantum yield of which is: ηj = A ji / (A ji + W ji ), (3.1) i

i

and corresponding branching ratios β ji = A ji /

A ji .

(3.2)

i

The values of A ji and W ji can be measured directly in some cases, calculated theoretically, or estimated using semi-empirical methods. Correlation between radiative and nonradiative relaxation rates is very important for consideration of potential of j → i transition for laser action. The classical 4-levels laser scheme is shown in Figure 12. After absorption of the pump energy (transition 0 → 3, B03 – Einstein absorption coefficient), followed by nonradiative W32 and radiative A32 relaxation, stimulated emission can be achieved on the transition 2 → 1 in case the population of the level 2 (N2 ) becomes more than that of the level 1 (N1 ). Laser action is possible if the gain for this 2 → 1 transition is positive: G(λ21 ) = σ21 (λ21 ) · (N2 − N1 ) − L > 0.

(3.3)

Here λ21 is the laser wavelength, σ21 (λ21 ) is the stimulated emission cross section at λ21 , and L is the total losses in laser rod and cavity. In this scheme, high values of B03 , σ21 , W32 , W10 and N = N2 − N1 are desirable for efficient laser action at transition 2 → 1. Probability A ji is the sum of magnetic dipole (md) and electric dipole (ed) transition probabilities. It is simple to calculate the probabilities of the radiative τ3

3 W32

A3i

τ2

2 B03

σ21

A2i

τ1

1

W10

A10

0

Figure 12. The 4-levels laser scheme. B03 – absorption at transition 0 → 3, W ji nonradiative multiphonon relaxation at j → i transitions, A ji radiative (luminescent) j → i transitions, τ j – lifetime of energy level “ j”. Figures near the levels are levels numbers.

22


md-transitions if the dispersion of crystalline refractive index n(λ) is known. Probabilities of the radiative ed-transitions may be calculated using semi-empirical methods and experimental data on absorption cross-section spectra, emission spectra, and life times of energy levels. The values of W ji can be measured directly, calculated theoretically or estimated using the experimental exponential relation, the so-called “energy gap law”. Based on the experimental results and analysis of the relation between W ji and energy gap E ji the following phenomenological dependence was obtained, which describes satisfactorily the experimental data: W ji (T, E ji ) = B · exp(−α · E ji ) · [1 − exp(h¯ ω0 )/kT]− p .

(3.4)

Here B and α are assumed to be defined for a given crystal, energy gap E ji = E j − E i is that between the level “ j” and the nearest lower level “i”, ω0 is the maximal frequency of phonon spectrum or “cut off”, and p = E ji /h¯ ω0 . As it follows from expression (3.4), the lower multiphonon relaxation rate at the given energy gap E ji will be found in crystals with narrower phonon spectrum, in which one of crystalline sub-lattices consists of heavy ions. Thus, the crystal-hosts on the basis of alkali-lead chlorides and bromides may be considered as the most promising for laser action in the IR. In the previous section, high frequency peaks in Raman spectra were found to be at h¯ ω0 = 203 and 138 cm−1 in KPC and KPB, respectively. Selected results of the experimental and theoretical determination of spectroscopic intracenter characteristics of inter-multiplet transitions, such as absorption cross section spectra, radiative and nonradiative probabilities, radiative life times of energy levels, and branching ratios obtained for the RE doped MPb2 Hal5 crystals, are considered in this chapter. 3.1. OPTICAL SPECTRA AND SPECTROSCOPIC PARAMETERS

The RE doped MPb2 Hal5 crystals reveal high values of peak absorption and emission cross-sections of RE ions. In contrast to fluorides, intensive absorption bands with maximal peak absorption cross-sections of RE3+ ions of order (1 ÷ 3) × 10−19 cm2 , located mainly in UV and visible spectral regions, are demonstrated in these crystals. As a result of low phonon-energy, several radiative transitions over a wide spectral region from the UV to mid-IR are exhibited in these new hosts doped with RE ions. 3.1.1. Low-temperature absorption and luminescence spectra Optical transitions in RE3+ :MPb2 Hal5 crystals are characterized by high oscillator strengths and large number of radiative transitions over a wide spectral range from the UV to mid-IR. The peculiarities of substitution of cations by RE ions in

23


TABLE 5. Stark level energies of Er3+ manifolds in KPb2 Cl5 crystal and total level splitting [73]. Er+ multiplet

4F

9/2

4I

9/2

4I

11/2

4I

13/2

4I

15/2

Energy level (cm−1 )

Overall level splitting (cm−1 )

15328, 15291, 15250, 15220, 15201 12513, 12501, 12444, 12427, 12349 10247, 10244, 10236, 10232, 10181, 10179 6675, 6663, 6644, 6550, 6539, 6530, 6513 241, 200, 159, 63, 38, 20, 5, 0

127 164 68 162 241

The error bars for this data are given as ±3 cm−1 for the 4 I15/2 manifold and ±1 cm−1 for the excited states

RE3+ :MPb2 Hal5 crystals are reflected in the optical absorption and photoluminescence spectra. The optical spectra at room temperature exhibit weakly structured bands. Stark component structure was determined for the ground and the first four excited erbium states in the Er:KPC crystals using spectroscopic measurements performed on oriented, single crystals at room and low (10 K) temperatures [73]. The results are presented in TABLE 5. The quantity and positions of the energy levels were consistent with a single erbium site in the host material. The conclusion was made that the erbium ion replaced only one of the two non-equivalent lead ion sites in the material lattice, with the assumption that a potassium vacancy compensates for the charge difference. 3.1.2. Absorption cross section spectra At present, the spectroscopic properties of RE ions are investigated in more detail in KPC host. Examples of room temperature absorption cross-sections spectra for the 4fn -configuration transitions in the RE3+ :KPb2 Cl5 (RE3+ = Pr, Nd, Tb, Dy, Ho, Er, Tm and Yb) crystals are shown in Figure 13 [34], [74–77]. Absorption cross-section spectra for Nd doped KPb2 Br5 and RbPb2 Br5 are presented in Figure 14. Absorption cross-sections were calculated from the absorption spectra measured for the samples with known average RE concentration. The KPC matrix enables doping with RE ions with concentrations of about several percent as maximum. The segregation coefficient is decreasing with changing of the RE ion from the first half of the lanthanide series to the second half (see the Section 2.1 and [78]). For example, in Nd:KPC crystals, the segregation (replacement) coefficient for neodymium is close to 1, K Nd = 0.86 [79]. Neodymium concentration in a boule slowly varies along the crystal length

24

LUDMILA ISAENKO ET AL. σabs , 10−20 cm2

σabs , 10−20 cm2

Pr:KPC

a)

1

10

Pr:KPC

I6, P0

3,0

3

F3, 3F4

2,0

6 3

4

P2

1,5

3

P1

1,0 1

D2

2

1

G4

0,5 0,0

500

550

600

650

1000

1500

σabs , 10−20 cm2

Nd:KPC

c) G5/2 +2G7/2

16

400

500

F5

0,6 F5/2+ H9/2

7

2

F5

4

7

F4 7F3

4

F3/2

0,2

0,0

700

800

2

900

4

6

F4

5

0,6 7

5

F5 F4

16

18

4

F2 7

F1,7F0

Dy:KPC

f)

3

6

F3

14

2

2000

3000

4000

−1

Wavenumber, cm

5000

6000

0

350

400

F9/2

I15/2

4

1000

4

1

0,0

4

F4 7F3

G11/2

7

4

0,2

7

4

7

0,4

12

6

( P, P)3/2 M19/2 4 4 4 I13/2+ K17/2+ I17/2 4 M21/2

7

10

6

F6-7F5

σabs , 10−20 cm2

4

e)

I11/2+ M5/2+ P7/2

Tb:KPC

0,8

8

Wavelength, µm

Wavelength, nm

7

F4

4

F9/2

H11/2 600

σabs , 10−20 cm2

5

7

0,4

4

2

0

d)

7

F6

F4

4

G9/2,7/2, 2K13/2

2

2

2

4

P1/2

4

G9/2,2K15/2

4

6

D1/2,3/2,5/2

12

2500

Tb:KPC

7 7

F7/2+4S3/2

14

0,8

F0,1,2,3

σabs , 10−20 cm2

2000

Wavelength, nm

Host cut-off

450

Wavelength, nm

8

H6, 3F2

3

2,5

8

0 400

10

b)

3,5

3

4

Absorption Cross Section

12

450

500

Wavelength, nm

Figure 13. Absorption cross-section spectra of RE3+ :KPC crystals in UV-VIS-IR spectral domains. RE=Pr (a, b); Nd (c), Tb (d, e), Dy (f, g), Ho (h, i), Er (j, k), Tm (l, m), Yb (n).

according to variations of neodymium concentration in the melt volume and depends on the crystal length. However, these changes are low compared with the fluoride crystals, for comparison in Nd:YLF KNd = 0.3. Since the distribution coefficient for rare-earth ions in KPC host depends on the RE and crystal growth method, the RE concentration has to be known in the sample under study. For this purpose, we used a simple non-destructive

25

NEW MONOCRYSTALS WITH LOW PHONON ENERGY σabs , 10−20 cm2

6

σabs , 10−20 cm2

Dy:KPC

6

g)

6

Ho:KPC

h)

14

H9/2+ F11/2

5

12

5

5

F1 , G 6

10 4

3

8 6

H13/2

H6

G2,3

5 5

6

6

6

1 F5/2

2

H11/2

3

G5

K8 5

3

F7/2

4

G4, K7

H5/2

5

S 2 , F4

5

F5

F2 5

5

6

5

6

6

2

H7/2+ F9/2

3

6

F3

0 400

0 500

1000

1500

2000

2500

3000

Wavelength, nm

σabs , 10−20 cm2

Ho:KPC

i)

1,2

5

500

600

700

800

Wavelength, nm

σabs , 10−20 cm2

3+

KPb2Cl5:Er , along Z

j)

4

G11/2

I7

1,0 0,8 5

H11/2

2

4

I5

0,0 800 1000 1200 1400 1600 1800 2000 2200 2400

300

350

400

σabs , 10−20 cm2

Er:KPC, along Z

k)

1,5 4

F9/2

4

1,0

4

4

F7/2

S3/2

450

500

550

600

Wavelength, nm

Wavelength, nm σabs , 10−20 cm2

F5/2, 3/2

5

4

0,4

G(H)9/2

2

I6

0,2

2

G9/2, 7/2+ K15/2

0,6

Tm:KPC, along Y 3

3,0 2,5

I13/2

1

F3, 2

l) 3

H4

D2

2,0 1,5 1

0,5

4 4

I11/2

G4

1,0

I9/2

0,5

0,0

600

800

1000

1200

1400

1600

0,0 300

400

500

600

700

800

900

Wavelength, nm

Wavelength, nm

Figure 13. Continued.

spectro-photometric method of determination of average rare-earth concentration in the sample described in [34]. The method is based on the comparison of the peak optical density Dλ in the reference line at the wavelength λ and the known peak absorption cross-section σa (λ) in a reference crystal sample with the known concentration of RE. Concentration of RE ions in this reference sample was determined by the X-ray spectral analysis performed with the electron-probing

26

LUDMILA ISAENKO ET AL. σabs , 10−20 cm2

k, cm−1

Tm:KPC, along Y

m) 3

H5

2,5

3

2,0

F4

1,5 1,0 0,5 0,0 1000

1200

1400

1600

1800

2000

Yb:KPC

n)

0,16

Absorption Coefficient

3,0

0,14 0,12 0,10 0,08 0,06 0,04 0,02 0,00 900

Wavelength, nm

950

1000

1050

1100

Wavelength, nm

Figure 13. Continued. σabs , 10−20 cm2

Nd:KPB

9

4

8

a)

2

Nd:RPB

b) 4

4

2,0

7 6

2

G5/2+ G7/2

2

F5/2+ H9/2

1,5

5 4 3 2

2 1

σabs , 10−20 cm2

G5/2+ G7/2

2 2

P1/2

4

G9/2,7/2

2

K13/2

4 4

K15/2

4

G9/2

2

0 400

500

600

1,0

2

F5/2+ H9/2

4

F7/2+ S3/2

4

700

K13/2

0,5

1000

F3/2

2

P1/2 G9/2

900

4

K15/2

2

800

4

F7/2+ S3/2

G9/2,7/2

2

F9/2 H11/2

Wavelength, nm

4

4 2

F3/2

2

4

H11/2 F9/2

0,0 400

500

600

700

800

900

1000

Wavelength, nm

Figure 14. Absorption cross-section spectra of Nd3+ :KPB (a) and Nd3+ :RPB (b) crystals in UV-VIS-IR spectral domains.

micro-analyzer Camebax by CAMEKA. The samples were cut off from different parts of the boule and prepared in the form of thin oriented polished plates. The absorption spectra of these samples were recorded with a Perkin-Elmer Lambda-900 spectrophotometer and the peak absorption cross-sections σabs (λ) were determined for each sample. The values of absorption cross-sections on the wavelength at the line maxip p mum σabs = σabs (λmax ), or “peak absorption cross-sections”, measured at room temperature for RE ions in KPC host, are gathered in TABLE 6. The following expression was taken for the integrated (efficient) cross-section σi, j (int): 1 K i, j (ν)dν, (3.5) σi, j (int) = σi, j (ν)dν = N where σi, j (ν) = K i, j (ν)/N is the absorption cross-section [in cm2 ] at frequency ν, and N is the concentration of RE3+ ions. The Pr:KPC crystals exhibit one of the most intensive absorption bands at 487 nm (transition 3 H4 → 3 P0 ) with a peak absorption cross-section


27

p

TABLE 6. The experimental maximal peak absorption cross sections σabs (λmax ) for the most intense bands in RE3+ :KPC crystals at room temperature. RE3+ ion

Pr Nd Tb Dy Er Tm Ho Yb

λmax , nm

487 589 3335 1297 379.4 797.9 453 982

p

σabs (λmax ), 10−20 cm2

Transition i → j

Reference

10.9 14.9 0.65 5.18 11 (15 K) 21.5 2.85 11 1.78

3 H → 1 I ,3 P 4 0 6 4I 4 9/2 → G5/2+7/2 7F → 7F 6 5 6H 6H 6 → 9/2 , F11/2 15/2

[75, 76] [74] This work [34] [50]

4 15/2 → G11/2 3H → 3H 4 6 5I → 5F , 5G 8 1 6 2F 2 5/2 → F7/2

[77] [76] [75, 76] [76]

4I

σabs (487 nm) = 1.09 × 10−19 cm2 . The intensity of other absorption bands (Figure 13 a and b), associated with transitions from 3 H4 ground state to excited levels 3 H6 + 3 F2 ; 3 F3,4 ; 3 P1 ; 3 P2 , are significantly lower. Room temperature absorption cross-section spectra for Nd:KPC were studied in [50,74,80]. Among transitions between the ground and excited neodymium levels, the highest integrated oscillator strengths in absorption spectrum correspond to the 4 I9/2 → (4 D3/2 , 4 D5/2 , 2 I11/2 ), 4 I9/2 → (4 G5/2 ,2 G7/2 ), 4 I9/2 → (4 S3/2 ,4 F7/2 ), and 4 I9/2 → (4 H9/2 ,4 F5/2 ) transitions (Figure 13c). The highest peak absorption p cross-section, σabs (589 nm) = 14.9 × 10−20 cm2 [74], corresponds to transition from the ground state to one of the group of excited levels 4 G5/2 , 2 G7/2 . The absorption spectrum of Nd:KPC shows bands matching the emission range of laser diodes. The band at 810 nm, 4 I9/2 → (4 H9/2 , 4 F5/2 ) transition, with the peak p absorption cross-section of σabs (810.4 nm) = 6.51 × 10−20 cm2 , is suitable for laser diode pumping. Optical properties of Nd ions in KPB and RPB crystals are studied in detail in [81]. The authors have presented the growth and physical properties of KPB and RPB crystals, and reported the results of the investigation of room-temperature absorption and emission spectra. A strong dependence of absorption cross-sections p on polarization was observed in the studied crystals. The values of σabs (λmax ) for RE ions measured at room temperature in KPB and RPB crystals are given in TABLE 7. p In Tb:KPC, the most intense absorption band around 4.3 µm, with σabs = −20 2 7 7 0.65 × 10 cm , corresponds to F6 → F5 transition. Absorption spectrum of Tb:KPC was studied also in [75, 76, 81–83], but the absorption cross-section spectrum was not determined. p

28

LUDMILA ISAENKO ET AL. p

TABLE 7. The experimental maximal peak absorption cross sections σabs (λmax ) for the most intense bands in Nd doped KPB and RPB crystals. Crystal

λmax , nm

Nd:KPB

592 591 812 812

Nd:RPB

TABLE 8.

p

σabs (λmax ), 10−20 cm2

Transition i → j

Reference

7.8 (Z) 28 2.0 (Z) 1.4 (Z)

4I

4 9/2 → G5/2+7/2 4 9/2 → G5/2+7/2 4I 4 2 9/2 → F5/2 + H9/2 4I 4 2 9/2 → F5/2 + H9/2

This work [81] This work [81]

4I

Absorption cross section for Dy:KPb2 Cl5 . Dy:KPb2 Cl5

Transition from 6H 15/2 to: 4M 6F

6 5/2 + P7/2

5/2 6H 6 7/2 + F9/2 6H 13/2

p

λ [nm]

σabs · 1020 [cm2 ]

352.6 810.4 1297 2820

2.4 0.99 5.18 2.19

At low temperature, the width of the lines becomes narrower and the peak intensity of the lines increases considerably. Thus, in Dy3+ :KPC, the peak absorpp tion cross-section σabs (λmax ) for transition 6 H15/2 → 6 H9/2 , 6 F11/2 was measured in [50] at low temperature (T = 15 K). It was found to be 11 × 10−20 cm2 , while at room temperature it is 5.18 × 10−20 cm2 (TABLE 8). In the Er:KPC crystal, the maximal peak absorption cross-section is p σabs (379.4 nm) = 21.5 × 10−20 cm2 in the Y (010) direction, and corresponds to a narrow (∆λ ≈ 0.9 nm) absorption band in the UV spectral range [77]. Apart from this narrow band, broad absorption bands suitable for the laser diode pumping were observed in the IR region. Namely, in the region of 960– 985 nm there is a broad band peaked at λ = 982.6 nm, with the peak absorption p cross-section σabs = 0.48 × 10−20 cm2 for Z-orientation (001), which corresponds to 4 I15/2 → 4 I11/2 transition (Figure 13 k); and in the region of λ = 798-810 nm, there is a band with a somewhat lower peak absorption cross-section p σa (799.6 nm) = 0.3 × 10−20 cm2 for Y-orientation (010), which corresponds to transition 4 I15/2 → 4 I9/2 . Room and low (10 K) temperature absorption cross-section spectra for three polarizations of the erbium manifolds with energy E < 16000 cm−1 (transitions

29


I15/2 → 4 Ij , j = 13/2, 11/2, 9/2 and 4 I15/2 → 4 F9/2 ) were investigated in [73]. Stark level energies of erbium ion in KPC crystal were determined and it was revealed that the erbium ion replaces only one of the two, non-equivalent, lead ion sites in the KPC matrix. The segregation coefficient for Er in KPC was found to be 0.5 [78].

4

3.1.3. Intensity parameters and radiative probabilities The knowledge of the probabilities of radiative transitions in rare-earth ions is useful for prediction of their possible laser applications. On the basis of the absorption cross-section spectra measurements, the characteristics of spontaneous radiative transitions were calculated with the standard Judd-Ofelt technique [84,85]. Oscilexp lator strengths f i, j (or line strengths Si, j ) for transitions from the ground state i to the excited multiplets j were calculated from the experimental absorption spectra in accordance with: mc2 mc2 exp exp f i, j = K (ν)dν = σ (int), (3.6) i, j N π e2 π e2 i, j exp

where m and e are the electron mass and charge, c is the light velocity, σi, j (int) is the experimental integrated (or effective) absorption cross-section of the i → j transition (in cm). The oscillator strength of the electric dipole transition i → j within the 4 f n configuration of the rare-earth ions in the crystal can be represented as the sum (t) 2 8π 2 mcνχ U S L J | ,

|S | | L| J t 3h(2J + 1)n 2 t (3.7) (t) where |S L| J | U S L J are the matrix elements of unit tensor operator, χ is the local field correction factor, χ = n(n 2 +2)2 /9 is for the dipole transition, n is the refractive index, 2J + 1 is the degeneracy of initial state, and t (t = 2, 4, 6) are the intensity parameters [84,85]. The oscillator strengths for the electric dipole ed,exp exp transitions are calculated from the expression f i, j = f i, j − f md . The oscillator strengths of magnetic dipole transitions f md are taken from [86]. By equating ed,exp experimental and calculated oscillator strengths, f i,ed,calc = f i, j , and solvj ing the obtained set of equations for the intensity parameters t by the least square method, one can find the values of t . These parameters for RE:MPb2 Hal5 crystals are given in TABLE 9. With intensity parameters from TABLE 9, the theoretical oscillator strengths for the absorption bands f ied,calc were calculated for Nd [74] and Er [77] ions in j KPC matrix, and they are listed in TABLES 10 and 11 accordingly. Good agreement between the experimental and calculated oscillator/line strengths is usually observed in case of limited number of transitions used for calculation, when the f i,ed,calc j

S L J , [S L] J =

30

LUDMILA ISAENKO ET AL. TABLE 9. Intensity parameters for RE:MPb2 Hal5 crystals RMS is root mean square error.

RE3+ doped crystal Pr:KPC Nd:KPC

Nd:KPB Nd:RPB Tb:KPC

Tb:KPB Dy:KPC

Er:KPC Er:KPB Ho:KPC Tm:KPC

2 ·10−20 , cm2

0 8.5 5.28 0.33 3.11 15.7 0.41 2.7 2.93−3.0 3.7 23 5.41 11.55 8.73 0.385 0.15 3.11 7.11

4 ·10−20 , cm2

6 ·10−20 , cm2

4.96 6.18 13.09 22.9 7.01 6.3 9.3 7.0 2.16− 0.995 4.3 3.3 0.99 1.41 1.87 1.099 3.64 1.89 4.915

0.57 4.8 7.96 12.74 0.47 3.0 2.6 0.72 0.129− 0.239 0.72 3.9 2.98 1.47 0.78 0.898 2.08 0.39 1.70

RMS, f i j (Si j ) 7.2 · 10−7 7.12 · 10−7

Number of transitions

Reference

8 13 6 4 11 7 9 6 6

[75, 76] [74] [80] [87] This work [81] [81] [75] [83]

(10-40)%

6 8 10

4.26 · 10−7 0.948 · 10−7 (0.38 · 10−20 ) 1 · 10−6 1.7 · 10−6

14 8 7 13 6

[81] [34] [50] [88] [77] [73] [89] [75, 76] [75, 76]

1.5 · 10−6 15% 3.1 · 10−7

most intensive absorption bands for “hypersensitive” transitions are not taken into account. In the case of satisfactory agreement between the calculated and experimental values of the oscillator strengths, it is possible to calculate the characteristics of radiative transitions with these intensity parameters t . Better coincidence between calculated and experimental results was obtained when only the lower energy levels were considered [73]. The following well-known expressions were used to determine the values of radiative characteristics: the oscillator strengths f j,i , the radiative probabilities A Tj,i , and branching ratios β Tj,i of the radiative transitions j → i: f jicalc = A Tji ([S L ]J , [S L]J ) =

gi calc f gj ij

(3.8)

8π 2 e2 ν 2ji n 2 (2Ji + 1) calc ([S L ]J , [S L]J ), (3.9) f mc (2J j + 1) ji

NEW MONOCRYSTALS WITH LOW PHONON ENERGY TABLE 10.

ed,exp

Experimental and calculated oscillator strengths ( f i, j exp

31

and f i,ed,calc ), integrated j

cross sections (σi, j (int) and σi,calc j (int)) of the dipole-dipole transitions i → j from the ground 4 3+ state I9/2 of Nd ion to excited levels in Nd:KPC crystals; ν¯ (i → j) – is the average transition is 7 · 10−7 [74]. frequency. Root mean square (RMS) error for f ied,calc j

4I

ed,exp

ν¯ (i → j), cm−1

Transitions i → j from term 4 I9/2 to: 13/2

4I

15/2 4F 3/2 4F 2 5/2 , H9/2 4F 7/2 4S 3/2 2H 11/2 4G 2 5/2 , G7/2 2K 4 4 13/2 , G7/2 , G9/2 2K 2 15/2 , G9/2 , 2 2 ( D, P)3/2 , 4 G11/2 2P 2 1/2 , D5/2 2P 2 2 3/2 , ( D, P)5/2 4D 4 2 3/2 , D5/2 , I11/2

β Tji

fi j

10−6

,

f ied,calc , j

10−6

exp

σi, j (int), 10−18 cm

σi,calc j (int),

10−18 cm

3850 5820 11300 12400 13300 14600 15800 17100 19000 21200

1.54 0.27 3.47 12.1 9.7 0.74 0.2 45.6 11.3 3.0

1.90 0.27 4.1 10.87 9.92 0.83 0.23 45.64 10.34 2.09

1.36 0.24 3.07 10.71 8.58 0.65 0.18 40.35 10 2.65

1.68 0.24 3.63 9.62 8.78 0.73 0.20 40.39 9.15 1.85

23300 26140 27900

1.22 0.08 23.3

1.20 0.07 24.41

1.08 0.07 20.62

1.06 0.06 21.60

AjiT = T. k Ajk

(3.10)

Here, ν is the average transition frequency in cm−1 , gi( j) = 2Ji( j) + 1 is the degeneracy of the i( j) level, and n is the refractive index at the frequency ν. The radiative lifetimes can be found from the total probabilities of radiative transitions from the level j:

−1 τ rad = A jk . (3.11) j k

The non-radiative transition probabilities, W jiN R , can be estimated using the values exp of the intrinsic lifetimes, τ j , experimentally measured in the samples with low RE concentration:

−1 exp NR τj = (A jk + W jk ) . (3.12) k

32 TABLE 11.

LUDMILA ISAENKO ET AL. ed,exp

Experimental and calculated oscillator strengths ( f i j exp

and f ied,calc ), integrated j

4 cross sections (σi, j (int) and σi,calc j (int)) of the dipole-dipole transitions i → j from the I15/2 ground state of Er3+ ion to the excited levels in Er3+ :KPC crystals. ν¯ (i → j) is the average transition frequency. RMS = 4.2 × 10−7 [77].

Transition i− > j 4I

13/2

4I

11/2

4I

9/2 4F 9/2 4S 3/2 2H 11/2 4F 7/2 4F 5/2 4F 3/2 2 G(H) 9/2 4G 11/2 4G 9/2 2K 15/2 4G 7/2

ν¯ (i → j), cm−1 6500 10160 12500 15300 18310 19200 20300 22020 22300 24300 26300 27100 27300 27700

ed,exp

fi j

10−6 ,

exp

f ied,calc j

σi, j (int),

σi,calc j (int),

1.32 0.76 0.56 2.81 0.43 18.3 2.09 0.52 0.29 0.69 32.3 2.00 0.96 0.46

1.17 0.56 0.34 2.31 0.62 16.11 1.81 0.48 0.19 0.88 28.7 2.73 1.47 0.46

1.17 0.62 0.5 2.48 0.38 16.2 1.85 0.46 0.26 0.61 28.6 1.77 0.50 0.41

1.32 (1.61∗ ) 0.63 0.38 2.61 0.70 18.2 2.05 0.54 0.22 0.99 32.4 3.08 1.66 (1.69∗ ) 0.52

10−6 ,

10−18 cm

10−18 cm

∗ ) The experimental values f ex p = f ed,exp + f md ij

The low RE concentration eliminated the influence of intercenter coupling processes. The calculated oscillator strengths, radiative probabilities, and branching ratios for radiative transitions between low energy RE levels in RE:KPC (RE = Pr, Nd, Tb and Er) crystals are summarized in TABLES 12–15, respectively. Nonradiative relaxation rates W N R are estimated within the Riseberg L.A. & Moos H.W. model [90]. 3.1.4. Multiphonon non-radiative relaxation rates The real emission ability of a crystal can be characterized by the luminescence quantum yield for transitions originating from the excited levels. The luminescence quantum yield strongly depends on the nonradiative relaxation rate W jiN R , the latter in its turn depends on the energy gap between neighboring energy levels E ji : η = j Ai j /( j Ai j + W jiN R ). (3.13)

33


calc , radiative probabilities A T , branching ratios TABLE 12. The calculated oscillator strengths f ji ji

β ji , radiative lifetimes τ rad and multiphonon non-radiative transition rates W N R for dipole-dipole ( j → i) transitions in Pr:KPC crystals [75]. Transition j→i 3H 5 3H 6 1G 4

1D 2

3P

0

3H 4 3H 5 3H 4 3F 4 3H 6 3H 5 1G 4 3F 3 3F 2 3H 6 3H 4 1G 4 3F 4 3H 6 3H 4

ν, ¯ cm −1

calc , f ji

10−6 2050 2570 4330 2700 5310 6980 7190 10408 11600 12500 16837 11250 13950 16560 20880

0.7 0.42 0.17 0.49 1.34 0.91 0.91 0.37 2.02 1.67 0.8 5.12 18.13 1.47 38.34

A Tji ,

β ji

τ rad , ms

∆E, cm −1

W N R, s −1

13.3 3.16 8.6 9.6 101 119 126 108 728 701 605 1730 9430 1077 44707

1 0.27 0.73 0.04 0.40 0.48 0.05 0.047 0.32 0.30 0.26 0.03 0.165 0.02 0.785

75 85

1900 2500

∼1 I13/2

F5/2-> I15/2

2,0

4

4 4 2

4

4

1

4

4

x5

4

0,4

G9/2-> I15/2

0,6

2

4

0,8

G11/2-> I15/2

1,0

F5/2-> I15/2

1,2

G11/2-> I13/2

4

1,4

H11/2-> I15/2

4

1,6

4

F7/2-> I15/2

1,8

2,2 Luminescence Intensity, a.u.

S3/2-> I15/2

2,0

4

Luminescence Intensity, a.u.

2,2

S3/2-> I15/2

KPC:Er

2

0,2 0,0

0,0 360 380 400 420 440 460 480 500 520 540 560 580

360 380 400 420 440 460 480 500 520 540 560 580

Wavelength, nm

Wavelength, nm

a)

b)

Figure 31. Emission spectra of Er3+ :KPC crystals upon LD excitation. a) Excitation by LD1 emitting at 975 nm; curve 2 is multiplied by 5 with respect to curve 1. b) Excitation by one LD1, emitting at λLD1 = 975 nm (curves 1, 2) and excitation by two laser diodes: LD1 emitting at λLD1 = 975 nm and LD2 emitting at λLD2 = 808 nm (curve 3). Curve 2 is multiplied by 5 with respect to curve 1. The spectrum 3 is normalized to a line near 495 nm, corresponding to transition 4F 4 7/2 → I15/2 . T = 300 K.

56

LUDMILA ISAENKO ET AL. EXCITION AND CONDUCTION BANDS 2

G7/2 4G 9/2 4G 11/2

2

ESA 380nm

H(G)9/2

408

4F 3/2

4F 5/2

450

2F 7/2 2H

11/2

4

495 Wij

530

S3/2

4

550

F9/2 Aij

ESA

4I 9/2 4I 11/2

L2 NC2

660

L1

800

980

L3

NC1

4

I13/2 LD1

LD2

SQ 1500

4I 15/2

Figure 32. The energy levels scheme and radiative and nonradiative transitions in the Er:KPC crystal under selective excitation by laser diodes LD1 (λLD1 = 975 nm) and LD2 (λLD2 = 808 nm). ESA – excited state absorption, SQ – selfquenching, NC1 and NC2 – nonradiative upconversion (ETU), thin solid arrows indicate luminescent transitions at the shortest wavelength. Figures near the arrows are the wavelengths in nm corresponding to the highest energy transitions. Laser transition at 4.4 µm is marked with bold arrow L1, the probable mid-IR laser transitions in Er:KPC crystal denoted with double dash arrows L2 (near 3.4 µm) and L3 (near 2.8 µm).

(Figure 32). In any case, population of the 4 F5/2 , 2 G9/2 and 4 G11/2 levels requires at least three photons at 975 nm. Corresponding luminescence bands originating from 4 F5/2 level (around 455 nm), from 2 G9/2 level (near 410 nm) and from 4 G11/2 level (around 385 and 507 nm), have lower intensity (note that curve 2 in Figure 31, corresponding to these transitions, is multiplied by 5). Pumping of Er:KPC with two laser diodes, LD1 (λLD1 = 975 nm) and LD2 (λLD2 = 808 nm), leads to significant increase of the luminescence from the 4 F5/2 level at 450 nm (Figure 31 b, curve 3). In the case of two-wavelength CW laser diode pumping, the 4 F5/2 level is populated due to two-step excitation: transitions 4 I15/2 → 4 I11/2 (GSA of LD1 emission) and 4 I11/2 → 4 F5/2,3/2 (ESA of LD2 emission), as shown in Figure 32. The last process is efficient only in the presence of LD1 emission, because of rather low absorption cross-section at 808 nm, which p is σabs (808 nm) = 0.09x10−20 cm2 .

57

3

7

5

1

4

3

3

5

2

2

1

6

2

4

1

0 0 50 100

Ti me ,

µs

Tim 150200 250 e, 300 µs

0 0 200 400 600 800 1000 1200

460 480 500 520 540 560 580 600 600

Wavelength, nm

650

700

750

800

850

b) 20 15

5 10

6

5 0

20

3

1

15 10

2

4

5 0

Wavelength, nm

c)

Ti

3

460 480 500 520 540 560 580 600

Ti

me

me

,µ

s

,µ

s

0

Luminecsence intensity, a.u.

a)

7

900

Wavelength, nm Luminecsence intensity, a.u.

Intensity, a.u.

6 4

Luminecsence intensity, a.u.


6000 600 650 700 750 800 850 900

Wavelength, nm

d)

Figure 33. Room temperature upconversion luminescence spectra of Er:KPC crystal under IR pulse laser excitation of the 4 I11/2 level at λexc = 980 nm. Pulse duration ∼15 ns. The spectra were recorded using CCD camera with delay = 0. Time between neighbouring spectra (gate width) was varied from 10 µs to 200 µs, each spectrum was recoded during the time interval (gate step) from 10 µs to 200 µs. a) Gate width = gate step = 10 µs; b) gate width = gate step = 40 µs; c) gate width = gate step = 100 µs; d) gate width = gate step = 200 µs. The numeration of the emission bands corresponds to transitions: 1–4 S3/2 → 4 I13/2 (850 nm); 2–4 I9/2 → 4 I13/2 (800 nm); 3–4 F7/2 → 4 I13/2 (712 nm); 4–4 F9/2 → 4 I15/2 (660 nm); 5–4 S3/2 → 4 I15/2 (540 nm); 6–2 H11/2 → 4 I15/2 (530 nm); 7–4 F7/2 → 4 I15/2 (490 nm).

Further experiments with short-pulse IR laser excitation provided direct evidence on the efficiency of ETU processes in Er:KPC crystal with Er concentration of about 2.7 at.%. The population dynamics of erbium levels was studied using short-pulse laser excitation at λexc = 980 nm. Fragments of time-resolved room-temperature luminescence spectra are presented in Figure 33 a-d. The luminescence bands in the visible spectral range (455–600 nm) correspond to the 4 F7/2 → 4 I15/2 (495 nm), 2 H11/2 → 4 I15/2 (530 nm) and 4 S3/2 → 4 I15/2 (545, 555 nm) transitions, respectively. As follows from Figure 33, and from study of luminescence kinetics, only the 4 F7/2 level is populated directly via two-step absorption (GSA and ESA). Measurements of luminescence kinetics obtained under the same excitation conditions by short laser pulses at 980 nm (Figure 34) have

58


1

Luminescence intensity

Luminescence intensity, a.u.

lg(Ilum /I0)

τ1exp = 10.7 µs 0,1

τ2exp = 150 µs

1

4 3 2 1

0,1

0,01 0,00

0,05

0,10

0,15

0,20

0,0

0,5

1,0

1,5

Time, ms

Time, ms

a)

b)

2,0

2,5

3,0

Figure 34. Luminescence kinetics for Er:KPC 2.7 at.% crystal under selective laser excitation of 4 I11/2 Er level (λexc = 980 nm, pulse duration ∼15 ns). a) Luminescence decay from 4 F7/2 level, transition 4 F7/2 → 4 I15/2 , λem = 495 nm. b) Curve 1 – the luminescence band at 380 nm; curve 2 – at 455 nm; curve 3 – at 660 nm; and curve 4 – at 800 nm, these bands correspond to 4G 4 4 4 4 4 4 4 11/2 → I15/2 , F5/2 → I15/2 , F9/2 → I15/2 , and I9/2 → I15/2 transitions, respectively.

shown that luminescence from level 4 F7/2 (Figure 34a) has no risetime and exhibits two components with exponential decay and lifetimes τ1 exp = 10.7 µs and τ2 exp ≈ 150 µs. The first component coincides with lifetime of the 4 F7/2 level, the second corresponds to ETU process (NC2 in Figure 32). Except the one-photon directly pumped 4 I11/2 level, emission from all other levels, namely 4 S3/2 (546 and 850 nm), 2 H11/2 (531 nm), 4 F5/2 (455 nm), 2 G(H)9/2 (408 nm), and 4 G11/2 (384 and 507 nm), occur with different risetimes and have complicated kinetics with non-exponential decay (Figure 34 b). This means that all these levels are populated due to ETU processes, which play the most important role in Er:KPC crystals under IR excitation. Optical properties of Er3+ -doped KPb2 Br5 crystals are reported in [89]. Under 975 nm diode laser pumping, Er:KPB revealed intense blue upconversion emission, whereas Er-doped KPb2 Cl5 (KPC), which has maximal phonon energy of 203 cm−1 , exhibited a dominant green Er3+ upconversion emission. The blue upconversion from Er:KPB can be attributed to emission from the 4 F7/2 excited state of Er3+ , which is quenched in most solid hosts due to strong multiphonon non-radiative decay. In KPB, the 4 F7/2 level becomes highly radiative with a room-temperature lifetime of ∼ 0.085 ms and estimated quantum efficiency of 94%. For comparison, the 4 F7/2 decay time in Er:KPC was only ∼ 0.011 ms at room temperature and the radiative quantum efficiency was estimated to be ∼ 9%. The other emission bands in Er:KPB crystals were observed in the IR at 1.5 µm (4 I13/2 → 4 I15/2 ), 1.7 µm (4 I9/2 → 4 I13/2 ), 2.0 µm (4 F9/2 → 4 I13/2 ), 2.7 µm (4 I11/2 → 4 I13/2 ), 3.6 µm (4 F9/2 → 4 I9/2 ), and 4.5 µm (4 I9/2 → 4 I11/2 ), indicating the potential of Er:KPB for IR laser applications.


59

Laser action of Er:KPC crystal in mid-IR, tunable in the range from 4.4 to 4.7 µm, was achieved in [45] at the 4 I11/2 → 4 I13/2 transition. This transition is labeled in Figure 32 by bold arrow, the probable mid-IR laser transitions in Er:KPC crystal are denoted with double dash arrows, L2 (near 3.4 µm) and L3 (near 2.8 µm). 5. Conclusion Experimental techniques for obtaining MPb2 Hal5 crystals of optical quality were developed, RE impurity structure, vibrational spectra, phase transitions and electronic excitations were studied, and RE segregation coefficients were estimated. Spectroscopic study of low-phonon-energy RE3+ :MPb2 Hal5 crystals grown by Bridgman techniques showed that their optical spectra exhibit broad nonstructured absorption and emission bands. The absorption spectrum of Nd, Er and Tm doped crystals shows bands matching the emission range of laser diodes. The RE3+ :KPb2 Cl5 crystals exhibit intense luminescence bands in the UV, visible and IR spectral ranges. Low nonradiative relaxation rates in the KPb2 Cl5 hosts provide a high luminescence quantum yield for transitions in the UV, visible, near- and mid-IR spectral regions. These features of the RE3+ :KPb2 Cl5 crystals create real possibilities for highly efficient laser action in mid-IR and make them promising active media for direct laser-diode-pumped solid-state lasers emitting in the nearand mid-IR spectral range up to 5 µm. The distinctions in phonon spectra for MPb2 Br5 and KPb2 Cl5 matrices lead to differences in luminescence properties of RE3+ :MPb2 Br5 and RE3+ :KPC crystals. The lower multiphonon relaxation rates in RE3+ :MPb2 Br5 crystals permit one to consider these crystals as promising active media for laser action at wavelengths longer than 5 µm. But the same reason causes difficulties in achieving laser action in RE3+ :MPb2 Br5 crystals under indirect laser diode pumping. Thus, low multiphonon relaxation rate from the 4 F5/2 Nd level in MPb2 Br5 matrices worsens the conditions for population of 4 F3/2 level. Consequently, direct laser diode pumping into the upper laser level is preferable for studied crystals. Moreover, energy transfer (self-quenching and upconversion) processes play a significant role in the creation of population inversion on the desirable laser transition levels and they have to be taken into account. The combination of high intensity of luminescent transitions, low multiphonon relaxation rates, together with efficient up-conversion processes give us an opportunity to consider RE3+ :MPb2 Hal5 crystals as one of the most promising active media not only for mid-IR, but also for visible and UV solid-state upconversion diode-laser-pumped lasers with extremely low Stokes (thermal) losses.

60


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ORTHORHOMBIC CRYSTALS OF LITHIUM THIOINDATE AND SELENOINDATE FOR NONLINEAR OPTICS IN THE MID-IR Orthorhombic Crystals of Lithium J.-J. ZONDY Institut National de Métrologie, Conservatoire National des Arts et Métiers (INM-CNAM), 61 rue du Landy, 93210 La Plaine Saint Denis, France V. PETROV∗ Max-Born-Institute for Nonlinear Optics and Ultrafast Spectroscopy, 2A Max-Born-Str., 12489 Berlin, Germany A. YELISSEYEV, L. ISAENKO, and S. LOBANOV Institute of Geology and Mineralogy, Siberian Branch of Russian Academy of Sciences, 3 Ac. Kopyug Av., 630090 Novosibirsk, Russia

Abstract. We review the optical and other relevant properties of two lithium indium compounds with wurtzite type structure, LiInS2 and LiInSe2 , which occupy a unique position among the mid-IR nonlinear crystals, having band-gaps at 347 nm and 433 nm, respectively. Realized and potentially interesting frequency conversion schemes with these two biaxial crystals are discussed. Keywords: Lithium thioindate, lithium selenoindate, nonlinear optical crystals, mid-infrared spectral range, down-conversion, optical parametric oscillators, optical parametric amplifiers, ultrashort laser pulses.

1. Introduction To date, only a few suitable nonlinear crystals combining a transparency extending into the mid-IR range above ∼5 µm (the upper limit of oxide materials) and largeenough birefringence to allow phase-matching over their transparency ranges are available. The binary and ternary birefringent noncentrosymmetric crystals now in use in that spectral range include the chalcopyrite semiconductors AgGaS2 (AGS), AgGaSe2 (AGSe), ZnGeP2 (ZGP) and CdGeAs2 (CGA), the defect chalcopyrite HgGa2 S4 (HGS), GaSe, CdSe, and Tl3 AsSe3 (TAS) [1]. Some other crystals like ∗ To whom correspondence should be addressed: e-mail: [email protected]

67 M. Ebrahim-Zadeh and I. T. Sorokina (eds.), Mid-Infrared Coherent Sources and Applications, 67–104. c 2008 Springer.

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proustite (Ag3 AsS3 ) and pyrargyrite (Ag3 SbS3 ) have already lost their importance because they were completely replaced by the more technological AGS while the growth technology of HgS was never developed [2]. The list of the nonoxide birefringent inorganic crystals ever used will be full if the elemental Se and Te are added: Their linear losses are, however, so high that at present they could be interesting (especially Te) only for diagnostic purposes of short pulses at longer wavelengths [2]. All these mid-IR crystals are uniaxial. All of them that are now available commercially or quasi-commercially (from laboratories) have their specific advantages but also some drawbacks: AGS and AGSe have low residual absorption but poor thermal conductivity and anisotropic thermal expansion with different sign, ZGP has excellent nonlinearity and thermal conductivity but multi-phonon and residual absorption limit its transparency from both sides so that pump wavelengths for optical parametric oscillators (OPOs) should lie above 2 µm which corresponds to less than 1/3 of its band-gap, CGA possesses extremely high nonlinearity but exhibits also absorption features and low temperatures are required to avoid the residual losses, HGS has a very high nonlinear figure of merit but its growth technology is very difficult and only small sizes are available, GaSe has large nonlinearity and birefringence but it is a soft, cleaving compound, with very low damage threshold, CdSe is transparent up to 18 µm but its birefringence and nonlinearity are quite modest, TAS exhibits rather low losses in its transparency range but its thermal conductivity is extremely low, and finally Te is a unique nonlinear material having in mind its extended wavelength range and superior nonlinear susceptibility but as already mentioned its applicability is limited by the high linear losses. Two approaches to develop alternative solutions and avoid these drawbacks in specific applications will be presented in two other Chapters of this book: These are the manufacturing of quasi-phase-matched orientation patterned structures with highly nonlinear but isotropic semiconductors, e.g. GaAs which has a mature technology [3], and the doping or mixing of nonlinear crystals to produce more complex quaternary compounds like Cdx Hg1−x Ga2 S4 and Agx Gax Ge1−x S2 [4]. The extremely difficult and specific for each compound growth technology and the complex and expensive methods necessary to characterize the properties make it really an event when new mid-IR nonlinear crystals can be added to the above short list. This Chapter is devoted to two such ternary chalcogenides whose growth technology was recently improved to such an extent that it was possible to perform extensive characterization and even realize some applications. These two materials, LiInS2 (LIS) and LiInSe2 (LISe), not only proved to be useful for the mid-IR spectral range but possess some unique properties which will definitely guarantee them a place among the other mid-IR nonlinear crystals if some technological issues are developed to an end. Moreover, their attractive features already stimulated the study of further crystals belonging to the same class, like LiGaS2 , LiGaSe2 , and LiGaTe2 which are now also under development [5, 6].

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Here, we will briefly review the history of LIS and LISe, and the growth methods used, summarize their properties relevant for nonlinear optics, and describe previously realized and possible future applications. 2. Development, growth, composition, and structure of LIS and LISe Single crystals of LIS were shown to crystallize in the β-NaFeO2 structure, which is a superstructure of the wurtzite type, by Hoppe as early as 1959 [7], although the compound itself was synthesized also earlier [8]. This means that LIS is an 9 orthorhombic crystal with space group Pna21 ≡ C2v and point group mm2. It is isostructural to the oxide nonlinear crystal LiGaO2 [7]. Such compounds have the same chemical formula as many chalcopyrites, AI BIII CVI 2 , but different structure when the monovalent element is an alkali metal (A = Li. . .Cs). LIS crystals with optical quality were grown for the first time by Boyd et al. at Bell Labs in 1973 [9]. Notwithstanding the small size and the poor quality of these first samples this group managed in their unprecedented manner to measure the transparency, linear dispersion, birefringence and nonlinear susceptibility of LIS. They grew the isostructural LISe in the same year but its characterization, comparative to LIS, was limited to electro-optic and pyroelectric properties [10]. Probably due to the growth difficulties, the development of LIS, LISe and other related compounds was slower than that of AGS and AGSe. Although Kish et al. [11] systematically described the structural and band-gap properties of the whole class of AI BIII CVI 2 compounds with A=alkali ion, B=Ga, In, Tl, and C=S, Se, Te, they did not place much attention on the development of the crystal growth and no further optical properties were analyzed. The same refers to the Japanese group of Kuriyama et al. at Hosei University who were more interested in the electrical and photo-emission properties. By the 1990-ies two groups, from Russia (Novosibirsk, the present authors) and Germany (Leipzig-Freiburg i. Br.), independently succeeded in the growth of some LiBC2 compounds. Most of the important results of the German group are summarized in the two dissertations (one of them devoted solely to LISe) [12, 13], and the references therein, but this group is unfortunately no more active. Their efforts were focused more on the crystal growth methods, creating phase diagrams, and crystallographic studies while optical aspects were restricted to transmission measurements near the band edge and infrared (reflection and Raman) spectroscopy. On the opposite, the activities of the Russian group were devoted more to the improvement of the crystal quality and the growth of large size single crystals as well as applications as nonlinear optical materials and that is why their activities included also profound optical characterization of the linear and nonlinear optical properties. The work on LIS crystals grown by this group which was performed in collaboration with several European partners was recently summarized in a comprehensive review [14]; a similar review on LISe was just submitted for publication [15].

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LIS and LISe are congruently melting compounds and can be grown from the melt using the three elements as starting materials. Boyd et al. grew LIS in graphite crucibles by directional solidification [9]. The melting point was around 880◦ C. The obtained crystals were either colourless or with yellow or red tinge. They used the same method to grow LISe and obtained deep red colour crystals [10]. Kamijoh and Kuriyama grew single crystals of LIS (colourless or light yellow in colour) of about 5 × 4 × 4 mm3 and LISe (deep red in colour) of about φ18 mm × 20 mm by directional solidification with a temperature gradient of 6◦ C/cm (LIS) and 4◦ C/cm (LISe) at a cooling rate of 2◦ C/h [16, 17]. They determined a melting temperature of 904◦ C for LISe [17]. Kish et al. [18, 19] and Kovach et al. [20] used the horizontal Bridgman-Stockbarger technique at a rate of 0.4. . . 0.8 mm/h to obtain single crystals of LIS with yellow tinge and sizes of up to 3 × 3 × 4 mm3 , and established a melting temperature of 990◦ C [20, 21]. The LIS growth parameters used for the directional solidification and the horizontal Bridgman-Stockbarger methods were described in [12]. The Bridgman-Stockbarger technique yielded larger single crystals (φ8 mm × 12 mm) which were colourless, yellow or red in colour [22]. An excess of Li and S had to be used to compensate the losses during evaporation and incorporation in the crucible [12, 16, 22]. The melting temperature of LIS was determined to be 980◦ C [22]. Phase diagrams of the system Li2 Se-In2 S3 can be found in [12,23]. The LISe growth parameters used for the directional solidification and vertical Bridgman-Stockbarger methods were described in [13]. LISe crystals as large as φ10 mm × 20 mm were obtained by directional solidification and their colour was yellow brownish [24]. The melting temperature was determined to be 897◦ C. Similarly, an excess of Li and Se was required in order to compensate the loss during the growth process [13, 17, 24]. The phase diagram of the system Li2 Se-In2 Se3 was also studied [13, 25]. In order to prevent the violent reaction between Li and S due to rise in temperature, Kuriyama and Kato [26] used LiIn alloys as a starting material for the growth of LIS. The crystals grown by this socalled indium solution method were colourless and transparent or light yellow in colour with a maximum size of 5 × 4 × 4 mm3 . More recently, Badikov et al. [27] grew LIS and LISe by the vertical Bridgman-Stockbarger technique starting with In2 S(e)3 , Li and S(e), and achieving crystal sizes of φ18 mm × 50–60 mm. They determined melting temperatures of 1030◦ C for LIS and 920◦ C for LISe. Finally, the isostructural mixed compound LiInSSe, which can be regarded as a solid solution LiIn(S1−x Sex )2 for x = 0.5, was also successfully grown by the same method achieving similar sizes [28]. We use a seeded Bridgman-Stockbarger process in a vertical two-zone furnace with counter pressure to grow large size single-crystal ingots of LIS and LISe. Details on the growth procedure can be found elsewhere [29, 30]. In principle, the synthesis and growth of LIS and LISe follows the same procedure as that for growing chalcopyrites, except for some refinements related to the volatility of the


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elements and the chemical reactivity of Li with the container walls. The purity of the starting materials is 99.999% (In, S, Se) and 99.9% (Li). The chalcogens are additionally purified by sublimation in vacuum while the metals are subjected to repeated zone melting and directional crystallization. Since the most volatile component, S or Se, has a high partial pressure at the temperature of the LIS(e) pyrosynthesis, the latter is carried out in a two-zone furnace to avoid the container explosion. The temperature of the “hot” zone, in which the crucible with the reaction mixture is placed, is 50. . .100◦ C higher that the melting temperature of the crystal. Our up-dated values for the melting temperatures are 1037 ± 7◦ C for LIS, which is close to [19, 27, 31], and 915 ± 5◦ C for LISe, which lies between the values specified by others [11, 17, 24, 27]. The temperature of the “cold” zone is selected in such a way that the vapour pressure does not exceed 2 atm. The synthesized compound is placed into a glasscarbon ampoule which is in turn mounted inside a sealed silica ampoule of larger diameter filled by dry Ar (0.5. . . 1 atm). The inner ampoule is necessary to prevent the outer quartz tube from reaction with Li. Such a double-wall growth ampoule containing the polycrystalline synthesis charge and a seed is placed in the furnace so that charge and the upper portion of the seed are melted. A temperature gradient of 10. . .15◦ C/cm is sufficient to maintain a stable growth interface in the furnace. Growth is accomplished by moving the melt interface slowly from the seed. The ampoule is shifted at a rate of 1. . . 10 mm/day. Initially we used (010) and (001) oriented seeds. However, since the thermal expansion of LIS and LISe is almost isotropic, in contrast to AGS and AGSe, the present state of the art allows to use any seed orientation in order to grow sufficiently large crystals along the required phase-matching directions. Typical dimensions of the single crystal ingots obtained are 15. . . 20 mm diameter and 30. . . 40 mm length. They are free of extended defects as inclusions, twins, cracks, etc. In order to improve the synthesis conditions for stoichiometric growth, the LIS(e) evaporation process was studied using an unique thermo-microscopic technique [30]. Incongruent sublimation at temperatures lower than the melting points was observed. According to chemical analysis, the vapour condensate consists of S(e) and later Li, which allows to account that the final compositions are shifted towards binary sesqui-chalcogenides. This depends on the pressure inside the ampoules. Incongruent sublimation is one of the reasons for deviation from stoichiometry of the as-grown crystals. Samples of stoichiometric composition are colourless for LIS and yellowish for LISe. Sometimes such crystals can be directly grown and no annealing is necessary. However, usually the as-grown ingots are cloudy (milky) and display a variety of tinges from colourless or slightly yellow (typical for LIS) to yellow or greenish (typical for LISe), depending on the growth conditions and initial reagent composition (Fig. 1, left). The milky features occur during cooling when fine-textured precipitates of a second phase appear. The second phase precipitates can be removed by annealing the as-grown ingots

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Figure 1.

As grown and annealed pieces of LiInSe2 (LISe) and LiInS2 (LIS).

in evacuated chamber with a suitable atmosphere close to the melting temperature. The annealing atmosphere depends on the initial charge composition which deviates from the stoichiometric one. Both, this deviation and the annealing procedure aim at achieving stoichiometric composition at the end. However, it is very easy to pass the stoichiometric point in the annealing process. In this case the colour can change, e.g. to rose for LIS and red for LISe, for chalcogen excess. This is related to additional absorption bands near the band edge although the transparency in the IR is restored almost to the theoretical level determined by the Fresnel losses. Such coloured samples with deviation from stoichiometry are shown on the right side of Fig. 1. The stoichiometry of the grown samples is investigated using differential dissolution technique combined with inductively-coupled plasma analysis [29]. As grown crystals may show e.g. up to 3% deficit of S(e)2 relative to Li + In, and up to 4% deficit of Li relative to In but after annealing also excess of S(e) could be observed [32]. A detailed structural analysis of LIS and LISe was performed by Kish et al. [18] and by Hönle et al. [33], respectively. The structure of LIS and LISe is formed by LiS(e)4 and InS(e)4 tetrahedrons, and the S(e)2− ions are arranged in hexagonal packing with tetragonal and octahedral cavities (tetra- and octapores). This β-NaFeO2 structure of LIS and LISe is less dense than the chalcopyrite structure of AGS and AGSe due to the presence of these empty cavities in the unit cell volume. Only half of the tetrapores are occupied by Li and In while all octapores are empty. The spontaneous polarization is due to the fact that in each bipyramid formed by two adjacent tetrapores only one is occupied by a cation. The unit ˚ b = 8.1 A, ˚ and c = 6.5 A ˚ for LIS, and cell parameters are roughly a = 6.9 A,


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˚ b = 8.4 A, ˚ and c = 6.8 A ˚ for LISe [34]. The exact lattice parameters a = 7.2 A, depend on the coloration, i.e. on the growth and annealing conditions, and the exact stoichiometry, but the structure of all LIS and LISe crystals is the same [34]. The presence of point defects and the influence of annealing on them has been studied in LIS by optical absorption and photoluminescence spectroscopy [22, 26, 29, 31, 35–38]. In principle the nature of such defects can be derived from the analysis of the composition and the structure. Typical examples are sulphur vacancies VS , interstitial sulphur Si after annealing, and antisite InLi defects. Similarly, point defects in LISe were studied by photoluminescence [37], optical absorption [34, 39], and nuclear magnetic resonance [32]. Point defects determine the crystal colour through their absorption bands which are affected by the annealing procedure. On the basis of the detailed study of the structural properties of LIS it has been suggested that the strength of the Li-S bond is weaker than that of the In-S bond (high mobility of the Li cations in the LIS lattice) and that this effect is due to the high ionicity of the Li-S bond [18]. That the Li-S(e) bond is weaker than the In-S(e) bond was confirmed also by other studies of LIS [14] and LISe [40]. Analyzing spectroscopic data it was possible to conclude that the Li-S(e) bonds in LIS and LISe are essentially ionic in nature and the structural properties (stability of the β-NaFeO2 structure) can be understood in terms of the average bond parameters [41]. 3. Band-gap, transparency, and IR cut-off of LIS and LISe Besides to more ionic bonds, the wurtzite-type structure of LIS and LISe is expected to lead to larger band-gaps in comparison to the Cu and Ag chalcopyrites [40]. The band-structure of LIS is of direct type (direct transitions between parabolic bands) [26, 31, 32, 34, 36]. The band-gap energy of LIS has been estimated at low and room temperature by photoluminescence [16, 35] and transmission [12, 19, 22, 26, 31, 42] measurements. Our updated value of 3.57 eV measured at room temperature with thin plates of LIS [14] is in good agreement with most of the previous transmission measurements [12, 22, 26, 31, 42]. Similarly, a lot of works dealt with the band-gap of LISe at low and room temperature using transmission [13,17,23,43–45], electrical resistivity [46], diffuse reflectance [47], and photoluminescence [37] measurements. Electronic structure calculations yielded a band-gap energy less than 2.1 eV [48]. The experimental results depend on the colour of the samples used, i.e. on the point defects present, and their interpretation and comparison are complicated: For instance, in one of the studies a band-gap at 2.03 eV was attributed to indirect or pseudodirect transitions in LISe but for a thickness of 4 µm a direct band-gap near 2.9 eV was also identified [45]. However, transmission measurements with yellow colour LISe indicated a direct band-gap [13, 23, 42, 44], and the results were very close to our updated value of

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Figure 2.

Polarized transmission spectra of LIS (a) and LISe (b) for a thickness of 5 mm.

2.86 eV [32, 34]. The polarization dependence of the band-gaps of LIS and LISe is only weakly pronounced [29, 34]. The room temperature unpolarized absorption measurements with the first optical quality LIS samples (light yellow in colour) indicated that the optical losses can be reduced to less than 0.25 cm−1 in the clear transparency range while the 1 cm−1 absorption level corresponded to 0.5 and 10 µm [9]. Other unpolarized transmission spectra of LIS with different thickness can be found elsewhere [19, 49–53]. Losses of 0.1. . .0.25 cm−1 in the clear transparency range and 1.1. . .2.3 cm−1 at CO2 (9.2. . .10.8 µm) laser wavelengths as well as a transparency window of 0.4. . .12.5 µm at the 10% level were specified for a thickness of 3.6 mm [49–52]. Careful measurements with polarized light showed that the 50% transmission level for a thickness of 5 mm extends from 0.5 to 9 µm while the clear transparency range with transmission defined by the Fresnel losses is from 0.8 to 8.1 µm, Fig. 2a [14]. Direct laser line measurements in the clear transmission range with different laser sources (e.g. at 2.53 µm) indicate a total loss coefficient (absorption and scattering) of ≈0.05 cm−1 [14,53]. The IR cut-off edge of LIS is independent of the colour and hence of the annealing procedure [53,54]. Transmission spectra of LISe were measured both for yellow and red coloration [27, 32, 34, 39, 52, 55]. They also reveal independence of the IR cut-off edge from the colour. The long-wave limit for the clear transparency does not extend significantly further into the mid-IR in comparison to LIS [32, 34, 52]. Polarized measurements with a 5 mm thick sample [15], see Fig. 2b, indicate that the 50% transmission level extends from 0.6 to 12 µm while the clear transparency range is roughly from 1 to 9 µm. Absorption coefficient of less that 0.05 cm−1 was specified near 1 µm for some special samples [27], but loss coefficients of < 0.1 cm−1 in the clear transmission range, and 0.5 and 1.2 cm−1 at 9.55 and 10.6 µm, respectively, were also given in the literature [52, 55]. The variation of the transmission at different points of the sample surface did not exceed 2% [55]. The transmission of LiInSSe extends to roughly 13.7 µm at the “0”-level and also shows the characteristic dip at 10 µm [28], like for LISe, see Fig. 2b. Raman studies of LIS have been performed with unpolarized [12, 20, 42] and polarized [14, 56] light. They were complemented by unpolarized IR absorption


75

[20], and unpolarized [57] and polarized [14, 42] IR reflectivity measurements which allowed to identify the vibrational modes, tabulated in [14, 56]. There are several important consequences of these results: Higher thermal conductivity and damage threshold in comparison to AGS and AGSe are expected for LIS as a result of the increased lattice phonon energy; the IR absorption edge of LIS is determined by multi phonon processes (three-phonon for the absorption onset near 8.1 µm and two-phonon for the cut-off at longer wavelengths) because the phonon spectrum of LIS is located at wavenumbers below 410 cm−1 . IR reflectivity and Raman spectra at room and low temperature were recorded for yellow LISe with polarized light [13, 42, 58]. The optical mode frequencies were tabulated in [13, 58]. No difference was observed for the frequencies between the red and yellow colour LISe [13]. As expected from reduced mass considerations the optical modes of LISe are shifted to lower frequencies due to the substitution of S by Se. The dominant line of the symmetric A1 mode lies at 268 cm−1 for LIS and at 161.5 cm−1 for LISe [58]. From absorption features of the transmission spectra and the maximum phonon energy of LISe (375 cm−1 ) it can be concluded that the onset of absorption near 10 µm is also due to threephonon absorption and the cut-off edge is set by two-phonon absorption. The fact that the IR cut-off edge of LISe is not substantially extended in comparison to LIS is associated with the role of the Li-S(e) sublattice vibrations while in AGS and AGSe, in the presence of the much heavier Ag ion, the high-frequency vibrations are related to the Ga-S(e) sublattice. 4. Dispersion and birefringence of LIS and LISe The three refractive indices of LIS were first measured and tabulated by Boyd et al. for light yellow crystals from 0.425 to 11 µm [9]. LIS is a negative biaxial crystal and the convention n X < n Y < n Z for the three refractive indices leads to the correspondence XYZ ≡ bac between the principal optical and crystallographic axes where c is the two-fold symmetry axis. The two indices n Y and n Z are very close and the birefringence is determined by the difference with n X . However, Sellmeier equations containing UV-poles and quadratic IR-terms were fitted to this data much later [59]. These equations were reproduced in several subsequent publications [34, 49–52, 60]. Another two-pole fit to the same data was suggested more recently [27]. However, no refinement with experimental phase-matching angles was performed. The experimentally observed deviations from the calculated angles made it necessary to refine the original fit using second harmonic generation (SHG) data for type-II phase matching in the X-Y and Y-Z planes in the 2.4. . .5.9 µm spectral range for the fundamental [38, 54, 61], and normal incidence difference-frequency generation (DFG) data in the X- Y plane between 6.6 and 7 µm [62]. The results for the two pole Sellmeier equations of the form n 2 = A1 + A3 /(λ2 − A2 ) + A5 /(λ2 − A4 ) [14], are reproduced in Table 1.

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TABLE 1. Coefficients of two-pole Sellmeier expansions for LIS and LISe (wavelength in µm). Crystal

LiInS2 (LIS)

LiInSe2 (LISe)

n

A1

A2

A3

A4

nX nY nZ nX nY nZ

6.686059 7.095493 7.256327 5.669848 5.676208 6.302234

0.05910334 0.06614640 0.06823652 0.09473786 0.06265155 0.04137438

0.1385833 0.1422326 0.1507200 0.1948525 0.2451579 0.2509052

897.7476 988.2024 983.0503 492.0924 432.8862 713.0767

A5 2047.46509 2511.08936 2626.10840 300.72708 205.05597 755.68622

Concerning LISe, the initial work of Negran et al. [10] contained only refractive index measurements at 633 nm. LISe is also negative biaxial with the correspondence XYZ ≡ bac, and the two refractive indices n Y and n Z are very close. Our index measurements in the 0.5–11 µm range with yellow colour LISe were tabulated in [39] where also one-pole Sellmeier equations with quadratic IR-terms were constructed. Additional refractive index measurements between 0.7 and 1.9 µm of yellow-greenish (as grown) and dark red (annealed) LISe indicated that the index of refraction is the same within the experimental error [32]. Another similar fit for the 0.5..10 µm spectral range appeared in [63] but its origin is unknown. An alternative measurement of the refractive indices of red colour LISe from 0.633 to 10 µm was published in [27], together with two-pole Sellmeier equations which were also reproduced elsewhere [55], and another index measurement with deep red LISe was used to create a further Sellmeier set based again on two poles [28]. The discrepancies between the available sets of Sellmeier equations, made it necessary to remeasure the refractive indices with high quality yellow LISe between 0.525 and 12 µm [15]. Starting with a two-pole fit to this new index values, our refinement was based on DFG data in the 5.9–8.1 µm range for the X-Y plane [64], the signal wavelength obtained at normal incidence in the X-Y plane of a 1.064 µm pumped LISe OPO [65], as well as SHG in the XY and X-Z planes near 2.9 and 2.25 µm, respectively [39]. The coefficients of the final Sellmeier set of equations are included in Table 1. Two-pole Sellmeier equations for LiInSSe were constructed by others using separate refractive index measurements from 0.5 to 11 µm [28]. The thermo-optic coefficients (1/n)dn/dT = A + BT of LIS were measured between T = −20 and +120◦ C at 0.477, 0.632, 1.06 and 3.391 µm by an experimental technique that exploits the shift of Fizeau fringes with temperature [61]. The wavelength dependence of the two parameters A and B can be approximated by analogous two-pole functional forms A = A1A + A3A /(λ2 − A2A ) + A5A /(λ2 − A4A ) and B = A1B + A3B /(λ2 − A2B )+ A5B /(λ2 − A4B ) for the three polarizations.

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TABLE 2. Dispersion of the parameters A and B of the thermo-optic coefficients of LIS and LISe defined by dn/dT = n( A + BT ). The wavelength is in µm and the temperature in ◦ C. crystal parameters A

B

A1A × 105 A2A × 10 A3A × 106 A4A × 10−2 A5A × 103 A1B × 109 A2B × 10 A3B × 109 A4B × 10−2 A5B × 106

LiInS2 (LIS)

LiInSe2 (LISe)

nX

nY

nZ

nX

nY

2.899680 1.207980 2.033761 2.210440 2.970535 19.87083 1.510404 1.860292 2.033450 2.500777

2.478267 1.150032 2.612463 1.937258 1.223207 1.523235 1.575449 2.601335 2.189817 −1.918712

3.315830 1.191312 2.555208 2.384285 3.649813 −6.564806 1.180506 4.291068 2.234460 −3.431015

2.78371 1.49498 5.4189 8.55280 7.32 – – – – –

4.26216 1.82457 4.9903 17.9166 13.97 – – – – –

nZ 3.58743 1.61387 6.2562 8.07974 8.73 – – – – –

The results from [14] are reproduced in Table 2. At 1064 nm and room temperature (293 K), dn X /dT = 3.725 × 10−5 K−1 , dn Y /dT = 4.545 × 10−5 K−1 , and dn Z /dT = 4.467 × 10−5 K−1 . The thermo-optic coefficients of yellow LISe were measured for 27 wavelengths between 0.625 and 12 µm at five temperatures between 20 and 150◦ C [66, 67]. A similar fitting procedure was used to obtain expressions for their wavelength dependence but in this case a first order approximation was sufficient, (1/n)dn/dT = A [15]. The corresponding coefficients for the three polarizations are included in Table 2. At 1064 nm, dn X /dT = 5.676 × 10−5 K−1 , dn Y /dT = 9.339 × 10−5 K−1 , and dn Z /dT = 7.368 × 10−5 K−1 . Above 3 µm where the wavelength dependence is only weakly pronounced, the thermo-optic coefficients of LISe are 1.5–2 times larger than those of LIS, they are comparable to the thermo-optic coefficients of AGSe and 2–3 times smaller than those of AGS [66, 67]. 5. Nonlinear susceptibility of LIS and LISe For the specified correspondence between the principal optical and the crystallographic axes of LIS and LISe, the effective second order nonlinearity deff for propagation in the principal planes can be calculated from [2]: deoe = doee = −(d24 sin2 ϕ + d15 cos2 ϕ) in the X- Y plane (1) doeo = deoo = −d24 sin θ in the Y-Z plane (2) dooe = d31 sin θ in the X-Z plane (θ < VZ ) (3)

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Figure 3. (a) Calculated angle V Z between the optic axis and the principal Z-axis of LIS and LISe in dependence on the wavelength. (b) Principal optical axes and types of interaction in a biaxial crystal. The two optic axes lie per definition in the X- Z plane. For LIS and LISe, XYZ ≡ bac holds.

with the subscripts “o” and “e” denoting the ordinary and extraordinary beams. LIS and LISe behave as optically negative uniaxial crystals in the X- Y and X- Z (for θ < VZ ) planes, and as optically positive uniaxial crystals in the Y-Z plane (Fig. 3). The situation θ > VZ for propagation in the X- Z plane is never reached in practice. General expressions for propagation outside the principal planes, which involve also d33 , can be found elsewhere [14, 15]. The wavelength dependence of the angle VZ (Fig. 3a) reflects the trends observed in the behaviour of the refractive indices. Thus at longer wavelengths, both for LIS and LISe, n Y and n Z get closer. The behaviour of VZ near the band-edge is expected, however, to be affected by defects (colour) and hence is of little importance. At present it is impossible to say whether n Y and n Z cross near the band-edge but this definitely does not happen in the regions of > 50% transparency (see Fig. 2). The first estimation of the nonlinear coefficients of LIS was performed by the Maker fringe (wedge) technique using non-phase-matched SHG at 10.6 µm [9]. The results included in Table 3 are rescaled using d33 (GaAs) = 83 pm/V [1]. We note that traditionally these coefficients are defined in the abc crystallographic frame and we assume that Kleinman symmetry holds, i.e. d24 = d32 and d31 = d15 [2]. It was also established that d31 and d24 have the same sign but the sign of d33 (LIS) remained undetermined [9]. The same authors concluded that the close values of d31 and d24 will lead to almost constant effective nonlinearity deff in the X-Y plane. Estimations of the nonlinear coefficients by the same method at 9.55 µm relative to ZGP gave practically the same result [49–51] if d36 (ZGP) = 75 pm/V is assumed [1, 2]. We previously published several preliminary estimations of the d31 and d24 nonlinear coefficients of LIS, mostly from SHG measurements [34, 38, 53, 54, 61], but also from the performance of an optical parametric amplifier (OPA) [60], assuming equal signs. However, they can be ignored because we incorporated all these results in a more systematic approach to derive consistent values taking

ORTHORHOMBIC CRYSTALS OF LITHIUM TABLE 3. crystal

SHG@

Nonlinear coefficients of LIS and LISe.

d31 [pm/V]

10.6 µm 6.14 ± 15% 2.59 µm 7.94 ± 20% 2.3 µm 7.25 ± 5% LiInSe2 (LISe) 2.3 µm 11.78 ± 5%

LiInS2 (LIS)

79

d24 [pm/V]

d33 [pm/V]

remarks

5.31 ± 15% −9.79 ± 15% wedge, relative to GaAs 5.73 ± 20% – SHG, relative to KTP 5.66 ± 10% −16 ± 25% SHG, relative to AGS 8.17 ± 10% −16 ± 25% SHG, relative to AGS

into account the wavelength dependence and the updated values for the reference samples [14]. We basically compared the results using two different kinds of SHG measurements. In one case the laser source in the range 2.4. . .2.6 µm was the idler output of a type-I LiNbO3 OPO (12 ns pulsewidth, 10 Hz repetition rate). Long LIS samples were used and hence the residual absorption and the beam walk-off effect, as well as the focusing effects, had to be taken into account in the derivation of the nonlinear coefficients. The three thick (5. . .7 mm) samples of LIS used had different coloration (light yellow for as grown and rose for annealed) and were cut for propagation in the X-Y and Y-Z planes. However, the results were independent of the coloration. The measurements were performed in the low depletion limit for the fundamental, relative to a dual-band antireflection coated KTiOPO4 (KTP) crystal cut for propagation in the X-Z plane. We used Gaussian beam SHG theory in the ns regime and put the results on an absolute basis using d24 (KTP) = 2.30 ± 0.2 pm/V [68]. The final results for d24 and d31 obtained for SHG at 2.59 µm are included in Table 3 [14]. In the other case we used 160 fs long pulses from a 1-kHz KTP OPA in the 2.3. . .2.85 µm spectral range but worked also in the low depletion limit to avoid complications from saturation effects and spatial dependence across the beam cross section. Three annealed samples of rose LIS were available, all of them 0.2 mm thick. They were cut for propagation in the X-Z plane, in the X-Y plane, and outside the principal planes, which allows to successively determine d31 , d24 and d33 , albeit with increasing error [14]. The measurement was relative to a type-I AGS crystal and put on an absolute basis using d36 (AGS) = 13.9 ± 2.8 pm/V [69]. It should be emphasized that the last value was measured in the same wavelength range and calibrated by the same d24 (KTP) value quoted above. The final results for d31 , d24 and d33 of LIS are given in Table 3 only with the relative error. One can see that there is very good agreement between the two measurements of d31 and d24 while for d33 we obtained a different sign [9]. A similar measurement with fs pulses was used in the first estimation of the two nonlinear coefficients d31 and d24 of LISe [39]. In order to improve the reliability and to extend the results also to d33 (LISe) we repeated this measurement performing it simultaneously and in an absolutely analogous manner as the above

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described measurement of the LIS nonlinearities with fs pulses. The three yellow LISe samples used were annealed and had the same thickness of 0.2 mm. The final results for d31 , d24 and d33 of LISe in Table 3 are given only with the relative error without taking into account the accuracy of d36 (AGS) for the same reference sample [15]. While the two nonlinear coefficients d31 and d24 of LISe are higher than in LIS the difference between the sulphide and selenide compounds is much smaller if compared to AGS and AGSe [1, 2]. The diagonal elements have the same magnitude within the experimental accuracy. The ratio of d24 /d31 for LIS (0.72. . .0.78) is close to the value of Boyd et al. [9] and this confirms that deff depends only weakly on the azimuthal angle for propagation in the X- Y plane. The same holds for LISe for which we obtained d24 /d31 = 0.69. The higher value of d33 makes it interesting to consider the behaviour of deff for propagation outside the principal planes. In some cases propagation outside the principal planes can ensure increased deff in type-I SHG (Fig. 4) while the curves for type-II SHG have a different character and maximum deff is achieved always in the X- Y plane.

Figure 4. Effective nonlinearity deff versus azimuthal angle ϕ for type-I (solid lines) and type-II (dashed lines) SHG in LIS (a) and LISe (b) outside the principal planes. The labels indicate the fundamental wavelengths. The curves start from the X-Z plane (ϕ = 0◦ ) and end at the X- Y plane (θ = 90◦ ) or start from the X-Y plane (θ = 90◦ ) and end at the Y- Z plane (ϕ = 90◦ ).


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Figure 5. Down conversion (DFG, OPA, OPO) outside the principal planes of LIS (a) and LISe (b) for a pump wavelength of 1064 nm and selected idler wavelengths (indicated in the figures). All curves start from the X- Z plane (ϕ = 0◦ ), where deff for type-II interaction (dashed lines) vanishes, and end at the X-Y plane (θ = 90◦ ) where deff for type-I interaction (solid lines) vanishes.

For various applications it is important to consider also the down conversion into the mid-IR of high power sources, e.g. lasers emitting at 1064 nm (Fig. 5). Calculations in the principal planes for the selected wavelengths indicate that the absolute negative extremum of the type-II deff curves which occurs in the X- Y plane is larger than the extremum of the type-I curves in the X- Z plane. Hence type-II interaction in the X-Y plane will be more efficient than type-I interaction in the X-Z plane. However, propagation outside the principal planes allows to increase the effective nonlinearity for type-I interaction (−7 < deff (θ, ϕ) < −7.5 pm/V for LIS and −8 < deff (θ, ϕ) < −9.6 pm/V for LISe) which can be advantageous since other parameters like e.g. the spectral acceptance can be better in type-I interaction [14, 15]. Another nonlinear parameter of higher order which plays an important role for high intensity ultrashort laser pulses is the two-photon absorption (TPA) coefficient. Since most high power fs laser systems rely on Ti: sapphire laser technology it is important to measure the TPA coefficient near 800 nm. In our initial

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measurement with a 1.5 mm thick LIS sample using 200 fs pulses at 800 nm the nonlinear losses were rather low and their intensity dependence could not be properly fitted by a TPA process. However, an upper limit of βT P A = 0.04 cm/GW (independent of the polarization) was derived while simultaneous measurement of a 0.3 mm thick AGS crystal yielded βT P A = 3.5 cm/GW±10% for o-polarization and βT P A = 5.6 cm/GW ± 20% for a mixed (o and e) polarization with reasonable fits [60]. A very similar upper limit of βT P A = 0.05 cm/GW was derived for LIS using another rose colour annealed sample of 5 mm length and 300 fs pulses at 820 nm [14]. An analogous measurement of a 3-mm thick annealed (yellow-brown) sample of LISe with 220 fs pulses at 820 nm showed that the TPA contribution can exceed the linear losses: The measured data were fitted by βT P A = 0.6 cm/GW [5]. Having in mind that typical peak pump intensities in fs OPAs are of the order of 50 GW/cm2 and the nonlinear crystals used are relatively short [5, 38, 60], it is clear that LIS with its extraordinary large band-gap lying in the UV (≈347 nm) is an unique mid-IR crystal that can be pumped by high power fs laser systems near 800 nm. This is obviously not the case with LISe while AGS will experience serious TPA problems even with much longer pulses. 6. Thermo-mechanical properties and damage resistivity of LIS and LISe The heat capacity at constant pressure of LIS and LISe has been measured previously from 200 to 550 K using polycrystalline samples [70]. The results at 300 K are C p = 90 and 96 Jmol−1 K−1 ± 1% for LIS and LISe, respectively. Measurements with single crystals of LISe yielded C p = 96.06 Jmol−1 K−1 ± 1.2% [71]. More recently we directly compared unoriented single crystals of rose LIS and LISe measuring C p with a differential scanning calorimeter in the temperature range 113–483 K [14, 66]. The results are partially reproduced in Fig. 6.

Figure 6. Heat capacity versus temperature for LIS and LISe (experimental points with error bars) and fitting results (curves).

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TABLE 4. Heat capacity C p = C0 − C1 /T − C2 /T 2 [Jmol−1 K−1 ] and thermal conductivity K = K 0 − K 1 T [Wm−1 K−1 ] of LIS and LISe where T is measured in K. crystal LiInS2 (LIS) LiInSe2 (LISe)

C0

C1

C2

K 0X

K 0Y

K 0Z

K 1X

K 1Y

K 1Z

112.98 114.02

3988 5708

139312 187540

– 6.739

– 7.70

– 8.539

– 0.00668

– 0.0101

– 0.0103

The values at 300 K are C p (LIS) = 92.9 ± 1.1 Jmol−1 K−1 and C p (LISe) = 98.1 ± 1.4 Jmol−1 K−1 . The obtained temperature dependence can be fitted by the function C p = C0 − C1 /T − C2 /T 2 and the coefficients are summarized in Table 4. It was established in [70] that the specific nature of the Li-S(e) bonds which has a considerable effect on the lattice vibrations gives rise to changes in the anharmonic properties in comparison to the chalcopyrites. This was confirmed in [66] by measurements on single crystals of LIS and LISe. The thermal conductivity of LIS along the principal optical axes was known at 300 K [72]: K X = 6.2 ± 0.5, K Y = 6.0 ± 0.5, and K Z = 7.6 ± 0.5 Wm−1 K−1 . We measured the thermal conductivity of red oriented LISe samples from 293 to 343 K [66, 67]. The results at 300 K are: K X = 4.7 ± 0.2, K Y = 4.7 ± 0.2, and K Z = 5.5 ± 0.3 Wm−1 K−1 . The temperature dependence can be approximated by linear fits the coefficients of which are included in Table 4 [67]. The values at room temperature were confirmed by an independent measurement at 302 K [73]: K X = 4.5 ± 0.3, K Y = 4.8 ± 0.2, and K Z = 5.8 ± 0.1 Wm−1 K−1 . Therefore the average value published for LISe in [55], comparable to AGS, should be an error. Thus the thermal conductivities of LIS and LISe are more than 4 times larger than the thermal conductivities of the corresponding chalcopyrite sulphide AGS and selenide AGSe. The thermal conductivity is related to the phonons which are responsible for the transfer of the thermal motion energy. The slightly lower thermal conductivity of LISe in comparison to LIS can be attributed to the lower energy of the phonon vibrations discussed in Section 3. The presence of the heavier metal ion (Ag) in AGS and AGSe explains their substantially lower thermal conductivity. The linear thermal expansion coefficients of LIS were measured by an absolute interferometric dilatometer from 253 to 393 K [14,61]: At room temperature (293 K): α X = (1.64±0.05)×10−5 K−1 , αY = (0.91±0.05)×10−5 K−1 , and α Z = (0.68±0.05)×10−5 K−1 . The temperature dependence can be approximated with linear functions. The coefficients obtained are given in Table 5. The linear expansion coefficients of red LISe were measured between 300 and 460 K [66,67]. The values obtained at room temperature (300 K) are: α X = (1.76 ± 0.18) × 10−5 K−1 , αY = (1.1 ± 0.16) × 10−5 K−1 , and α Z = (0.87 ± 0.11) × 10−5 K−1 .

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TABLE 5. Thermal expansion coefficients α = α0 + α1 T + α2 T 2 [10−6 K−1 ] of LIS and LISe where the temperature is in K. crystal

α0X α0Y α0Z

α1X

α1Y

α1Z

α2X

α2Y

α2Z

LiInS2 12.2 6.93 4.06 0.0144 0.0072 0.0093 – – – LiInSe2 7.0 30.3 1.0 0.0463 −0.1051 0.0417 −3.67 × 10−5 1.359 × 10−4 −5.38 × 10−5

They are rather close to the values known for LISe from measurements of the changes of the unit cell parameters in the 303. . . 773 K temperature range [13]: α X = 1.98 × 10−5 K−1 , αY = 0.936 × 10−5 K−1 , and α Z = 0.64 × 10−5 K−1 . The parameters obtained for quadratic fits of the temperature dependence are included in Table 5 [66,67]. Although the thermal expansion of LIS and LISe is anisotropic, the signs of the linear expansion coefficients are the same in contrast to the uniaxial chalcopyrites AGS and AGSe. This property is an essential advantage in relation to the crystal growth and mechanical stability of dielectric coatings. The damage properties of LIS were studied at 5 µm with a free electron laser [34,54]. At a pulse duration of 500 fs the damage threshold was 1.1 J/cm2 but this is the fluence of the 5 µs macropulse consisting of fs pulses at 1 GHz. No surface damage was observed in LIS up to 140 GW/cm2 using amplified 200 fs pulses at 800 nm [60]. However, at the repetition rate of 1 kHz, gray tracking phenomena were observed which were attributed to the absorption of the non-phase-matched second harmonic generated at 400 nm because a similar effect was produced by unamplified fs pulses at 400 nm. These gray tracks were partially reversible and increased the crystal absorption mainly in the UV and visible while in the near-IR their effect was weaker. With a conventional lamp source it was established that the gray track formation is maximized near 360 nm but was absent for illumination above 450 nm [38]. Interpretation of these effects can be found in [14]. At 1.064 nm, the CW damage threshold of LIS should lie above 120 kW/cm2 while measurements with 10 ns pulses at 10 Hz yielded a damage threshold of roughly 1 J/cm2 or 100 MW/cm2 which is quite high [14]. In several papers the damage threshold of LIS was determined at 9.55 µm with 36 ns long pulses [49–51], the last result being 214 MW/cm2 which is roughly 50% above the values determined for AGS and AGSe. The damage threshold of LISe measured at this wavelength was even higher: 248 ± 16 MW/cm2 [55]. Illumination of LISe with amplified 200 fs pulses near 820 nm produced also gray tracks but no crystal damage was observed up to 50 GW/cm2 [5]. Some other properties of LIS and LISe which are not necessarily related to nonlinear optics have also been studied: Besides the already mentioned photoluminescence and electrical properties, citations for which can be found in [14, 15],


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we want to mention here the pyroelectric, piezoelectric, and electro-optic effects in LIS [10, 14, 61, 74] and LISe [10, 15]. 7. Phase-matching in LIS and LISe The biaxial phase-matching loci for collinear SHG in LIS and LISe can be categorized using the classification of Hobden [75]. The computation is based on relatively simple transcendental equations [76]. Figure 7 illustrates the different SHG classes for LIS and LISe at several representative fundamental wavelengths. The surface of the unit sphere is projected onto the X-Z plane of the crystal. The direction of the wave vectors of the interacting waves for phase-matching as given by their interception with the surface of the unit sphere is plotted. The stereographic projection of the first octant is presented only but the loci in the other octants can be obtained by mirror reflections across the principal planes.

Figure 7. Stereographic projections of the SHG in the first octant of LIS (a and b) and LISe (c and d) calculated for wavelengths representative of the Hobden classes. Type-I (ss-f) interaction (solid lines) and type-II (fs-f≡sf-f) interaction (dashed lines).

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J. -J. ZONDY ET AL. TABLE 6. Hobden classes and transition wavelengths in nm for LIS and LISe.

crystal/classes 14 → 13 13 → 11 11 → 10 10 → 9 9 → 10 10 → 11 11 → 13 13 → 14 LiInS2 (LIS) 1617 LiInSe2 (LISe) 1860

1783 2078

2353 2672

2675 3051

5493 7799

6111 8259

8224 10881

8710 11071

Figure 8. SHG phase-matching in the principal planes of LIS (solid lines) and LISe (dashed lines) and inverse group velocity mismatch, GVM (∆31 = 1/v 3 − 1/v 1 and ∆32 = 1/v 3 − 1/v 2 where v 1 , v 2 , v 3 denote the group velocities at λ1 , λ2 , and λ3 ) for the cases where deff = 0. The thin dashed lines indicate the correspondence between the two branches of the tuning and GVM curves.

The transitional (fundamental) wavelengths between the different Hobden classes are summarized in Table 6. They correspond to propagation directions along the Y or Z principal optical axes (noncritical phase-matching) either for the ss-f or the fs-f (≡sf-f) polarization configurations. As can be seen from Fig. 7, double solutions for the angles exist (e.g. for Hobden’s class 9) which is equivalent to the existence of points outside the principal planes where ∂ϕ/∂θ = 0 holds. This means that noncritical phasematching in one direction can also occur outside the principal planes (e.g. at ϕ ≈ 26.7◦ , θ ≈ 74.35◦ for ss-f type SHG at 4 µm and at ϕ ≈ 23.2◦ , θ ≈ 70.3◦ for ss-f type SHG at 5 µm in LIS and LISe, respectively). The SHG phase-matching directions in the principal planes of LIS and LISe are shown in the lower part of Fig. 8. The transitional wavelengths from Table 5


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can be easily identified in Fig. 8. The SHG ranges for LIS (LISe) where deff = 0 are 1783–8224 nm (2078–10881 nm) for type-I (oo-e) phase-matching in the X-Z plane, 2353–6111 nm (2672–8259 nm) for type-II (eo-e) phase-matching in the X-Y plane, and 2353–2675 nm and 5493–6111 nm (2672–3051 nm and 7799– 8259 nm) for type-II (oe-o) phase-matching in the Y- Z plane. We observe an interesting feature in these crystals: The SHG limits with deff = 0 are larger for propagation outside the principal planes where type-I phase-matching down to 1617 nm and up to 8710 nm in LIS, and down to 1860 nm and up to 11071 nm in LISe is possible. Under the convention n X < n Y < n Z the largest birefringence and consequently the shortest SHG wavelength is obviously achieved for type-I interaction and propagation along the Y-axis. However, when the Y-axis is approached in the principal planes X-Y or Y-Z of LIS and LISe, deff for type-I phase-matching vanishes and this is true also for the limiting case of propagation along the Y-axis. This is the reason why propagation outside the principal planes can be used, e.g., to shorten the SHG lower wavelength limit (Fig. 7). A similar situation has been observed previously in KTP [77]. It is seen from Fig. 8 that in the Y-Z plane the type-II interaction is quasi angle-noncritical which ensures a large acceptance angle and a small walk-off angle. In contrast, type-I interaction in the X-Z plane and type-II interaction in the X-Y plane have regions of quasi wavelength-noncritical phase-matching centered at 3889 and 3803 nm for LIS, and at 5223 and 4919 nm for LISe, respectively. Further analysis of the angular acceptance and the walk-off angle dependence can be found elsewhere [14, 15]. The chosen presentation of the inverse group velocity mismatch, GVM, in the upper part of Fig. 8 is equivalent to the spectral acceptance but contains the sign as additional information. Note that in the case of type-I SHG the spectral acceptance is given by 0.886/|∆31 | where the indices are related to λ1 ≥ λ2 > λ3 with 1/λ3 = 1/λ1 +1/λ2 . The two parameters ∆31 and ∆32 simultaneously vanish at 3889 nm (LIS) and 5223 nm (LISe) in the X-Z plane which means large spectral acceptance for SHG of short pulses and necessity to consider higher order effects (group velocity dispersion). The situation is different for type-II interaction in the X-Y plane: here ∆32 = −∆31 at 3803 nm (LIS) and 4919 nm (LISe), at 2915 nm (LIS) and 3701 nm (LISe) ∆32 vanishes, and at 4946 nm (LIS) and 6328 nm (LISe) ∆31 vanishes but in none of these cases an extremum of the spectral acceptance occurs because in type-II SHG of short pulses all three waves should be considered as broad-band. The spectral acceptance is smallest in the Y-Z plane and this can be used for spectral narrowing. Type-I phase-matching in the X-Z plane for non-degenerate three-wave interactions is presented in Fig. 9 where two branches of the solution can be seen. The whole transparency range of LIS and LISe can be covered for 0◦ ≤ θ ≤ 40◦ in the X-Z plane but deff increases with the phase-matching angle θ. Note that

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Figure 9. Type-I (oo-e) phase-matching for sum and difference frequency mixing or optical parametric amplification in the X-Z plane of LIS (a) and LISe (b). The uncritical configurations are shown by thick lines. The curves are terminated by the transparency ranges of the crystals.

deff = 0 in the uncritical (θ = 0◦ ) configuration and that the situation θ > VZ , is never reached. At larger angles θ a retracing behaviour in the left branch is observed: e.g. in the case of OPO one and the same pump wavelength λ P ≡ λ3 corresponds to two pairs (λ I ≡ λ1 , λ S ≡ λ2 ) of idler and signal wavelengths. In such regions the spectral acceptance is very large. Thus, e.g. for θ = 40◦ (LIS) and 45◦ (LISe) in Figs. 9a and b, respectively, at λ1 ≈ 11.4 µm, λ2 ≈ 0.963 µm and λ3 ≈ 0.888 µm for LIS, and at λ1 ≈ 9.64 µm, λ2 ≈ 1.94 µm and λ3 ≈ 1.615 µm for LISe, all three group velocities are very close and the absolute values of the GVM parameters do not exceed 20 fs/mm. Such phase-matching configurations are especially suitable for frequency down-conversion of fs pulses or generation of fs quasi continuum. In OPAs, however, seeding must be used for control of the spectral bandwidth. In the regions near the degeneracy points (SHG points) one has on the other hand ∆21 ≈ 0 but the wave at λ3 has in general a different group velocity. Such a regime is attractive for broad-band parametric amplification in the field of a narrow-band pump pulse as in the case of chirped pulse optical parametric amplification. Increasing the phase-matching angle (curves for θ = 45◦ in Fig. 9) the two branches merge into a closed contour and the point is approached where SHG phase-matching only for a single wavelength is possible, see Fig. 8. In this limit all three group velocities are again very close but the tunability is very limited. The curves for type-II phase-matching (Fig. 10) have a completely different shape. The two branches of the solution are represented by curves of opposite curvature which can cross at two points where phase-matching for degenerate DFG or SHG is realized. With decreasing phase-matching angle these branches separate and a single crossing point is reached (near ϕ = 50◦ for LIS and between ϕ = 40◦ and 50◦ for LISe) which corresponds to the single SHG solutions in Fig. 8. For yet smaller angles no crossing occurs and the degeneracy point is not reached.


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Figure 10. Type-II (eo-e and oe-e) phase-matching for sum and difference frequency mixing or optical parametric amplification in the X-Y plane of LIS (a) and LISe (b). The uncritical configurations are shown by thick lines. The curves are terminated by the transparency range of the crystals.

For all phase-matching angles presented we observe again a retracing behaviour at longer λ P ≡ λ3 : For each λ3 two couples (λ I ≡ λ1 , λ S ≡ λ2 ) are phase-matched. At the points where these two pairs merge into one (at the maximum λ3 permitting phase-matching) the waves at λ1 and λ2 have equal group velocities and similar to the cases discussed for Fig. 9, broad-band parametric amplification in the field of a narrow-band pump wave can be realized. The deviation from the pump group velocity remains, however, essential. Thus e.g. at ϕ = 90◦ and λ3 = 3310 nm (LIS) and λ3 = 4330 nm (LISe), ∆21 ≈ 0, and ∆31 ≈ ∆32 ≈ −1.65 ps/cm (LIS) and ∆31 ≈ ∆32 ≈ −1.57 ps/cm (LISe). Improved group velocity matching with the pump wave occurs for these points at smaller phase-matching angle ϕ, in accordance with Fig. 8. The GVM depends on the specific wavelengths chosen. At λ3 = 1064 nm (a case interesting for parametric down-conversion) ∆21 (X-Z) < ∆21 (X-Y) is fulfilled in the main part of the transparency ranges of LIS and LISe. This means that type-II phase-matching in the X-Y plane is more advantageous for development of narrow-band parametric generators or oscillators.

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Crystals of LiInSSe or various compositions between LIS and LISe occupy an intermediate position also with respect to the phase-matching properties. Some phase-matching analysis for LiInSSe and estimations of the acceptable composition variations for various phase-matched processes can be found elsewhere [28, 78]. 8. Nonlinear frequency conversion with LIS and LISe The first phase-matched nonlinear process realized in 2000 with LIS was SHG from 2.35 to 2.65 µm in the X-Y and Y-Z planes using a 10 ns LiNbO3 OPO operating at 10 Hz [34, 38, 53, 61]. These measurements were complemented with SHG between 3.85 and 6 µm of a free electron laser [34, 38, 54]. They all served basically to test the validity of the existing Sellmeier equations, for preliminary estimations of the nonlinearity, and to establish the equivalence of the phasematching properties for the yellow (as grown) and rose (annealed) LIS. The purpose of the first SHG experiments in the X-Y and X-Z planes of LISe, using fs pulses between 2.1 and 2.8 µm, was similar [39]. LIS is not phase-matchable for SHG at CO2 laser wavelengths. The CO2 laser SHG efficiency obtained with LISe shows that this selenide crystal cannot compete with AGSe for this important application [52,55,63]: The SHG external efficiency obtained with a 6.2 mm thick LISe crystal using 33 ns long pulses was 2.6% in terms of peak power and 1.5% in terms of energy for a peak pump intensity of 38.5 MW/cm2 at 9.55 µm, and the obtained second harmonic energy was 7.2 mJ; somewhat higher efficiency, 4.3% in terms of peak power, was reported at 9.26 µm. In the following three subsections we will present three different applications realized so far with LIS and LISe. 8.1. MID-IR FEMTOSECOND OPA [5, 14]

For the production of ultrashort mid-IR pulses, it is highly desirable to realize direct down-conversion from the 800 nm spectral range where the most widely spread Ti:sapphire fs sources operate [79]. LIS was the first nonlinear optical crystal for which such a process was demonstrated in 2001 using only a 1.5 mm thick uncoated sample which allowed the direct conversion of amplified 200 fs pulses at 800 nm and 1 kHz to the mid-IR, reaching 9 µm by type-II phase-matching in the X-Y plane [60]. This was possible because this material allowed to avoid TPA near 800 nm to a great extent. Nevertheless, as can be seen from Fig. 11 the GVM in LIS is still rather large for pumping near 800 nm and in particular the idler pulse travels much faster than the other two. This makes it difficult to achieve high parametric gain with such a seeded OPA using fs pump pulses. In a subsequent experiment, the parametric gain in terms of pulse energy was considerably increased by lengthening the pump pulses to 300 fs and using a 5 mm thick uncoated LIS crystal which was


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Figure 11. Calculated inverse GVM at λ P = λ3 = 820 (a) and 1250 nm (b) for type-II interaction in the X-Y plane of LIS and LISe: ∆ S P = 1/v S − 1/v P (dashed lines), ∆ I P = 1/v I − 1/v P (dotted lines), and ∆ I S = 1/v I − 1/v S (solid lines). The Sellmeier equations used for LIS and LISe are from Table 1.

Figure 12. Idler spectra that demonstrate the achieved tunability with the continuum seeded LIS OPA pumped at 820 nm. The labels indicate the FWHM.

again rose (annealed). The tunability obtained with this sample is illustrated in Fig. 12. Although more than 80 nJ were achieved for the idler energy between 8 and 12 µm, the gain was still rather low having in mind that the OPA stage, seeded by a spectral portion of continuum, was pumped by 150 µJ pulses at 820 nm with a peak on-axis pump intensity of 60 GW/cm2 [14, 38]. As a consequence the idler pulse duration was also just below 600 fs although the pulses were almost transform limited (time-bandwidth product equal to 0.44 assuming Gaussian pulse shapes) [14]. Using a similar set-up which is explained in more detail in another Chapter of this book [4], we directly compared LIS and LISe under identical pump and seed conditions. In this case both samples (cut for type-II phase-matching in the X-Y plane) were uncoated, annealed and 3 mm thick. The OPA was pumped at 820 nm by 220 fs, 230 µJ pulses at 1 kHz [5] and the peak on-axis pump intensity was 50 GW/cm2 . It was seeded by continuum generated with ≈30 µJ of pump radiation in a 2-mm thick sapphire plate by selecting ≈10 nm wide spectral portions with the use of interference filters. The GVM in LISe is even larger and

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Figure 13. Idler energy measured with 3-mm thick samples of LIS and LISe used in an OPA pumped at 820 nm by fs pulses. Type-II phase-matching in the X-Y plane is used.

the TPA effect is rather strong. Consequently, the performance of this crystal was inferior in comparison to LIS, see Fig. 13. This is a good example of a situation where although the effective nonlinearity is higher, the performance of a given crystal is limited by other factors. Very recently, LIS was used in a similar OPA pumped at 1240 nm by fs pulses with an energy of 160 µJ produced by a Cr: forsterite amplifier system [80]. In that case the continuum generated by the second harmonic of the pump wave was preamplified in two LiB3 O5 stages. The pump pulses used for the LIS OPA stage were 100–140 fs long and the pump intensity was between 140 and 200 GW/cm2 . The uncoated crystal was 3 mm thick and cut for propagation in the X-Y plane. Although tuning from 8 to 10.8 µm was demonstrated, the external conversion efficiency in terms of energy was only 0.6%, and the maximum idler energy – only 1 µJ at 9.5 µm. Thus this scheme, although containing two additional stages, did not improve the conversion efficiency (either overall or in the last OPA stage) in comparison to the use of crystals with higher nonlinearity [4]. The important conclusion is that, as long as TPA can be avoided, the higher effective nonlinearity can compensate for the larger GVM. It can be seen from Fig. 11 that the point of matched group velocities in LISe is shifted towards longer idler wavelengths in comparison to LIS and that longer pump wavelengths provide better chance to achieve this regime within the transparency ranges of the crystals. The large band-gap values of LIS and LISe ensure lower GVM, and lower TPA and Kerr-type nonlinearity n 2 can be expected. However, only LIS is applicable for pumping near 800 nm while its second-order nonlinearity is moderate. Near λ P = 1250 nm, it is clear that LISe can be preferable over LIS but for this pump wavelength also other crystals like AGS and HGS are applicable. LIS could be very useful for pumping with ps amplified Ti:sapphire laser systems which are also tunable because in that case TPA plays also essential role but longer crystals can be used. On the other hand


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LISe might prove advantageous for ps OPAs and optical parametric generators (OPGs) pumped near 1 µm (Nd or Yb based amplifier systems with duration in the 1-30 ps range) because in this case the low GVM and the high damage threshold would play a more essential role. 8.2. CONTINUOUS-WAVE DFG OF MID-IR RADIATION [62, 64]

DFG with CW laser sources has been studied with LIS and LISe in order to produce narrow-band mid-IR radiation for high resolution spectroscopy [62, 64]. If both laser sources have linewdths 99.5%) mirror at λ S with 98% transmission at 1064 nm (λ P ) and 90% at λ I , Ag: highly reflecting (>98.5%) mirror for all three waves.


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Figure 18. (a) Output idler energy versus pump energy at 1064 nm (a), and versus repetition rate for a pump energy of 8 mJ (b), at normal incidence to the LISe crystal.

effects. The identical slopes of the three curves in Fig. 18a indicate that scaling of the output energy can be expected at higher pump energies. The pulse-to-pulse fluctuations observed in the output energy of the OPO were of the order of ±15% which is consistent with the ±10% pump pulse fluctuations. Substantial improvement of the present results in terms of output energy and tunability in the mid-IR can be expected. However, to utilize the high thermal conductivity of LISe and its high damage threshold it will be necessary to improve the quality of the antireflection coatings and to reduce the residual absorption losses. Once these problems are solved, LISe crystals could be useful for 1064 nm pumped OPOs also at kHz repetition rates. We note that among the new chalcogenide compounds under development, HGS and mixed quaternary crystals of the same type with higher nonlinearities but poorer thermal conductivities have recently demonstrated their capabilities in Nd:YAG laser pumped ns OPOs [4]. 9. Conclusion The interest in the chalcogenides LIS and LISe was motivated by several remarkable properties distinct from those of the matured AGS, AGSe or ZGP crystals. These properties are related more or less to the different nature of the Li-S(e) ionic bonds: (1) Both compounds display larger band-gap energy in comparison to other sulphide or selenide nonlinear crystals and this allows to pump them at relatively short wavelengths without the onset of TPA; (2) Their thermal conductivities are substantially larger than those of AGS(e), owing to the increase in lattice phonon energy and Debye temperature which, together with the smaller thermo-optic coefficients (relative to AGS), at equivalent residual absorption losses, will minimize the thermal lensing effects; (3) Their wurtzite-type lattice structure is less prone to stresses and laminar defects – no sign anisotropy in the thermal expansion coefficients like in AGS(e); and (4) Owing to their orthorhombic structure, LIS and LISe are pyroelectric (existence of a spontaneous macroscopic polarization).

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From the binary or ternary mid-IR crystals now in use, LIS and LISe are the only biaxial crystals, which in general means extended phase-matching capabilities. Future applications of LISe and LIS in the mid-IR could be related also to the utilization of propagation schemes outside the principal planes. The transparency range of both LIS and LISe corresponds to the one of AGS and it can be expected that they can develop into an interesting alternative to this mature crystal with specific advantages in various applications above ∼5 µm (the limit for oxide nonlinear crystals) up to about 12 µm. Most of the attractive features specified before, together with the increased damage resistivity, obviously point out high peak and/or average power applications. In many cases these advantages could compensate for the slightly lower effective nonlinearity. Ultrafast frequency conversion schemes based on LIS and LISe are interesting basically because they allow conversion of conventional fs pulse sources from the near to the mid-IR. While the large band-gap helps to avoid TPA and decrease the temporal walk-off, the possibility to pump LIS near 800 nm is attractive also for single (or sub-) cycle pulse generation in the mid-IR by mixing different spectral components of extremely short (sub-15 fs) pulses from Ti:sapphire laser systems. Ultrafast (fs or ps) down-conversion schemes like DFG, OPA or OPG pumped in the near-IR by amplified systems operating at 0.01–100 kHz require relatively short crystal lengths and the average powers are relatively low. The realization of high repetition rate (∼100 MHz) fs or ps synchronously pumped OPOs (SPOPOS) in the mid-IR will also profit from the lower GVM and the absence of TPA. Such devices based on LIS or LISe could be pumped either near 800 nm where the pump sources are tunable, or near 1 µm with fixed wavelength pump sources. Especially in ps SPOPOs, however, it is expected that thermal effects related to the residual losses could also play an essential role. The use of longer crystals for down conversion of ns pulses or CW radiation will depend even more critically on the thermal management and the level of residual losses in LIS and LISe in the region of clear transparency. As long as the loss level, e.g. at 1064 nm, is not reduced to the one typical of productionquality AGS (0.01–0.02 cm−1 ) it will be difficult to utilize the advantages of LIS and LISe related to their superior thermo-mechanical properties and realize novel operational regimes like CW or kHz repetition rate OPOs. CW OPOs offer the advantage of >1000 times narrower emission linewidths over pulsed OPOs owing to their single-frequency oscillation capability stemming from the homogeneous character of the parametric gain in the steady-state regime (the gain saturates as soon as a mode-pair starts to oscillate). CW operation of an OPO based on a non-oxide crystal has been to-date only demonstrated with AGS pumped at 845 nm, by resonating both the signal and idler waves at 1267 and 2535 nm, respectively, in an uncritically phase-matched configuration [83,84]. This pioneering experiment allowed to highlight the severe limitations associated with the use of chalcogenide mid-IR materials in CW OPOs, as compared with


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technologically mature oxide-based materials [85]. The output performance of these CW AGS-based OPOs was clamped to about 2 mW at ∼1.5 times the oscillation threshold (∼100 mW) of the doubly-resonant cavity, as a result of strong thermal lensing effects due to the low thermal conductivity of AGS, and despite the extremely low losses of the selected samples (0.005–0.01 cm−1 measured at 1064 nm). Owing to their more than 4 times larger thermal conductivities (as compared to AGS) and lower thermo-optic coefficients, LIS and LISe are potentially better candidates for implementing CW OPOs in the deep mid-IR. However, due to the present status of the residual losses within their clear transparency ranges (about 0.05 cm−1 at 1064 nm, higher than the above quoted values for production quality AGS, and much higher as compared to the < 0.001 cm−1 loss levels typical for oxide materials), CW parametric oscillation with LIS and LISe is precluded by the still large cavity round-trip loss. Further progress in the growth technology of LIS and LISe is still needed to bring down their residual loss to a level similar to that in AGS and compatible with the parametric gain in the CW regime (typically 100-1000 times lower than with high peak power ns pump lasers). Thus the work to obtain improved stoichiometry crystals of LIS and LISe so as to reduce the number of point defects responsible of the residual transmission loss, especially near the short wave transmission edge, continues. However, for several of the above mentioned applications, it will be also necessary to develop highly resistant antireflection coatings with damage thresholds at least comparable to those of the uncoated crystals. Acknowledgements This work was written in the frame of Project D/0427481 supported by the German-French bilateral programme PROCOPE. Most of the results presented were achieved in the frame of the INCO-Copernicus contract IC15-CT98-0814 within the International Cooperation of the 4th Framework Programme, and with the partial support of Grant 04-02-16334 from the Russian Foundation for basic research and the RUS 01/223 Project of BMBF (Germany) for cooperation with Russia. We acknowledge the participation of F. Noack and F. Rotermund from the Max-Born-Institute in the fs frequency conversion experiments and thank W. Chen (Université du Littoral Côte d’Opale, Dunkerque, France) for provision of the experimental data used in Subsection 8.2 prior to publication. References 1. D. N. Nikogosyan, Nonlinear optical crystals: A complete survey (Springer, 2005). 2. V. G. Dmitriev, G. G. Gurzadyan, and D. N. Nikogosyan, Handbook of Nonlinear Optical Crystals, Third Revised Edition (Springer, 1999).

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QUATERNARY NONLINEAR OPTICAL CRYSTALS FOR THE MID-INFRARED SPECTRAL RANGE FROM 5 TO 12 µm Quaternary Nonlinear Optical Crystals V. PETROV∗ Max-Born-Institute for Nonlinear Optics and Ultrafast Spectroscopy, 2A Max-Born-Str., 12489 Berlin, Germany V. BADIKOV and V. PANYUTIN High Technologies Laboratory, Kuban State University 149 Stavropolskaya, 350040 Krasnodar, Russia

Abstract. We review all known optical and other relevant properties of the two solid solutions Cdx Hg1−x Ga2 S4 (x = 0. . .1) and Agx Gax Ge1−x S2 (x = 0.17. . .0.5) emphasizing their unique advantages as nonlinear optical crystals for the mid-IR spectral range between 5 and 12 µm and describe all frequency conversion schemes realized so far with them as well as future potential applications. Keywords: Ternary and quaternary semiconductors, defect chalcopyrites, solid solutions, nonlinear optical crystals, mid-infrared spectral range, down-conversion, optical parametric oscillators, optical parametric amplifiers, ultrashort laser pulses.

1. Introduction II IV V The chalcopyrite semiconductors with chemical formulae AI BIII CVI 2 and A B C2 (uniaxial crystals with 42m point group symmetry) are at present the most widely used nonlinear optical materials for the deep mid-IR range above 5 µm extending to roughly 20 µm [1]. A great number of ternary compounds belonging to these two classes exist [2], however, optical properties have been studied only for few of them because of the lack of high-quality defect-free crystals [3]. Unfortunately in many cases the birefringence is not sufficient for phase-matching. The phase-matchable chalcopyrites that have been primarily studied in the past 35 years are AgGaS2 (AGS) and AgGaSe2 (AGSe) belonging to the AI BIII CVI 2 class, ∗ To whom correspondence should be addressed: e-mail: [email protected]


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and ZnGeP2 (ZGP) and CdGeAs2 (CGA) belonging to the AII BIV CV 2 class [1, 4]. AGS, AGSe and ZGP are nowadays commercially available. The materials efforts required for the growth technology of a new crystal are enormous and in some cases birefringent chalcopyrites that had been already characterized but had no specific advantages were not developed further, e.g. ZnSiAs2 [3], while in other cases empirical predictions based on first-principles calculations seem advantageous, e.g. CdSiP2 [5]. One exception is the newly discovered LiGaTe2 (LGT) belonging to the AI BIII CVI 2 class [6], for which a phase-matched frequency conversion process was immediately demonstrated. A third type of related compounds, VI the so-called defect chalcopyrites AII BIII 2 C4 with point group 4, possess substantially increased second order nonlinear susceptibility in comparison to their chalcopyrite counterparts especially in relation to their band-gaps [7,8], but in fact only one such crystal, HgGa2 S4 (HGS), has been used so far for phase-matched frequency conversion [4]. Having in mind the very limited number of technologically mature nonlinear optical crystals for the above spectral range it is clear that mixed versions of such crystals are potentially interesting since they provide the opportunity to tailor the energy band-gap and the overall transparency window, the refractive index and the birefringence as well as the nonlinear susceptibility and the thermo-optical properties. In addition it might happen that the growth of large sizes with good optical quality is easier with a mixed crystal than with one of the parent ternary compounds. The engineering of the optical properties and especially the birefringence is similar to the periodic poling of ferroelectric crystals where this is normally connected with utilization of the maximum nonlinear coefficient using identical polarization of the three waves. However, on the one hand such ferroelectric materials are basically oxides which are not transparent above 5 µm. The only known exception, the monoclinic Sn2 P2 S6 [9], has a phase transition to a centrosymmetric paraelectric phase at the relatively low temperature of 338 K. An alternative here is the realization of quasi phase-matching in orientation-patterned GaAs [10] which is a great technological challenge. On the other hand solid solutions relying on the birefringence offer additional advantages in comparison to the quasi phasematching materials especially in the case of high intensities and short laser pulses: The tailoring of the band-gap allows to avoid two-photon absorption (TPA) and the variation of the group velocity mismatch (GVM) in combination with the use of different polarizations can ensure longer interaction lengths. A great number of quaternary crystals belonging to the chalcopyrite and defect chalcopyrite families have been grown and studied from crystallographical point of view but their optical characterization has been restricted basically to the band-gap evaluation. In the past, only three such mixed chalcopyrites were demonstrated to be useful for phase-matched optical frequency conversion processes: AgGax In1−x S2 , [11] AgGax In1−x Se2 , [12] and CdGe(Px As1−x )2 [13] exhibit complete solubility since the parent compounds have identical

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structure and their properties vary smoothly with the composition. In all three cases the idea has been to extend the phase-matching capability (especially towards uncritical interaction in the case of the negative crystals) by reducing the birefringence (AgInS2 , AgInSe2 , and CdGeP2 do not possess sufficient birefringence for phase-matching within their transparency ranges). Moreover, the Incontaining components increase the nonlinearity of the quaternary mixtures while CdGeP2 substantially extends the transmission of CGA to shorter wavelengths. Unfortunately, practical applications of CdGe(Px As1−x )2 and AgGax In1−x S2 were limited to demonstration of their phase-matching capability [13–15]. The only mixed chalcopyrite crystal which has been extensively studied is AgGax In1−x Se2 because it is interesting for uncritical second harmonic generation (SHG) of CO2 laser radiation. This compound is the only quaternary crystal of this type included in the Handbook [4] containing extensive literature on its properties and applications; several systematic studies on it appeared more recently [16–18]. The present Chapter is devoted to two different sulphide classes of mixed quaternary nonlinear optical crystals for the mid-IR spectral range between 5 and 12 µm: The first one is represented by Cdx Hg1−x Ga2 S4 , a complete solid solution with two parent compounds possessing the same defect chalcopyrite structure, and the second one consists of Agx Gax Ge1−x S2 which has AGS as a parent compound in the limit x = 1 but does not represent complete solid solution because the compound in the limit x = 0, GeS2 , exhibits different crystallographic structure. Although single crystals both of Cdx Hg1−x Ga2 S4 and Agx Gax Ge1−x S2 were grown as early as 1980 [19, 20] it was only very recently that the growth technology was substantially improved to allow optical characterization and implementation. We will review all the known optical and related properties of the above compounds and present all the applications realized up to now emphasizing the specific advantages and future potential. 2. Mixed defect chalcopyrites Cdx Hg1−x Ga2 S4 2.1. GROWTH AND PROPERTIES OF CGS, HGS, AND CHGS

The crystal growth conditions and the properties of Cdx Hg1−x Ga2 S4 (CHGS) are closely related to those of the two isostructural parent compounds CdGa2 S4 (CGS) and HGS. Such defect chalcopyrites can be obtained in polycrystalline form by fusion of the three components or the binary compounds, grown in small sizes by chemical transport reactions or in larger sizes from the melt. Both ternary compounds CGS and HGS were first synthesized by sintering of the binary constituents by Hahn et al. in 1955 [21]. The obtained polycrystalline samples were used to establish their defect chalcopyrite structure (space group S42 − I 4). High optical quality crystals of CGS with large (>1 cm) size were reported for the first time with the Bridgman-Stockbarger technique [22–25]. The last two

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papers also review earlier work on the growth and properties of CGS. Feigelson and Route [24] indicate a congruent melting character of CGS and a melting temperature of 980 ± 5◦ C. Different phase diagrams for the system CdS − Ga2 S3 can be found in the literature [24, 25]. According to Anosova et al. [25], the solid solutions existing on the basis of CGS extend for CdS content from 47.5 to 50.5 mol % and the point of complete melting of the stoichiometric composition of CGS is 990 ± 2◦ C. In general, in order to achieve homogeneous composition of the grown boule it is necessary to have a charge corresponding to the maximum melting temperature: According to our latest estimations this maximum melting temperature (995 ± 2◦ C) corresponds to slight (0.5 mol %) CdS deficit. The situation with the growth of HGS is similar but much more complicated. Large size (>1 cm) crystals of good optical quality were reported for the first time by Badikov et al. in 1979 using the vertical Bridgman-Stockbarger technique [26, 27]. This earlier work was reviewed in more detail by Rychik [28]. The main difficulty in growing HGS in comparison to CGS is the much higher partial vapour pressure of HgS which leads to substantial deviation of the composition of the grown boule from that of the charge. There is some controversy about the melting character of HGS [26,28–30]. Congruent melting at 880◦ C and incongruent melting at 886◦ C were reported in the corresponding literature [26, 27, 29]. According to Rychik [28], solid solutions on the basis of HGS exist for HgS content between 45 and 50.5 mol % and HGS melts continuously changing its composition with a temperature of complete melting (882 ± 2◦ C) corresponding to a solid solution with 48 mol % HgS. Our updated value for the melting temperature which we believe refers to the stoichiometric composition is 920 ± 2◦ C. Similarly to CGS, the grown HGS boules exhibit increasing HgS content along the height and post-growth annealing is required to improve the homogeneity. Depending on the excess of HgS in the charge, which decreases the crystallization temperature, both orange and yellow HGS can be grown. The nature of the distribution of the components and phases of the crystallized HGS depends on the initial charge composition, the temperature gradient of the furnace, the duration and temperature of the initial annealing, the diameter and the height of the boule, and the volume of the free space [31]. The great technological difficulties are still the limiting factor for the size of the grown HGS boules which amounts to several cc while for CGS the volume can be almost 100 times larger. A lot of studies were devoted to the band-gaps of CGS and HGS. For crystals grown by chemical transport reaction from the vapour phase, indirect band-gaps of 3.40 eV (CGS) and 2.79 eV (HGS) as well as direct band-gaps of 3.44 eV (CGS) and 2.84 eV (HGS) were reported at room temperature [32]. Direct transitions with band-gaps at 3.58 eV (CGS) and 2.79 eV (HGS) were derived later [33]. These results are in agreement with a recent model for calculation of the bandgaps based on an empirical correction beyond the local-density approximation [34]. However, the exact value of the band-gap depends on the growth method.


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It is larger for crystals obtained by chemical transport reaction which are normally colourless (CGS) [32] or yellow (HGS) [32], and lower for crystals grown from the melt which often have a yellow (CGS) [24] or orange colour (HGS) [35] indicating different stoichiometry. Thus the colour can be related to the exact stoichiometry: It is colourless for CGS with maximum CdS content [25] and yellow for HGS with maximum HgS content [28]. In fact in HGS the observed phases were even more (red and black) but the stable phases are only orange and yellow in colour [26, 27]. Unfortunately, at present there are no reliable measurements which relate the colour of CGS and HGS to the exact stoichiometric composition although there are indications that colourless CGS [24] and yellow HGS [36] are closest to the exact stoichiometry. The band-gaps of CGS [37] and HGS [38, 39] exhibit only weak dependence on the polarization. The first data on the refractive index of CGS published by Hobden [40] was limited to the 435.8-706.5 nm spectral range. Hobden established that in this wavelength range the birefringence of CGS is rather small. It remains below 0.006 up to 2 µm [41]. The low birefringence of CGS is due to an accidental isotropy point determined at 487.2 [40], 487.5 [42] (refractive index data from 0.45 to 0.6 µm in this work) or 488.2 nm [41]. Below this point CGS is positive uniaxial. The existence of an isotropic point is a consequence of the fact that being a negative crystal CGS has such a band structure that the band-gap for the o-polarization is larger [37, 43]. The position of the isotropic point depends on the exact composition and it has been shown that this is the parameter most sensitive to deviations from the stoichiometry along the height of the grown boule [25]. Both the position of the isotropic point and the birefringence are temperature dependent [40, 44], however, it is not possible to increase the birefringence to a level suitable for phase-matching. The two refractive indices of CGS measured and tabulated in the 0.405–13 µm spectral range by Suslikov et al. [43] were used later to fit onepole Sellmeier expansions with quadratic IR terms [45]. Another tabulation of the refractive indices of stoichiometric CGS between 0.6 and 11.5 µm can be found in Anosova et al. [25], together with similar data for 0.5 mol % excess of CdS, as well as, in the 0.48–1.2 µm spectral range, for 1 mol % deficit of CdS. The former data has been used as a basis to construct two-pole Sellmeier equations for CGS which were published later [46]. The first data on the refractive index of orange HGS published by Levine et al. [35] included only few wavelengths in the visible and near-IR just as a demonstration of the feasibility of this crystal for birefringent phase-matching. The refractive indices for the orange phase were measured and tabulated between 0.5495 and 11 µm first by Badikov et al. [26] who fitted two-pole Sellmeier equations for description of the dispersion; another such fit to the same data appeared recently [47]. In some other publications the authors claim to have fitted Sellmeier equations that are equally good for the two phases [36,39,48,49]. Refractive index data on yellow phase HGS (assumed there to correspond to the stoichiometric

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composition) was reported for the 0.5–10.6 µm range by Rychik [28]. The main difference concerns the ordinary index of refraction. This same work contains alternative data on orange HGS (assumed composition Hg0.923 Ga2 S3.923 ) in the 0.5264–10.6 µm spectral range and their variation with temperature. The resulting two-pole Sellmeier equations for the yellow phase were recently reproduced with some typographical errors rectified [46]. They predict slightly different angles, e.g. 1–3 degrees lower θ for type-I processes, in comparison to the orange phase [26]. Experimentally deviations of roughly 2◦ were observed for SHG near 9.25 µm but it was established that the angular acceptance is independent of the phase [50]. From the measurements at 20 and 148◦ C for the orange phase [28] it can be concluded that the thermo-optic coefficients of HGS do not significantly depend on the wavelength in the 1.064–6.43 µm spectral range. The average values, dn o /dT = 5.4 × 10−5 K−1 and dn e /dT = 5.6 × 10−5 K−1 , indicate rather weak dependence of the phase-matching angles on the crystal temperature or in other words large temperature acceptance. This was fully confirmed by more recent measurements of the thermo-optic coefficients at 0.633, 1.064, 3.39 and 10.6 µm over the −20. . .100◦ C range by temperature scanning Fabry-Perot interferometer [51]. These results were summarized by fitting the two parameters in the dependence (1/n o,e )dn o,e /dT = Ao,e + Bo,e T for the four wavelengths (Table 1). The magnitude of the effect was directly compared to AGS for which the thermo-optic coefficients appeared to be roughly three times larger. The first refinement of the Sellmeier expansions of HGS based on phasematched measurements (SHG between 2 and 10 µm) was performed by Takaoka and Kato [52]. Their formulae are especially useful for the orange phase HGS although the material used was mostly yellow in colour. Finally, a recent refinement of the two-pole Sellmeier expansion for the orange phase [50] was based on SHG near 9.25 µm and the index data published previously [26]. Both CGS and HGS were introduced as nonlinear optical materials by Levine et al. who first managed to grow sufficiently large sizes from the melt in order to measure the transparency (0.45–13 µm for CGS and 0.55–13 µm for HGS) and the nonlinear coefficient d36 [35, 53]. These transparency ranges were not essentially modified in subsequent work [23, 24, 26]. The yellow phase HGS is slightly more TABLE 1.

Thermo-optic coefficients [K−1 ] of HGS where T is in K (reproduced from [51]).

wavelength [µm] dn o /dT = n o (Ao + Bo T ) dn e /dT = n e (Ae + Be T )

Ao × 105 Bo × 108 Ae × 105 Be × 108

0.633

1.064

3.39

10.6

3.43 4.45 3.46 4.44

2.37 2.8 2.49 2.56

2.05 2.26 2.11 2.29

2.03 1.69 2.07 2.13


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transparent in the visible [38,39]. Badikov et al. specified an absorption coefficient of 0.05 cm−1 (3.5 cm long CGS) and 0.1 cm−1 (4 cm long HGS) for the region of good transparency [23, 27]. Ren et al. [39] gave 0.1–0.2 cm−1 losses for HGS in the 0.9–8.5 µm spectral range and 0.2–0.57 cm−1 at CO2 laser wavelengths as well as cut-off wavelengths of 490 nm (yellow phase) and 507.5 nm (orange phase) in the visible, and 14.3 µm in the mid-IR for a sample thickness of appr. 3 mm. Although still typically about 0.05 cm−1 the losses in exceptional crystals of HGS grown recently were less than 0.02 cm−1 at 1064 nm. The occurrence of some absorption features in HGS is discussed by Badikov et al. [50]. The mid-IR cut-off edges of CGS and HGS are defined by the onset of two-phonon absorption [37]. Using the Maker-fringe technique at 1064 nm, Levine et al. established that for both orange HGS and CGS, d36 is roughly 80 times larger than d11 (SiO2 ) which gives 24 pm/V [35, 53] assuming d11 (SiO2 ) = 0.3 pm/V as a generally accepted value [54] but the size and quality of their samples resulted in relative large errors: ±30% for HGS and ±15% for CGS. As explained for CGS, such a nonlinear coefficient is close to the maximum limit that can be expected for a crystal with such a large band-gap: The intrinsic nonlinearity is expected to be about a factor of 2 higher than in the chalcopyrite counterpart AGS according to bond charge calculation models [53]. The nonlinear figure of merit of CGS and HGS is increased with respect to that of AGS because the large number of vacancies in the defect chalcopyrite structure results in lower average bond density and hence linear susceptibility. The effective nonlinearity for negative crystals of the crystallographic class 4 is given, assuming Kleinman symmetry, by dooe = (d36 sin 2ϕ + d31 cos 2ϕ) sin θ deoe = doee = (d36 cos 2ϕ − d31 sin 2ϕ) sin 2θ

(type-I) (type-II).

(1) (2)

Badikov et al. were able to estimate both coefficients for orange HGS, again by the Maker-fringe method at 1064 nm, but relative to AGS [27]. The result is d36 = 27.2 pm/V ± 15% and d31 = ±d36 /3 using d36 (AGS) = 15.1 pm/V as corrected by Miller’s rule to 1064 nm [55]. Analogous measurements at 9.55 µm relative to ZGP gave, with d36 (ZGP) = 75 pm/V [4], d36 = 35.2 ± 15% pm/V [36, 39, 48, 49]. Takaoka and Kato [52] obtained a similar ratio for the two coefficients (d31 = 0.37d36 ) and a value of d36 = 0.9d36 (AGSe) for phase-matched SHG at 5.3 µm which equals ≈30 pm/V ± 10% at this wavelength when rescaled using d36 (AGSe) = 29.5 pm/V (at 10.2 µm) and Miller’s rule [56]. An absolute determination of d36 for orange HGS by SHG near 9.25 µm was reported recently using 8.4 mm thick samples [50]: The result was 32 ± 5 pm/V and the conversion efficiency was actually independent of the colour. Although our most recent comparison of 0.5 mm thick samples by SHG of fs pulses at 3.5 µm confirmed the ratio d36 (HGS)/d36 (AGS) = 1.8 established in [27], the nonlinearity of HGS is still closer to that of the selenide compound AGSe. This is the essential advantage of HGS because according to its transparency range it basically competes

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with AGS which exhibits considerably lower nonlinearity. We also estimated the ratio d31 /d36 from non-phase-matched oo-e type SHG at 1064 nm by rotation of 1.5 mm thick wedges cut at ϕ = 0◦ , θ = 90◦ about the c-axis: Taking care to avoid Maker fringes we obtained 0.166 ± 0.007 and 0.174 ± 0.007 for CGS and HGS, respectively. The relative sign of d36 and d31 is still unknown because of difficulties to determine the +Z orientation of the polar four-fold symmetry axis c. Quantum-mechanical calculations of the nonlinear susceptibilities predict equal sign of the two nonlinear coefficients [57]. Nevertheless, for practical applications it is clear that this situation requires selection of the azimuthal angle ϕ in such a way that only d36 remains active in Eq. (1)–(2). This ensures deff values that are only ≈7% (or less) lower than the maximum achievable values. The damage resistivity of HGS strongly depends on the temporal regime. No damage occurred for CW radiation at 10.6 µm up to 16 W/cm2 [58]. On the other hand in the same work surface damage occurred at 60 MW/cm2 after ten shots with 30 ns pulses at 1064 nm. In another work, optical breakdown was observed in the same regime for 200 MW/cm2 (60 ns pulses at 1064 nm) [59]. This high damage threshold was not confirmed by Takaoka and Kato who reported 40 MW/cm2 [52]. More recent measurements with 30 ns pulses at 1064 nm gave also 40 MW/cm2 as a surface damage threshold of orange HGS for a single shot [50]. However, the damage mechanism is obviously sensitive to the flux and not to the incident intensity: Thus, e.g., we observed no damage in orange HGS up to 400 MW/cm2 for pulses of 1 ns at 1064 nm and 1 kHz. Comparative measurements with other crystals were performed at 9.55 µm with 30 ns pulses: The damage threshold of yellow HGS (310 MW/cm2 ) was slightly higher than for orange HGS (294 MW/cm2 ) [60]. It should be outlined that these values were about two times lower in AGS and AGSe. Damage with fs pulses occurs normally as a result of self-focusing. Such damage was not observed for a thickness of 2 mm up to 170 GW/cm2 at 820 nm with 200 fs long pulses (1 kHz) [45] and for a thickness of 4.5 mm up to 160 GW/cm2 at 1250 nm with 180 fs long pulses (1 kHz) [61]. In the latter case also no nonlinear losses were detected as can be expected from the band-gap value. The TPA coefficient has been measured for CGS at 581 nm with 35 ps long pulses: It amounts to βT P A = 8 ± 0.3 and 11 ± 2 cm/GW for the o- and e-polarization, respectively [62]. Some thermo-mechanical properties of HGS were also studied recently. The heat capacity at constant pressure amounts to C p = 435±57 and 395±45 Jkg−1 K−1 for the orange and yellow phase, respectively. The thermal conductivity amounts to K ⊥c = 2.36 ± 0.24 and 2.31 ± 0.07 Wm−1 K−1 , and K //c = 2.49 ± 0.05 and 2.85 ± 0.10 Wm−1 K−1 , for yellow and orange HGS, respectively [50]. Higher conductivity (3.9 Wm−1 K−1 ) was given in [47] for an unspecified orientation. These values are roughly two times higher than in AGS and AGSe. The thermal expansion of the orange phase is anisotropic (α⊥c = 11.17 × 10−6 K−1 and α//c = 4.04×10−6 K−1 ) but the signs are equal, in contrast to AGS and AGSe [51].


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HGS is at present a well established nonlinear optical crystal with superior nonlinearity which has found numerous applications: Up-conversion of CO2 laser radiation [59], SHG of CO2 laser radiation in the 9.25–9.55 µm wavelength range [36, 39, 47, 49, 52], SHG of tunable OPO (optical parametric oscillator) radiation between 2 and 5 µm [52], tunable ns-OPO operation with 1064 nm pumping [52, 63], tunable ps parametric superfluorescence or optical parametric generator (OPG) [50], tunable fs optical parametric amplifier (OPA) pumped at 1250 nm [61, 64], and difference frequency generation (DFG) of fs pulses in the mid-IR [65]. As already explained, actually both ternary compounds, CGS and HGS, are themselves solid solutions but with narrow solubility ranges. Since they are isostructural, the quaternary mixture CHGS or Cx H1−x GS is a complete solution with x = 0. . .1. On the one hand this is an attractive property because in principle any desired composition can be grown but on the other hand this leads to enormous difficulties to ensure homogeneity of the boule. During the growth by the vertical Bridgman-Stockbarger method, the composition of CHGS changes. This is a consequence of the fact that in the phase diagram of CHGS the liquidus and solidus curves are separated by a temperature interval which depends on the composition and vanishes only for x = 0 and 1. Hence, the component with higher melting point crystallizes first. Thus, in the lower part of the boule the content of Cd is larger than in the charge because CGS crystallizes at higher temperature while in the upper part of the boule the content of Hg is larger. There is also radial variation of the composition caused by the radial temperature gradient and the curvature of the crystallization front, and the part of HGS increases with the distance from the centre. The inhomogeneous composition results in variation of the birefringence and hence limits the useful size of the manufactured elements. Variations of x ≈ 0.01/cm would lead to index changes not exceeding 0.001. . . 0.002/cm, depending on the wavelength. Since in most cases one does not need all three dimensions to be large it is possible to solve the problem by selecting the material from the axial region of the boule. This is so because for conversion of low-power narrow-bandwidth radiation, normally long crystals with small aperture are sufficient while the conversion of fs pulses and the energy scaling in such schemes require large aperture but rather thin samples. The varying composition offers on the other hand the possibility to tune (e.g. an OPO with a fixed pump wavelength) by translation of the CHGS sample preserving the uncritical synchronism. Crystals of Cx H1−x GS were grown by the Bridgman-Stockbarger method using quartz ampoules with an inner diameter of 18 mm and wall thickness of 4.5 mm. Elements Hg, Cd, Ga, and S with 99.9999% purity were used to presynthesize the charge. The ampoule with the charge was sealed off at a residual air pressure of 1 × 10−5 torr. The ratio of the charge and free space in the ampoule was 1:1. The crystals were grown on oriented seeds, at 2–6 mm/day using

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(a)

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(b)

Figure 1. (a) As grown Cd0.26 Hg0.74 Ga2 S4 boule – the scale shown is 5 mm per division. (b) A processed Cdx Hg1−x Ga2 S4 element (θ = 90◦ , ϕ = 45◦ ) with antireflection coatings on its 30.6 × 8 mm2 faces and a thickness of 11 mm used for the tunable OPO operation described in 2.2.3. with x varying between 0.21 and 0.25 along the 30.6 mm dimension.

different temperature gradients (2. . .10◦ C/cm) [66]. The grown boules (see Fig. 1) allowed to process elements with sizes as large as 3 cc. The composition of the grown boules was studied by the inductively coupled plasma – optical emission spectrometry (ICP-OES) method. Using 5 plates with a thickness of about 1 mm cut perpendicular to the growth direction from two different boules we established that the variation of the composition is rather smooth. The lowest gradients of the parameter x along the height that can be currently achieved are of the order of −0.05 cm−1 . The radial gradient is expected to be smaller. Previously we published Sellmeier expansions of Cx H1−x GS for x = 0.2, 0.4, 0.6 and 0.8 but the composition specified was that of the charge [46]. Some “interpolated” Sellmeier equations for x = 0.1, 0.2, 0.3 and 0.4 appeared also elsewhere [67, 68]. It is possible to establish a more adequate relation between the refractive index variation and the exact chemical composition. To this aim two 20◦ prisms with 10 × 10 mm2 surfaces were prepared from boules with measured composition corresponding to x = 0.27 and 0.33 and the index of refraction was measured between 0.55 and 10 µm by the autocollimation method. The results were then fitted by two-pole Sellmeier expansions of the form n 2 = A1 + A3 /(λ2 − A2 ) + A5 /(λ2 − A4 ). The coefficients obtained are summarized in Table 2. They give deviations not exceeding 3 × 10−3 from the experimental values of the index n. More detailed interpolated Sellmeier parameters for x = 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, and 0.5 based on the same data can be found elsewhere [66]. The derived Sellmeier equations can be used to compute the birefringence. This parameter is more adequate for characterization of the chemical composition because it is almost independent of the wavelength in the 2. . .8 µm spectral range. Its dependence on the composition is well pronounced because the two parent compounds exhibit very different birefringence. Figure 2 shows the calculated birefringence ∆n(x, λ) = n o (x, λ) − n e (x, λ) for different compositions and wavelengths. For x = 0.2 and 0.4 we used the Sellmeier coefficients valid for

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QUATERNARY NONLINEAR OPTICAL CRYSTALS TABLE 2.

Sellmeier expansion coefficients for two compositions of Cdx Hg1−x Ga2 S4 .

Cdx Hg1−x Ga2 S4 Cd0.27 Hg0.73 Ga2 S4 Cd0.33 Hg0.67 Ga2 S4

n

A1

A2

no ne no ne

7.813921 7.784219 6.771355 6.775125

842 878 552 595

A3 1785.748 1953.555 626.4785 749.8960

A4

A5

0.0753347 0.0797939 0.0561378 0.0635720

0.2207567 0.2043484 0.2339643 0.2179198

birefringence ∆n

0.05 λ =1µm λ =2µm λ =4µm λ =8µm

0.04

0.03

0.02

0.0

0.2 0.4 composition parameter x

Figure 2. Birefringence of CHGS versus composition for several wavelengths.

the charge composition [46], while for HGS we applied both the older Sellmeier equations of Badikov et al. [26], and those improved by Takaoka and Kato [52]. As can be seen from Fig. 2, linear dependence of the birefringence is obtained for a rather large range of the composition parameter x. The refractive indices of the quaternary compound can be related to those of the parent compounds using some fundamental parameters as the band-gap [43]. However, for practical purposes, as soon as reliable Sellmeier equations are constituted for several compositions, a good approximation is to interpolate n 2 . Unfortunately, at present there are no reliable measurements of the nonlinear coefficients of CHGS. From OPO experiments, there are only indications that for x < 0.33 d36 is similar to that of HGS [51]. From theoretical point of view it can be expected that the nonlinearity of the quaternary compound CHGS is somewhat reduced in comparison to HGS because of the increased band-gap [8, 69]. Some other optical characteristics of mixed Cx H1−x GS crystals are also known. The band-gap of the solid solution Cx H1−x GS depends linearly on x in the whole range x = 0. . .1 in agreement with calculations of the electronic band structure of the mixture [70]. The transmission spectra shown in Figs. 3a and b as well as similar measurements published elsewhere [38, 48, 51, 67, 68], clearly indicate that the transparency of Cx H1−x GS is substantially extended in the visible

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V. PETROV ET AL. 80 transmission [%]

(a) 60 40 HgGa2S4 Cd0.65Hg0.35Ga2S4

20 0 0.4 0.5 0.6

transmission [%]

80 60 40

2 4 6 8 10 12 14 wavelength [µm]

(b) Cd0.35Hg0.65Ga2S4 60 40

e o

20

20 0

0 475

500 525 550 wavelength [nm]

1

10 wavelength [µm]

Figure 3. Transmission of Cx H1−x GS relative to HGS. The unpolarized spectra in (a) are recorded with a 2-mm thick Cx H1−x GS sample (θ = 69◦ , ϕ = 45◦ , x = 0.65 measured in the crystal) and a 2-mm thick HGS sample (θ = 40◦ , ϕ = 45◦ ). The polarized spectra in (b) are recorded with a 3-mm thick Cx H1−x GS sample (θ = 87◦ , ϕ = 45◦ , x = 0.35 in the charge).

in comparison to HGS. A minimum loss coefficient of 0.05 cm−1 for the region of high transparency was specified [51] although in exceptional cases less than 0.02 cm−1 have been measured at 1064 nm. As can be expected for the composition in Fig. 3b, the band-gap is larger for the e-polarized beam. The absorption features observed seem common to Cx H1−x GS and HGS [50]. The transmission of a 8 × 6 mm2 C0.35 H0.65 GS plate of ≈2 mm thickness in the transparency range was found to vary by less than 0.9% across the surface and the loss coefficient estimated near 9.55 µm was 0.2. Also for this process it is obviously preferable to design an element with θ = 90◦ and varying composition. This application is, however, restricted to special cases (high intensities and short crystals) because the losses near 9.55 µm in HGS and CHGS which are likely related to multi phonon absorption are not negligible. Finally, the high nonlinearity of a nonlinear crystal is important not only for down-conversion of pulsed laser radiation but also for that of CW laser sources whose intensity is much lower which makes it difficult to achieve reasonable conversion efficiency. That is why it is common to apply very tight focusing in that case where the exact beam parameters depend on the crystal length available and the spatial walk-off effect caused by the birefringence. The latter can be eliminated under conditions of uncritical phase-matching, however, whether such conditions can be realized or not depends on the available wavelengths and the temperature tuning is normally rather limited. While the future realization of a 1.064 µm pumped CW OPO based on CHGS will depend on the availability of low loss (< 0.01 cm−1 ) CHGS crystals, it should be outlined that such mid-OPOs do not exist at present and the existence of uncritical phase-matching seems an essential prerequisite for this. DFG is at present the only available technique to produce tunable narrow-band (or even single-frequency) CW radiation in the mid-IR by down conversion. While for shorter input wavelengths it is possible to use type-I AGS and uncritical temperature tuning this does not necessarily provide the higher conversion efficiency and the broader tunability [72]. This is so because the effective nonlinearity of AGS (or HGS) in type-II interaction can be much larger and compensate for the limited interaction length. It is obvious that optimum conditions will be given if uncritical phase-matching in CHGS is engineered by its composition. Since the temperature sensitivity is low, also in this case one can utilize the smoothly varying compostion as an advantage and tune by translation of the nonlinear element. 3. Orthorhombic Agx Gax Ge1−x S2 crystals 3.1. GROWTH AND PROPERTIES OF AGGS

As already mentioned in the Introduction, in the case of Agx Gax Ge1−x S2 (AGGS) the two compounds in the limits x = 0 and x = 1 are not isostructural. This has two basic consequences: The solid solutions Agx Gax Ge1−x S2 exist only in a limited range for the parameter x, and their properties are related to a much lesser extent to the properties of AGS and GeS2 . While the chalcopyrite AGS with point group 42m has mature growth technology and is a well established and characterized nonlinear optical crystal [1, 4], little information is available on GeS2 . The space group of GeS2 (single crystallites) was determined to be

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19 C2v − Fdd2 (point group mm2) as early as 1936 [73]. However, it turned out that at normal pressure and temperature this compound has two modifications. The refinement of the structure of the low-temperature phase yielded lower symmetry and monoclinic non-centrosymmetric space group Cs2 − Pc (point group m) [74]. The other phase, high-temperature GeS2 , has a centrosymmetric monoclinic space 5 group C2h − P21 /c (point group 2/m) [74]. Its band-gap amounts to 3.2 eV [75]. Orthorhombic symmetry of the quaternary compound AgGaGeS4 belonging to the AGGS class (Agx Gax Ge1−x S2 , x = 0.5) was established first when studying polycrystalline samples [76]. Almost simultaneously a profound analysis of single crystals of AgGaGeS4 appeared [77] which was based on the analogy with the 19 GeS2 structure suggested by Zachariasen [73]. The non-centrosymmetric C2v − Fdd2 “diamond” structure was ascribed to AgGaGeS4 (orthorhombic symmetry class mm2). The structure of AgGaGeS4 results from the substitution of Ge4+ by Ga3+ in the GeS2 cation sublattice. The valence deficiency is compensated by Ag+ ions filling the tetrahedral vacancies. Similarly to HGS and CHGS, the initial work on single crystal growth of AGGS compounds in large sizes by the Bridgman-Stockbarger technique from the melt was motivated by the possibility for visualization of mid-IR radiation by up-conversion. In that early work, the phase diagram of AgGaS2 − GeS2 was studied and orthorhombic solid solutions Agx Gax Ge1−x S2 were identified for x = 0.1 . . . 0.5 [20]. Single crystals of these compounds with a diameter of 20 mm and length of 50 mm were grown as early as 1980 [20]. More details were published, however, in 1991 [78]. The phase diagram of the AgGaS2 -GeS2 system showed that for 0.7 < x < 1 (at 1103 K) a pure tetragonal modification of Agx Gax Ge1−x S2 is formed which is isostructural to AGS but for 0.17 < x < 0.54 (also at 1103 K) a pure orthorhombic modification exists the structure of which can be assumed to be that of AgGaGeS4 . Glass formation was observed in the vicinity of GeS2 (x < 0.1) and recent powder SHG tests indicate that the structure in the limit x → 0 is centosymmetric. The above ranges are separated by intermediate regions where two phases exist. At lower temperatures the solubility of AGS in the orthorhombic phase decreases from its maximum value of 54%. The liquidus curve of this phase is almost horizontal. AgGaGeS4 has a melting point of 1118 K. The melting point increases with the GeS2 content to 1123 K and then remains constant. The orthorhombic solid solutions melt in a narrow temperature range which does not exceed 10◦ C. This range also decreases with the GeS2 content which means that better conditions for homogeneous composition are given but this is accompanied also by the trend towards glass formation at small values of x. At lower temperature also the solubility of GeS2 in the tetragonal phase decreases from its maximum value of 30 mol %. The tetragonal modification of Agx Gax Ge1−x S2 was studied later also by Chbani et al. [79] who found only AgGaGeS4 in the phase diagram of the Ag2 S-Ga2 S3 -GeS2 system but their results concerning the stability of AgGaGeS4 contradict the above


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observations. The section AgGaS2 -GeS2 of this phase diagram was recently reconsidered [80]. These authors obtained also a narrow region of solubility of AGS in GeS2 (x < 0.02 at 720 K) with the monoclinic symmetry of high-temperature GeS2 [74]. According to their phase diagram the pure orthorhombic phase extends over a narrower range (0.45 < x < 0.52 at 720 K). As a consequence of the phase diagram it is difficult to grow high quality tetragonal AGGS crystals. Several “discrete” orthorhombic single crystals with x = 0.17, 0.20, 0.25, 0.33 and 0.5 were grown for the initial crystallographic and optical studies [78]. These solid solutions of the form AgGaS2 -nGeS2 can be represented alternatively by the formula AgGaGen S2(n+1) , n = 1 . . . 5. According to more recent growth experiences the upper limit for the orthorhombic phase corresponds to n = 14 but it should be emphasized that in the general case n is not limited to a natural number. For brevity we use further also the notation AGGS(n). Quartz ampoules of 24 mm diameter and 120 mm length are used for the synthesis of AGGS(n) with 99.9999% purity Ag, Ga, Ge and S taken in stoichiometric ratios. The ampoules are sealed off after reaching a pressure of 2 × 10−5 Torr. The melt is produced in a horizontal oven. The quality of the grown crystals depends on the chemical composition of the charge, the temperature gradient in the furnace and the rate of the growth. Deviation of the crystal composition from the average value of x leads to decomposition of the solid solutions and the appearance of scattering centres upon cooling. This effect is stronger towards the boundary values of x. Typical temperature gradients used in the furnace for the growth of the different AGGS(n) compounds are between 3 and 6 K/mm. For instance, the decomposition of the solid solution AgGaGeS4 caused by the temperature gradient at the crystallization front can be completely avoided at 3 K/mm. The temperature in the furnace is stabilized with an accuracy of ±0.5 K. Characteristic average rates for the growth of high optical quality AGGS(n) crystals range from 2 to 8 mm/day for the different compounds. The present state of the art permits the growth of single crystals of AGGS(n) as large as 60–80 mm in length and 22 mm in diameter (Fig. 12) with an optical homogeneity of δn < 1 × 10−4 cm−1 achieved after post growth thermal annealing in a furnace for 30 days. Further information on the growth conditions of AgGaGeS4 was published very recently also by other authors [81, 82]; in both cases the temperature gradient was larger but the growth rate was lower. This composition is also the most studied one: The deviation from stoichiometry of the grown crystals measured by chemical microanalysis does not exceed ±0.01 for x [83, 84]. Besides the evolution of the crystal lattice parameters and the melting temperature of the orthorhombic phase with the parameter x, the work of Badikov et. al. [78] contained some basic information on the optical properties of AGGS(n). The band-gap lies between those of AGS and GeS2 but changes only weakly with the composition: It increases from 2.78 eV for AgGaGeS4 to 2.81 eV for

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(a)

(b)

Figure 12. (a) AgGaGeS4 and fabricated optical elements from it: The size of the left one is 10 × 10 × 30 mm3 . (b) Boule (φ18 mm × 60 mm) and optical elements made of AgGaGe4 S10 .

birefringence na-nc

0.20 AGGS (exp.1991) AGS AGGS (calc.)

0.16 0.12

0.08

0.04 0.0

0.2

0.4 0.6 0.8 1.0 composition parameter x

Figure 13. Birefringence of the biaxial AGGS(n) versus composition for n = 1 . . . 5 in comparison to the birefringence of the uniaxial AGS (half full symbol) at 700 nm. The open symbols represent the original data from [78] while the solid symbols connected with a line are based on calculations using the recently constructed two-pole Sellmeier expansions.

AgGaGe5 S12 (n = 5). For all compositions (n = 1 . . . 5) the optical losses were less than 0.1 cm−1 both at 505 and 694 nm. The most interesting feature discovered, however, was the drastical increase of the birefringence in comparison to AGS (Fig. 13). This effect is unique if compared to CHGS or the other mixed systems mentioned in the Introduction in which the birefringence is in general reduced with respect to the phase-matchable parent compound. The data obtained for the refractive index of AgGaGeS4 in the 0.5–11.5 µm range in 1980 [20] was published only recently [85] together with a system of two-pole Sellmeier equations [48, 49, 83, 85]. Another two-pole fit [86] and a simplified one-pole fit with a quadratic IR-term [38, 84] based on the same data also appeared. Limited data on the refractive index was available also for AGGS(n = 2 . . . 5) but Sellmeier equations existed only for n = 5 [48, 49, 87]. In an effort to construct reliable Sellmeier equations we combined these data with measurements of the angle between the two optic axes (Fig. 14) and SHG measurements in two of the principal planes using ns-pulses at 1064 nm (n = 3, 4, 5) as well as fs-pulses tunable from 1.7 to 4.5 µm (n = 1 and 4). The obtained


129

30

(a)

angle Vc [˚]

25 20 15 10 5 0 −5 0.1

0.2

0.3 0.4 parameter x

0.5

Z optic axis

nY

−

(b) θ +

nx VZ

+

nx

no

nY nZ

X

ne

nX

ne no nY ne no nZ

0.6

nZ

Y

−

ϕ

Figure 14. (a) Measured angle Vc between the optic axis and the c-axis of Agx Gax Ge1−x S2 at 633 nm in dependence on the x-parameter (solid triangles and fit) and calculated values (open triangles). (b) Principal optical axes and types of interaction in a biaxial crystal. The two optic axes lie per definition in the X-Z plane. V Z is the angle of one of them with the Z-axis, V Z = 90◦ − |Vc |. For AGGS(n), XYZ ≡ cba (n = 1) and XYZ ≡ cab (n = 2 . . . 5) hold.

two-pole expansions of the form n 2 = A1 + A3 /(λ2 − A2 ) + A5 /(λ2 − A4 ) are valid for the 0.5–11.5 µm spectral range [88]. More recently Miyata et al. constructed a refined Sellmeier expansion for AgGaGeS4 based on DFG (between 2.2 and 11.8 µm) and SHG (at 1.6 µm) phase-matching data which contains one pole and a quadratic IR term [89], fitting well also published angles for SHG near 9.55 µm [90]. For all compounds AGGS(n = 1 . . . 5), c is the two-fold polar axis and de f f is maximized for propagation along the b-axis [85, 88]. However, the correspondence between the crystallographic axes abc and the principal optical axes XYZ defined by n X < n Y < n Z is not the same for the whole class: XYZ = cab holds for n = 2 . . . 5, and XYZ = cba for n = 1(AgGaGeS4 ). This means that the two optic axes of the biaxial crystals AGGS(n) lie in the c-b plane for n = 2 . . . 5 and move to the c-a plane in the case n = 1. This can be seen from Fig. 14 which

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shows the angle between one of the optic axes and the c-axis. The transition between the two crystallographic planes is illustrated assuming a different sign of this angle Vc . According to Fig. 14 all AGGS crystals are negative biaxial. The refractive index n c = n X is substantially smaller than n a , n b which are rather close (quasi uniaxiality). This difference determines the birefringence. In contrast to what was believed previously [49, 83, 85], there is no crossing point of n a and n b in AgGaGeS4 and n b < n a is fulfilled in the whole transparency range. The different correspondence between the crystallographic and principal optical axes leads to different expressions for de f f . In the principal planes de f f is given for n = 2–5 by: in the X-Y plane (3) dooe = d32 sin ϕ 2 2 deeo = d32 sin θ + d31 cos θ in the Y-Z plane (4) dooe = d31 cos θ in the X-Z plane (θ < VZ ). (5) In the case of AgGaGeS4 these expressions defined in the XYZ frame remain unchanged due to the unchanged assignment n X = n c , however, the two coefficients should be exchanged in them (d31 ↔ d32 ) because for orthorhombic crystals they are traditionally defined in the abc frame. Note that for phasematching reasons the situation θ > VZ in AGGS is never realized in practice. Thus only type-I interaction is effective in these crystals. The transmission of AgGaGeS4 determined with a 2.1 mm thick crystal extends from 0.44 to 14 µm at the “0”-level and from 0.445 to 11.9 µm at the 10% level [48,49,83,84]. The measurement near the absorption edge in Fig. 15(a) with a 3-mm thick sample indicates weak dependence on the polarization and good agreement with the previously estimated band-gap of 2.78 eV which corresponds to 446 nm [78]. Typically the losses in the clear transparency range amount to 0.05 cm−1 , in exceptional cases lower losses (0.01–0.02 cm−1 at 1064 nm) have been achieved. A loss coefficient of 0.05 cm−1 has been also reported at 2.05 µm in a first attempt to grow AgGaGeS4 [82]. It can be expected that improvement of the growth technology will allow to reduce the loss level to 0.01 cm−1 and even below. Between 500 and 700 nm the losses increase but remain below 0.1 cm−1 while near 9.55 µm < 0.3 cm−1 were reported [48, 49, 83, 84]. In the good transparency region the transmission variation is of the order of 1–2% for an area of 10 × 15 mm2 and it is more pronounced below 1 µm [83]. Measurements with thin samples for higher n (Fig. 15b) reveal that the short-wave transparency limit is extended down to 410 nm at the “0”-level in accordance with the increasing band-gap (updated value of ≈3.0 eV from this curve). The same measurement indicates that the IR cut-off edge is probably related to two-phonon absorption which poses a limit for the practical applications. Unfortunately we are not aware of any experimental data on the vibrational modes. The latter have been only theoretically classified for AgGaGeS4 [91].


transmission [%]

80

131

(a) AgGaGeS4

60 60

40

40 20 0 425

20 0

E//c E//b E//a 450 475 500 wavelength [nm]

525

1

10 wavelength [µm]

transmission [%]

80

(b)

60

AgGaGe4S10

40 20 0

1

10 wavelength [µm]

Figure 15. Unpolarized transmission of a 3-mm thick AGGS (n = 1) plate (a) and 0.5-mm thick AGGS (n = 4) plate (b). The inset in (a) shows the polarization dependence near the band edge where the transmission is given also in % for a thickness of 3 mm.

The nonlinear coefficients of AgGaGeS4 were initially measured by the Maker fringe method at 1064 nm relative to AGS [20, 85]: Averaging these data and assuming Kleinman symmetry gives d31 = 12.3 ± 15% pm/V, d32 = −5.4 ± 15% pm/V, and d33 = 6.3 ± 15% pm/V. The diagonal element d33 plays a role only outside the principal planes. Another estimation by the same method relative to ZGP gave as a result, without specifying the sign, d31 = 13 ± 15% pm/V and d32 = 8 ± 15% pm/V at 9.55 µm [48, 49, 83, 84]. A rather indirect comparison with LiInS2 in a fs-OPA pumped at 820 nm and generating an idler wave at 7 µm gave d31 (AgGaGeS4 ) = 12 ± 20% pm/V [85]. To improve the reliability of the data on the nonlinear coefficients we performed phase-matched SHG measurements [88]. The two nonlinear coefficients of AGGS(n = 1, 4) were first estimated relative to AGS using the idler pulses of a 1 kHz fs OPA pumped at 800 nm. Two plates of AgGaGeS4 cut at θ = 57.7◦ in the X-Z plane and ϕ = 29◦ in the X-Y plane, two plates of AgGaGe4 S10 cut at θ = 59◦ in the X-Z plane and ϕ = 14.5◦ in the X-Y plane, and a reference plate of AGS (θ = 35.3◦ for type-I, oo-e interaction), all with thickness 0.5–0.52 mm, were used for these SHG measurements. From relative SHG

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V. PETROV ET AL. TABLE 3. Nonlinear coefficients of AGGS for SHG at 1064 nm. Agx Gax Ge1−x S2 nonlinear coefficient d31 [pm/V] d32 [pm/V]

AgGaGeS4

AgGaGe3 S8

fs pulses 10.2 −6.2

ns pulses 13.65

AgGaGe4 S10 fs pulses 11.7 −8.7

ns pulses 13.8

efficiencies at 3.5 µm, using a MgO-LiNbO3 crystal in the fs OPA, we derived d31 (AgGaGeS4 ), d32 (AgGaGeS4 ), and d31 (AgGaGe4 S10 ), and from SHG at 1.7 µm using a β-BaB2 O4 crystal in the fs OPA we estimated d32 (AgGaGe4 S10 ). The results after rescaling to SHG at 1064 nm by Miller’s rule, are included in Table 3. These experiments provided no information about the relative sign. A comparison of the SHG efficiency obtained at 1064 nm with a 1-mm Zcut plate of AgGaGe4 S10 at θ = 13.5◦ and that obtained with a 5-mm thick X-cut, temperature-tuned LiB3 O5 crystal using 1-ns pulses at 1 kHz gave, with d32 (LiB3 O5 ) = 0.85 pm/V [4], 13.8 pm/V for d31 (AgGaGe4 S10 ). A similar experiment with a ≈2-mm thick AgGaGe3 S8 plate (phase-matching at θ = 3.2◦ ) gave 13.65 pm/V for d31 (AgGaGe3 S8 ). The error introduced in the relative SHG measurements should be of the order of ±5%. All this data summarized in Table 3 is in good agreement with the previous estimations for AGGS(n = 1) using the Maker fringe technique. On the other hand it reveals that there is no pronounced trend in the dependence of the nonlinearity on the composition. A surface damage threshold of 50 MW/cm2 was reported with 30 ns pulses at 1064 nm and 10 Hz in the initial work devoted to all AGGS(n) compounds [20]. Very recently a zero-probability damage threshold of 73 MW/cm2 (1.1 J/cm2 ) was estimated for AgGaGeS4 at 2.05 µm using 15 ns long pulses at 10 kHz [82]. The damage occurred always at the exit crystal face. The same compound was also studied at 9.55 µm with 30-ns pulses and compared to other crystals: The damage threshold of 230 MW/cm2 obtained is somewhat lower than the damage threshold of CHGS but still considerably larger than the values obtained for AGS and AGSe [60]. Optical damage or formation of colour centers were not detected in a 2.8 mm thick AgGaGeS4 sample up to 170 GW/cm2 with 80-fs pulses at 820 nm and 1 kHz [85]. Reversible nonlinear losses were observed in the same work at much lower intensities (50 GW/cm2 ) but could not be fitted by a simple TPA process. Data on some thermal properties is available only for AgGaGeS4 : The heat capacity amounts to C p = 448 ± 8 Jkg−1 K−1 and the thermal conductivity measured with an unoriented sample is K = 0.399 ± 0.002 Wm−1 K−1 which is lower in comparison to CHGS [82]. A thermal conductivity lower than that of the parent

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compounds is not unexpected for a solid solution. However, this issue deserves more attention in the future because it is unclear why the damage threshold of this material is then so high. 3.2. POTENTIAL AND FREQUENCY CONVERSION SCHEMES REALIZED WITH QUATERNARY AGGS CRYSTALS

The unique advantage of the AGGS(n) crystals over any other mid-IR materials is the engineerable birefringence which can be extremely large. These compounds are one of the few examples of biaxial nonlinear crystals for the mid-IR. Furthermore, they exhibit higher damage resistivity in comparison to AGS, the basic commercial material for the 5–12 µm spectral range. The biaxial character of the AGGS compounds offers much more possibilities for phase-matched configurations including uncritical phase-matching. These crystals behave like negative uniaxial in the X-Y and X-Z planes and as positive uniaxial in the Y-Z plane (Fig. 14b). Since d31 > d32 , most interesting for practical applications seems the engineerable by composition uncritical phase-matching along the b-axis. According to the obtained Sellmeier equations, variation of the composition parameter x from 0.17 to 0.5 ensures fulfillment of the uncritical condition for type-I SHG along the b-axis with maximum de f f = d31 for fundamental wavelengths ranging from 1015 to 1477 nm [88]. Table 4 summarizes the fundamental wavelengths for uncritical type-I SHG along the Z and Y principal optical axes of the AGGS(n = 1 . . . 5) crystals together with the corresponding angular acceptances in the two principal planes ∆θ TABLE 4. planes. AGGS(n) n 1 2 3 4 5

Phase-matching properties of AGGS(n = 1 . . . 5) for type-I SHG in the principal

uncritical along Z λ [nm] 1484 10778 1146 13140 1064 14101 1046 14658 1015 14483

θ(X-Z) 2.68◦ 8.03◦ 1.80◦ 6.91◦ 1.64◦ 6.59◦ 1.61◦ 6.39◦ 1.51◦ 6.44◦

θ (Y-Z) 2.81◦ 7.59◦ 1.86◦ 6.20◦ 1.64◦ 5.95◦ 1.54◦ 5.83◦ 1.51◦ 5.82◦

uncritical along Y λ [nm] 1477 10840 1079 13838 998 14909 986 15443 945 15627

ϕ(X-Y) 2.67◦ 8.00◦ 1.60◦ 6.57◦ 1.43◦ 6.24◦ 1.41◦ 6.05◦ 1.30◦ 5.98◦

θ (Y-Z) 2.79◦ 7.56◦ 1.65◦ 5.92◦ 1.43◦ 5.61◦ 1.35◦ 5.50◦ 1.28◦ 5.42◦

uncritical λ [nm] X-Z

X-Y

4234

4250

4183

–

4141

–

4126

–

4056

–

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GVM [ps/cm]

20 10

10

10

0

0

0

−10

∆31 (oo-e)

−20

20

wavelength [µm]

15

40

60

-10

∆31 (ee-o)

80 15

20

40

-10

60

12

12

9

9

9

6

oo-e

3 0

0

X

20

40 ϕ [˚]

60

Y

20

40

60

80

60

80

6

ee-o

3 80 0

∆31 (oo-e)

80 15

12

6

AgGaGeS4 AgGaGe5S12

20

40 60 90˚−θ [˚]

oo-e

3 80 0

Z

20

40 θ [˚]

X

Figure 16. Type-I SHG phase-matching in the principal planes of AGGS(n = 1, 5). The dashed lines indicate the correspondence between the two branches of the tuning and GVM curves. Some experimentally obtained points are shown by symbols.

or ∆ϕ (FWHM) calculated from the second derivative of the wave mismatch for a crystal length of 1 cm (these parameters scale with the square root of the crystal length). It can be seen from Fig. 16 that the tuning behaviour of AGGS(n = 1) is quite symmetric in the X-Y and X-Z planes and that there is no phase-matching in the vicinity of the X-axis where de f f vanishes. However, this is not the case for AGGS(n > 1). Although the upper wavelength limit of the tunability in the X-Y plane seems larger in this case, it should be kept in mind that this region is outside the validity of the Sellmeier equations and the transparency range. The tunability in the Y-Z plane is very limited for all n = 1 . . . 5 and defined by the wavelength pairs given in Table 4. This means that the interaction in this plane is quasi anglenoncritical which ensures large acceptance and small walk-off angles [85]. On the opposite, one or two regions exist in the X-Y and X-Z planes where the three-wave interaction is quasi wavelength-noncritical. The wavelengths at which this occurs (also given in Table 4) correspond to vanishing GVM which means large spectral acceptance for SHG of short pulses where the second derivative of the wavemismatch comes into play. Note that in the case of SHG the spectral acceptance is given simply by 0.886/|∆31 | where the indices are related to λ1 ≥ λ2 > λ3 with 1/λ3 = 1/λ1 + 1/λ2 . The spectral acceptance is smallest in the Y-Z plane and this can be used for spectral narrowing.


wavelengths λ2 and λ1 [µm]

10

40˚ 45˚ 50˚ 55˚ 60˚ 70˚ 90˚

ϕ = 35˚

40˚45˚50˚55˚60˚70˚90˚

30˚

1 AgGaGeS4

(a) 0.5

wavelengths λ2 and λ1 [µm]

ϕ =35˚

135

θ =55˚

1 wavelength λ3 [µm] θ =55˚

5

50˚ 45˚ 40˚

10 50˚ 45˚ 40˚ 35˚ 30˚ 20˚

1

0˚

(b) 0.5

AgGaGe5S12 1 wavelength λ3 [µm]

5

Figure 17. Type-I (oo-e) phase-matching for sum and difference frequency mixing or optical parametric amplification in the X-Y plane of AgGaGeS4 (a) and the X-Z plane of AgGaGe5 S12 (b) where de f f is maximized. The uncritical configurations are shown by thick lines. The curves are terminated by the transparency range of the crystals. 1/λ3 = 1/λ1 +1/λ2 holds with λ1 ≥ λ2 > λ3 .

The smaller value of the diagonal element d33 of the nonlinear susceptibility indicates that propagation outside the principal planes is not expected to be advantageous in any aspect. Having in mind that d31 > d32 we present for the general case in Fig. 17 interaction only in the plane with superior de f f . The solutions for type-I phase-matching in Fig. 17 consist of two branches which eventually merge at larger angles (see the ϕ = 30◦ curve in Fig. 17a) forming a closed contour. The left branch corresponding to shorter λ3 provides broader tunability at a given crystal cut. Note that in the limit of uncritical phase-matching the wavelength tunability is not very large and gets even narrower with increasing n. At some phase-matching angles, retracing behaviour can be observed within the transparency range: e.g. in the case of parametric interaction one and the same pump wavelength λ P ≡ λ3 corresponds to two pairs (λ I ≡ λ1 , λ S ≡ λ2 ) of idler

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and signal wavelengths (e.g. curve ϕ = 30◦ in Fig. 17a). In this region the spectral acceptance is very large. Thus for ϕ = 30◦ in Fig. 17a, λ3 = 1604 nm, λ2 = 2072 nm and λ1 ≈ 7.1 µm, we have ∆32 ≈ ∆31 ≈ 10 fs/mm. Such a phasematching configuration is especially suitable for frequency conversion of fs pulses or generation of fs quasi continuum and in this case higher order effects (group velocity dispersion) have to be taken into account. Near degeneracy (SHG points) one has on the other hand vanishing ∆21 but the wave at λ3 has in general different group velocity. Equality of all three group velocities is reached again only at the maximum allowed phase-matching angle when the contours in Fig. 17 degenerate into a point corresponding to SHG at 4250 and 4056 nm, respectively (compare Fig. 16 and Table 4). This happens at ϕ ≈ 28.8◦ (Fig. 17a) and θ = 57.8◦ (Fig. 17b) and that is why no closed contour is seen in Fig. 17b for the chosen angle interval. Spectrally, the regions of low GVM are quite narrow. The first experimentally realized phase-matched process with AgGaGeS4 was up-conversion of 10.6 µm radiation to 507 nm by mixing with powerful laser radiation at 532 nm [78]. In the next two subsections we will describe two different applications of AGGS(n) crystals which we realized more recently.

60

60

40

40

20

20

0

3

4

5

6

7

8

9 10 11 12 idler wavelength λI [µm]

0

phase-matching angle ϕ [˚]

idler energy [nJ]

3.2.1. Optical parametric amplification in AGG S(n = 1) As an OPA, we studied a 2.8-mm thick uncoated sample of AgGaGeS4 with an aperture of 7×6 mm2 , cut at ϕ = 37◦ in the X-Y plane. The crystal was pumped at 820 nm with 220 fs, 230 µ J pulses from a 1 kHz-Ti:sapphire regenerative amplifier at a peak axial intensity of 50 GW/cm2 as described in Subsection 2.2.2., see Fig. 7. This pump intensity was sufficiently low to avoid TPA but the conversion efficiency was also relatively low. The experimentally achieved tuning range for the idler was from 3.8 to 11 µm. The obtained idler energy and the measured phase-matching angles are shown in Fig. 18. The computed curve is based on the Sellmeier expansions from [88].

Figure 18. Measured idler energy (circles) and phase-matching angle ϕ (squares), and comparison with a calculation for the tuning of the AgGaGeS4 OPA (curve) pumped at 820 nm.

QUATERNARY NONLINEAR OPTICAL CRYSTALS (a)

137

(b)

164nm

318nm

7.0

9.0

7.5

idler wavelength λI [µm]

9.5

10.0

idler wavelength λI [µm]

Figure 19. Spectra of the idler pulses generated by the AgGaGeS4 OPA at λ I = 7.2 µm (a) and λ I = 9.5 µm (b).

(b)

(a)

890 fs

620 fs

−1

0 delay [ps]

1

−1

0

1

delay [ps]

Figure 20. Cross correlation functions of the idler pulses corresponding to the spectra in Fig. 19 at λ I = 7.2 µm (a) and at λ I = 9.5 µm (b). The deconvolved FWHM amounts to 570 fs (a) and 860 fs (b) assuming Gaussian pulse shapes.

The idler spectra recorded at 7.2 and 9.5 µm are presented in Fig. 19 and the CCFs are shown in Fig. 20. The measured idler pulse duration near 7.2 µm was 570 fs (FWHM) and the idler pulses were nearly Fourier-limited assuming Gaussian temporal shapes (time-bandwidth product of 0.54). At 9.5 µm the FWHM of 860 fs leads to a time-bandwidth product (0.91), about 2 times the Fourier limit. The pulse lengths achieved are representative of the large GVM between the idler pulses and the other two pulses: At λ I = 7.2 µm the idler runs about 1.3 ps and at 9.5 µm – about 1.1 ps ahead of the pump pulse within 2.8 mm of AgGaGeS4 . The increase of the pulse duration with increasing idler wavelength is attributed to the lower parametric gain according to the angle and wavelength dependence.

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The nonlinear losses in the AgGaGeS4 sample at the applied pump intensity were about 10%. It is expected that the increased band-gap for n > 1 will allow pumping of other AGGS(n) compounds in the 800 nm range at high intensity without nonlinear losses. Although the GVM is slightly better, the AGGS(n) compounds seem inferior to CHGS for this application because their nonlinearity is substantially lower. Nevertheless, angle tuning is obviously facilitated away from the uncritical configuration and in this case their use could be advantageous because the increase of the GeS2 content increases both the birefringence and the band-gap while in the case of CHGS the increase of the CHS content increases the band-gap but reduces the birefringence. 3.2.2. Phase-matched SHG in AGG S(n = 3 . . . 5) at 1064 nm The AGGS compounds have not only larger birefringence than AGS but also the dispersion of their refractive indices has a different behaviour. In particular, there is no isotropic point in the visible and the birefringence remains relatively large (Fig. 13). From the estimated phase-matching properties it is predicted that uncritically phase-matched SHG should be possible down to ≈1 µm for the fundamental, with the second harmonic approaching the transparency cutoff limit (Table 4). Due to the superior characteristics in comparison to LiB3 O5 or KTiOPO4 it is expected that such crystals can find applications in low-power microlasers with intracavity SHG including single-frequency designs. SHG in the X-Z plane was studied near 1064 nm with three different Qswitched Nd:YAG lasers delivering 1 ns (at 1 kHz), and 10 and 150 ns (at 10 Hz) pulses, and tunable 30 ps idler pulses from a 10-Hz optical parametric generator pumped by the third harmonic of a Nd:YAG amplifier. The AGGS(n = 3, 4, 5) samples used were Z-cut and had a thickness from 1 to 4 mm [88]. The results obtained at 1064 nm are summarized in Fig. 21. The numerical data and the Sellmeier expansions used for the calculation are from [88].

phase-matching angle θ [˚]

30 25 20

AgGaGe3S8 AgGaGe4S10 AgGaGe5S12

15 10 5 0 1000

1020

1040

1060

1080

1100

fundamental wavelength [nm]

Figure 21. Measurement of phase-matched SHG at 1064 nm with different samples of AGGS(n = 3, 4, 5) in the X-Z plane. The curves show the calculated phase-matching angles.


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The average phase-matching angle for AGGS(n = 3) at 1064 nm is ≈1.9◦ which is very close to the calculated one (θ = 1.88◦ ). Thus AgGaGe3 S8 turns out to be the most suitable candidate for SHG at 1064 nm. It is the first time a non-oxide inorganic crystal has been shown to be phase-matchable for SHG at 1064 nm. Obviously gradients in the composition result in slight variation of the birefringence. It is clear from Table 4 that the deviations from θ = 0◦ in AgGaGe3 S8 seen in Fig. 21 are comparable to the angular acceptance ∆θ. The thermo-optic coefficients for the AgGaGen S2(n+1) compounds are unknown at present but with a 2-mm thick Z-cut AgGaGe3 S8 sample we established that the average deviation of ≈1.9◦ from the uncritical phase-matching direction can be eliminated at a temperature of about 130◦ C. The basic advantage of the AGGS crystals for this application relative to oxide crystals like LiB3 O5 and KTiOPO4 are the increased nonlinear coefficients, typical for any sulphide crystal. Additional advantages are the uncritical phase-matching with maximized effective nonlinearity, increased angular acceptance, vanishing walk-off and type-I interaction (in comparison to KTiOPO4 ), and the possibility to operate close to room temperature with much higher efficiency (in comparison to LiB3 O5 ). Although the spectral acceptance of the AGGS compounds is narrower, this can be compensated for by taking a shorter crystal since the difference in de f f is much larger. 3.2.3. Further potential applications of AGGS SHG has been realized with crystals of AgGaGeS4 also near 9.55 µm [48, 49, 83, 90]. Using 33 ns long pulses with a peak intensity of 38.5 MW/cm2 and a 2.1 mm thick crystal, a peak power of 43 kW was achieved for the second harmonic which corresponded to roughly 0.6% external efficiency in terms of peak power and 0.3% in terms of energy (0.7 mJ achieved in the second harmonic). Although according to Table 4 AgGaGeS4 and also the other AGGS crystals, in contrast to the CHGS compounds, are phase-matchable for SHG in the whole spectral range of the CO2 laser and this has been experimentally verified for AgGaGeS4 up to 10.3 µm [86], they exhibit, similarly to the CHGS crystals, significant absorption which is the restricting factor for this application. This problem can be obviously solved with the related selenide quaternary compounds of the same type which are at present under study [78]. According to the same table, at short wavelengths, AGGS compounds with tailored composition could be useful for uncritical SHG along the Z-axis of different Nd3+ , Yb3+ , Er3+ or Cr4+ -lasers. Propagation along the Y-axis allows uncritical phase-matching at yet shorter wavelengths which could be useful for InGaAs laser diodes. In the case of AgGaGeS4 this corresponds also to de f f = d31 .

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4. Conclusion This chapter contains a complete survey of two quaternary nonlinear optical crystals with variable composition. As typically for sulphides their upper transparency edge limits their usefulness to about 12 µm. While their main field of application should lie above 5 µm which is roughly the limit for oxide nonlinear crystals, it should be outlined that both CHGS and AGGS are also capable of spanning the gap to the visible and near-IR because their band-gaps are sufficiently large. In this sense these two crystals which are in their development stage have to compete in the first place with AGS with its mature technology. In addition to the increased nonlinearity and the better thermo-mechanical and damage properties, which are characteristic also for its parent compound HGS, CHGS can offer the easier growth in larger sizes with potentially lower internal loss level than HGS. The variable composition offers unique potential for applications related to the possibility of having uncritical phase-matching with maximum effective nonlinearity and without spatial walk-off. These include down conversion, by DFG or OPO, of CW laser sources from the visible/near-IR and in some cases ns-OPOs. Especially tuning by the composition, preserving the uncritical phase-matching condition, seems very promising because temperature tuning is very limited. These schemes require normally longer samples. Thus the main problem in their realization (except for DFG) is the present level of losses in the region of clear transparency. Since CHGS is a complete solid solution there are some fundamental limits for the achievable homogeneity of the grown crystals. However, in many cases this limitation can be circumvented by the use of shorter crystals because the nonlinear susceptibility is relatively high. This has been already demonstrated for a 10 Hz CHGS OPO with 30 ns pump pulses at 1064 nm. Nevertheless, as soon as the loss level is not reduced to the one typical of production-quality AGS (0.01 cm−1 ) it looks like that CHGS crystals can find more applications with fs and ps pulses. In this case the interaction length is relatively short and the nonlinear elements are not longer than several millimetres. We have demonstrated such OPA operation with high energy fs pulses at 1 kHz for pump wavelengths down to the range of Ti:sapphire laser systems. This was possible due to the relatively large band-gap which can be also tailored by the composition. The latter holds also for the GVM parameters which determine the actual interaction length in the case of ultrashort pulses. Using such amplified fs or ps pulses at 0.01–100 kHz it is not essential to have uncritical phase-matching because the beam cross sections are relatively large. However, realization of high repetition (∼100 MHz) fs or ps SPOPOs in the mid-IR will rely, in addition to the suitable GVM and the absence of TPA, on the existence of uncriticality because of the tighter focusing. Such devices based on CHGS could be pumped either near 800 nm where the pump sources can be tunable, or near 1 µm with fixed wavelength pump sources. Thermal effects


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related to the residual absorption have to be considered in ns OPOs operating at kHz repetition rates and in ps SPOPOs. The orthorhombic AGGS crystals could be advantageous over the CHGS crystals whenever larger crystal sizes are required because their homogeneity is superior and the losses can be potentially reduced to a lower (e.g. 0.005 cm−1 ) level. The more stable composition is a consequence of their phase diagram and the fact that they are partial solid solutions. Since their slightly lower (by 10–20%) nonlinear susceptibility in comparison to AGS is compensated for by the increased damage threshold they are also interesting for ns OPOs pumped at 1064 nm. The unique properties of the AGGS compounds are related to the extraordinary large birefringence. This allows phase-matching of down conversion processes with very short input wavelength(s) and also up conversion and in particular SHG to wavelengths approaching their band-gap which is also slightly increased with respect to AGS. For a number of wavelength combinations this can be combined with uncritical phase-matching utilizing the maximum effective nonlinearity which can exceed that achievable with AGS. Thus, offering higher nonlinearity, they can even compete in the visible/near-IR with oxide crystals. Their biaxial nature provides greater variety of phase-matching schemes and in particular quasi angle-uncritical or wavelength-uncritical configurations. They are one of the very few biaxial crystals that gained importance in the mid-IR. Finally, we note that implementation of both CHGS and AGGS crystals in cavity arrangements like OPOs will depend on the development of low-loss antireflection coatings which in some cases can contribute to further increase of the surface damage resistivity. Acknowledgements The first optical characterization of the CHGS and AGGS crystals was undertaken in the 1980-ies by N. K. Trotsenko from the Laboratory of Crystal Growth, Kuban State University. His results played a major role for the evaluation of the potential of these mixed compounds and stimulated further activities on the optimization of their growth technology. We acknowledge the essential contributions of G. Shevyrdyaeva from the High Technologies Laboratory in the development of this technology. We thank further K. V. Mitin from “Astrofizika” Research and Production Association (Moscow) for providing information and discussions on the ns OPO operation of CHGS, S. G. Sheina (High Technologies Laboratory) and V. I. Chizhikov (Kuban State University) for discussions concerning the crystal growth and the optical properties, respectively, and F. Noack, F. Rotermund, and G. Xu from the Max-Born-Institute for participation in some of the short pulse laser experiments.

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47. S. Das, U. Chatterjee, C. Ghosh, S. Gangopadhyay, Yu. M. Andreev, G. Lanskii, and V. V. Badikov, Tunable middle infrared radiation with HgGa2 S4 crystal, Opt. Commun. 259(2), 868–872 (2006); Corrigendum 263(2), 352 (2006). 48. M. V. Kabanov, Yu. M. Andreev, V. V. Badikov, and P. P. Geiko, Parametric frequency conversion based on new nonlinear crystals, Russ. Phys. J. 46(8), 835–846 (2003) [transl. from Izv. Vysshikh Uchebnykh Zavedenii, Fizika 46(8), 84–94 (2003)]. 49. Yu. M. Andreev, P. P. Geiko, and M. V. Kabanov, New crystals for frequency-tunable lasers, Optoelectronics, Instrumentation and Data Processing 40(5), 96–106 (2004) [transl. from Avtometriya 40(5), 119–133 (2004)]. 50. V. V. Badikov, N. V. Kuzmin, V. B. Laptev, A. L. Malinovsky, K. V. Mitin, G. S. Nazarov, E. A. Ryabov, A. M. Seryogin, and N. I. Schebetova, A study of the optical and thermal properties of nonlinear mercury thiogallate crystals, Quantum Electron. 34(5), 451–456 (2004) [transl. from Kvantovaya Elektron. 34(5), 451–456 (2004)]. 51. V. Badikov, A. Fintisova, V. Panutin, S. Sheina, S. Scherbakov, G. Shevyrdyaeva, A. Don, K. Mitin, N. Schebetova, A. Seryogin, V. Sinaisky, N. Kuzmin, V. Laptev, A. Malinovsky, E. Ryabov, J. Mangin, G. Gadret, J.-C. Jules, G. Mennerat, C. Pasquer, and J.-C. de Miscault, Hg1−x Cdx Ga2 S4 crystals as new materials for mid-infrared parametric oscillators pumped by Nd:YAG lasers, Conference on Lasers and Electro-Optics CLEO’04, San Francisco (CA), USA, May 16–21, 2004, paper CThT44, CLEO/IQEC Technical Digest CD-ROM. 52. E. Takaoka and K. Kato, Tunable IR generation in HgGa2 S4 , Conference on Lasers and Electro-Optics CLEO’98, San Francisco (CA), USA, May 3–8, 1998, paper CWF39, 1998 OSA Technical Digest Series Vol. 6, pp. 253–254. 53. B. F. Levine, C. G. Bethea, and H. M. Kasper, Nonlinear optical susceptibility of thiogallate CdGa2 S4 , IEEE J. Quantum Electron. 10(12), 904–906 (1974). 54. D. A. Roberts, Simplified characterization of uniaxial and biaxial nonlinear optical crystals: A plea for standardization of nomenclature and conventions, IEEE J. Quantum Electron. 28(10), 2057–2074 (1992). 55. J.-J. Zondy, D. Touahri, and O. Acef, Absolute value of the d36 nonlinear coefficient of AgGaS2 : prospect for a low-threshold doubly resonant oscillator-based 3:1 frequency divider, J. Opt. Soc. Am. 14(10), 2481–2497 (1997). 56. J.-J. Zondy, Experimental investigation of single and twin AgGaSe2 crystals for CW 10.2 µm SHG, Opt. Commun. 119(3–4), 320–326 (1995). 57. A. A. Martynov and A. E. Rozenson, Quantum-mechanical calculation of linear and nonlinear susceptibilities of an HgGa2 S4 crystal in the transparency range, Sov. Phys. Semicond. 14(10), 1137–1139 (1980) [transl. from Fiz. Tekh. Poluprovodn. 14(10), 1908–1912 (1980)]. 58. S. A. Andreev, N. P. Andreeva, V. V. Badikov, I. N. Matveev, and S. M. Pshenichnikov, Frequency up-conversion in a mercury thiogallate crystal, Sov. J. Quantum Electron 10(9), 1157–1158 (1980) [transl. from Kvantovaya Elektron. 7(9), 2003–2006 (1980)]. 59. S. A. Komarov, A. N. Meleshko, S. A. Pleshanov, and V. S. Solomatin, Efficient conversion of CO2 laser radiation in the nonlinear crystal HgGa2 S4 , Sov. Tech. Phys. Lett. 6(7), 375–376 (1980) [transl. from Pis’ma Zh. Tekh. Fiz. 6(7), 870–873 (1980)]. 60. Yu. M. Andreev, V. V. Badikov, V. G. Voevodin, L. G. Geiko, P. P. Geiko, M. V. Ivashchenko, A. I. Karapuzikov, and I. V. Sherstov, Radiation resistance of nonlinear crystals at a wavelength of 9.55 µm, Quantum Electron. 31(12), 1075–1078 (2001) [transl. from Kvantovaya Elektron. 31(12), 1075–1078 (2001)].

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61. F. Rotermund and V. Petrov, Femtosecond noncollinear optical parametric amplification in the mid-infrared range with 1.25 µm pumping, Jpn. J. Appl. Phys. 40(5A), 3195–3200 (2001). 62. K. R. Allakhverdiev, Z. Yu. Salaeva, and A. B. Orun, Two-photon absorption in CdGa2 S4 and CdGa2 S3.96 Se0.04 crystals, Opt. Commun. 167(1–6), 95–98 (1999). 63. V. V. Badikov, A. K. Don, K. V. Mitin, A. M. Seregin, V. V. Sinaiskii, and N. I. Schebetova, A HgGa2 S4 optical parametric oscillator, Quantum Electron. 33(9), 831–832 (2003) [transl. from Kvantovaya Elektron. 33(9) 831–832 (2003)]. 64. F. Rotermund and V. Petrov, Mercury thiogallate mid-infrared femtosecond optical parametric generator pumped at 1.25 µm by a Cr:forsterite regenerative amplifier, Opt. Lett. 25(10), 746– 748 (2000). 65. F. Rotermund, V. Petrov, and F. Noack, Difference-frequency generation of intense femtosecond pulses in the mid-IR (4–12 µm) using HgGa2 S4 and AgGaS2 , Opt. Commun. 185(1–3), 177–183 (2000). 66. V. V. Badikov, A. K. Don, K. V. Mitin, A. M. Seryogin, V. V. Sinaiskiy, and N. I. Schebetova, Optical parametric oscillator on an Hg1−x Cdx Ga2 S4 crystal, Quantum Electron. 35(9), 853– 856 (2005) [transl. from Kvantovaya Elektron. 35(9), 853–856 (2005)]. 67. D. Ren, J. Huang, X. Hu, Y. Qu, Y. Andreev, P. Geiko, and V. Badikov, Efficient CO2 frequency doubling with Hg1−x Cdx Ga2 S4 , Proc. SPIE 5397, 205–211 (2004). 68. J.-Z. Huang, D.-M. Ren, X.-Y. Hu, Y.-C. Qu, Y. Andreev, P. Geiko, V. Badikov, and G. Lanskii, Nonlinear optical properties of mixed Cd0.35 Hg0.65 Ga2 S4 crystal, Acta Phys. Sinica 53(11), 3761–3765 (2004), in Chinese. 69. S.-P. Huang, D.-S. Wu, X.-D. Li, Y.-Z. Lan, H. Zhang, Y.-J. Gong, F.-F. Li, J. Shen, and W.-D. Cheng, Band structures, chemical bonding, and frequency-dependent optical properties of nonlinear optical crystals HgGa2 S4 and Hg0.5 Cd0.5 Ga2 S4 , Chin. Phys. 14(8), 1631–1638 (2005). 70. V. L. Paniutin, B. E. Ponedelnikov, A. E. Rosenson, and V. I. Tchijikov, Structures de bande des solutions solids Cd1−x Hgx Ga2 S4 et CdGa2 (S1−x Sex )4 , J. Physique 41(9), 1025–1029 (1980). 71. V. Petrov, F. Rotermund, and F. Noack, Generation of high-power femtosecond light pulses at 1 kHz in the mid-infrared spectral range between 3 and 12 µm by second-order nonlinear processes in optical crystals, J. Opt. A: Pure Appl. Opt. 3(3), R1–R19 (2001). 72. V. Petrov, C. Rempel, K.-P. Stolberg, and W. Schade, Widely tunable continuous-wave midinfrared laser source based on difference-frequency generation in AgGaS2 , Appl. Opt. 37(21), 4925–4928 (1998). 73. W. H. Zachariasen, The crystal structure of germanium disulphide, J. Chem. Phys. 4(9), 618– 619 (1936). 74. D. I. Bletskan, I. M. Mitrovtsii, V. A. Stefanovich, M. V. Potorii, Yu. V. Voroshilov, and V. Yu. Slivka, Polimorphism of germanium disulfide, Sov. Phys. Crystallogr. 32(2), 224–229 (1987) [transl. from Kristallographiya 32(2), 385–393 (1987)]. 75. A. V. Golubkov, G. B. Dubrovskii, and A. I. Shelykh, Preparation and properties of GeS2 single crystals, Semiconductors 32(7), 734–735 (1998) [transl. from Fiz. Tekh. Poluprovodn. 32(7), 827–828 (1998)]. 76. O. H. Hughes, J. C. Woolley, S. A. Lopez-Rivera, and B. R. Pamplin, Quaternary adamantine selenides and tellurides of the form I III IV VI4 , Sol. State Commun. 35(8), 573–575 (1980).


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77. E. A. Pobedimskaya, L. L. Alimova, N. V. Belov, and V. V. Badikov, Crystal structure of silver germanogallium sulfide and GeS2 , Sov. Phys. Dokl. 26(3), 259–260 (1981) [transl. from Dokl. Akad. Nauk SSSR 257(3), 611–614 (1981)]. 78. V. V. Badikov, A. G. Tyulyupa, G. S. Shevyrdyaeva, and S. G. Sheina, Solid solutions in the AgGaS2 -GeS2 and AgGaSe2 -GeSe2 systems, Inorg. Mater. 27(2), 177–180 (1991) [transl. from Izv. Akad. Nauk SSSR: Neorganicheskie Materialy 27(2), 248–252 (1991)]. 79. N. Chbani, A.-M. Loireau-Lozac’h, J. Rivet, and J. Dugue, Systeme pseudo-ternaire Ag2 S-Ga2 S3 -GeS2 : Diagramme de phases-domaine vitreux, J. Sol. State Chem. 117(1), 189–200 (1995). 80. I. D. Olekseyuk, G. P. Gorgut, and M. V. Shevtchuk, Phase equilibria in the AgGaS2 -GeS2 systems, Polish J. Chem. 76(7), 915–919 (2002). 81. O. M. Yurchenko, I. D. Olekseyuk, O. V. Parasyuk, and V. Z. Pankevich, Single crystal growth and properties of AgGaGeS4 , J. Cryst. Growth 275(1–2), e1983–e1985 (2005). 82. P. G. Schunemann, K. T. Zawilski, and T. M. Pollak, Horizontal gradient freeze growth of AgGaGeS4 and AgGaGe5 Se12 , J. Cryst. Growth 287(2), 248–251 (2006). 83. D.-M. Ren, J.-Z. Huang, Y.-C. Qu, X.-Y. Hu, Y. Andreev, P. Geiko, V. Badikov, and A. Shaiduko, Optical properties and frequency conversion with AgGaGeS4 crystal, Chin. Phys. 13(9), 1468–1473 (2004). 84. Yu. M. Andreev, L. G. Geiko, P. P. Geiko, V. V. Badikov, and S. G. Grechin, Optical properties of the new nonlinear crystal AgGaGeS4 , Prikladnaya Fizika (Applied Physics), (2), 102–108 (2002), in Russian. 85. V. Petrov, V. Badikov, G. Shevyrdyaeva, V. Panyutin, and V. Chizhikov, Phase-matching properties and optical parametric amplification in single crystals of AgGaGeS4 , Opt. Mat. 26(3), 217–222 (2004). 86. S. Das, C. Ghosh, S. Gangopadhyay, Y. M. Andreev, and V. V. Badikov, AgGaGeS4 crystals for nonlinear laser device applications, Jpn. J. Appl. Phys. 45(7), 5795–5797 (2006). 87. V. Badikov, G. Shevyrdyaeva, V. Panyutin, V. Petrov, and F. Noack, Phase-matched second harmonic generation at 1064 nm in quaternary crystals of silver thiogermanogallate, Conference on Lasers and Electro-Optics, CLEO 2005, Baltimore (MD), USA, May 22–27, 2005, Technical Digest CD-ROM, paper CFL3. 88. V. Badikov, G. Shevyrdyaeva, V. Chizhikov, V. Panyutin, G. Xu, V. Petrov, and F. Noack, Phase-matched second-harmonic generation at 1064 nm in quaternary crystals of silver thiogermanogallate, Appl. Phys. Lett. 87(24), 2411131–3 (2005). 89. K. Miyata, V. Petrov, and K. Kato, Phase-matching properties for AgGaGeS4 , Appl. Opt. 46(23), 5728–5731 (2007). 90. T.-J. Wang, Z.-H. Kang, H.-Z. Zhang, Z.-S. Feng, Y. Jiang, J.-Y. Gao, Y. M. Andreev, G. V. Lanskii, and A. V. Shaiduko, Model and experimental investigation of frequency conversion in AgGaGex S2(1+x) (x = 0, 1) crystals, J. Phys. D: Appl. Phys. 40(5), 1357–1362 (2007). 91. O. B. Shcherbina, On the dynamics of the crystal lattice of silver thiogermanogallate, In Collection Optical properties and growth conditions of silver and mercury thiogallates, pp. 73–81, Kuban State University, Krasnodar 1982 (VINITI, Moscow, 1982), in Russian.


MICROSTRUCTURED SEMICONDUCTORS FOR MID-INFRARED NONLINEAR OPTICS Microstructured Semiconductors P. S. KUO and M. M. FEJER∗ E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305 USA

Abstract. Microstructured semiconductors patterned with regions of different crystallographic orientations can be used to quasi-phasematch nonlinear interactions. This chapter reviews the fabrication, properties, and applications of these materials. Keywords: Nonlinear optical materials; mid-infrared; frequency conversion; quasi-phase-matched; semiconductors; orientation-patterned gallium arsenide GaAs.

1. Introduction Since its practical inception in the 1990s, quasi-phasematching (QPM) in periodically-poled ferroelectrics has proven to be a very useful technique for bulk and guided-wave quadratic nonlinear optical devices [1,2]. One fundamental issue limiting the use of oxide ferroelectrics is their multi-phonon absorption, which generally limits their use to interactions involving wavelengths shorter than 4–5 µm. Practical application of non-oxide ferroelectrics has not been possible, so alternative materials systems suitable for QPM in the mid-infrared are of interest. The zincblende semiconductors, such as GaAs, ZnSe, and GaP, have large nonlinear susceptibilities, low optical absorption, and transparency well into the mid-IR, and so have long been used for mid-IR nonlinear optics. However, their optical isotropy, a consequence of their cubic crystal structure, precludes birefringent phasematching, which has severely limited the applicability of these materials. A number of QPM techniques based on stacks of crystal plates with alternating orientation have been explored, but fabrication has proved to be challenging, again limiting their applicability [3, 4]. More recently, epitaxial growth of orientation-patterned materials, with lithographically controlled patterns, has greatly opened the range of applicability of these materials. ∗ To whom correspondence should be addressed.


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The best developed of these materials is orientation-patterned GaAs (OPGaAs), which has been fabricated in both thin-film (microns) and thick-film (up to ∼1 mm) form, suitable for guided-wave and bulk devices, respectively. Among the device results reported to date are optical parametric oscillators (OPOs) tunable from 2.1–11 µm, an optical parametric generation (OPG) device producing a continuum from 4–11 µm, THz generation with 3% quantum efficiency, and a single-frequency difference frequency generation (DFG) source tunable from 7.4–9 µm. Section 2 is an overview of the properties of zincblende semiconductors, emphasizing GaAs and including the interesting polarization effects that result from the linear optical isotropy and the high symmetry of the nonlinear susceptibility. In section 3, fabrication methods for microstructured zincblende semiconductors are discussed. Emphasis is given to all-epitaxial, lithographically controlled approaches. Section 4 describes bulk QPM device results in 43 m materials, and Section 5 is a summary including future directions for research. 2. Properties of zincblende semiconductors Table 1 shows key material properties for selected zincblende semiconductors. They share several intrinsic properties that make them attractive for mid-IR nonlinear optics. Essential for mid-IR operation are their low phonon energies, which lead to long-wavelength multi-phonon absorption edges and allow operation beyond 10-µm wavelengths. The large nonlinear susceptibilities (in the case of GaAs, approximately four times larger than d33 of LiNbO3 ) is particularly important for mid-IR interactions, where the basic wavelength scaling of quadratic TABLE 1. Properties [5–12] of several zincblende semiconductor nonlinear optical materials in comparison to LiNbO3 . Material Transparency Refractive Range (µm) Index1

di j Thermal Conductivity 2,3 (W/m-K) (pm/V)

dn/dT (10−4 K−1 )

GaAs GaP ZnSe LiNbO3

107 45 25 23

2.9 1.2 0.7 0.44

0.9–17 0.5–11 0.5–20 0.4–4.5

3.34 3.03 2.44 2.134

52 110 19 4.6

1 At room temperature, 2 µm wavelength. 2 d is d for all entries except for LiNbO , which is d . ij 14 3 33 3 Nonlinear coefficient is scaled using Miller’s rule to doubling of λ

f = 2 µm. 4 Refractive index and thermo-optic coefficient given for extraordinary wave of LiNbO . 3

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151

nonlinear mixing poses challenges for efficient operation. Their high thermal conductivities are advantageous for minimizing the temperature rise in applications involving high average powers. In the remainder of this section, the properties of GaAs are discussed in more detail, as it is currently the best developed of the microstructured semiconductors. 2.1. DISPERSION

Recalling that for QPM interactions, the required period, , for the sign reversals in the nonlinear susceptibility are given by twice the coherence length, i.e. = (n 3 /λ3 − n 2 /λ2 − n 1 /λ1 )−1 ,

(1)

precise dispersion relations are required for designing QPM structures for specific interactions. Furthermore, accurate thermo-optic coefficients are needed in order to compute temperature tuning rates and effects of self-heating such as thermal lensing. Careful measurements of the dispersion of GaAs and its temperature dependence have been made by Skauli [6]. The form of the fit to this data, 2 2 < ε2 > G3 A E 1 − (h¯ ω)2 E 2 − (h¯ ω)2 n 2 (h¯ ω) = 1 + ln + + 2 ln 2 2 2 2 π π E 0 − (h¯ ω) E 1 − (h¯ ω) E 3 − (h¯ ω)2 (2) was proposed by Pikhtin [9], who also gives useful dispersion relations for a number of other semiconductors. Skauli [6] modified this functional form by allowing the parameters E 0 , E 1 , E 2 , and E 3 to vary with temperature so that dn/dT and d2 n/dT 2 data could also be described. Tuning behavior predicted with these relations agree well with experimental data across the entire mid-IR range. Figure 1 shows the phasematched signal-idler pairs as a function of the QPM period for a number of pump wavelengths, along with the periods required for QPM SHG. It can be seen that periods of several 10’s of microns up to approximately 100 µm are typically required. 2.2. NONLINEAR SUSCEPTIBILITIES

The nonlinear susceptibility tensor has only three non-zero elements, d14 , d25 , and d36 , which are equal by symmetry. There are a variety of measurements of d14 available in the literature [6,9]. Recent measurements based on QPM SHG in OPGaAs at 4 µm pump wavelength, made relative to a sample of PPLN, yielded a value of d14 = 94 ± 10 pm/V [8]. The high symmetry of the nonlinear tensor and the isotropy of the refractive index enable nonlinear interactions with an unusual variety of polarization combi¯ nations. In OP-GaAs experiments, the waves typically propagate along the [110]

152

2.8 0 3.0 µm 6µ 3.2 m 5µ m 4.0 0µ m

m 0µ 2.1

12

1.3

1.0

6µ m 2µ 1.5 m 5µ m


Wavelength (µm)

10 8 6 4 2 0

0

50

100

150

200

QPM period (µm)

Figure 1. Phasematched signal-idler pairs in GaAs (at 20◦ C) as a function of QPM period (abscissa) and pump wavelength (top label). The dashed line plots the phasematched SHG wavelengths.

crystal direction. When all three polarizations are aligned parallel to √ [111], the effective nonlinear coefficient de f f , is maximized with a value of 2d14 / 3. When one of the waves is polarized along the [110] direction (for definiteness, say it is the pump), it can be shown that de f f = d14 , constant for all signal polarizations so long as the idler wave is complementarily polarized. As a result, OP-GaAs can be used in polarization-insensitive optical parametric amplification [13] or in an optical parametric oscillator that is pumped with an unpolarized laser. An important factor limiting high peak power operation of GaAs devices is undesired higher-order nonlinear processes such as two- and three-photon absorption, self-focusing, and self-phase modulation. Figure 2 shows the wavelength dependence of the multiphoton absorption coefficients [14,15], as measured by zscan methods, where the total absorptivity is given by α(I ) = α1 + α2 I + α3 I 2 , where I is the intensity. The measured data are compared to the simple two-band models from Wherrett [16] and are in good agreement. It can be seen that, as expected, two-photon and three-photon effects become significant for wavelengths shorter than 1.7 and 2.5 µm, respectively. The wavelength dependence of the nonlinear refractive index, defined as n(I ) = n 0 + n 2 I , is shown in Fig. 3, and is also in reasonable agreement with theory [17].


153

Figure 2. Measured and theoretical (a) two-photon and (b) three-photon absorption coefficients in GaAs with electric field polarized along [110].

Figure 3. Measured and theoretical wavelength dependence of nonlinear refractive index in GaAs with electric field polarized along [110].

154


3. Fabrication of microstructured zincblende semiconductors The crystallographic x, y, and z axes in the zincblende (point group 43 m) structure are four-fold rotation-inversion axes. Thus, a 90◦ rotation around one of these axes inverts the crystal structure, and changes the sign of the nonlinear susceptibility tensor, as required for QPM. Unlike ferroelectrics, in which fields applied to the crystal after growth can reorient the bistable spontaneous polarization, there is no mechanism for post-growth reorientation of the crystal axes in zincblende semiconductors. There are two general approaches to accomplish this reorientation in zincblende materials: assembling stacks of suitably rotated plates, and growth of the crystal on a “template” substrate suitably patterned to control the orientation of the grown film, as illustrated in Fig. 4. These methods are discussed in sections 3.1 and 3.2. 3.1. STACKED PLATE METHODS

The potential of III-V and II-VI zincblende semiconductors was recognized early in the development of nonlinear optical materials. The earliest efforts to develop QPM media based on these materials involved fabrication of stacks of thin plates of alternating rotation to flip the sign of the effective nonlinear coefficient. The plots were oriented at Brewster’s angle to minimize Fresnel reflections at the many interfaces [3, 18]. While these early experiments demonstrated the principle, the difficulty in accurately fabricating the thin plates with the accuracy and flatness required, and the high scatter losses associated with the many interfaces limited the practical application of this technique. Subsequently, a diffusion-bonding technique, in which the stack of plates was fused into a single block by heating under uniaxial stress in a reducing atmosphere was explored to reduce the interface loss effects [4,19]. More recently, the use of a deposited layer of a soft, index-matched chalcogenide glass on each wafer interface to enable high quality bonding at lower-temperatures has been demonstrated [20]. While it was possible to fabricate (a) Stack of plates

+ - + - + - + Bond

+-+- +-+-

(b) Orientation template

-

-

+

-

-

Grow

- + - + - + +

Figure 4. Illustration of two approaches to fabricating QPM structures with zincblende materials.

155


low-loss stacks by these means [20, 21], the fabrication challenges posed by the tolerances on the numerous thin plates precluded wide-spread application of these approaches in mid-IR devices. Stacked-plate methods have recently seen use at THz frequencies, where the thicker plates required by the longer coherence lengths obtained in this spectral region ease the fabrication challenges. These are discussed further in Chapter II.9 of this volume. 3.2. ORIENTATION-PATTERNED GROWTH

The difficulty in fabricating suitable stacks of plates for QPM in zincblende semiconductors suggests that a monolithic structure, with lithographic control of the long-range order of the pattern, would be more widely applicable. In templatecontrolled growth, a substrate is patterned lithographically such that the orientation of subsequently grown films is controlled by the pattern on the substrate. Multi-layer, thin-film growth on such a template, for example by molecular-beam epitaxy (MBE) or organometallic vapor-phase epitaxy (OMVPE), can produce a QPM waveguide device, while thick-film growth on the template, for example by hydride vapor-phase epitaxy (HVPE) can produce a “bulk” (∼millimeter-thick) film for QPM interactions. 3.2.1. Early work on orientation templates Templates developed to date involve fabrication of a film of rotated orientation on a substrate, followed by lithography and etching to reveal strips of the original substrate separated by strips of the rotated film, as sketched in Fig. 5. Subsequently grown films take on the orientation of the surface on which they nucleate, and hence, on such a patterned substrate, take on a periodic orientation. Under appropriate conditions, the boundaries between the regions grow up vertically, preserving the orientation pattern through the entire thickness of the film. 1) GaAs wafer +

(100)

2) Epitaxial growth of thin, Nonpolar Ge layer inverted GaAs layer -

3) Pattern photoresist

(100)

(011)

(011)

5) Epitaxial regrowth of orientation-patterned film (100)

-

+

-

+

(011)

4) Chemical etching -

+

-

+

-

+

-

+

(011) (011)

(011)

Figure 5. Sketch of process flow for fabrication of an orientation-patterned GaAs template.

156


Clearly, a key step in any template-controlled method is the fabrication of the initial rotated layer. The first demonstrated method, based on /orientation effects resulting from the lattice-mismatched heteroepitaxial growth of CdTe and ZnTe films on GaAs substrates demonstrated the principle, but the propagation losses in ZnTe/ZnSe waveguides grown on these templates were too large for practical application [22]. The next method developed was based on diffusion bonding two [100] GaAs wafers, rotated 90◦ around [100] with respect to eachother, on one of which there had previously been grown a thin GaAs film on an AlGaAs release layer. Etching off the release layer left behind the thin film on the other wafer, with orientation rotated by 90◦ [23, 24]. Successful QPM waveguide devices have been demonstrated based on this method, and are discussed in section 5.1. 3.2.2. Orientation templates based on polar-on-nonpolar epitaxy Currently, the most widely used templates are based on lattice-matched heteroepitaxy of GaAs/Ge films on GaAs substrates. The method is based on the observation (see Fig. 6) that interchanging the Ga and As atoms in a GaAs lattice results in the same structure as would a 90◦ rotation of the original structure around [100]. Thus, noting the alternating layers of Ga and As along a [100] axis of GaAs, inserting a double layer of Ga (or As) would result in the crystal above the double layer being rotated 90◦ compared to that below the layer. While it is not possible to grow such a structure, growth of a thin Ge film, which is nonpolar and can accommodate subsequent growth initiated with either a Ga or an As layer, does allow the growth of a film whose orientation is rotated with respect to the substrate [25, 26]. With this as the key step, the process illustrated in Fig. 5, can be used to create an orientation template. With subsequent thin film growth, e.g. GaAs/AlGaAs, a QPM waveguide can be formed [27] (section 5.1), while with thick film (typically HVPE) growth, a bulk QPM medium is formed [28, 29]. We focus on the latter in this and the following sections, as these are better developed at present. (a) Ga As

(b) +d

-d

[001] Nonpolar Ge layer [110]

[110]

Figure 6. (a) Atomic structure in GaAs and its inverted structure; (b) insertion of a nonpolar Ge layer allows growth of the inverted crystal above the original crystal.


157

3.2.3. HVPE growth of thick GaAs films on orientation templates Template fabrication is reproducible and is no longer a significant issue for thick film devices; details of the current process can be found in Ref. [30]. The growth of thick films on the templates remains a work in progress. Key issues for the growth include the fidelity of the domain pattern as it grows up through the film, the maximum thickness that can be grown before parasitic processes in the reactor limit the growth rate, the density of free carriers (which cause absorption in the mid-IR), and other sources of absorption and scatter loss. Details of the HVPE growth process for thick OP-GaAs films, and its optimization are beyond the scope of this article. We confine ourselves to a sketch of the current capabilities and remaining challenges. Both atmospheric-pressure [31] and low-pressure HVPE [28] have been applied to the growth of OP-GaAs. The latter has the advantage of much higher growth rates; up to ∼100 µm/hr has been demonstrated successfully. At these rates, a 0.5-mm-thick film can be grown in only 5 hours. The thickest films grown in a single run have been ∼750-µm thick. Films in excess of 1-mm thick have been grown in multiple growth runs, but the quality of the interface between the layers is problematic. Domains with periods down to 40 µm have been grown reliably through 0.5-mm-thick films, and down to 20 µm in 200-µm thick films. Densities of free carriers below 1 · 1013 cm−3 are obtained, so that free carrier absorption in the mid-IR is negligible. Characterization of extrinsic scatter and absorption losses is an ongoing process; results depend on parameters of the growth process. Total losses of ∼0.01 cm−1 have been observed at 2-µm wavelengths. Fig. 7 shows stain-etched cross sections of typical OP-GaAs films.

Figure 7. Stain-etched cross-sections of OP-GaAs films with 80 µm period, where (a) is a short run that yielded a 220-µm thick film and demonstrates the characteristic “triangle-flat” free-surface shape, and (b) is a recent 700-µm-thick film with high domain fidelity throughout the thickness.

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4. QPM in bulk microstructured zincblende semiconductors 4.1. MID-IR SHG

Single-pass SHG is of course well known both as a useful method to generate coherent radiation at wavelengths for which convenient laser sources are unavailable and as a convenient method for characterizing the linear and nonlinear properties of new media. QPM interactions in GaAs bring the usual advantage of noncritical phasematching at any desired wavelength, the option of engineering multiple devices on a chip [32, 33], and tailoring the tuning properties through aperiodic or chirped QPM gratings [34, 35]. The large nonlinear susceptibility and noncritical phasematching available in QPM GaAs are particularly important in the mid-IR, where the decrease in mixing efficiency with increasing wavelength makes design of efficient devices difficult. For SHG, the optimum efficiency is obtained for focusing slightly tighter than confocal, i.e. for a confocal parameter of the pump beam slightly shorter than the length of the crystal. For such operation, and neglecting the dispersion of the nonlinear susceptibility and the refractive index, the efficiency scales as [36] P2ω /Pω = ηc L Pω

(3)

where the confocal efficiency, ηc , is given by ηc = 16π 2 de2f f h/ε0 cn 2 λ3

(4)

where λ is the pump wavelength, n is the average refractive index, L is the length of the crystal, ε0 is the permittivity of free space, and c the speed of light. h is the Boyd and Kleinman focusing parameter, taking the value 0.8 for confocal focusing and 1.2 for the optimum, tighter than confocal focus. The material figure of merit is seen to be de2f f /n 2 , which is approximately 10 times larger for QPM GaAs than for PPLN, indicating an advantage for GaAs even in spectral regions where both materials are transparent. Taking de f f = (2/π) × 94 pm/V = 60 pm/V, n = 3.3 and h = 0.8, we find ηc ≈ 0.16 [W−1 cm−1 ]/λ3 [µm], where we use the nonlinear susceptibility for 4-µ m SHG [8], and neglect its wavelength dependence. For SHG of 10-µ m radiation in a 5-cm-long crystal, we find an efficiency of 0.08%/W, so that >100 W power would be necessary for efficient operation, suggesting either pulsed pumps or intracavity operation. The strong wavelength scaling substantially reduces the required power at shorter wavelengths, e.g. for a 5-µm pump the efficiency in a 5-cm-long crystal increases to 0.6%/W. Careful SHG measurements at 4-µm fundamental wavelength [8] were used to measure the nonlinear susceptibility of OP-GaAs (section 2.2), and SHG at a number of wavelengths in OP-GaAs was used to refine dispersion models for GaAs [6]. SHG of CO2 lasers has been carried out in DB-GaAs [4, 19], and OPGaAs [28, 31], with efficiencies comparable to those theoretically predicted.


159

4.2. MID-IR DFG

Tunable, narrow-linewidth sources in the mid-IR are of interest for various spectroscopic sensor applications. Difference-frequency generation of near-IR sources is an attractive option, as it can be based on well-developed pumps from telecom applications, e.g. at 1.3- or 1.5-µm wavelengths, preserves the linewidth and stability of those pumps with no further engineering effort, and can be tuned very broadly (several hundred cm−1 ) in the mid-IR [37, 38]. Offsetting those advantages are relatively low output powers (∼1 mW for 1 W pumps) in bulk configurations. Waveguide devices (section 5.1) have the potential to increase the efficiency by several orders of magnitude, but have not yet been operated in the mid-IR in QPM GaAs. The efficiency for DFG of gaussian beams involves more complicated focusing considerations than for SHG. Assuming that the interaction is well off degeneracy, and the two pumps are focused so that the nonlinear polarization (and hence the generated difference frequency) has a confocal parameter equal to the length of the crystal, the output power can be approximated by PD F G = η D F G,c L Pp1 Pp2

(5)

such that the confocal mixing efficiency is given by η D F G ≈ 8π 2 de2f f /n 2 cε0 λ3D F G = 9.8 × 10−2 [W−1 cm−1 ]/λ3D F G

(6)

where the parameters are the same as those defined following Eq. 4. To generate 1 mW of power at 7 µm would require two near-IR pumps of ∼1 W power. Experiments with tunable 1.5-µm and 1.3-µm sources of 1 W and 30 mW powers, respectively, have shown efficiencies in an OP-GaAs crystal within a factor of 2-3 of the above estimates at DFG wavelengths from 7–9 µm [39, 40]. While the DFG tuning range when varying one pump with the other fixed is rather narrow (2 cm−1 for a 17-mm-long crystal), by tuning the two pumps in synchronism, DFG tuning over a range of 55 cm−1 was demonstrated. With an OP-GaAs sample containing four QPM sections, tuning from 7.2 µm to 9.4 µm was demonstrated, shown in Fig. 8 [40], and applied to a number of spectroscopic measurements [41]. Wavelengths as long as 16 µm have been generated by QPM DFG in DB-GaAs [42]. 4.3. OPTICAL PARAMETRIC OSCILLATORS

Optical parametric oscillators (OPOs) offer greater ease of tuning and higher efficiencies than DFG devices, at the price of requiring that the pump power exceed a threshold value before there is any output and not necessarily preserving the linewidth of the pump laser. The threshold condition for a singly resonant OPO

160

P. S. KUO AND M. M. FEJER 23.8 micron period 25.7 micron period 26.7 micron period 29.7 micron period

1.0

DFG Intensity (a.u.)

0.8

0.6

0.4

0.2

0.0 7.2

7.6

8.0

8.4

8.8

9.2

9.6

Idler Wavelength (µm) Figure 8. DFG idler wavelength tuning in OP-GaAs for several QPM periods achieved by synchronously tuning both pumps. For comparison, the narrow curves show the idler when only one pump is tuned. Continuous tuning over this range would be possible in suitable multi-grating sample.

is that the parametric gain equal the cavity losses. For an OPO operating near degeneracy, the theoretical gain is the same as the conversion efficiency for SHG, so with the results of section 4.1, we see that for a 2-µm-pumped OPO with near 4-µm outputs, the gain is 0.3%/W-cm, or 1.5%/W for a 5-cm-long crystal. Thus, with low-loss crystals and cavities, pump power thresholds of several watts can be anticipated. To date, CW OPOs have not been demonstrated in GaAs, but excellent results have been obtained with nanosecond near-IR pumps [43, 44]. Two-photon absorption of the pulsed pump leads to preference for pump wavelengths longer than the two-photon edge, 1.7 µm. An OP-GaAs OPO was pumped with 1.75-to 2.05-µm wavelength, 6-ns pulses from a PPLN OPO that was in turn pumped with a Q-switched Nd:YAG laser (Fig. 9). By tuning the pump wavelength, the OP-GaAs OPO yielded continuous output from 2.07 to 3.08 µm (signal) and 5.8 to 11 µm (idler), as seen in Fig. 10. The output wavelengths were only limited by the OPO mirror reflectivities, so with proper mirrors, tuning from 2–11 µm is possible [44]. 4.4. ULTRAFAST INTERACTIONS

In devices operating with ultrafast pulses, the additional consideration of the group velocity mismatch between the interacting waves must be considered. When the group delay difference through the length of the crystal becomes comparable to the duration of the pulses, the gain is significantly reduced below that calculated


161

Figure 9. Schematic diagram of the OP-GaAs OPO described in Refs. [43, 44]. The inset shows a stain-etched cross-section of the 61.2 µm period OP-GaAs grating.

Figure 10. Measured OP-GaAs OPO tuning curve with respect to the pump wavelength (solid circles). Theoretical tuning calculated from dispersion relation in Ref. [7].

from quasi-stationary analysis [35]. Here, we summarize some simple conclusions for ultrafast SHG. Fig. 11 shows the group velocity mismatch parameter, δν, where δν = 1/u ω − 1/u 2ω (7) such that u i = (dω/dk)|ωi is the group velocity at the fundamental or second harmonic. The length over which a pump pulse will walk off the generated harmonic is L g = τ/ |δν|, where τ is the pulse length. If we choose the length for the crystal

162


1/|δν| (mm/ps)

1000

100

10

1

0.1 2

4

6

8

10

Fundamental Wavelength (µm) Figure 11. Inverse group velocity mismatch parameter for SHG in OP-GaAs.

to be 2L g , then for confocal focusing, it can be seen that the efficiency will scale only with the pulse energy. For transform-limited Gaussian pulses [35], U2ω /Uω = ηU F Uω

(8)

where U2ω and Uω are the pulse energies at the fundamental and harmonic, respectively, and ηU F = 76.7de2f f /ε0 cn 2 λ3ω δν. (9) We see that the material figure of merit depends on de2f f /n 2 δν. The efficiency is nearly constant at 50%/nJ over much of the mid-IR (see Fig. 12), so that efficient SHG can obtained with nJ or sub-nJ pulses. The near-constancy of the efficiency across much of the spectrum reflects the λ−3 decrease in efficiency for CW confocally focused SHG with increasing wavelength being compensated by the decreasing dispersion and hence the smaller value of δν. These SHG results are again closely related to the gain for near-degenerate parametric amplification. The high gains available with nanojoule pulses suggest that low-pump-threshold synchronously-pumped parametric oscillation should be readily obtained. Such work is in progress, but has not yet been demonstrated. The high parametric gains and wide gain bandwidths have been used to obtain greater than octave-bandwidth continua in the mid-IR based on optical parametric generation (OPG) [45]. Pumping a 166.6-µm period OP-GaAs grating with 3.28-µm wavelength, 1-ps duration pulses with energy up to 2 µJ, the observed OPG spectrum was more than an octave wide, spanning from 4.5 to 10.7 µm measured 20 dB down from the peak (see Fig. 13). Conversion efficiencies up to 15% were measured. The pump wavelength was chosen such that the degenerate wavelength was near the zero-group-velocity-dispersion point in GaAs, which helped broaden the OPG spectrum, as can be seen from the near-vertical QPM

163


Conversion Eff. (%/nJ)

200

150

100

50

0 2

4

6

8

10

Fundamental Wavelength (µm) Figure 12. Conversion efficiency for ultrafast SHG in OP-GaAs. The crystal length is chosen to be twice the walkoff length, L g , and the pump is confocally focused.

Spectral Density (a.u.)

1

b

0.1

0.01

a 1E-3

1E-4

4

5

6

7

8

9

10

11

12

Wavelength (µm) Figure 13. OPG spectrum for a 3.28 µm pump at 1.4 µJ energy. Dips at 5 and 9.5 µm (marked by a and b) are due to phase-matched sum frequency generation.

curve in Fig. 1. At the high pump intensities used here, cascaded sum frequency generation (manifesting as dips in the OPG spectrum) and higher order nonlinearities (self-phase modulation and self-focusing) were observed. Such a broadband, spatially coherent light source has potential applications for spectroscopy as it can be highly collimated or tightly focused. Efforts are underway to take advantage of the broad parametric gain bandwidth and high gains in other parametric devices such as synchronously pumped OPOs.

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4.5. THZ

QPM GaAs is also of interest for THz generation by DFG or optical rectification of near-IR pulses. The low losses at both IR and THz frequencies and engineerable non-critical phasematching for a range of THz frequencies allows efficient and tunable THz generation of near-diffraction limited beams. Near-IR to THz quantum efficiencies as high as 3%, outputs from 0.8–3 THz, and average output powers of 1 mW have been obtained [46]. These applications are discussed in detail in Chapter II.4 of this volume, so will not be elaborated here. 5. Current research directions 5.1. WAVEGUIDES

Guided-wave interactions can confine radiation to transverse dimensions on the order of the wavelength over arbitrary lengths, lifting the tradeoff between confinement and interaction length that limits the efficiency of bulk interactions. The efficiency then scales quadratically with the length of the device, with typical coefficients for mid-IR DFG in the range of 0.1–1%/W-cm2 , so that milliwatt mid-IR powers could be obtained with τ2 ,

(1)

i.e. the total lower state lifetime τ2 is shorter than the time to inject electrons from the n=3 to the n=2 levels. Following the active region is the injection/relaxation region. As its name suggests, the purpose of this region is to enable a cooling down of the electron distribution, as well as an increase of its energy compared to the band edge, in order to enable injection in the next period. These two functions are conveniently provided by a graded-gap region, usually obtained by a digital alloy with a varying duty cycle. This region also provides an “electron reservoir” that will feed the carriers to the next period.

PROGRESS IN QUANTUM CASCADE LASERS

173

As shown in Fig. 1 b), a very attractive feature of lasers based on intersubband transitions is the fact that cascading the active region periods is especially easy and almost comes naturally. In a cascade laser, the gain region consists of a large (typically N p = 10 − 100) number of repeated periods. Electrons are then “recycled” from period to period as they cascade down the structure. Cascading has two main advantages. Firstly, by increasing the size of the region in which gain occurs, it will decrease the population density requirement for each individual active region period. This allows a reduction of the threshold current density of the device. In addition, a single electron is able to potentially emit a number N p of photons, increasing the slope efficiency. Both effects are obtained at the cost of a larger applied bias. In essence, in a cascade laser, one is exchanging a lower operating current for a larger operating voltage. This enables a large reduction of the device’s ohmic losses, especially in the mid- or far-infrared were the photon energy is very small. For practical applications, the quantum cascade laser offers some key advantages: for the first time it allows the design of semiconductor lasers in a very wide operating wavelength range in the mid-infrared out of the same technologicallymastered, large-bandgap semiconductor material such as GaAs/AlGaAs or InGaAs/AlInAs/InP. In addition, being based on a fundamentally different operating mechanism, it is the only mid-infrared semiconductor laser to operate at room temperature. Mid-infrared quantum cascade laser sources are particularly well adapted for chemical spectroscopy in both medical (Menzel et al., 2001; Kosterev et al., 2001) and atmospheric (Kosterev et al., 1999) applications. They are also interesting candidates for free space telecommunication (Blaser et al., 2001; Martini et al., 2002). As shown in Fig. 2 where the maximum operating temperature of quantum cascade lasers in pulsed (dots) and in continuous wave (squares) is plotted as

Figure 2. Maximum operating temperature in pulsed operation (dots) and in continuous wave (squares), as reported in the literature.

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JEROME FAIST ET AL.

a function of operating wavelength, much of the mid-infrared is now covered by continuous wave operating quantum cascade lasers (Beck et al., 2002; Evans et al., 2004; Yu et al., 2003; Yu et al., 2006). An other important achievement in quantum cascade laser research is the realization of a terahertz quantum cascade laser operating at λ = 66 µm (Köhler et al., 2002; Rochat et al., 2002). Work on these structures have concentrated on various issues such as the development of new active region designs: − Based on optical phonon extraction, pioneered by the MIT group of Q. Hu. This structure holds the record performance in terms of high temperature operation (164K) (Williams et al., 2005). − Based on a combination of optical phonon extraction and bound-to-continuum active region demonstrated (Scalari et al., 2005) in our group. − Various combination of schemes (multistage, double phonon extraction, etc.) (Kohler et al., 2004; Barbieri et al., 2004). As shown in Fig. 2, although excellent progress have been made in extending the wavelength coverage of terahertz quantum cascade lasers, their maximum operating temperature remains clearly below the range reachable by a thermoelectric Peltier cooler. 2. Optimization of doping level The optimization of quantum cascade lasers, with the aim of obtaining devices operating at room temperature with low threshold currents, was initially focused on the quantum design. A very successful approach was the two phonon resonance active region design which avoids an electron extraction bottleneck (Faist et al., 2002) and in which the ratio τ32 /τ2 is especially favorable. However, an other important parameter to study is the doping level of the active region. We present here a systematic change of the active region doping in a InAlAs-InGaAs/InP lasers emitting at 9 µm. Recently, a similar study based on GaAs/AlGaAs lasers emitting in the mid-infrared region was presented (Giehler et al., 2003). It demonstrated the influence of free-carrier absorption on both the optical losses and the threshold current density (Giehler et al., 2004). The core of the devices was grown by molecular beam epitaxy (MBE) of lattice matched InGaAs/InAlAs layers on a n-doped InP (Si, 2×1017 cm−3 ) substrate which also acts as a bottom cladding layer. The top cladding layer (InP, Si, 1×1017 cm−3 , 2.5 µm thickness) as well as the top contact layer (InP, Si, 7 × 1018 cm−3 , 0.85 µm thickness) and the capping layer (InGaAs, Si, 2 − 3 × 1019 cm−3 , 10 nm thickness) were grown by metalorganic vapor phase epitaxy (MOVPE). The core of the waveguide consists of a 35 period active region placed between a lower and an upper wave guiding layer (InGaAs, Si, 6 × 1016 cm−3 , with thicknesses of


175

n-do

ped

n-do

ped

5 4 g 3 2 1

Injector Active region Figure 3. Schematic conduction band energy diagram of a two phonon resonance active region and moduli squared of the relevant wave functions under an applied electric field of 36 kV/cm.

0.2 µm and 0.3 µm respectively). The layer thicknesses in angstroms starting from the injection barrier are as follows: 40/19/7/58/9/57/9/50/22/34/14/33/13/32/15/ 31/19/30/23/29/25/29/ where In0.52 Al0.48 As barrier layers are in bold, In0.53 Ga0.47 As well layers in roman, and doped layers underlined. The design of this active region (Hofstetter et al., 2001) is based on four quantum wells. A double-phonon resonance between the coupled three lower lasing energy states (levels 1, 2 and 3, see Fig. 3) enables both a short electron lifetime on the lower lasing state 3 and an efficient carrier extraction. The thin first injector well prevents a too large overlap of the wave functions of the injector ground state g with the lower lasing state and maintains a high injection efficiency. For four different sheet densities n s , one wafer per doping level was grown: Si, 2.6×1011 , 2.1×1011 , 1.5×1011 and 1.0×1011 cm−2 (corresponding to the runs n67, n72, n69, and n71, respectively). Lasers were fabricated with a standard processing procedure using wet chemical etching (HBr/HNO3 /H2 O, 1:1:10 solution) to define 24 µm wide ridges. The waveguides were then covered with a 300 nm isolation layer of Si3 N4 and top contacted with Ti/Au (10/1000 nm).

176

JEROME FAIST ET AL. Current Density [kA/cm2] 4

6

8

10

12

1.5

303 K 1.5% duty cycle

12 Voltage [V]

2

1.0 8 2.6 x 1011cm−2 0.5 2.1 x 1011cm−2 1.5 x 1011cm−2 1.0 x 1011cm−2

4

0 0

2

4

6

8

Peak Power [W]

0

0 10

Current [A]

Figure 4. Current-voltage and current-optical peak power characteristics of 3 mm-long and 24 µm-wide lasers in pulsed mode at room temperature for four different doping concentrations.

Processing was completed by sample thinning and back contact metallization (Ge/Au/Ag/Au, 12/27/50/100 nm). Devices were cleaved into 3 mm long stripes, then mounted junction-up on copper heatsinks, and tested on a Peltier cooler. Average output power measured by calibrated thermopile detector and voltage characteristics as a function of current of four differently doped QCL’s are presented in Fig. 4. The lasers were operated at a temperature of 303 K and under 100 ns long pulses with a repetition frequency of 100 kHz (Alpes Lasers TPG 128 pulse generator). The measured threshold current densities increase linearly with the doping concentration. The samples with the lowest doping concentration (1.0 × 1011 cm−2 ) shows a threshold of 2.6 kA/cm2 whereas the one with the highest doping density (2.6 × 1011 cm−2 ) have a value of 4.0 kA/cm2 . Similarly, the maximum operating current increases linearly with the doping concentration from a value of 7.2 kA/cm2 (Pmax = 460 mW) to a maximum value of 13.5 kA/cm2 (Pmax = 1.2 W). The doping concentration therefore determines the current laser’s dynamic range. The best laser performance results from a compromise between high output power and small current consumption necessary for continuous wave operation. The linear dependence of the maximum current density JN D R , which corresponds to the negative differential resistance (NDR) for all doping concentrations, is shown in Fig. 5 (solid squares). The resonant tunneling of electrons between the injector g and the upper lasing state 4 was first derived by Kasarinov and Suris (Kazarinov and Suris, 1971; Kazarinov and Suris, 1972; Sirtori et al., 1998), and can be described by the following expression: J = q Ns

2||2 τ⊥ 1 + 2 τ⊥2 + 4||2 τ4 τ⊥

(2)


177

J [kA/cm2]

15 Models (2) and (3) Models with add.n=1x1011cm−2 n67, n72, n69, n71 n120 JNDR

10

303 K 1.5% duty cycle

5

JTH

0

0

1

2

3

Doping level [1110cm−2]

Figure 5. The threshold current density JT H in open squares and the maximum current density J NDR in solid squares as a function of sheet densities corresponding to the doping study (n67, n72, n69, n71). The corresponding calculated curves from models based on resonant tunneling (2) and rate equation (4) are represented in solid lines. In dashed lines, fitted curves corresponding to an extrapolated doping offset of n offset = 1.0×1011 cm−2 added to the active region doping are shown. Open and solid circles represent the threshold and the maximum current densities respectively of a laser grown after a longer MBE running time (n120).

where = E g − E 4 = qd(F − Fr ),

d = |z gg − z 44 |

where q is the electronic charge, 2h¯ || (3.5 meV) is the energy splitting at resonance between the ground state of the injector and the upper lasing state, h¯ is the energy detuning from resonance, d is the spatial separation between the centroids of the two electron probability distributions, F is the average electric field applied over the distance d and Fr is the electric field which brings the upper lasing state 4 and the ground state g of the injector into resonance. The linear variation of the maximum current with the doping concentration suggests that the electron-electron scattering contribution to the upper state lifetime τ4 is negligible. We therefore assume a computed value of τ4 = 0.56 ps based on the emission and absorption of bulk optical phonons. Similarly, the measured intersubband luminescence as a function of doping density shows no dependence of linewidth with the carrier concentration. This suggests a constant in plane dephasing lifetime τ⊥ = 0.04 ps. The sheet density Ns is the electron density in the injector ground state g. This electron density is approximated by Ns = n s Ntrans , where n s corresponds to the total sheet density in the injector region and Ntrans to the density of electrons which contribute to the transport in the active region. The transport carrier density can be written as Ntrans = J τ/q, where τ is the time of the electron transit in a period of the active region of length L p (59.8 nm). An approximate value of the electron transport time τ = 1.4 ps is obtained by multiplying the optical phonon emission time τ ph (0.2 ps) with the number

178

JEROME FAIST ET AL.

of optical phonon energy steps after the first intersubband scattering event of F·L p − 1 = 7 (where h¯ ω L O = 34 meV is the optical phonon energy). From this N= hω ¯ LO estimation, the calculated curve deduced from the Equ. 2 at resonance ( = 0) is displayed in Fig. 5 (solid line). The experimental data (solid squares) are shifted relative to the theoretical curve which has a zero value for the maximum current (JNDR = 0) for an undoped structure (n s = 0). A better agreement between theory and experiment is obtained if an extrapolated n-type sheet carrier density of n offset = 1.0 × 1011 cm−2 is added to the active region doping (dashed line). The dependence of the threshold current density JT H on the doping concentration (open squares) is also linear as shown in Fig. 5. The model used for describing the variation of the threshold current density with doping density is based on a rate equation approach and can be written as (Faist et al., 2000): JT H = q 2

z2

) 1 (α/ gc + n therm 3 τ4 1 − τ3 /τ43

(3)

ij is the gain cross section, n therm is the thermal population in where gc = 4πq 3 0 nλ 2γi j L p the lower lasing state and can be neglected in our case, λ is the emission wavelength, n (3.26) is the mode refractive index, 2γi j (18 meV) is the full width at half maximum of the transition in energy units determined from the luminescence spectrum, z i j (2.5 nm) is the dipole matrix element and (65%) is the overlap factor. The time constant τ43 (3.39 ps) represents the lifetime of the transition 4→3 derived from the optical-phonon emission processes and τ3 (0.18 ps) is the lifetime of the electron in the lower state of the radiative transition. The total optical losses α = αm + αw are the sum of the mirror losses αm (4.3 cm−1 ) and undoped + αwabs contain the the waveguide losses αw . The waveguide losses αw = αw undoped (4.6 cm−1 ) and the calculated losses of the undoped waveguide structure αw free carrier absorption losses for the different doping concentrations αwabs (22.8, 18.9, 14.7 and 10.0 cm−1 for 2.6×1011 , 2.1×1011 , 1.5×1011 and 1.0×1011 cm−2 , respectively). Following this model, the calculated curve (solid line) reproduces the linear variation of the threshold current density with the doping density, as shown in Fig. 5. Good agreement between theory (dashed line) and experimental values (open squares) is obtained if we include an estimated doping offset of n offset = 1.0 × 1011 cm−2 . Usually, the background impurity level tends to decrease with time in an ultra high vacuum environment. In order to check this, a sample identical to n72 was grown after about 2 months of continuous operation of the MBE system. The measured values of JNDR and JT H of this device (n120) are reported in Fig. 5 (solid and open circles respectively). As expected, both values are lower and correspond to a situation where the background doping of the MBE had dropped to a value below N V = 0.2 × 1017 cm−3 (n offset = 0.2 × 1011 cm−2 ). Considering the device n120 (2.1 × 1011 cm−2 ) and the sample n71 (1.0 × 1011 cm−2 ) with its


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added background doping (0.2 × 1011 cm−2 and 1.0 × 1011 cm−2 respectively), a comparable total doping concentration is obtained with a similar threshold current density as shown in Fig. 5. The larger dynamical range between the threshold density and the maximum current density observed for the sample with a cleaner environment (n120) is attributed to a higher quality material. 3. High power devices For a number of quantum cascade laser applications, especially long-path remote sensing and countermeasures, large peak and average powers are essential. In a quantum cascade laser, electrons are injected from period to period, emitting photons at each step. For this reason, the power is expected to grow linearely with the number of periods in the active region. Scaling of the optical power was demonstrated already by Gmachl et al. (Gmachl et al., 1999) in a series of experiments. However, for a fixed waveguide width, as the number of periods increases, the overlap factor of each individual period with the optical mode will decrease as they are inserted in a region with lower optical field. As a result the threshold current density will saturate (Gmachl et al., 1999) as the overlap factor of the gain medium reaches unity. It was shown that the slope efficiency also decreases below the ideal value (Gresch et al., 2006). For non-identical overlap factor of the individual stages, the slope efficiency may be computed and yields: Np i )2 dS N p ( i=1 (4) = dJ αtot q N p N p 2 i=1 i The second term on the right hand side of the above equation (called ηv in the following text) weights the reduction of the slope efficiency caused by vertical hole burning. Evaluating ηv for a hypothetical, symmetric slab waveguide with 3 µm thick active region (n eff = 3.3) and InP cladding, at a wavelength of 4.3 µm, yields ηv = 86 %. Our calculations show that with the waveguide design we present in this letter this value improves to 99.4 %. The maximum slope-efficiency is obtained when all i are the same, meaning that the optical mode should have a rectangular profile. In addition we observe a big improvement of beam quality and delay of the onset of gain compression which results in high peak-power. Saturation of the gain medium will naturally occur for the periods of the active region at the peak of the optical mode. Again, onset of saturation will then occur for an optical power smaller by a factor of two for a structure that employs the traditional waveguide described above as compared to one with a ideal rectangular shaped optical mode profile. Such an optical mode profile can be achieved by inserting a gain medium separated in three groups of periods by two InGaAs buffer layers, and further separated from the cladding layers

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by thick InGaAs waveguiding layers. This separation also helps to maintain the electrical stability of the structure. Fig. 6 shows the refractive index profile, as well as the 1D-simulated intensity of the fundamental mode of one of the three samples (N505) used in this study. The optical mode profile has a large spatial extention and very little penetration into the cladding layers. Waveguide losses are therefore mainly governed by the losses in the active regions and InGaAs buffer layers. Our structures were grown by MBE in the InP-based strain-compensated In0.61 Ga0.39 As/In0.45 Al0.55 As material system. The active regions of samples N505 and N513 are based on a 4.5 µm bound-to-continuum design but changing growth conditions resulted in a shorter emission wavelength (λ = 4.3 µm) for N505. The sequence of the layers is 46,9,14, (20,2,19), (7,2,7), (18,2,17), (8,2,7), (16,2,15), (11,2,10), (12,2,12), (10,2,9), 23, 22, 20, 23, 19, 25, 18, 30, 17, 34, 16, 36, 16 ˚ and (.) dewhere AlInAs-(bold) and InGaAs-layer thicknesses are given in A notes composite AlInAs-AlAs-AlInAs barriers and InGaAs-InAs-InGaAs wells, respectively. The underlined layers are doped with Si (n = 2.3 × 1017 cm−3 N505, n = 1.7 × 1017 cm−3 N513). The composite layers were added to reduce carrierleakage into the continuum (Semtsiv et al., 2004). The active region of N515 is described by Blaser et al. (Blaser et al., 2005) but we changed the doping to n = 1.2 × 1017 cm−3 . In the case of N505 and N513 growth starts with the usual InP-to-InGaAs grading layers and is then followed by a 1 µm thick InGaAs (n = 4 × 1016 cm−3 )


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buffer layer lattice-matched on InP. The gain region consists in three stacks where each stack is composed of 17 injector/active region stages, separated by 0.5 µm thick InGaAs buffer layers. A 900 nm thick InGaAs buffer layer terminates the waveguide core and the top-cladding layer consists in AlInAs with a total thickness of 2 µm. The grown structures were processed into 14 to 24 µm wide ridge waveguides using photolithography and wet etching. Laser devices with lengths up to 5.3 mm were cleaved and soldered with indium on copper mounts. To increase output power the devices were HR-coated on the back facet using Al2 O3 /Au/Al2 O3 coating. Measurement of the far-field emission pattern (bottom) shows a narrow, Gaussian profile with 29.4◦ FWHM in the growth- and 13.3◦ in the perpendicular direction. Calculation of the far-field in the growth direction (dashed line in Fig. 6) yields a FWHM of 31.1◦ which is in good agreement with the measured values. We did not measure the far-fields for N513 and N515 but calculations yield values of 32.7◦ and 35.6◦ . This value is significantly lower than the one measured a similar device (Blaser et al., 2005) using a conventional waveguide (68◦ ) or the value of 49◦ reported by Yu et al. (Yu et al., 2005). Figure 7 shows the peak power and voltage as a function of current for the devices N505 and N513. The measurements were done in pulsed mode with 1 % duty-cycle (100 kHz, 100 ns pulse width) in a TE-cooled laser housing. The optical power was directly collected by a cone optics and redirected to a thermopile power meter. For sample N505 operating close to λ = 4.3 µm, with a 5 mm long and 21 µm wide cavity, a threshold current density of 3.0 kAcm−2 and a peak power of 2.2 W were measured. These values improved to 1.8 kAcm−2 and 5.0 W at −30◦ C. For sample N513 at a slightly longer wavelength (λ = 4.55 µm), at 30◦ C we measured a maximal peak power of 2.1 W with d P/d I = 1.1 W/A. These values improved to a maximum peak power of 4 W and a slope efficiency of d P/d I = 1.8 W/A, a threshold current density is 1.3 kAcm−2 at −30◦ C. At this temperature, a maximum wall plug efficiency of 4.4 % is achieved. We attribute the difference between our threshold currents and the lower values achieved by Yu et al. (Yu et al., 2005) to the lower material strain used, that enabled thermoionic current from the upper state above the barriers. As a result we observed an exponential dependence of the threshold current density with temperature J = J0 exp(T /T0 ) with a characteristic temperature T0 of 150K compared to their value of 190 K (Yu et al., 2005). The device N515 (3.4 mm×20 µm, HR-coated), operating at λ ≈ 5.2 µm, was measured over a wider temperature range. To this aim, the device was mounted on a He flow-cryostat where the heat-sink temperature can be varied between 4 and 320 K. The emitted light was collected by Ge f/0.8 optics and refocalized on the thermopile head of our power meter using a ZnSe f/1.5 aspheric lens. Figure 8 shows the current-voltage-power characteristics of the device. At 15 K we

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measure a maximal peak power of more than 14 W and an initial slope efficiency of 11 W/A. The wall-plug efficiency ηwp reaches up to 34 %. At −33◦ C we still measure 7.2 W peak power and the slope- and wall-plug efficiencies are 7.3 W/A and 16 %, respectively. The threshold currents vary between 0.29 kAcm−2 at 15 and 78 K and 1.1 kAcm−2 at 280 K. The slope efficiency, that can be expressed by dP hν αm τeff = Np dI q αtot τeff + τ2

(5)

where αtot = αw + αm is the total optical loss and iτeff = τ3 (1 − τ2 /τ32 ), (Ajili et al., 2004) depends strongly on the waveguide losses. For sample N515, using hν = 248 meV Np = 60, a HR-coating with R = 1 and neglecting the lower state population τ2 = 0, the predicted value (d P/d I ≈ 5 W/A) is smaller than the measured one (d P/d I = 11 W/A) at cryogenic temperature. The difference originated in the temperature dependence of the waveguide losses. In Fig. 9 the average power of three devices in function of the duty-cycle at −30◦ C and 30◦ C are shown. Maximal average power of 290 mW at −30◦ C was obtained with device N515 at a duty-cycle of 8 %. This behaviour is expected because of the poor thermal conductivity of the active waveguide core. Thinner


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ridges as well as an InP top cladding could significantly improve the performances of these devices. For this reason, another device, N810, was designed and grown. It included an active region similar to the one of N513 and emitting at λ = 4.8 µm with slightly larger band discontinuities. The active region also exhibited a lower doping level (Si: n s = 8.8 × 1010 cm−2 ). The waveguide was similar, with one individual activeregion stack composed of 20 periods instead of 17. The waveguiding and spacer layers are the same as for the other structures but the top-cladding consists in a 2 µm thick layer of InP (Si: n = 1 × 1017 cm−3 ), followed by a 400 nm thick InGaAs contact layer (Si: n = 2 × 1018 cm−3 ). The performances of a relatively

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short (3mm long) device with a high reflectivity backfacet coating is shown in Fig. 10. The performances did indeed improve significantly, with, at 30◦ C, a power of 3W reached at a current of 1.75A instead of a power of 2W at a current of 8A. The wallplug efficiency reaches then 6.7% at 30◦ C and 12% at −30◦ C. 4. Linewidth enhancement factor In contrast to conventional semiconductor lasers which are based on interband transitions, QCL’s are based on intersubband transitions. A fundamental difference between these two transitions is the fact that the latter displays a delta-like joint density of states, which results in a symmetric gain curve. Using the Kramers-Kronig transformation to obtain the refractive index from the gain curves, we see that the expected refractive index change will be zero at the gain peak. The linewidth enhancement factor α is defined by the ratio of the real part to the imaginary part of the refractive index change (Henry, 1982; Vahala and Yariv, 1983). As a result, a low linewidth enhancement factor is expected in a structure designed to lase at the gain peak curves. This has strong implications for device performance. In particular, the laser linewidth, proportional to (1+α 2 ), is strongly reduced compared to interband lasers for which the linewidth enhancement factor is commonly between 2–8 (Osinski and Buus, 1987). Moreover, this implies intersubband lasers should have a negligible chirp, and thus their optical output should have a negligible frequency modulation with a modulating drive current.

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Figure 11. Setup for measuring the linewidth enhancement factor, α, based on a mixing of a high-frequency modulated distributed feedback quantum cascade laser (QCL-2) with a reference distributed feedback quantum cascade laser (QCL-1). The beams are superimposed using a ZnSe beam splitter and mixed onto a high-speed HgCdTe detector connected to a spectrum analyzer.

The first reported value of QCL linewidth enhancement factor (Faist et al., 1995) (α = 0.1), was based on a sub-threshold gain measurements with HakkiPaoli technique. These experiments were based on the measurement of the fringe contrast of Fabry-Perot modes. The real part of the refractive index is then obtained by Kramers-Kronig transformation of the measured gain data. Recently, another linewidth enhancement factor measurement with a value of α = −0.5 was reported (Lerttamrab et al., 2003; Kim et al., 2004). This value of α was extracted from wavelength shift of the Fabry-Perot resonances with current below threshold. A direct measurement of the linewidth enhancement factor that uses a variant of the experiment proposed by Harder et al. (Harder et al., 1983) is presented here. The optical setup is shown schematically in Fig. 11. Unlike the original setup, the optical spectrum is no longer measured with a scanning Fabry-Perot interferometer. It is obtained by optically mixing a reference distributed feedback (DFB) laser with a test DFB laser under modulation on a fast, room temperature, HgCdTe detector (Vigo SA, PEML-3). Care was taken to avoid optical feedback in the QCL’s by making a slight misalignment of the detector. The detected intensity is proportional to the term provided by the mixing of the two beams, and is given by: I (t) = I0 [1 +

m cos(t)] × cos[(ω1 − ω2 )t + β cos(t + ψ)] 2

(6)

where ω1 and ω2 are the frequencies of the reference and the test laser, respectively. The parameter β = − 12 αm is the phase modulation index and is proportional to the linewidth enhancement factor α and to the intensity modulation index m as previously reported (Harder et al., 1983). The reference intensity I0 corresponds to the intensity of the mixing without current modulation (m = 0).

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As will be shown later, the phase ψ depends on the device heating by the current modulation and its calculated value is ψ = − π2 . The detector signal is measured by a 9 kHz - 3 GHz spectrum analyzer (Agilent, E4402B) via a 38 dB amplifier. The two DFB QCL’s (Alpes Lasers SA) used in this experiment are based on a bound-to-continuum design (Blaser et al., 2005). The lasers operate under constant currents of 461 mA at 263 K for the reference laser and of 316 mA at 243 K for the test laser. The electrical powers are generated by stabilized current sources (ILX Lightwave, LDC-3744 and LDX-3232) and the temperatures are controlled by Peltier coolers monitored with commercial suppliers (Alpes Lasers, TC-51). Under these conditions, single mode emissions at 5.46 µm with average optical powers of 10 and 5 mW for the reference and test lasers, respectively, are observed. The mixing of the two lasers results in a beating spectrum. At 100 MHz, with a sweep time of 5 ms and a resolution bandwidth of 1 MHz, a typical beat note has a full width at half maximum of 6 MHz. The measured linewidth is attributed to fluctuations of the drive currents and, to a lesser extent, to the fluctuation of heat-sink temperatures. A small sinusoidal current modulation is added to the drive direct current via a Bias-T and is fed to the test laser. The latter is connected to a 50-Ohm cable by short ( 2 MHz) yields: m I (Udc + dU I ) π 2 mod d I dc Tact = Tsink + Udc Idc Rth + cos t − (7) C V 2 where Tact is the temperature of the active region, Tsink the temperature of the heatsink and Rth = 6.3 K/W the thermal resistance (Blaser et al., 2005). The calculated phase difference between induced temperature Tact and the power source P is − π2 . This phase difference is attributed to the time delay between the temperature response and the current modulation. The optical frequency deviation is related to the induced-temperature modu1 lation by ν = − 4π αm = ∂∂νT (Tact − Tsink ). The expression for the linewidth enhancement factor is given by: Imod (Udc + dU I ) d I dc ∂ν (8) 2 C V ∂T The RF power P through the device generates an optical signal with a temperatureinduced FM modulation having a dephasing of ψ = − π2 with the AM modulation. This value is in agreement with the asymmetry observed in the amplitude spectrum for an increasing amount of FM modulation. By expanding Equ. 6 1, the spectral density of the radiation at center line ω1 − ω2 and for the first sidebands at ω1 − ω2 ± are given respectively by: I0 2 (9) J (β) I 2 (ω1 − ω2 ) = 4 0 I0 2 m2 J1 (β) + [J0 (β) + J2 (β)]2 ∓ I 2 (ω1 − ω2 ± ) = 4 16 m (10) J1 (β)[J0 (β) + J2 (β)] 2 α = −2π

where Jn (β) is the n th order Bessel function. From these equations, the linewidth enhancement factor is found by measuring the ratio of the first sideband to the center line amplitudes for an intensity modulation index of m = 0.4. The corresponding values of the linewidth enhancement factor are 8.2 ± 0.3, 2.0 ± 1.0, 0.8 ± 1.4 and 1.0 ± 1.6 for 20, 80, 500 and 990 MHz respectively. As reported in the Fig. 13, these experimental values of α are in agreement with the simple thermal model (Equ. 8) and confirm the assumptions concerning the temperature behavior of the device. This temperature-induced FM modulation below about 100 MHz is also observed in interband lasers (Kobayashi et al., 1982). For 500 MHz, the difference of the first sideband amplitudes is used to deduce the linewidth enhancement factor. This technique has a better accuracy with a value of α = 0.02 ± 0.2.


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For a laser emission close to its gain peak (5.44 µm), a linewidth enhancement factor of α = 0.06 is expected (Maulini et al., 2005). The accuracy of the measurements is limited by the current stabilization. Due to the current instabilities, the beat note has a large frequency excursion. This effect limits the signal integration time and the accuracy on the mean of the sideband amplitudes. An accurate determination of α is then expected with a better current stabilization (Taubman et al., 2002). 5. Acknowledgements The authors would like to thank Stephane Blaser (Alpes Lasers SA), Richard Maulini, Nicolas Hoyler for various contributions. This work was financially supported by the Swiss National Science Foundation under the NCCR project Quantum photonics as well as the European Community project ANSWER. References Ajili, L., G. Scalari, J. Faist, H. Beere, E. Linfield, D. Ritchie, and G. Davies: 2004, ‘High power quantum-cascade lasers operating at λ ∼ 87 and 130 µm’. Appl. Phys. Lett. 85(18), 3986–3988. Barbieri, S., J. Alton, H. Beere, J. Fowler, E. Linfield, and D. Ritchie: 2004, ‘2.9 THz quantum cascade lasers operating up 70 K in continuous wave’. Appl. Phys. Lett. 85(10), 1674–1676. Beck, M., D. Hofstetter, T. Aellen, J. Faist, U. Oesterle, M. Ilegems, E. Gini, and H. Melchior: 2002, ‘Continuous wave operation of a mid-infrared semiconductor laser at room temperature’. Science 295, 301–305.

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Blaser, S., D. Hofstetter, M. Beck, and J. Faist: 2001, ‘Free-space optical data link using Peltiercooled quantum cascade laser’. IEE Elect. Lett. 37(12), 778–780. Blaser, S., D. Yarekha, L. Hvozdara, Y. Bonetti, A. Muller, M. Giovannini, and J. Faist: 2005, ‘Room-temperature, continuous-wave, single-mode quantum-cascade lasers at λ ∼ 5.4 µm’. Appl. Phys. Lett. 86, 41109–1–41109–3. Evans, A., J. Yu, J. David, L. Doris, K. Mi, S. Slivken, and M. Razeghi: 2004, ‘High-temperature, high-power, continuous-wave operation of buried heterostructure quantum-cascade lasers’. Appl. Phys. Lett. 84(03), 314–316. Faist, J., F. Capasso, C. Sirtori, D. Sivco, and A. Cho: 2000, ‘Quantum cascade lasers’. In: H. Liu and F. Capasso (eds.): Intersubband transitions in quantum wells: Physics and device applications II, Vol. 66. Academic Press, Chapt. 1, pp. 1–83. Faist, J., F. Capasso, C. Sirtori, D. Sivco, A. Hutchinson, and A. Cho: 1995, ‘Continuous wave operation of a vertical transition quantum cascade laser above T=80 K’. Appl. Phys. Lett. 67(21), 3057–3059. Faist, J., F. Capasso, D. Sivco, C. Sirtori, A. Hutchinson, and A. Cho: 1994, ‘Quantum cascade laser’. Science 264, 553–556. Faist, J., D. Hofstetter, M. Beck, T. Aellen, M. Rochat, and S. Blaser: 2002, ‘Bound-to-continuum and two-phonon resonance quantum cascade lasers for high duty cycle, high temperature operation’. IEEE J. Quantum Electron. 38(6), 533–546. Giehler, M., R. Hey, H. Kostial, S. Cronenberg, T. Ohtsuka, and L. Schrottke: 2003, ‘Lasing properties of GaAs/(Al,Ga)As quantum-cascade lasers as a function of injector doping density’. Appl. Phys. Lett. 82(5), 671–673. Giehler, M., H. Kostial, R. Hey, and H. Grahn: 2004, ‘Effect of free-carrier absorption on the threshold current density of GaAs/(Al,Ga)As quantum-cascade lasers’. J. Appl. Phys. 96(9), 4755–4761. Gmachl, C., F. Capasso, A. Tredicucci, D. Sivco, R. Köhler, A. Hutchinson, and A. Cho: 1999, ‘Dependence of the device performance on the number of stages in quantum-cascade lasers’. IEEE J. Select. Topics Quantum Electron. 5(3), 808–816. Gresch, T., M. Giovannini, N. Hoyler, and J. Faist: 2006, ‘Quantum cascade lasers with large optical waveguides’. IEEE Photon. Technol. Lett. 18(3), 544–547. Harder, C., K. Vahala, and A. Yariv: 1983, ‘Measurement of the linewidth enhancement factor α of semiconductor lasers’. Appl. Phys. Lett. 42(04), 328–330. Henry, C.: 1982, ‘Theory of the linewidth of semiconductor lasers’. IEEE J. Quantum Electron. 18(02), 259–264. Hofstetter, D., M. Beck, T. Aellen, and J. Faist: 2001, ‘High-temperature operation of distributed feedback quantum-cascade lasers at 5.3 µm’. Appl. Phys. Lett. 78(4), 396–398. Kazarinov, R. and R. Suris: 1971, ‘Possibility of the amplification of electromagnetic waves in a semiconductor with a superlattice’. Sov. Phys. Semicond. 5(4), 707–709. Kazarinov, R. and R. Suris: 1972, ‘Electric and electromagnetic properties of semiconductors with a superlattice’. Sov. Phys. Semicond. 6(1), 120–131. Kim, J., M. Lerttamrab, S. Chuang, C. Gmachl, D. Sivco, F. Capasso, and A. Cho: 2004, ‘Theoretical and experimental study of optical gain and linewidth enhancement factor of type-I quantum-cascade lasers’. IEEE J. Quantum Electron. 40(12), 1663–1674.


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HIGH-BRIGHTNESS 2.X µm SEMICONDUCTOR LASERS

M. RATTUNDE∗ , M. T. KELEMEN, N. SCHULZ, C. PFAHLER, C. MANZ, J. SCHMITZ, G. KAUFEL and J. WAGNER Fraunhofer-Institut für Angewandte Festkörperphysik (IAF), Tullastrasse 72, 79108 Freiburg, Germany

Abstract. There is an increasing number of applications, which require compact and robust laser sources emitting in the 2–3 µm wavelength range. Based on semiconductor lasers, highly-efficient, small-footprint laser systems can be realized, having a long lifetime and the potential of reduced costs due to their mass-production capability. In recent years, semiconductor lasers based on the III–V compound semiconductor material system (AlGaIn)(AsSb), emitting in the 1.8 µm to 3.0 µm wavelength regime (in the following abbreviated as 2.X µm) have reached a considerable level of maturity regarding spectral coverage, output power and device reliability. For the majority of the potential applications of these GaSb-based lasers, output power is not the only criterion, but the combination of high output power and good beam quality, i.e. high brightness, is the ultimate goal. This is more difficult to achieve for edge-emitting semiconductor lasers, than e.g. with classical solid state lasers. In this chapter we will give an overview of the recent advances concerning GaSbbased 2.X µm semiconductor lasers and describe the route to high brightness lasers, based on this material system. Keywords: GaSb, 2 µm, high brightness, high power, semiconductor diode laser, tapered diode laser, optically pumped semiconductor disk laser, VECSEL.

1. Introduction The 2.X µm wavelength range is of special importance for applications, such as gas detection, medical diagnostics, laser surgery, optical pumping of longer wavelength solid-state lasers, material processing and security applications. As there are characteristic absorption lines of a variety of relevant gases in this wavelength range [1], such lasers are in particular useful for high resolution molecular spectroscopic gas detection for industrial process monitoring or environmental control. Continuous wave (CW) output powers at room temperature of a few 10 mW are required for these applications, together with a good spectral purity and a certain tunability. Furthermore, LIDAR-measurements and optical free-space ∗ To whom correspondence should be addressed. Marcel Rattunde, Fraunhofer-Institut für

Angewandte Festkörperphysik, Tullastrasse 72, 79108 Freiburg, Germany; e-mail: marcel. [email protected] 193 M. Ebrahim-Zadeh and I. T. Sorokina (eds.), Mid-Infrared Coherent Sources and Applications, 193–224. c 2008 Springer.

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telecommunications can be carried out within the 2–2.5 µm atmospheric transparency window. Because of the distinct absorption spectrum of human tissue in the present spectral range [2], medical diagnostic, such as noninvasive optical blood glucose monitoring [3], and laser surgery [2] are other promising applications. For the latter, output powers exceeding 10 W are required. Given this wide range of applications of lasers in material processing, not all can be dealt with using state-of-the-art GaAs-based high-power diode lasers, emitting around 1 µm. For example the welding of transparent plastic requires high power lasers emitting at 2 µm, an application which is currently addressed by Ho-YAG solid state laser systems [4]. High-power semiconductor lasers emitting at around 2 µm, with their potentially lower cost and compactness can replace those laser systems. Finally, optical pumping of solid state lasers emitting at longer wavelengths [5, 6] and security related applications, such as directed infrared countermeasures, are further areas where high brightness 2.X µm semiconductor lasers will find use. The (AlGaIn)(AsSb) material system constitutes an ideal basis for the realization of diode lasers in this wavelength regime. GaInAsSb, grown either lattice matched to GaSb or deliberately strained with a direct band gap energy corresponding to wavelengths between 1.7 µm and well above 3 µm, can be used for the active layer. For the barrier and cladding layers, AlGaAsSb grown lattice matched to GaSb with various compositions, is well suited because of its larger band gap energy and lower refractive index than GaInAsSb. Starting with the first III–V mid-IR laser in 1963, based on InAs homojunctions and a low-temperature emission at 3.1 µm [7], double-heterostructure (DH) lasers were developed subsequently with a GaInAsSb active region and AlGaAsSb barriers, grown on GaSb-substrates. These lasers showed already excellent performance at room temperature in the 2.0 to 2.5 µm range [8, 9]. For the 3 to 4 µm range, DH-lasers employing InAsSb/AlGaAsSb layer sequences on GaSb or InAsSb/InAsPSb layers on InAs-substrates were fabricated with a maximum operating temperature of around 170 K in pulsed operation [10–12]. In 1992, the concept of strained quantum-well (QW) lasers was for the first time implemented in GaSb-based lasers [13] yielding significant improvements in both laser output power and maximum operating temperature [14]. Nowadays GaInAsSb/AlGaAsSb type-I QW lasers can be operated at room temperature in CW-operation up to wavelength of 3.04 µm [15] and in pulsed mode up to wavelength of 3.26 µm [16]. For even longer emission wavelengths towards 4 µm, type-II laser concepts, such as the interband W-laser [17] and the interband cascade laser [18] seem to outperform type-I QW-lasers with InAsSb active layers, mostly because of the possibility to suppress CHHS-Auger recombination in these type-II heterostructures [19]. And it waits to be seen, how the performance of short wavelength quantum cascade lasers (QCLs) will evolve, which have reached emission wavelengths as short as 3.54 µm in pulsed mode up to now [20].


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In this chapter, we will focus on recent developments in GaInAsSb/AlGaAsSb type-I semiconductor lasers grown on GaSb-substrates for the 2.X µm wavelength range. 2. III-Sb based material system 2.1. MATERIAL PROPERTIES

The quaternary semiconductor Alx Ga1−x Asy Sb1−y is the ideal material for barrier-, waveguide-, window-, absorbing- and cladding layers in III-Sb based semiconductor lasers. Furthermore, efficient distributed Bragg reflectors (DBR) can be fabricated using AlAs0.08 Sb0.92 /GaSb layer pairs. Because of the large width of the individual DBR layers as well as of the whole layer stack, they are almost exclusively grown lattice matched to the GaSb-substrate; this can be achieved by adding a small amount of As to the AlGaSb to form Alx Ga1−x Asy Sb1−y with y = 0.08 x [21]. The direct band gap for AlGaAsSb at 300 K, lattice matched to GaSb, is given by Eg (Γ ) = 2.297 x + 0.727(1 − x) − 0.48 x(1 − x)eV [21]. The ternary alloy Alx Ga1−x Sb has the specific property of changing the character of the fundamental band gap twice upon increasing Al-content: From direct, with the -conduction band minimum being lowest in energy, to indirect, with the L-point minima being lowest in energy for Al-contents above 25% and to the X-point minima being lowest for an Al-content beyond approx. 45% [21–23]. For AlGaAsSb lattice matched to GaSb, a similar behavior is expected as only a small amount of As is added, although some calculations suggest a direct to indirect crossover at an Al-concentration of only 14% [21]. For the active layers, Ga1−x Inx Asy Sb1−y is used which has a direct bandgap for all alloy compositions and which is lattice matched to GaSb if the condition y = 0.913x is fulfilled [21, 24]. The band-edge profile for Ga1−x Inx Asy Sb1−y grown on GaSb is shown in Fig. 2.1 for two extreme cases, namely (a) compressively strained GaInSb with increasing compressive strain εzz upon increasing In content x according to the relation εzz = +0.063 · x (Fig. 2.1a) and (b) GaInAsSb lattice matched to GaSb by appropriate simultaneous adjustment of In und As contents x and y according to y = 0.913x (Fig. 2.1b). Also shown are as a reference the band edges of AlGaAsSb lattice matched to GaSb with an Al content of 30%. The latter represents a typical barrier material, used by many different groups in their GaSb-based QW lasers [25, 26]. All material data for this calculation have been taken from Ref. 21. Starting with GaSb on the left hand side of each diagram, the GaInAsSb band gap decreases with increasing In content in both cases. Without the addition of As (Fig. 2.1a), i.e. for Ga1−x Inx Sb, the GaInSb is compressively strained, and due to the effect of this biaxial in-plane strain on the band structure, a type-I band alignment is formed with regard to the chosen AlGaAsSb barrier material in the whole composition range with the

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Figure 2.1. Relative positions of the conduction band (cb), heavy-hole (hh), light-hole (lh), and split-off (so) valence band vs. In-content for the active region QW material Ga1−x Inx Asy Sb1−y grown on GaSb; for comparison conduction and valence band edges of the Al0.3 Ga0.7 As0.02 Sb0.98 barriers are also indicated (gray lines). Two cases are shown: (a) compressively strained QW material with y = 0 (b) lattice matched material with y = 0.913x. For the strained GaInAsSb in (a), the strain εzz is given by +0.063x.

heavy hole (hh) band as the topmost valence band. But due to the increasing strain upon increasing In content, the maximum emission wavelength achievable with this ternary compound is limited by the critical layer thickness for pseudomorphic growth of GaInSb on GaSb. For material lattice matched to GaSb with y = 0.913x (Fig. 2.1b), the band offset in the valence band ∆EV decreases with increasing In-content x and leads to a type-II band alignment with respect to the AlGaAsSb barrier material for x > 0.35. Similar is true for tensile strained material. Therefore compressively strained GaInAsSb is favorable in order to allow sufficient confinement of also the holes in the active QWs. This is especially important for GaSb-based lasers emitting at longer wavelength towards 3 µm (see section 3.1). 2.2. GROWTH

Although there are some reports of GaSb-based lasers grown by metal-organic vapor phase epitaxy (MOVPE) [27], molecular beam epitaxy (MBE) is most widely used [14, 28]. The laser structures are mostly grown on (100)-oriented

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Figure 2.2. Temperature-dependent spinodal isotherms for Ga1−x Inx Asy Sb1−y (solid lines) after Ref. 29. The dashed line indicates the composition for lattice-matching to GaSb.

n-doped GaSb substrates. A state-of-the-art MBE system is typically equipped with valved cracker effusion cells for the group-V elements As and Sb, providing precisely controlled fluxes of As2 and predominantly Sb2 as required for the growth of mixed group-V ternaries and quaternaries. The group-III elements Al, Ga, and In as well as the p- and n-type dopants Be and Te are supplied from conventional effusion cells, where GaTe or Sb2 Te3 is used as the Te doping source. The lower cladding layer is grown at higher temperatures (around 550◦ C) than the laser core and the top-cladding layer (around 475◦ C). Growing the top cladding layer at a lower temperature than the bottom cladding ensures that the GaInAsSbQWs do not degrade due to In-inter-diffusion during growth of the former [28]. Growth of the barrier and cladding material AlGaAsSb lattice matched to GaSb lies in a stable growth regime for all Al-concentrations for growth temperature above 400◦ C, i.e. no phase separation occurs [14]. However, the active layer material GaInAsSb is not miscible for the entire composition range. In Fig. 2.2 the calculated spinodal isotherms for GaInAsSb are shown, indicating the growth temperature dependent boundaries for unstable alloys [29]. For GaInAsSb lattice matched to GaSb, there is a miscibility gap between approximately 20% and 85% In-content for the growth temperatures around 500◦ C. MBE growth is still possible within the miscibility gap, but the material quality tends to deteriorate. Compressively strained GaInAsSb with high In and low As concentration has the advantage of avoiding this miscibility gap to some extent. 3. High brightness GaSb-based diode lasers In this section, recent developments in the area of high-brightness edgeemitting semiconductor diode lasers emitting in the 2.X µm wavelength range are described. In order to realize high-brightness diode lasers, various laser

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parameters, such as modal gain, internal losses, serial resistance, and thermal impedance as well as the waveguiding structure have to be optimized simultaneously in order to combine a high output power with a good beam quality. 3.1. ACTIVE REGION DESIGN

The active region of GaSb-based 2.X µm diode lasers is made out of strained Ga1−x Inx Asy Sb1−y QWs, embedded between AlGaAsSb barriers. Using a quaternary material for the active layer adds an additional degree of freedom to the design of QWs compared to a ternary material (such as the well known GaInAs/GaAs materials combination): By changing the composition, two of the three relevant parameters bandgap Eg , strain εzz , and band offsets E can be adjusted individually within certain limits. An increase of the emission wavelength can be achieved by an increase either of the In-content or of the As-content in the GaInAsSb QW-layers. The former will raise the amount of compressive strain in the active QW, and thus decrease the critical layer thickness, and increase the valence band offset EV and hence the hole confinement, while the latter will decrease both strain and EV (see Fig. 2.1). The hole confinement is a critical factor for GaSb-based diode lasers. It affects to a great extent the threshold current density, as a shallower valence band offset EV increases the heterobarrier leakage-current [30,31]. A constant valence band offset EV between the GaInAsSb active layer and the barriers (i.e. independent of the emission wavelength) is achieved if the As-content is 0.32 times the In-content [32]. The correlation between the strain εzz and the emission wavelength of the active layers, satisfying the above condition, is shown as dashed line in Fig. 3.1a; here a QW width of 10 nm and lattice-matched Al0.3 Ga0.7 As0.02 Sb0.98 barriers have been assumed. Thus, as a rule of thumb, the strain-wavelength data of a laser structure should lie on or above that line in order to ensure sufficient hole confinement. The symbols in Fig. 3.1a represent experimental data from different laser structures [32]. The squares and circles denote structures for which only the composition of the GaInAsSb QWs was changed, while all other epitaxial layers of a standard broadened waveguide design were kept constant (details of this waveguide structure are discussed in Sect. 3.2). For the same set of samples, the threshold current density Jth is plotted in Fig. 3.1b versus the emission wavelength. For the laser structures displayed by squares, mainly the In-content was increased to shift the emission towards longer wavelengths, resulting in an increasing compressive strain. All data points lie well above the dashed line in Fig. 3.1a. Consequently, the active regions of all structures are expected to exhibit a sufficient valence band offset, resulting in a low threshold current density in the range of 148 to 190 A/cm2 (49 to 63 A/cm2 per QW) over the entire wavelength

(a) 0.02

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Figure 3.1. (a) Lattice mismatch (a/a0 )⊥ as well as the resulting strain εzz vs. the PL emission wavelength for lasers with different GaInAsSb QW-active regions. The squares denote samples, for which the wavelength variation was mainly due to a change in the In-content, while the open circles represent samples, for which the As-content was increased in order to increase the lasing wavelength. The asterisk denotes a sample with the new waveguide design, as discussed in Sect. 3.2. The dashed curve is derived from the condition, that the As-content is 0.32 times the In content, i.e. a constant hole confinement [32]. (b) Threshold current density Jth vs. emission wavelength for the different samples shown in Fig. 3.1. All measurements were performed using 1000 µm long diode lasers with uncoated factes at a heatsink temperature of 280 K in CW-operation [32].

range from 1.9 to 2.4 µm as can be seen from Fig. 3.1b. In contrast to this, the open circles denote samples where the As-content rather than the In content was increased in order to achieve a longer lasing wavelength, which results in a decreasing strain and shallower valence band offset (Fig. 2.1). The consequence is a dramatic increase of the threshold current density (Fig. 3.1b) due to increased heterobarrier leakage. For longer emission wavelengths, close to 3 µm, the condition for sufficient hole confinement (dashed line, Fig. 3.1a) is difficult to fulfill, as this would result in heavily strained QWs and a critical layer thickness in the order of the width of the QWs. Possible solutions for this is the use of strain compensation, i.e. employing tensile strained barriers to avoid the accumulation of compressive strain in particular in a multiple QW active region and thus the onset of relaxation [33], or alternatively the use of quinternary AlGaInAsSb barriers instead of quaternary AlGaAsSb to improve the hole confinement [16]. A more radical approach to deal with the strain issue is to employ a metamorphic AlInSb buffer layer between GaSb substrate and the laser structure, in order to generate an artificial substrate with a lattice constant larger than that of GaSb [34]. Furthermore, there is evidence that for wavelengths above approx. 2.6 µm, Auger recombination is becoming increasingly important as a non-radiative loss mechanism [35], leading to a further increase of the threshold current. As an illustration of the above, Fig. 3.2 displays the threshold current density at room temperature per QW for various laser structures reported by different groups.

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Figure 3.2. Threshold current density per QW close to room temperature vs. emission wavelength for laser samples from MIT (open squares) [36], Sarnoff Corp. / Univ. of Stony Brook (closed squares) [37–39], CEM2, Montpellier (closed circles) [40, 41], WSI, Munich (open stars) [15, 16] and Fraunhofer IAF (closed stars) [32,42]. The resonator length of the diode lasers was in the range of 1 to 2 mm.

4

Figure 3.3. Refractive index profile (solid line, left scale) and calculated optical mode intensity (dashed line, right scale) for (a) the conventional broadened waveguide design and (b) for the improved design [32, 44].

3.2. VERTICAL EPITAXIAL STRUCTURE

The epitaxial layer sequence design is probably the most critical feature in the design of an edge emitting diode laser, as it directly affects the internal laser parameters (internal losses αi and internal efficiency ηi ) as well as the series resistance of the laser and thus its high-power performance. Furthermore, the vertical structure defines the optical waveguide and that way the beam quality and the fast-axis beam divergence. The vast majority of 2.X µm diode lasers reported to date has been realized using the broadened waveguide or large optical cavity (LOC) design [43], whose refractive index profile is shown in Fig. 3.3a. The LOC design is characterized by a high Al-content in the AlGaAsSb cladding layers of typically 84% and a wide waveguide core section with two separate confinement layers (SCL)


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typically 400 nm in width enclosing the QW active region. This waveguide structure, which has been used so far almost exclusively for GaSb-based diode lasers [15, 16, 25, 26, 28, 30, 31, 35–41, 43] with only minor variations in the Al-content of the cladding layers (84%–90%) and the width of the SCL (300–600 nm), has the advantage of a large optical confinement factor (QW ) of the QWs forming the gain region, leading to a high modal gain and enabling low threshold current densities. At the same time the overlap of the optical mode with the doped cladding layers (Clad ) is small, which results in low free carrier absorption losses αi [43, 44]. The drawback of LOC design applied to GaSb-based 2.X µm diode lasers is the very large beam divergence in the fast axis with a full width at half maximum (FWHM) in the range of 63◦ –67◦ [45–47]. Because of this large beam divergence, the light-coupling efficiency into an optical system of finite aperture is reduced, leading to a limitation of usable power of the device. Therefore, it is necessary to have a fast axis beam divergence of ≤45◦ FWHM for state-of-the-art collecting optics. Recently our group has presented an improved vertical waveguide design with a reduced fast axis beam divergence of 44◦ FWHM and the same favorable output power and power efficiency as the broadened waveguide structure [32, 48]. The goal was to design a vertical waveguide structure which combines a significant broader optical mode inside the waveguide with an optical confinement for the QWs (QW ) comparable to that of the conventional broadened waveguide design. The latter requirement is crucial in order to maintain a low threshold current, as a marked loss in QW cannot be compensated by the adjustment of any other design parameter. The refractive index profile of the resulting improved waveguide structure is shown in Fig. 3.3b. This improved structure is based on a narrow optical waveguide with only 140 nm wide Al0.3 Ga0.7 As0.02 Sb0.98 SCLs and a reduced Alcontent in the AlGaAsSb cladding layers of 50%, resulting in a lower refractive index step between the cladding and the waveguide layers. As the internal losses are dominated by the absorption due to free carriers in the p-cladding with a cross section of σP = 4.6 · 10−17 [44], the Be-doping in the inner part of the p-cladding was reduced. In this way the internal losses αi could be kept as low as for a conventional broadened waveguide design, in spite of the much larger overlap of the optical mode with the cladding layers. In order to verify this improved waveguide concept, two laser structures have been fabricated side by side, one with a conventional LOC waveguide and the other with the improved waveguide design, as shown in Fig. 3.3 a and b. The active region was identical for both structures, employing Ga0.64 In0.36 As0.10 Sb0.90 QWs with εzz = 1.5% strain and an emission wavelength of 2.3 µm at room temperature. The strain-wavelength data point for this laser structure is indicated in Fig. 3.1 by an asterisk; it can be seen that, according to the overall design rule derived in Sect. 3.1, the hole confinement in the active region is expected to be sufficient.

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The measured far field distribution in the fast axis is shown in Fig. 3.4 for both laser structures. The large beam divergence of the broadened waveguide laser of 67◦ FWHM (120◦ full width at 1/e2 ) is reduced to 44◦ FWHM (77◦ full width at 1/e2 ). This strong decrease in the fast axis divergence will drastically increase the coupling efficiency of the laser light into an optical system, thus increasing the overall power efficiency. In Fig. 3.5a, the threshold current density Jth is plotted versus the resonator length for both laser structures. Despite the large differences between the


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two waveguide structures and the resulting different optical mode profiles, the threshold current density remains the same for the improved waveguide structure as for the LOC structure. This was achieved by a balanced adjustment of the waveguide width, the refractive index step n and the doping profile in the p-cladding layer. In order to derive the internal parameters αi and ηi , the inverse differential quantum efficiency 1/ηd is plotted in Fig. 3.5b versus the resonator length. The differential efficiency ηd is comparable for both structure, with even slightly higher values for the improved waveguide structure (lower values of 1/ηd ). From the intersection of the linear fit to the experimental data with the ordinate, the internal efficiency ηi can be determined, while the internal losses αi are to be derived from a combination of both the intersection and the slope. Within the measurement uncertainty, both structure show comparable values of the internal parameters with ηi around 70–80% and αi in the range of 8–9 cm−1 . The latter implies that the adjusted doping profile in the p-cladding is effective in compensating the higher confinement factor with cladding layer Clad , keeping the overlap of the optical mode with the free holes in the p-type cladding, and thus the internal losses αi , constant. The turn on-voltage (0.7 V) and series resistance (200 m for a 1500×64 µm2 geometry, or 5260 −1 cm−2 ) was also identical in both structures, despite the lower Be-doping in the inner part of the p-cladding of the improved waveguide. This implies that the p-doping level is still high enough to ensure a low series resistance for the AlGaAsSb cladding layers with an Al-content of 50% as used in the improved waveguide structure [48]. Further fine-tuning of the improved waveguide design and the doping profile resulted in a laser emitting at 2.3 µm with very low internal losses of αi = 5 cm−1 , an internal efficiency of ηi = 86% and an even further reduced fast axis beam divergence of 40◦ FWHM [49]. 3.3. BROAD-AREA LASERS

High power diode lasers emitting at wavelengths between 2 µm and 3 µm have significant potential as compact and efficient light sources in the fields of direct materials processing, laser surgery and therapy as well as defense related applications. For all these applications an output power in the Multiwatt range is required. As an overview, Fig. 3.6 displays the max. output power for single emitters in CW operation close to room temperature for high-power diode laser report by various groups. So far, they all suffer from a large fast axis beam divergence due to the broadened waveguide design employed. In order to demonstrate, that the improved waveguide concept described in Sect. 3.2 is applicable also to high power diode lasers, we fabricated broad-area (BA) lasers emitting at 2 µm based on the improved waveguide structure displayed in Fig. 3.3b. The triple-QW active region of this laser structure is composed of

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Figure 3.6. Maximum output power for 2.X µm single emitters in CW operation close to room temperature, for samples from Sarnoff Coop. / Univ. of Stony Brook (closed squares) [37–39], CEM2, Montpellier (closed circles) [40], WSI, Munich (open stars) [15] and Fraunhofer IAF (closed stars) [48].

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ternary Ga0.81 In0.19 Sb QWs with a compressive strain of εzz = 1.5%. 150 µm wide gain-guided broad area lasers were fabricated using standard optical lithography in combination with dry etching techniques for lateral patterning, and lift-off metallization for p-contact formation. Backside processing started with substrate thinning followed by the deposition of the n-contact metallization and annealing. The facets are coated with high-reflective/antireflective (HR/AR) films with 95% and 3% reflectivity. 3.3.1. Single emitter Figure 3.7 shows the output power- and voltage-vs.-current characteristics and the current dependent wall-plug efficiency of a 1000 × 150 µm2 single broad-area diode laser. The devices were mounted junction side down on gold-coated copper heat sinks (c-mounts). The measurements were performed at a heat sink temperature of 20◦ C in continuous wave (CW) mode. The threshold current is 0.33 A corresponding to a threshold current density of 220 A/cm2 . A high output power


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of 1.96 W is obtained at an operation current of 7.9 A. For higher currents thermal rollover sets in. A slope efficiency of 0.32 W/A, corresponding to an external quantum efficiency of 50% results in a wall-plug efficiency of more than 26%, which is remarkably high for diode lasers emitting at 2 µm. The measured far field distribution in the fast axis showed the same reduced beam width as shown in Fig. 3.4. In Figure 3.8 the shifts of the emission wavelength of a broad-area single emitter with temperature (1.2 nm/K) and as a function of dissipated power (8.6 nm/W) are given. Whereas the wavelength shift with power loss is measured in CW operation, the emission wavelength as a function of temperature has been measured in pulsed mode 10% above threshold current to avoid self-heating effects. From both measurements the thermal resistance of the c-mount packaging has been extracted to be 7 K/W. In order to explore the power limitation of these diode lasers when thermal effects are excluded, devices were tested in pulsed mode (0.5 µs pulse width, 0.01% duty cycle). In this way, a record value in output power of 9.1 W is achieved for GaSb-based diode lasers at a driving current of 30 A, limited by the power supply. No catastrophic optical mirror damage occurred at the front facet in the current regime applied. The power density at the emitting facet is estimated to be about 6 MW/cm2 at 30 A. The long-term reliability of these diode lasers has been tested by aging a limited number of devices at a heat sink temperature of 20◦ C. A batch of five devices has been tested under constant current at 3 A (Fig. 3.9). The initial output power is about 0.9 W. All devices show only gradual degradation (1 W power capability of a BA-laser is provided by the tapered laser approach. The tapered diode laser, schematically shown in Fig. 3.12, can be described as a combination of the RW- and BA-laser concept [52]. For GaSb-based tapered diode lasers, Choi et al. reported 120-mW diffraction-limited CW output power from a 2-mm-long device at 2.04 m [53]. By increasing the device length to 2.4 mm, the diffraction-limited CW output power from a broadened-waveguide tapered laser could be increased to 600 mW at 2.05 µm wavelength [54]. Based on laser structures described in Sect. 3.2 and 3.3, we have pushed the nearly diffraction limited output power towards 1.5 W [57]. The lateral structure of the tapered diode lasers discussed here has been fabricated as follows. The ridge-waveguide (RW) section, deflecting grooves and gain-guided tapered section have been defined by dry chemical etching. RW width and height are chosen carefully for the propagating wave to fill the taper angle of 6◦ . After depositing the p-metal layers followed by a lift-off processing step, the substrate was thinned. Backside processing was finished by depositing the n-contact metallization. The laser resonator consists of a 500 µm long RW section followed by a tapered section with a length of 2000 µm (Fig. 3.12). The rear facet is HR-coated with a reflectivity of 97% while the output facet was AR-coated with a reflectivity of 1%. The devices were finally mounted junction-side-down

Figure 3.12.

Schematic drawing of a gain guided tapered laser with ridge-waveguide design.

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on Au-coated copper heat sinks using In solder. The device is uniformly pumped through evenly spread bond wires. In Fig. 3.13a, the CW output power versus current characteristic recorded at a heat sink temperature of 20 C, is shown together with the corresponding power conversion efficiency. The threshold current is 0.6 A and the initial slope efficiency amounts to 0.25 W/A, leading to a differential quantum efficiency of 39%. The maximum output power equals 1.54 W at a current of 9 A. The maximum power conversion efficiency approaches 18% at 2.5 A. From Rth = dT/dPloss , we determined the thermal resistance Rth of the devices to be 6 K/W. To show the enormous potential of these lasers when thermal limitations were overcome, we also performed pulsed measurements with 10 µs pulses at 250 Hz repetition rate (0.25% duty cycle) (Fig. 3.13b). Under these conditions, a maximum peak power of 5 W is reached at the maximum available current of 30 A, still limited by the onset of thermal roll-over rather than by COMD. The beam quality parameter M2 as well as the brightness are plotted against CW output power in Fig. 3.14a. M2 was measured according to ISO 11146 and is calculated with the common 1/e2 cut method. In the whole power range, the tapered diode laser shows a nearly diffraction-limited behavior corresponding to a M2 value well below 1.7; i.e., the device shows nearly diffraction-limited behavior up to a record value of 1.5 W, corresponding to a maximum brightness of 32 MW/cm2 sr, which is over an order of magnitude higher than for the RWlaser in Sect. 3.4. Also shown in Fig. 3.14a is the intensity profile recorded in the beam waist when performing the M2 measurement at a CW power level of 1.5 W. Comparing this profile with a Gaussian beam one can estimate the power in the central lobe at a given power level. The present device reaches 1.3 W (88% of total power) in the central lobe which again confirms the good beam quality of these devices.

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Figure 3.15. Color-coded lasing spectra for (a) constant pulsed current in the tapered section and variable CW current in the RW-section and (b) constant CW current in the RW-section and variable pulsed current in the tapered section [58].

An important phenomenon occurring in tapered diode lasers is the astigmatism. The source-point in fast axis orientation is located at the output facet whereas in slow axis direction this point lies inside the tapered diode laser. The distance between these two source-points is called astigmatism and is in general current and temperature dependent. In Fig. 3.14b, the measured astigmatism is plotted against the CW operation current at a heat sink temperature of 20 C. Up to a maximum CW current of 6 A, the focal point shifts away from the facets by 160 µm, corresponding to a change of 22% relative to the astigmatism near threshold.


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Figure 4.1. (a) Schematic OPSDL set-up: The laser cavity is formed by a distributed Bragg reflector integrated in the OPSDL chip and an external out-coupling mirror. A pump laser is focused on the chip surface yielding a pump spot typically 50–500 µm in diameter. (b) Maximal CW output powers vs. emission wavelength, for direct OPSDL emission and for wavelengths emitted via second harmonic generation (SHG). Data were taken from Ref. 63,64,71,73 and 81–83.

Another interesting feature of the above tapered laser approach is the possibility to contact the RW section and the tapered section separately, including applying current pulses to one of the two sections [58]. That way the lasing wavelength of a tapered diode laser can be controlled by the current injected into the RW section, while the total power output is adjusted separately by the current supplied to the tapered section (see Fig. 3.15) [58]. With this setup, a high brightness seed- or pump-source for solid state lasers or rare earth doped fiber amplifiers can be realized, which combine a stable lasing spectra with an adjustable output power. 4. GaSb-based optically pumped semiconductor disk lasers 4.1. INTRODUCTION

Optically pumped semiconductor disk lasers (OPSDLs), also referred to as vertical-external-cavity surface-emitting lasers (VECSELs), have emerged recently as a new category of semiconductor lasers [59, 60]. As can be seen from Fig. 4.1 (a), the overall layout of an OPSDL is similar to that of a classical optically pumped solid-state disk laser, with the solid-state gain medium being replaced by a semiconductor chip. The OPSDL concept has been shown to be capable of multiple-Watt output powers [63, 64] and laser emission in circular, nearly diffraction-limited beams even at high power levels [59, 60]; the combination of these properties is in general not achievable using conventional edge-emitting diode lasers described in the

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preceding sections. Thus, an OPSDL combines the advantages of semiconductor lasers (efficiency, wavelength versatility) with those of a conventional solid-state laser (simultaneously high beam quality and output power). Using additional intra-cavity optical elements, further functionalities such as passive mode-locking [65], wavelength tunability [66], single-longitudinal mode operation [72] or second harmonic generation [64] have been demonstrated recently. Research activities in this class of lasers are predominantly focused on AlGaAs/GaInAs/GaAs-based devices emitting at wavelengths in the 0.8–1 µm range where the highest output powers have been realized so far (Fig. 4.1 (b)). Heading towards longer wavelengths, the output powers of GaInNAs-, and GaInAsP-based OPSDLs drop off rapidly [71, 72]. At wavelengths above 2 µm, there have been only few reports so far on OPSDLs [73, 74]. The output power of these GaSb-based lasers was limited to the several mW range, mainly as a result of premature thermal roll-over due to device overheating. Because of strong molecular absorption lines in this spectral range, these tunable, single-frequency devices are useful for intra-cavity gas absorption spectroscopy where such low output powers are deemed to be sufficient. However, there is a demand for high-brightness 2.X µm laser sources, intended for the applications mentioned in Chapter 1. In the following sections, concepts to realize high-performance long-wavelength OPSDLs are presented and laser operation results are shown for GaSb-based devices emitting in the 2.3 µm wavelength range. 4.2. EPITAXIAL LAYER STRUCTURE AND SAMPLE CHARACTERIZATION

An OPSDL chip is composed of an epitaxially grown distributed Bragg reflector (DBR) of high reflectivity (R>99%) acting as cavity mirror and an active region where the laser radiation is generated. The active region itself consists of a number of quantum wells that are embedded between thick barrier layers having a higher band gap energy and usually serving also as pump absorbing layers (“barrier pumping”). For a low laser threshold, the active region is designed as a resonant periodic gain (RPG) structure [61, 62], i.e. with the quantum wells being positioned in the antinodes of the standing-wave-type laser intensity distribution that is formed in the cavity (see Fig. 4.2 (a)). On top of the active region, a window layer of high-band gap material is grown to prevent non-radiative carrier recombination at the top surface. (AlGaIn)(AsSb)-based OPSDL structures are typically grown by molecular beam epitaxy (MBE) on GaSb substrates [73, 75]. Due to the large design wavelengths, the total epitaxial layer structure thicknesses are in the 10–12 µm range which is challenging but can be mastered by state-of-the-art MBE technology. Post-growth processing, such as lateral structuring and contact metallization, is in general not necessary.


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Figure 4.2. (a) Solid lines: Calculated band energy profiles of conduction band (CB) and valence band (VB) of a GaSb-based OPSDL structure, displayed in growth direction. Dotted line: Simulated optical intensity at the microcavity resonance wavelength. (b) Solid line: reflectivity spectrum of an OPSDL structure recorded at an incidence angle of 10◦ . Dashed line: room temperature PL spectrum taken from the cleaved facet of the OPSDL chip.

For structural characterization, the reflectivity spectrum of an OPSDL structure is recorded, as depicted in Fig. 4.2 (b). The spectrum of this structure exhibits a nearly rectangular DBR high-reflectivity band between 2.2 and 2.45 µm, interrupted by a strong dip at 2.29 µm. The dip arises from absorption within the quantum wells that is enhanced by a microcavity resonance. Laser emission eventually occurs at the resonance wavelength (cf. Fig. 4.3 (b)). As second characterization method, the sample’s photoluminescence (PL) spectrum is measured. The PL spectrum basically reflects the intrinsic quantum well gain spectrum. Under typical lasing conditions, the gain maximum should match the microcavity resonance and thus the laser emission wavelength [76]. As can be seen from Fig. 4.2 (b), the PL peak is directly located at the resonance position which is a precondition for a good laser performance. 4.3. THERMAL MANAGEMENT

By absorption of the incident pump photons, a significant amount of heat is generated in the active region counteracting stable OPSDL operation without appropriate heat sinking. Consequences are a premature thermal roll-over [75] and the risk of sample damages even at moderate pump power levels. Thermal simulations have shown that for GaSb-based OPSDLs the insertion of an intra-cavity heat spreader is an efficient means for heat removal from the active region [67]. Using the liquid capillary bonding technique [78], transparent heat spreaders can be bonded to the chip’s top surface in close proximity to the active region where the heat is generated without any absorbing glue or soldering layer. Due to its outstanding thermal and optical properties, the heat spreader material

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of choice is in general single-crystalline diamond [71, 72]. Recent work on GaSb-based OPSDLs [75, 76] has evidenced that polycrystalline chemical vapor deposition (CVD) diamond [79] can also be used as intra-cavity heat spreader material, representing a lower-cost alternative to single-crystalline diamond. 4.4. OPSDL DEVICE PERFORMANCE

A typical 2.X µm OPSDL setup consists of a diamond-bonded OPSDL chip placed at the end of a plan-concave linear resonator (Fig. 4.1) about 49–50 mm in length (external mirror curvature: −50 mm). A Nd:YAG pump laser emitting at 1.064 µm served as pump source, focused to a slightly elliptical spot 50–150 µm in diameter, depending on alignment. In this configuration, lasing threshold is reached at typical pump power densities of 730–1000 W/cm2 for out-coupling rates between 0.6 and 2.5% [75]. In Fig. 4.3 (a), temperature-dependent CW power transfer characteristics of the OPSDL at 3.6% out-coupling are shown. At a heatsink temperature of −20◦ C, a pump-power limited output power of 1.5 W was reached at a slope efficiency of 17%. The CW output power at 10◦ C still exceeds 1 W. For these high-power measurements, the resonator has been aligned for optimal overlap between pump spot and the cavity mode on the chip, yielding a beam propagation factor of M 2 ≈ 3 at maximum output power. Typical CW output powers of GaSb-based OPSDLs not utilizing a diamond heat spreader are in the several mW range [73, 75], which evidences the efficient heat extraction from the OPSDL active region by means of the diamond heat spreader. A further increase in OPSDL output power is expected using higher pump powers and higher out-coupling rates. Fig. 4.3 (b) shows the emission spectrum of the diamond-bonded laser. Peak emission wavelength is 2.295 µm. As an intra-cavity etalon is formed by the

Figure 4.3. (a) CW output power vs. absorbed pump power of a diamond-bonded OPSDL for several heat sink temperatures. (b) CW emission spectrum of the diamond-bonded OPSDL (heat sink temperature: 10◦ C) at an absorbed pump power of 1 W.


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0.25 mm-thick uncoated diamond heat spreader, several longitudinal modes with a separation corresponding to the free spectral range of the etalon are activated. Using a thinner diamond heat spreader with a larger mode separation may enforce single-longitudinal mode operation, as already demonstrated at shorter emission wavelengths [72]. As already stated in section 4.1, OPSDLs are in general capable of emission in circular symmetric beams with beam qualities close to the diffraction limit. This has also been verified for GaSb-based OPSDLs where by an appropriate resonator alignment laser emission in a pure TEM00 mode was obtained [76]. The M 2 values determined in this configuration were 1.05 (measured at 1/e2 beam intensity) and 1.13 (at the second moment beam width), both values being very close to the diffraction limit of an ideal Gaussian beam. Typically, the output power in singletransverse mode configuration is somewhat lower than the maximal achievable output power [59]. For the present 2.X µm OPSDL, the maximal TEM00 mode output power is in the order of 70% of Pmax . 4.5. IN-WELL OPTICAL PUMPING

The OPSDLs described in the previous sections of this chapter were so-called barrier-pumped devices, i.e. with the incident pump radiation mainly being absorbed in the barrier layers of the active region. The advantages of this optical pumping scheme are 1) strong pump absorption in the barrier layers due to large total barrier thicknesses and 2) insensitivity to the pump wavelength, unless the pump photon energy is below the barrier band gap energy. On the other hand, a disadvantage of this approach is a large mismatch between the pump photon and the emitted photon energy (also referred to as “quantum deficit”), which exceeds 50% for the GaSb-based OPSDLs discussed above (see Fig. 4.4 (a)) [73,76]. Such a large quantum deficit represents a major limitation to the overall OPSDL power efficiency. This energy difference can be significantly reduced by employing the “in-well” pumping concept. Here, the pump photon energy is chosen very close to the energy of the emitted photons, resulting in the absorption of the pump photons directly in the quantum wells rather than in the barrier layers (Fig. 4.4 (b)). In-well pumping of an OPSDL has been demonstrated first for an AlGaAs/GaAs-based laser emitting at 850 nm, which was pumped at 808 nm [68]. This device suffered from a low pump absorption of 14% since the total thickness of the absorbing quantum wells was as low as 100 nm and the incident pump light passed the quantum wells just once. A much larger pump absorption of 70% was achieved in a subsequent experiment for an in-well pumped GaInAs/GaAs-based OPSDL emitting at 980 nm [69, 70]. The high pump absorption was achieved by pumping into a microcavity resonance of the OPSDL chip. Since the microcavity modes shift towards shorter wavelengths with increasing incidence angle [69, 70], the

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Figure 4.4. Band edge profile in conduction band (CB) and heavy hole band (HH) of a GaInAsSb quantum well designed for emission at 2.35 µm. (a) Barrier pumping: electron-hole pairs are generated by pump absorption (pump wavelength: 1.064 µm) in the barrier layers and recombine via photon emission in the quantum well. (b) In-well pumping: electron-hole pairs are generated directly in the quantum well by absorption of long-wavelength pump light (pump wavelength: 1.94 µm). In contrast to barrier pumping, the quantum deficit is considerably reduced.

laser resonance itself could be used for enhancing the pump light absorption when pumping at 940 nm at a large external angle of incidence. Compared to barrierpumping the same OPSDL at 800 nm, the slope efficiency and the output power under in-well pumping could be nearly doubled. The approach of resonant in-well pumping has recently been adapted also for a GaSb-based 2.35 µm OPSDL [77]. Due to a very low quantum well absorption coefficient at wavelengths close to the emission wavelength, a pump wavelength of 1.9–2.0 µm was chosen yielding a quantum deficit of 18%. Since pump and emission wavelength are separated by ∼400 nm from each other, the laser resonance itself cannot be used for resonant pump absorption. Instead, a more complex epitaxial layer structure exhibiting two separate resonances with two associated DBR high reflectivity bands was employed (Fig. 4.5). That way, the pump wavelength can be chosen independent of the laser emission wavelength. Despite of a low single-pass pump absorption of 2.5 µm. Semicond. Sci. Technol. 19, 655 (2004).


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32. M. Rattunde, E. Geerlings, J. Schmitz, G. Kaufel, J. Weber, M. Mikulla and J. Wagner: GaSbbased 1.9-2.4 µm quantum-well diode lasers with low beam divergence. Proc. SPIE 5738, 138 (2005) 33. W. Li, J.B. Héroux, H. Shao, W.I. Wang : Strain-compensated InGaAsSb/AlGaAsSb midinfrared quantum-well lasers. Appl. Phys. Lett. 84, 2016 (2004) 34. E.A. Pease, L.R. Dawson, L.G. Vaughn, P. Rotella, L.F. Lester: 2.5–3.5 µm optically pumped GaInSb/AlGaInSb multiple quantum well lasers grown on AlInSb metamorphic buffer layers. J. Appl. Phys. 93, 3177 (2003). 35. D. Garbuzov, M. Maiorov, H. Lee, V. Khalfin, R. Martinelli, J. Connolly: Temperature dependence of continuous wave threshold current for 2.3–2.6 µm InGaAsSb/AlGaAsSb separate confinement heterostructure quantum well semiconductor diode lasers. Appl. Phys. Lett. 74, 2990 (1999) 36. G. Turner, H. Choi, M. Manfra: Ultralow-threshold (50 A/cm2 ) strained single-quantum-well GaInAsSb/AlGaAsSb lasers emitting at 2.05 µm. Appl. Phys. Lett. 72, 876 (1998) 37. J.G. Kim, L. Shterengas, R.U. Martinelli, G.L. Belenky, D.Z. Garbuzov, W.K. Chan : Roomtemperature 2.5 µm InGaAsSb/AlGaAsSb diode lasers emitting 1 W continuous wave. Appl. Phys. Lett. 81, 3146 (2002) 38. J.G. Kim, L. Shterengas, R.U. Martinelli, G.L. Belenky: High-power room-temperature continuous wave operation of 2.7 and 2.8 µm In(Al)GaAsSb/GaSb diode lasers. Appl. Phys. Lett. 83, 1926 (2003) 39. D. Garbuzov, R. Martinelli, H. Lee, R. Menna, P. York, L. DiMarco, M. Harvey, R. Matarese, S. Narayan and J. Connolly: 4W quasi-continous wave output power from 2 µm AlGaAsSb/InGaAsSb single quantum well broadened waveguide laser diodes. Appl. Phys. Lett. 70, 2931 (1997) 40. A. Salhi, Y. Rouillard, A. Pérona, P. Grech, M. Garcia, C. Sitori: Low-threshold GaInAsSb/AlGaAsSb quantum well laser diodes emitting near 2.3 µm. Semicond. Sci. Technol. 19, 260 (2004) 41. A. Salhi, Y. Rouillard, J. Angellier, P. Grech and A. Vicet: 2.61 µm GaInAsSb/AlGaAsSb type I quantum well laser diodes with low threshold. Electron. Lett. 40, 424 (2004) 42. M. Rattunde, C. Mermelstein, J. Schmitz, R. Kiefer, W. Pletschen, M. Walther and J. Wagner: Comprehensive modelling of the electro-optical-thermal behavior of (AlGaIn)(AsSb)-based 2 µm diode lasers, Appl. Phys. Lett. 80, 4085 (2002) 43. D.Z. Garbuzov, R.U. Martinelli, H. Lee, P.K. York, R.J. Menna, J.C. Connolly, S.Y. Narayan: Ultralow-loss broadened-waveguide high-power 2 µm AlGaAsSb/InGaAsSb/GaSb separateconfinement quantum-well lasers. Appl. Phys. Lett. 69, 2006 (1996) 44. M. Rattunde, J.Schmitz, R.Kiefer and J. Wagner: Comprehensive analysis of the internal losses in 2.0 µm (AlGaIn)(AsSb) quantum-well diode lasers, Appl. Phys. Lett 84, 4750 (2004) 45. G. Belenky, J. Kim, L. Shterengas, A. Gourevitch, and R. Martinelli: High-power 2.3 µm laser array emitting 10 W CW at room temperature, Electron. Lett. 40, 737, (2004). 46. C. Mermelstein, M. Rattunde, J. Schmitz, S. Simanowski, R. Kiefer, M. Walther and J. Wagner: Sb-based mid infrared diode lasers, Mat. Res. Sic. Proc. 692, 365 (2002) 47. H. Choi, G. Turner, J. Walpole, M. Manfra, and M. Connors: Low-Threshold, high-power, highbrightness GaInAsSb/AlGaAsSb quantum-well lasers emitting at 2.05 µm, Proc. SPIE 3284, 268 (1998).

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48. M. Rattunde, J. Schmitz, G. Kaufel, M. Kelemen, J. Weber, and J. Wagner: GaSb-based 2.X µm quantum-well diode-lasers with low beam divergence and high output power, Appl. Phys. Lett. 88, 081115 (2006) 49. M. Rattunde, J. Schmitz, G. Kaufel and J. Wagner, to be published in IEEE Photon. Technol. Lett. 50. L. Shterengas, G. L. Belenky, A. Gourevitch, D. Donetsky, J. G. Kim, R. U. Martinelli, D. Westerfeld, High-Power 2.3-µm GaSb-Based Linear Laser Array, IEEE Photon. Techn. Lett., Vol. 16, no. 10, pp. 2218–2220, 2004 51. M. T. Kelemen, J. Weber, M. Rattunde, C. Pfahler, G. Kaufel, R. Moritz, C. Manz, M. Mikulla, and J. Wagner, High-power diode laser arrays at 2 µm for materials processing, Proc. LIM 2005, Munich, pp. 713–718, 2005 52. J. N. Walpole, “Semiconductor amplifiers and lasers with tapered gain regions,” Opt. Quantum Electron., vol. 28, pp. 623–645, 1996 53. H. K. Choi, J. N. Walpole, G. W. Turner, S. J. Eglash, L. J. Missaggia, and M. K. Connors, “GaInAsSb-AlGaAsSb tapered lasers emitting at 2 µm,” IEEE Photon. Technol. Lett., vol. 5, no. 10, pp. 1117–1119, 1993 54. H. K. Choi, J. N.Walpole, G.W. Turner,M. K. Connors, L. J. Missaggia, and M. J. Manfra, “GaInAsSb-AlGaAsSb tapered lasers emitting at 2.05 µm with 0.6-W diffraction-limited power,” IEEE Photon. Technol. Lett., vol. 10, no. 7, pp. 938–940, 1998 55. K. Boucke, J. Rogg, M. T. Kelemen, R. Poprawe, and G. Weimann, “Numerical simulations of novel high-power high-brightness diode laser structures”, Proc. SPIE 4283, p. 586, 2001 56. M. Kelemen, J. Weber, M. Rattunde, G. Kaufel, J. Schmitz, R. Moritz, M. Mikulla and J. Wagner, High-power 1.9 µm diode laser arrays with reduced far-field angle, IEEE Photon. Technol. Lett. 18, 628 (2006) 57. C. Pfahler, G. Kaufel, M. T. Kelemen, M. Mikulla, M. Rattunde, J. Schmitz, and J. Wagner, GaSb-based Tapered Diode lasers at 1.93 µm with 1.5 W Nearly Diffraction Limited Power, IEEE Photon. Technol. Lett. 18, 758–760 (2006) 58. C. Pfahler, M. Eichhorn, M. Kelemen, G. Kaufel, M. Mikulla, J. Schmitz and J. Wagner, Gain saturation and high-power pulsed opaeration of GaSb-based tabered diode lasers with separately contacted ridge and tapered section, Appl. Phys. Lett. 89, 021107 (2006) 59. M. Kuznetsov, F. Hakimi, R. Spraque, and A. Mooradian, High-Power (>0.5-W CW) Diode-Pumped Vertical-External-Cavity Surface-Emitting Semiconductor Lasers with Circular TEM00 Beams, IEEE Photon. Technol. Lett. 9, 1063–1065 (1997). 60. M. Kuznetsov, F. Hakimi, R. Spraque, and A. Mooradian, Design and Characteristics of High-Power (>0.5-W CW) Diode-Pumped Vertical-External-Cavity Surface-Emitting Semiconductor Lasers with Circular TEM00 Beams, IEEE J. Sel. Top. Quantum Electron. 5, 561–573 (1999). 61. M. Raja, S. Brueck, M. Osinski, C. Schaus, J. McInerney, T. Brennan, and B. Hammons, Resonant Periodic Gain Surface-Emitting Semiconductor Lasers, IEEE J. Quantum Electron. 25, 1500–1512 (1989). 62. S. W. Corzine, R. S. Geels, J. W. Scott, R.-H. Yan, and L. A. Coldren, Design of Fabry-Perot Surface-Emitting Lasers with a Periodic Gain Structure, IEEE J. Quantum Electron. 25, 1513– 1524 (1989).


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BROADBAND MID-INFRARED SOLID-STATE LASERS Broadband Mid-Infrared Lasers IRINA T. SOROKINA Photonics Institute, Vienna University of Technology e-mail: [email protected] also with Department of Physics, Norwegian University of Science and Technology e-mail: [email protected]

Abstract. A survey of broadband Co2+ - and Cr2+ -based lasers is presented. These mid-IR sources, operating in the very interesting “molecular fingerprint” region between ∼1.6 and 3.5 µm offer the broadest bandwidth from all solid-state vibronic lasers. The emphasize is made on Cr2+ -doped lasers, which have not only the widest and the highest gain, but also operate at room-temperature and produce the shortest pulses of only several optical cycles around 2.5 µm directly from the resonator. Ten years after their invention, Cr2+ -doped lasers have come of age and emerge in applications, demanding high power and extreme bandwidth. The paper reviews advances in the existing and novel Cr2+ -based lasers, such as mixed Cr2+ :ZnSx Se1−x , Cr2+ :CdMnTe and Cr2+ :CdZnTe lasers, which are likely to extend these features even further, and briefly describes a number of novel and yet upcoming applications. The first steps towards electrically pumped nanocrystalline lasers are described and the underlying physics is outlined. Keywords: Transition metal doped II-VI; Cr2+ :ZnSe; Cr2+ :ZnS; Cr2+ :CdSe; tunable mid-infrared lasers; ultrashort-pulsed mid-infrared lasers; mid-infrared random lasers.

1. Introduction 1.1. MOTIVATION

The big advantage of crystalline solid-state lasers is their ability to generate the widest among known modern lasers spectra directly from the resonator. The ultimately broad bandwidth can be achieved either in color-center lasers (otherwise called F-center lasers) or in transition metal ion doped lasers. However, the main drawbacks of the first group of sources include the use of insulating vacuum, and the necessity of cryogenic cooling, especially in the mid-infrared region. In the seventies and eighties the F-center lasers, including commercial ones, have found a widespread use in various applications, especially in high-resolution spectroscopy requiring high spectral or temporal resolution, and in frequency standards. However, with the rapid progress in the last decade in room-temperature 225 M. Ebrahim-Zadeh and I. T. Sorokina (eds.), Mid-Infrared Coherent Sources and Applications, 225–260. c 2008 Springer.

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ion-doped crystalline lasers the F-center lasers lost their practical meaning. For this reason we will concentrate in this chapter on transition-metal ion doped crystalline lasers with the special emphasize on chromium doped II-VI compound based lasers as the most successful room-temperature diode-pumpable sources in the wave-length range between ∼2 and ∼3.5 µm. The mid-infrared (mid-IR) wavelength range, which is also often called a “molecular fingerprint” region, and in particular, the range between 2 and 5 µm is characterized by the presence of the strong fundamental and overtone vibrational absorption lines of atmospheric constituents, vapours and other gases. Those include, e.g.: water vapour (H2 O), filling the whole range between 2.5 and 3 µm with maximum around 2.7 µm, carbon monoxide (CO) with strong features around 2.3–2.4 µm, carbon dioxide (CO2 ) absorbing around 2.7–2.8 µm, nitrous oxide (N2 O), having several absorption features all through 2–4 µm range, as well as many other species. The ability of broadband solid-state lasers to spectrally cover in a single shot or by rapidly tuning the laser the widest wavelength range, containing all the above molecular absorption lines, is the main advantage of these compact and user friendly coherent sources. Detection of low concentrations of these and other molecules, constituting air pollutants or green-house gases for the purpose of environmental diagnostics or even the human breath for the purpose of medical diagnostics is currently done using laser systems, which are based mainly on nonlinear optical conversion techniques and include optical parametric oscillators (OPO) and difference frequency generators. OPO is almost an ideal solution, but rather complex and costly. Another possibility would be to employ semiconductor lasers, including heterojunction lasers, lead-salt, antimonite and quantum cascade lasers (QCL), which are probably the simplest and the most cost effective sources in the Mid-IR wavelength region. However, they provide narrow tuning ranges (compare ∼140 cm−1 tuning range of a quantum cascade laser and ∼1800 cm−1 tuning range of a Cr:ZnSe laser) and limited output power levels at room temperature. Besides, even at cryotemperatures the QCLs operate so far only above 3.4 µm, and this hurdle is not going to be overtaken easily in the near future [1]. The crystalline solid-state lasers [2], on the other hand, which operate at room-temperature and have the largest relative bandwidth of ∼45% of the central wavelength of the laser, can provide very high power levels retaining the good beam quality and narrow spectral linewidth at the wide tuning range. In combination with near-infrared diode lasers as pump sources these lasers can offer stability, efficiency and compactness as well as the broad spectral coverage and tuning ranges, which are generally inaccessible for semiconductor lasers. 1.2. APPLICATIONS

For femtochemistry, molecular time-resolved measurements, molecular spectroscopy, trace gas analysis, biomedical applications, etc. one should directly

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Biological tissue absorption due to water content

1000

1

10

Cr:ZnSe tuning range (2.0-3.1µm)

100

100 aminesN-H

Penetration depth (µm)

Tissue absorption (cm−1)

10000

hydroxylO-H 10

1000 2.0

2.5

3.0

3.5

Wavelength (µm) Figure 1. Typical absorption and penetration depth of the biological tissue, as well as the typical absorption ranges of some important radicals.

reach molecular frequencies. Mid-IR tunable and femtosecond sources are required, which would possess sufficient bandwidth and have a good spatial coherence (preferably TEM00 mode), be low-cost, compact, directly diodepumpable. Availability, since recently, of the room-temperature diode-pumped broadband tunable solid-state lasers as simple and compact alternative to semiconductor lasers and nonlinear optical frequency conversion devices in this wavelength region is a significant step forward in remote sensing and trace gas detection (for details see Chapter 3.5), as well as in other medical applications (Chapter 3.6). Indeed, as it can be seen in Fig. 1, biological tissue has a maximum of absorption around ∼2.9 µm mostly due to the water content. Therefore, such medical applications as ophthalmology, tissue cutting and welding, neurosurgery, dermatology and bioimaging would benefit from broadband and rapidly tunable coherent sources in this wavelength region. For further details on these applications the reader is referred to Chapter 3.6. The ultrabroad gain bandwidth of some laser crystals allows generation of the ultimately short pulses of only few optical cycles. Such pulses, especially in the mid-infrared range are unique diagnostic tools for numerous transient processes on the femtosecond scale. These lasers are also attractive for such applications as MIR free-space communications, optical frequency standards as well as optical coherence tomography (OCT).

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2. Bandwidth and wavelength scaling rules In this section we will analyse implications of the large band-width and the long operation wavelenght on the laser properties of continuous-wave tunable, as well as femtosecond lasers. First of all, we must clearly define the notion of bandwidth. The gain bandwidth is one of the most important characteristics, determining the ability of the laser material to be tuned and to produce short pulses. Generally speaking, the laser transitions in the mid-infrared tend to be broadband. Indeed, the widths of the individual states (in energy units) are determined by the particular crystal-lattice interaction and inhomogeneous broadening, which are characteristic for the given ion and host. The transition bandwidth hν (in energy units) is then the sum of the widths of the transitions between the upper and lower states. Since the transition energy hν is inversely proportional to the wavelength, the relative bandwidth of the transition ν/ν = λ/λ increases towards the infrared. To provide the fair comparison of the bandwidth of the materials the spectra are plotted in the semi-logarithmic scale, keeping λ/λ constant. Central wavelength also dramatically influences the laser threshold. In Ref. [2] the following scaling rule for the required pump intensity at threshold could be obtained: 1 λ n 2 1 Ith ∝ , (1) F O M η Q E λ0 λ40 where η Q E is the quantum yield of the transition, defined as: τ ηQ E = (2) τrad and FOM (figure of merit) is the ratio of absorption coefficients at the pump wavelength and at the lasing wavelength. One important conclusion, arising from the formula, is that the threshold power density scales with the bandwidth. This explains the relatively high threshold, characteristic for the broadband materials. Only the progress in the pump sources, when the laser pumping became available, made the laser action of the broadband materials possible. As a result, the first Argon-laser pumped tunable Ti:sapphire appeared [3, 4], followed by a number of exciting developments in the femtosecond pulse generation [5–8]. Nowdays there exists only a limited number of directly diode-pumped broadband solid-state lasers. The materials, which proved to be easily diode-pumpable, include (in the order of increasing wavelength): Cr:LiSAF [9] and Cr:LiSGaF [10, 11], Cr:YAG [OLCrYAG], and since recently also Cr:ZnSe [13] and Cr:ZnS [14]. The further analysis of the formula (2) shows that there is a factor λ4 in the denominator, which effectively decreases the threshold for the longer wavelength transitions. For the mid-infrared this is a very encouraging factor. Provided that the active material has a high FOM and a high quantum yield (like it is the case in e.g., Cr:ZnSe) this makes direct diode-pumping in the mid-IR feasible. To get a feeling


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of what difference the λ−4 factor can produce, compare e.g. the otherwise quite similar Ti:sapphire (λ0 = 780 nm) and Cr:ZnSe (λ0 = 2450 nm): the threshold intensity differs by two orders of magnitude! Therefore, the direct diode-pumping of Ti:sapphire will remain a challenge even if high-power blue-green laser diodes become available. This makes any nonlinear-optical conversion systems based on Ti:sapphire laser more expensive and costly than the mentioned above directly diode-pumped lasers. What concerns the ultrashort pulse generation, the first three mentioned lasers generate pulses as short as five optical cycle pulses, whereas Cr:ZnSe generates so far down to 10 optical cycles [15, 16] with a good outlook to match Ti.sapphire in generation of single optical cycle pulses. With recent progress in ultrashort-pulse generation from the Cr:ZnSe laser (for details see the following Section of this Chapter), which allowed for the first time the generation of ultraintense light pulses comprising merely several electric field oscillation cycles at 2.5 µm wavelength, new applications start to appear. For example, long wavelength ultrashort pulses can prove to be beneficial for XUV and X-Ray generation in comparison to near-infrared ultrashort pulses from Ti:sapphire. The detailed analysis of this phenomenon is given in Chapter 3.7. Here we will give only a brief explanation of the physics involved. Consider a schematic diagram of a high-harmonic generation (Fig. 2). Indeed, the arising intensity gradient of the ultrashort pulse propagating through some noble gas allows electrons to survive in their bound atomic state up to external field strengths a few times higher than the binding Coulomb field and gives rise to ionization rates comparable to the light frequency. After ionization in a high field of an ultrashort pulse (Fig. 2a) an electron is torn apart from the nucleous and then ruturns back after a half-cycle, having acquired the ponderomotive energy U p from the light field. For a given light field this energy has a certain maximum, which defines a cut-off wavelength for high-harmonic generation process (Fig. 2b). The cut-off energy is given by the following formula: e2 E 2 Ipeak λ2 (3) (h¯ ω)cut−off = Wb + Up = Wb + 3.17 4mω2

Figure 2. Illustration of a typical high-harmonic generation. (adopted from Ref. [17])

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where the field frequency is in the denominator. We thus see, that by the given peak intensity, which is limited by the full ionization, the cut-off energy scales as λ2 ! It should not be forgotten, that the pulse width also scales with the wavelength: τpulse =

const λ2 λ = const · ∝λ· ν λ λ

(4)

so that the pulse duration is proportional to the wavelength and the number of optical cycles of the electric field of the pulse. We can therefore rewrite the cut-off energy using the pulse energy flux J in the following form: (h¯ ω)cut−off

Jpulse 2 λ ∝ Jpulse · λ τpulse

(5)

Thus, to reach a given cut-off frequency using a mid-infrared driving source we would need less energy in the pulse. As an illustrative example, when moving from 800 nm wavelength of a Ti:sapphire laser to 2.5 µm wavelength of a Cr:ZnSe laser we need to apply about an order of magnitude lower pulse intensities, or a few times lower pulse energies. Thus, a compact table-top femtosecond Cr:ZnSe laser can do the same job as the currently used more powerful, and therefore more complex Ti:sapphire laser system. In other words, size and cost of the femtosecond laser system scales as λ−1 ! 3. TM2+ -based solid-state lasers 3.1. HISTORICAL PERSPECTIVE AND STATE-OF-THE-ART SOURCES

Historically, the first tunable continuous-wave solid-state lasers were those based on the divalent 3d transition-metal ions (TM2+ ). It should be noted that the existing TM2+ -ions, lasing on the 3d-3d transitions in the mid-IR, can be divided into two major groups: those ions, which occupy octahedral sites (like e.g. Ni2+ and Co2+ in halides), and those, which can be found in tetrahedral positions (like e.g. Cr2+ , Fe2+ , Ni2+ and Co2+ in chalcogenides). The electric-dipole transitions of the ions in octahedral sites (possessing inversion symmetry) are parity forbidden and have therefore generally low oscillator strength and long lifetime. The ions in the tetrahedral sites, lacking inversion symmetry, are characterized by the high oscillator strength and short lifetime. The other distinguishing feature of the TM2+ -ions in tetrahedral sites is the relatively low crystal-field splittings, placing optical transitions further into the infrared. Broadband transition-metal ion doped solid-state lasers are being frequently used as a constituent driving part of the optical parametric devices. At the same time they represent an attractive and simple alternative to these somewhat more

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Emission cross-sect. (a. u.)

BROADBAND MID-INFRARED LASERS Co:MgF2

Cr:CdSe

Cr:ZnSSe Cr:ZnSe

1500

2000

2500 Wavelength (nm)

Cr:ZnS 3000

3500

Figure 3. Gain curves of the existing ultrabroadband mid-infrared lasers at room temperature.

complex and costly devices in the mid-infrared. Indeed, only this type of lasers allows tuning ranges reaching ∼0.5 λ0 and few optical cycle pulses. In the recent years along with the Ti:sapphire based lasers systems, parametrically converting radiation to the mid-infrared, a lot of attention of researchers was devoted towards the alternative compact and cost effective continuous-wave and ultrashort pulsed sources based on Cr2+ -doped crystals of the II-VI family. In the last decade a number of such sources have been developed in the “molecular fingerprint” range between ∼2 and 3.5 µm (Fig. 3). The first really ultrabroadband laser was a Co2+ :MgF2 laser, which could be tuned between 1.75 and 2.16 µm as early as 1964 [18]. The necessity for cryogenic cooling hindered commercial development of this device. Further advent of the laser pumping allowed tight focusing of the pump beam into the laser medium and therefore partially compensated for the low emission-cross section. Using laser pumping and cryogenic cooling, CW operation has been achieved in Co2+ as well as in Ni2+ -doped MgF2 [19,20]. Later also the pulsed room-temperature operation has been achieved [21]. The active mode-locking of Co2+ :MgF2 laser was demonstrated in Ref. [22]. With the rapid development of the cryogenic cooling technique in the last years one may expect the revival of interest towards this laser. At longer wavelengths (beyond 2 µm) the multiphonon relaxation processes set the fundamental limit for obtaining continuous-wave room-temperature laser operation from vibronic transitions. Because of this the majority of the known vibronically broadened laser transitions in the mid-infrared are quenched at room temperature. The major break-through in this respect came with the invention in the middle of nineties by the group of scientists at the Lawrence Livermore National Laboratory of the new class of transition-metal doped zinc chalcogenides [23–25]. Shortly afterwards similar families of transition-metal doped cadmium chalcogenides based on CdSe [26, 27] as well as on CdTe and compounds [28, 29] were proposed simultaneously by the other two groups. Since that time TM2+ -ions

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have been incorporated into several binary and ternary II-VI compounds, including ZnSe, ZnS, ZnTe, CdSe, CdS, Cd1− Mnx Te, Cd1−x Znx Te, ZnMgSe and ZnMgSeTe. In all these crystals TM2+ ions occupy low crystalline field tetrahedral sites coordinated by the heavy selenide, telluride or sulphide anions. The low maximum phonon frequency in chalcogenides (compare: 240 cm−1 in ZnSe and e.g. 850 cm−1 in YAG) leads to the decrease of the nonradiative decay rate and increase of the fluorescence quantum yield. At room-temperature the latter is close to unity in Cr:ZnSe and is comparably high in other chalcogenide materials. This provides Cr:ZnSe the highest gain among vibronic lasers and enables efficient room-temperature operation. It is not a surprise that in the following years Cr:ZnSe draw a lot of attention as a room-temperature broadly tunable continuous-wave (CW) laser operating around 2.5 µm [30–32], and since very recently also as a source of ultrashort pulses [15, 16]. Besides Cr2+ ion, Fe2+ was successfully used as a lasing ion in ZnSe (for references and details see Chapter 2.4). Availability of Cr2+ -based lasers in the infrared is therefore of primary importance for many applications, all of which can be found in the Part III of the present book. Consideration of TM2+ -doped lasers in this Section will be limited to Co2+ and Cr2+ -doped materials, with the emphasis on Cr2+ :ZnSe and Cr2+ :ZnS as materials providing superior laser performance so far. 3.2. Co:MgF2 LASER

Co2+ ions in octahedral sites have the 3d8 configuration. The free ion term 4 F splits into 4 T1 , 4 T2 , and 4 A2 levels with 4 T1 level being the ground state. The absorption bands resulting from the 4 T1 → 4 T2 transition around 8000 cm−1 and 4 T1 → 4 A2 transition around 18000 cm−1 [33] allow pumping with 1.32 µm Nd-laser and 514 nm Ar-laser correspondingly (Fig. 4). The large configurational coordinate offset of the upper laser level 4 T2 results in the broadband infrared luminescence spectrum (Fig. 5) ranging from 1.5 to over 2.3 µm and corresponding to the 4 T2 → 4 A2 transition. The unusually broad bandwidth is explained not only by the vibronic nature of the transition, but also by the fact that the ground state is split into six sublevels spread over 1300 cm−1 , each having an associated vibronic transition [18,34]. The corresponding zero-phonon lines lie between 1.47 and 1.85 µm. As a result, the luminescence spectrum is a sum of the six zerophonon lines and related sidebands, which can be clearly seen in Fig. 5a. ESA in the 4 T2 → 4 A2 and 4 T2 → 4 T1 transitions in Co2+ :MgF2 and Co2+ :ZnF2 have been found to reduce efficiency in laser operation of these crystals [35]. ESA also effectively decreases the gain cross-section and leads to a large saturation fluence of 100 J/cm2 [36]. It is also important to note that the main problem of Co2+ : MgF2 is the rapid decrease of the upper laser level lifetime with temperature (Fig. 6), which drops

233

BROADBAND MID-INFRARED LASERS 2

4

A1

3

2

T1 (e t2 4)

T2

2

T1

20

4

P

3 4 T2 (e t2 )

4

ESA

G

4

E/B

2

A 2 (e 4 t2 3 )

Laser

(a) 4

T2

4

F

Pump

10

4

2

T1

0

4

0

1

2

Dq/B

E T 1 (e 2t 25)

Figure 4. Tanabe-Sugano diagram for an octahedrally coordinated Co2+ ion (3d 7 configuration). Free-ion terms are shwn to the left. The excited-state absorption (ESA) transition is spin-allowed and affects the effective cross-sections and laser efficiency [2]. b)

Luminescence (a.u.)

a)

1400

1600

1800

2000

2200

Wavelength (nm)

Figure 5. a) Luminescence spectrum of Co2+ :MgF2 [37] at 77 K and b) the corresponding tuning curve [38].

Lifeteime (ms)

1

0.1

0

50

100

150

200

250

300

Temperature (K)

Figure 6.

Temperature dependence of the fluorescence lifetime of Co2+ :MgF2 [34].

234

IRINA T. SOROKINA

from 1.3 msec at 77 K down to 36 µsec at 300 K [34]. Similar lifetime behaviour has been reported for KMgF3 by Sturge [Sturge73] and is assumed to be caused by the increased rate of non-radiative decay due to multiphonon emission [34]. For this reason all these lasers need liquid-nitrogen cooling to maintain lifetimes in the millisecond range. The good news is that the thermal conductivity of Co2+ :MgF2 of 0.3 W/ (m · K), Mohs hardness of 6, and the negligibly small dn/dT [21] partially compensate the above mentioned deficiencies. This allows pumping at high power levels without deterioration of the output characteristics. Rines et al [36] could generate as much as 6.5 W of average output power in the pulsed regime at 2.05 µm with a repetition rate of 9 Hz and a pump energy of 2.7 J. Cryogenically cooled CW Co2+ : MgF2 laser exhibited high energy conversion efficiency of 31% at 1.3 µm, and high output power of 1 W at 1.86 µm [39]. Moulton demonstrated more than 4 W of output power in TEM00 mode at 1.92 µm in CW regime at 15 W of pump power [34]. No indication of output power saturation due to heating effects was observed. A few years ago, Di Lieto realized a high power broadly tunable Co2+ : MgF2 CW laser [38]. Using 12 W Nd:YAG laser at 1.3 µm as a pump source, he could achieve up to 3 W output power in TEM00 mode at 1.67 µm, and 2 W at 1.77 µm. The slope efficiency of 32% compares with the best values reported in other works, and the broad continuous tuning range between 1.6 and 2.1 µm (Fig. 5b) makes this laser a practical tool for spectroscopic [38] and solid-state laser pumping purposes [32]. The room-temperature pulsed operation is possible in Co2+ -doped lasers at the expense of the higher threshold and lower slope efficiency [21, 35, 36]. However, in this case the active medium should be pumped on a timescale short enough compared to the upper state lifetime of 36 µs. In the pulsed regime a Nd:YAlO3 pumped Co2+ : MgF2 laser has been tuned over the broad wavelength range between 1.5 and 2.3 µm [34]. This laser has finally matured to the commercially available laser system [21]. Taking into account the rapid developments in cryogenic technique, which we evidence in the recent years, one may expect further developments in Co2+ : MgF2 lasers. This may lead in the future to the compact user-friendly high power, broadly tunable, and maybe even ultrashort-pulsed lasers in the very interesting wavelength range between 1.6 and 2.3 µm. 3.3. Cr2+ -DOPED II-VI LASERS

The Cr2+ ions reside in II-VI hosts in tetrahedral sites. These sites do not possess inversion symmetry and are characterized by the high oscillator strength (high cross-sections) and short lifetime of typically a few microseconds. The other distinguishing feature of the Cr2+ -ions in tetrahedral sites is the relatively low


235

Figure 7. Tanabe-Sugano (a) and configurational (b) diagrams of the energy level splitting of Cr2+ ions in tetrahedral configuration. Only two quintet states, 5 E and 5 T2 are available for laser transitions. Note the Jahn-Teller splitting of the lower level (two of three branches are shown).

crystal-field splitting, placing optical transitions into infrared. The Cr2+ ions in the above crystals have the simplest (similarly to Ti3+ ion in sapphire) single electron configuration e2 t 2 2 . The Two levels (5 T2 and 5 E) originate from the crystal-field splitting of the 5 D ground state of the free-ion with d 4 configuration, which is the only quintet state (Fig. 7). Since all the higher lying states are singlets or triplets, the excited state absorption (ESA) transitions from the upper state are spin-forbidden. Altogether this ensures that Cr:ZnSe has the highest gain among all vibronic solid-state lasers and enables efficient broadband room-temperature operation. As a result, Cr2+ -doped II-VI lasers provide access to the 2–4 µm wavelength region, exhibit smooth tunability at the highest possible efficiency, Watt-level output powers and narrow spectral linewidth, which are generally inaccessible for semiconductor lasers. One of the crystals of this family, Cr2+ :ZnSe, exhibited efficient room-temperature diode-pumped continuous-wave and mode-locked operation also in the ceramic form. These lasers are nowadays probably the simplest and the most cost effective light sources in this wavelength region [78,90,91]. 3.3.1. Material and spectroscopic properties The material and spectroscopic properties of the most important crystalline hosts for Cr2+ ion are summarized in Tables 1 and 2 respectively. Among the listed crystals especially Cr2+ :ZnSe and Cr2+ :ZnS are distinguished by their remarkable characteristics, combining the ultrabroad bandwidth, the high emission crosssection of the order of 10−18 cm2 [24], the negligibly low excited state absorption

236

IRINA T. SOROKINA TABLE 1.

Material properties of the Cr2+ -doped laser crystals. CdSe

Cdx Mn1−x Te Ti3+ : Al2 O3

ZnSe

ZnS

Crystal structure

cubic

Lattice constant ˚ (A) Transparency range (µm) Hardness (Knoop) Thermal conductivity (W/m◦ C) dn/dT (10−6 /◦ C) Thermal expansion (10−6 /◦ C) Bandgap (eV) Refractive index (at llas ) Third-order nonlinearity n 2 (10−20 m2 /W) Second-order nonlinearity (pm/W)

5.67

mixed-polytype cubic, uniaxial 5.4 6.05 (cubic)

0.5–20

0.4–14

0.8–18

6.487–0.146x a = 4.765 c = 13.001 1–28 0.35–5.5

120 18

160 17 (uniaxial) 27 (cubic)

70 4

45(x = 1) 7.5(x = 1)

2000 27

70 7.3

46 6.4

98 4.9

100 4.5 (5.9)

12 8.4

2.8 2.45

3.8 2.27

1.7 2.47

1.5 2.7

8 1.76

170 (at 1.8 µm)

90 (at 1.3 µm)

1300 (at 1.5 µm)

−2700 (at 1.06 µm)

3 (at 0.8 µm)

30

8

18

60

Absent

cubic

uniaxial

(ESA) [42], with the fairly good chemical and mechanical stability and the thermal conductivity approaching that of sapphire. The laser induced damage threshold was measured to be 2.3 GW/cm2 in ZnSe (compare with 6 GW/cm2 in diamond) [43]. Here it is worth noting that the laser induced damage threshold generally correlates with the bandgap and is therefore the highest in ZnS and the lowest in CdTe [44]. The authors of Ref. [45] showed that the damage threshold irradiance in CdTe, ZnSe and CdS is independent of the focal radius and scales as t −1/2 (where t is the laser pulse duration), which is characteristic of surface damage due to surface contamination. It achieves 1.96 GW/cm2 (at 42 ps pulse duration) in CdTe and 14.9 GW/cm2 in ZnSe (at 34 ps pulse duration). This is a reasonable value to enable high power laser applications of Cr:ZnSe. The only drawback of Cr:ZnSe and Cr:ZnS materials is the relatively high thermal lensing parameter dn/dT (∼70·10−6 K−1 in Cr:ZnSe, 46·10−6 K−1 in ZnS compared to 12·10−6 K−1 in sapphire). However, the latter is compensated by the generally low thermal load due to the absence of such parasitic processes as ESA or upconversion.

237

BROADBAND MID-INFRARED LASERS TABLE 2. Spectroscopic and laser characteristics of Cr2+ -doped laser materials.

Peak emission cross-section σem (10−20 cm2 ) max (nm) λlum Peak absorption cross-section σabs (10−20 cm2 ) max (nm) λabs τem (µs) at 300 K Saturation intensity em (kW/cm2 ) Isat Luminescence bandwidth (nm) Relative bandwidth Optical quantum efficiency Slope efficiency (%) CW output power (W) Output energy (average power) Mode-locked output power (mW) Pulse duration Diode-pumping

ZnSe

ZnS

CdSe (pulsed)

Cd0.55 Mn0.45 Te Ti3+ : (pulsed) Al2 O3

130 90 [24]

140 75 [24]

200

170

39 [40] 45 [41]

2450 110 87 [24]

2350 100 52 [24]

2200 300

2480 170

780 6.5

1780 5.5 8 [24] 11

1680 4.3 8 [24] 14

1900 6

1900 4.8

500 3

8

10

210

900

800

550

770

300

0.41 1

0.34 0.73

0.25 1

0.31 1

0.38 0.9

53 1.8 0.43 mJ (18 W) 120 (fs) 400 (ps) 80 fs yes

71 0.7 0.1 mJ

48 – 0.8 mJ

64 – 0.6 mJ

140

–

–

35 up tp 10 >1 J >10 W up to 3000

1 ps yes

– no

– yes

5 fs no

The spectroscopic properties of Cr2+ (d4 ) ion in II-VI compounds have been extensively studied since back in the sixties (see e.g., [46–49]) and later in the seventies-eighties (see e.g., [50–56]). The first thorough spectroscopic investigation of Cr2+ -doped chalcogenides as laser materials and measurement of absorption and emission cross-sections were carried out in Refs. [23, 24]. The absorption and emission spectra of Cr2+ ion in Cr:ZnSe, Cr:ZnS and Cr:CdSe are depicted in Fig. 8 and Fig. 3 respectively. A broad absorption band centered around ∼1.8 µm in Cr:ZnSe, around ∼1.7 µm in Cr:ZnS and around 1.9 µm in Cd-compounds allows pumping by Tm-doped lasers, which are available as pulsed and continuous-wave sources of over 100 W average power [2] and recently also as fiber lasers with even higher power. The spectroscopy of

238

IRINA T. SOROKINA

Figure 8.

Absorption spectra of Cr:ZnS, Cr:ZnSe and Cr:CdSe.

Cr2+ -doped II-VI materials has been extensively reviewed in Ref. [58] from the laser point of view. It should be noted here that these media are characterized by high transition cross-section, µs lifetime and relatively low thermal quenching at room temperature, all being the results of inversion symmetry at the Cr2+ site (Table 2). Another important point is the additional broadening of the fluorescence spectrum due to the large Jahn-Teller splitting of the ground state, reaching 340 cm−1 and 300 cm−1 in Cr.ZnSe and Cr:ZnS respectively [49]. The direct measurement of the emission life-time τ in in Cr2+ :ZnSe has been carried out by several authors [51–54]. All of them report Cr2+ lifetime in various chalcogenides to be a few microseconds and not quenched up to ∼300 K. The extensive lifetime measurements were carried out in the last years for mainly polycrystalline [59] as well as for single crystalline Cr2+ :ZnSe crystals [60]. The latter study report only negligible increase of the lifetime from 5.4 µs at 77 K to 5.6 µs at 300 K. They also correlate with the similar investigations in Cr2+ :CdSe [61] and report concentration quenching of Cr2+ lifetime. In Fig. 9 we provide a direct comparison between the temperature dependent lifetime of Cr:ZnSe and Ti:sapphire. It is interesting to note that whereas the lifetime of Ti:sapphire is somewhat quenched at room temperature, this does not happen to Cr:ZnSe, which has a quantum yield close to unity. The data on lifetime lead to the absorption and emission cross-sections of 1.1 × 10−18 cm2 and 1.3 × 10−18 cm2 correspondingly [2, 60]. The strong reabsorption has been reported [60], which might compromise the lifetime. These data should be taken into account when designing the laser based on these crystals. The spectroscopic investigation in Cr2+ :ZnS has been reported in Ref. [62]. Among other II-VI compounds ZnS is distinguished by the largest energy gap of 3.8 eV, the smallest lattice constant and the correspondingly blue shifted fluorescence peaking around 2.1 µm (the corresponding emission cross-section peaking around 2.3 µm). As in case of Cr2+ :ZnSe the measurements yielded decreased (in comparison to 11 µs in Ref. [23]) radiative lifetime of 5 µs and correspondingly corrected absorption and emission cross sections of ∼1 × 10−18 cm2 and

239

BROADBAND MID-INFRARED LASERS 7 Cr:ZnS 76% at 300K

Fluorescence lifetime (µs)

6

Cr:ZnSe 98% at 300K

5 4 3

Ti:Sapphire 81% at 300K

2 1 0 100

200

300

400

500

Temperature (K)

Figure 9. Temperature dependence of the active ion lifetime in Cr:ZnSe, Cr:ZnS and Ti:sapphire.

1.4 × 10−18 cm2 respectively. Cr2+ :ZnS, otherwise very similar to Cr2+ :ZnSe, is characterized by a more rapid onset of the thermally activated nonradiative decay with temperature (Fig. 9). Relatively to the 77 K lifetime the room-temperature lifetime drops by ∼24%. The difference between Cr:ZnSe and Cr:ZnS may be explained by a higher maximum phonon frequency in this crystal (compare ∼250 cm−1 in ZnSe [63] and ∼350 cm−1 in ZnS [64]). On the positive side there are the lowest dn/dT and the best hardness and the highest damage threshold among the Cr2+ -doped media. All this makes Cr:ZnS especially attractive for high power applications. Cr2+ :CdSe [26, 27, 65–67] has a somewhat larger lattice constant than 2+ Cr :ZnS and Cr2+ :ZnSe (Table 1). The Cr2+ emission is therefore shifted by 100–200 nm towards the infrared and spreads out to over 3.5 µm. If not rather inferior to Cr2+ :ZnS and Cr2+ :ZnSe thermo-optical properties, this laser crystal would be a perfect candidate for continuous-wave lasing beyond 3 µm. Similarly to Cr2+ :ZnSe and due to the same reason, the lifetime of 6 µs in Cr2+ :CdSe does not change between 60 and 300 K [26]. The peak absorption and emission cross-sections were measured to be 3 × 10−18 cm2 and 2 × 10−18 cm2 respectively [26]. 3.3.2. Broadly tunable Cr2+ -based lasers Since the first demonstrations in 1995 at Lawrence Livermore National Lab the laser related research largely focused around Cr2+ :ZnSe, Cr2+ :ZnS and Cr2+ :CdSe lasers. The implemented so far pump sources include: tunable

240

IRINA T. SOROKINA

Co2+ :MgF2 laser [23, 24, 32], 1.9–2.1 µm Tm3+ , Ho3+ -lasers [30, 42], ∼1.6 µm Er-fiber lasers [14, 68, 69], 1.8 µm Tm:fiber laser [86], ∼1.6 µm NaCl:OH color center laser [31], ∼1.6 µm Raman-shifted Nd:YAG laser [70], ∼1.6 µm Raman-fiber laser [71] as well as 1.6–1.9 µm InGaAsP/InP semiconductor lasers [13, 14, 72, 73]. The direct diode-pumping yields the highest wall-plug efficiency. However, for high-power generation a 1.8–1.9 µm Tm-fiber laser may be the best choice. Since the first experimental demonstration the performance of these materials has greatly improved. At the initial stage experiments concentrated on the pulsed regime using a Co:MgF2 laser at 1.86 µm as a pump source. Using the grating in the Littrow configuration tunability over 2150–2800 nm was achieved. However, the laser emitted a relatively broad linewidth of ∼40 nm. Later these results were improved and 45% slope efficiency was demonstrated in Ref. [74]. The first diodepumping in the pulsed mode was demonstrated in Ref. [75]. Cr:ZnSe material is also suitable for power scaling. The lifetime quenching does not exceed 25% up to the concentration levels of 1 × 1019 cm−3 [60], corresponding to >10 cm−1 peak absorption coefficient, a typical figure for Yb:YAG thin disk lasers. In the pulsed mode, Schepler et. al. have demonstrated in the thin disk configuration 4.2 W of output power at 10 kHz repetion rate [67, 76]. The laser yielded up to 1.4 W in continuous-wave mode. The pump wavelength of 1.89 µm required relatively thick samples for good absorption. An optimized Cr:ZnSe thin disk laser design with reduced disk thickness and proper pump wavelength should be able to produce much higher output power in a good transversal mode. In a classical pumping arrangement Alford et al further scaled the output power in the pulsed regime up to 18.5 W at 30 W absorbed power pumped by the Q-switched Tm:YAlO3 laser at 7 kHz repetition rate (Fig. 10). Slope efficiency

Figure 10.

Output power and tuning of a high-power pulsed Cr:ZnSe laser [77].


241

of 65% (59% optical-to-optical efficiency) has been demonstrated [77]. In this experiment tunability between 2.1 and 2.85 µm was achieved at up to 10 W output power. Based on the analysis of the mechanical, thermal, spectroscopic, and laser properties of Cr:ZnSe, the output powers over 10 W in CW regime and several Watts in the mode-locked or amplifier regime can be anticipated. To this point the following record parameters were demonstrated from this laser: 1) the output power up to 18.5 W in gain-switched regime [77]; 2) the output power up to 1.8 W in a polarized TEM00 mode [78]; 3) the highest efficiency exceeding 70% in the pulsed mode [79]; 4) the broadest tuning bandwidth of 1100 nm between 2000 and 3100 nm in CW regime from the conventional resonator (see Fig. 4 in Chapter III.5 of this book) and the bandwidth of 1300 nm between 1800 and 3100 nm in the intracavity pumping arrangement [80]; 5) narrow-linewidth 600 MHz operation without any intracavity etalons [58] as well as single longitudinal mode operation with 20 MHz linewidth, using intracavity etalons [81]; 6) 350 nm tuning range at 65 mW output power in the diode-pumped regime [13] (450 nm in Cr:ZnS [14]); 7) parametrical conversion of 2.5 µm radiation of Cr :ZnSe to 4–4.85 µm [82], and 8), the active [83, 84] and passivemode-locking [15, 16, 85] with pulses as short as 4 ps at 400 mW of output power, and 80 fs at 80 mW, in active and passive mode-locking regimes, respectively. The most impressive results have been obtained so far using the Cr2+ :ZnSe crystals. The Cr2+ :ZnS crystal was less studied as a laser material due to the lack of good optical quality single crystals. Having similar spectroscopic properties to Cr:ZnSe, Cr:ZnS is known to have a larger bandgap, better hardness, a higher thermal shock parameter (7.1 and 5.3 W/m1/2 in Cr:ZnS and Cr:ZnSe, respectively [23]), and the lower dn/dT than in Cr:ZnSe (Table 1). At the same time, the temperature quenching of the Cr:ZnS lifetime starts at lower temperatures, than in Cr:ZnSe (Fig. 9), which might be a serious disadvantage, especially in CW applications. With proper cooling, however, the power handling capability of this material should be on par or better than that of Cr:ZnSe, making Cr:ZnS attractive for high-power applications. Our experiments with equally doped Cr:ZnS and Cr:ZnSe (e.g. with the same thermal load per unit length) showed, that Cr:ZnS performed at least as good as Cr:ZnSe. The pulsed laser operation of Cr:ZnS laser has been first reported in [23,24,87]. The spectroscopic study and the first continuous wave operation was reported in [88]. Using Er-fiber pumping up to 700 mW room temperature tunable over 700 nm (between 2.1–2.8 µm) CW operation was demonstrated [14]. Tuning over 400 nm between 2250–2650 nm in the directly diode-pumped configuration [14] as well as an Er-fiber pumped CW microchip laser at 2320 nm were recently demonstrated [69]. An advantage of Cr:ZnS is the shift of the absorption peak by about 100 nm to the blue (Fig. 8), allowing a convenient pumping of this material with available 1.6-µm telecommunications diodes [14].

242

IRINA T. SOROKINA

Another important issue is extending the operation range of the Cr2+ -doped lasers, especially beyond 3-µm wavelength. This could be obtained by using other II-VI compounds with a larger lattice constant and hence lower crystalline field (see Fig. 7a). For example, hosts like CdSe [26, 27], CdTe [89], and CdMnTe [28, 29] also allow room temperature operation with Cr2+ ion. Tuning up to the record 3.4 µm in the pulsed regime was demonstrated in Cr:CdSe [66]. It makes sense to consider other mixed ternary and quaternary compounds that would provide both a control over the central wavelength and the additional inhomogeneous broadening of the spectrum, as it will be shown in the next section. Finally, maybe one of the most interesting advantages of these materials is the availability of the technologically developed and low cost polycrystalline material. The existing technologies of producing ceramic ZnSe, such as a chemical vapour deposition (CVD) method or the hot-press method of powders, result in high optical quality low-cost substrates of arbitrary size. Many of the above reported results were obtained with ceramic active media, which allow also directly diode-pumped CW tunable and actively mode-locked operation [90, 91]. With proper optimization, a directly diode-pumped femtosecond ceramic laser could be created. This would be a most practical source of few-cycle light pulses. 3.3.3. Ultrashort-pulsed Cr2+ :ZnSe and Cr2+ :ZnS lasers Direct femtosecond laser sources, producing only few optical cycle pulses in the mid-IR range between 2 and 3 µm, are highly important for such applications as nano- and micro-structuring in semiconductors (e.g. for fabrication of Si-photonic structures), wavelength conversion towards shorter (X-ray), as well as longer (up to THz) wavelength ranges, time-resolved spectroscopy, trace-gas sensing, as well as for continuum generation in the mid-IR. Such pulses in the mid-infrared spectral region can be used as unique diagnostic tools for investigation of numerous transient processes on the femtosecond scale. The broadly tunable ultrashort pulsed lasers in this wavelength range are also attractive for such applications as optical coherence tomography, ophthalmology, and dermatology in medicine. They can be also be used for pumping mid-IR OPOs to produce even longer wavelengths [82, 92]. Nowadays, femtosecond pulses in this wavelength range are being produced by multi-stage parametric frequency converters based on Ti:sapphire laser, which are rather bulk and inefficient in comparison to the directly diode-pumped Cr:chalcogenide lasers, emitting in this wavelength region. In the last few years picosecond mode-locking, both active and passive, has been achieved in Cr2+ :ZnSe [83–85, 93] and Cr2+ :ZnS laser [94]. The first works used an acousto-optic modulator to mode-lock the laser with the shortest pulses being 4 ps [83, 84] at up to 400 mW output power. Later, the first semiconductor saturable absorber (SESAM) mode-locked Cr2+ :ZnSe laser generating 11 ps pulses at 2.5 µm at 400 mW output power was demonstrated [85]. The pulse


243

Figure 11. Chirped mirrors for the Cr:ZnSe laser.

duration was presumed to be limited by some intrinsic limitation like an etalon. For some time the reported pulse durations were in the picosecond range. To overcome a picosecond barrier in Cr2+ lasers became therefore a highly desirable, but also a very challenging task. Recently we could finally identify the physical cause of this picosecond barrier, which was due to the water absorption lines in the resonator around 2.5 µm. As a result, we could report the first femtosecond Cr:ZnSe laser, passively mode-locked by an InAs/GaSb SESAM and generating 106 fs pulses at up to 75 mW power around 2.5 µm wavelength [15]. Later, optimization of the dispersion compensation schemes with the use of chirped mirrors (Fig. 11) allowed to demonstrate for the first time a chirped-mirror controlled femtosecond laser oscillator (Fig. 12), generating the shortest reported so far 80 fs pulses (10 optical cycles) at 80 mW output power (Fig. 13). Dispersion compensation by chirped mirrors is a very challenging task in the mid-IR due to the necessity to design and fabricate especially thick multilayer mirrors. This causes additional absorption losses at large penetration depth at the long-wavelength side, as evidenced by Fig. 11. Solving this technological problem would allow generation of even broader spectra with corresponding pulse shortening. Finally we should note that Cr:ZnSe is capable of power-scaling and producing up to 1 µJ pulses directly from the oscillator. In Ref. [95] the analytic theory of a chirped pulsed oscillator (CPO) mode-locked by SESAM and operating in the

244

IRINA T. SOROKINA Cr2+:ZnSe

R=100

R=75 f=40 Er:fiber

CM

λ=1.61 µm

CM CM

OC 2-6%

SESAM on heatsink

R=50

YAG

FWHM 137 fs Pulse FWHM 81 fs (Gaussian)

6

2

4

Round-trip GDD (fs )

SHG intensity (rel. units)

8

Spectral intensity

Figure 12. Schematic diagram of a femtosecond Cr:ZnSe laser. The pump at 1.61 µm and the output radiation are polarized in the plane of the figure. OC, output coupler. CM, chirped mirror.

0

4 mm ZnSe 3.1 mm YAG 4x CM

2

−1000 −2000

0 −200

−100

0

100

Time delay (fs)

200

2300

2400

2500

2600

Wavelength (nm)

Figure 13. Autocorrelation trace, spectrum and round-trip GDD for a Cr:ZnSe laser using a combination of chirped mirrors and the thin YAG plate for dispersion compensation.

positive dispersion regime was developed. Application of the developed theory to the analysis of the Cr-chalcogenides CPOs demonstrated their high potential to generate µJ-level sub-100 fs pulses at 2.5 µm. The most promising candidates are Cr:ZnS and Cr:ZnSe, which could potentially even outperform Ti:Sapphire CPO in terms of achievable pulse energy. 3.3.4. Engineering of the new Cr-doped II-VI laser media. The crystal field engineering of Cr-doped II-VI materials proved to be successful in several cases. The central frequency of the vibronic transition is defined by the crystal-field splitting. In case of Cr2+ , the splitting is proportional to the crystal field parameter Dq/B, which inversely scales with the unit cell size: λ0 = c/ν0 ∝ (Dq/B)−1 ∝ a0

(5)

where a0 is the unit cell size. For example, changing the unit cell size from a0 = ˚ in Cr:ZnS through a0 = 5.67 A ˚ in Cr:ZnSe to a0 = 6.05 A ˚ in Cr:CdSe one 5.4 A decreases the crystal field splitting correspondingly. This shifts the absorption and emission wavelengths gradually towards longer wavelengths (Fig. 3 and Fig. 8). This is an example of simple crystal field engineering with binary A I I B V I compounds. The more complex methods involve design of the laser media based


245

on ternary compounds (A I I B I I )C V I like, e.g. Cr2+ :Cdx Mn1−x Te compounds. These represent an interesting alternative to selenide or sulfide laser materials [28, 29, 89, 96–99]. Besides the fluorescence wavelength shift, the chemical composition would also affect the bandgap (in Cdx Mn1−x Te, it can be increased from 1.44 eV to 2.3 eV by varying x between 1 and 0.55). The only disadvantage, preventing their use in continuous-wave lasers, remains the relatively poor thermal properties of these crystals (Table 1). The radiative lifetimes in Cr2+ :Cdx Mn1−x Te compounds vary between 3.2 and 4.5 µs depending upon the crystal composition [100]. Relatively to the 77 K lifetimes the room-temperature lifetimes are quenched by ∼35% in Cr2+ :CdTe, and by ∼62% in Cr2+ :Cd0.85 Mn0.15 Te [100]. In the latter crystal the absorption and emission cross-section were measured to be 1.4 × 10−18 cm2 and 1.3 × 10−18 cm2 respectively [97]. These values are close to those in Cr2+ :ZnSe and Cr2+ :ZnS. Another incentive to engineer these materials is that it is easier to grow them in comparison to selenides [100]. Free-running operation of the pure Cr2+ :CdTe, has been reported in [89]. The laser delivered 132 µJ at 2 Hz repetition rate, when pumped by 1.4 mJ from a Cr,Tm,Ho:YAG laser at 2.09 µm. In Cd0.85 Mn0.15 Te tuning has been accomplished by using a quartz birefringent filtre and extended from 2.3 to 2.6 µm [96], as well as by a grating in a Littrow configuration and extended between 2.17 and 3.01 µm [99]. Output energies as high as 0.6 mJ could be achieved at absorbed pump energy of ∼1.6 mJ. The first CW and direct diodepumped operation was demonstrated as well [72], however, at the expense of the output power, which in CW regime did not exceed 6 mW (15 mW in the pulsed regime). In a similar way more recently Cr2+ :Cdx Zn1−x Te has been developed. The laser operated at room-temperature in continuous-wave regime. However, the output power was limited to only a few mW due to the poor thermal conductivity and strong thermal lensing in this material like in the case of CdMnTe [101]. The third way to make a mixed compound is to create a ternary system A I I (B V I C V I ), like e.g. Cr:ZnSx Se1−x [102]. There is an important difference to the previous case: since Cr2+ substitutes an AII ion, mixing of the BVI CVI ions occurs in the immediate neighbourhood of the chromium ion. Opposite to Cr:CdMnTe, where changing of the lattice parameter merely shifts the emission spectrum towards longer wavelength, in the latter case the crystal field experienced by the Cr2+ ion should be strongly affected by mixing and one may expect a large inhomogeneous broadening. Undoped solid solutions of ZnSx Se1−x [103] are used as substrates for epitaxial growth of blue-emitting diodes, as well as active media for e-beam longitudinally pumped lasers. In our work, we realized diffusion doping of this crystal grown by seeded chemical vapor transport. Based on the Raman and infrared absorption spectra we determined the content of ZnS to be 42% (crystal composition ZnS0.42 Se0.58 ).

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The results of the absorption and room-temperature luminescence measurements are given in Fig. 14 and summarized in Table 3. As seen in Fig. 1, the high-quality absorption due to predominantly Cr2+ ions could be obtained in this crystal with peak absorption coefficient of 9.5 cm−1 the maximum around 1.69 µm. The room-temperature lifetime was measured to be 3.7 µs, which is close to the corresponding value measured in concentrated Cr2+ :ZnS and

Figure 14. Comparison of the absorption (upper graph) and fluorescence (lower graph) spectra of Cr:ZnSe, Cr:ZnS, and Cr:ZnSSe [104]. The emission spectra are corrected for the detector and spectrometer response. TABLE 3. Main spectroscopical data of Cr:ZnSSe in comparison with Cr:ZnSe and Cr:ZnS [104].

Absorption peak (nm) Absorption width (nm) Gain peak (nm) Gain bandwidth (nm) Lifetime at 300 K (µs)

Cr:ZnS

Cr:ZnSSe

Cr:ZnSe

1695 350 2315 800 4.3

1696 400 2410 930 3.7

1770 355 2400 850 4.8

247


30 20 10

Air

95

Transmission, %

40

Cr:ZnSSe Cr:ZnSe

Output power (rel.u.)

Output power (mW)

100

Cr:ZnSSe, pump 1.67 µm OC2%, slope eff.16% OC4%, slope eff.24%

50

90

0 0

a)

100 200 Absorbed pump power (mW)

300

2200

2400 2600 Wavelength, nm

2800

b)

Figure 15. Output characteristics (a) and tuning (b) of the Cr:ZnSSe laser. For comparison, tuning curve of the ceramic Cr:ZnSe is given [105]

Cr2+ :ZnSe, as are the corresponding values for absorption and emission cross sections. However, emission bandwidth is noticeably broader than in Cr:ZnS or Cr:ZnSe and is peaked at the same wavelength as in Cr:ZnSe (Fig. 14). Thus, Cr2+ :ZnSSe represents an interesting alternative to pure selenides and sulphides. The only disadvantage may be the higher maximum phonon frequency in this crystal (compare ∼350 cm−1 in ZnS0.42 Se0.58 [104] with ∼250 cm−1 in ZnSe). Similar to Cr2+ :ZnS, this leads to the more rapid onset of nonradiative decay in this crystal relative to Cr2+ :ZnSe. At room temperature, the quantum yield is about 76%. In the laser experiments, we used a 1-mm thick polished plate of polycrystalline Cr:ZnS0.42 Se0.58 in the conventional three-mirror configuration (as in Ref. [14]). Without additional cooling, the laser operated at room temperature in continuous-wave regime, producing ∼30 mW of output power at 3% output coupling with 170-mW threshold pump power. These results could be further improved using the Co:MgF2 laser at 1.67 µm. The laser output characteristics are given in Fig. 15a. The threshold was measured to be less than 80 mW of absorbed power at 2% output coupling. For comparison, in the similar cavity, Cr:ZnS exhibits 210 mW and Cr:ZnSe few tens of mW threshold. Without additional cooling, the laser operated at room temperature in continuous-wave regime around 2480 nm, producing ∼50 mW of output power with 4% output coupling at 600 mW of incident pump power, and 24% slope efficiency. Using a dry fused silica Brewster prism as a tuning element, we were able to demonstrate tunability over ∼560 nm: from 2099 to 2658 nm (Fig. 15b). In order to provide a fair comparison, a tuning curve of the polycrystalline Cr:ZnSe sample of comparable quality in similar conditions is given. The tuning range of Cr:ZnS0.42 Se0.58 significantly exceeds that of the Cr:ZnSe on the short wavelength side. The long wavelength cutoff for both samples was due to the water vapor absorption in the cavity, as shown by the air transmission curve.

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Summarizing, Cr:ZnS0.42 Se0.58 represents an interesting alternative to Cr:ZnS and Cr:ZnSe, when having the largest possible emission bandwidth is an issue. However, more work has to be done in order to achieve the same high optical quality as in Cr:ZnSe crystals. 3.3.5. Nanocrystalline Cr 2+ :ZnSe and Cr 2+ :ZnS powder lasers As already discussed, the Cr2+ -doped laser materials are characterized by high gain and an intrinsically low lasing threshold, as well as by such remarkable spectroscopic features as the absence of excited state absorption and high quantum yield. The active media can be obtained by diffusion doping of metallic chromium into the ceramic ZnSe. Along with several other techniques of producing ceramic ZnSe, the latter is often obtained by hot-pressing the micro- and nanocrystalline ZnSe powder. A somewhat odd (but not without good reason) question arises as to whether it would be possible to get laser action from Cr2+ :ZnSe or any other Cr2+ -doped II-VI compound in the powder form? Indeed, random powder lasers is a hot topic in the modern photonics research. For extensive reviews on this subject the reader is referred to Refs. [106–108]. This type of laser has been extensively studied since the first proposal in 1966 by Ambartsumyan et .al. [109] of lasers with nonresonant feedback, and demonstrated in ZnO by Nikitenko et. al. [110] and in Nd3+ :LaMoO4 by Markushev et. al. [111]. During the last decade, a great variety of random powder lasers has been developed, all of them emitting in the UV to near infrared wavelength range. Recently, we reported the first eye-safe midinfrared ion-doped semiconductor random lasers based on Cr2+ :ZnSe [112] and Cr2+ :ZnS [113] powders operating around 2.4 µm and 2.3 µm, respectively. The experimental details can be found in Ref. [78] At pump energy flux comparable to the absorption saturation flux Jsat of bulk Cr:ZnSe and Cr:ZnS (i.e. between 0.3Jsat -0.3Jsat ) we observe the dramatic shortening of the emission lifetime (Fig. 16a), the threshold-like behavior of the emission intensity (Fig. 16b), and the radical narrowing of the emission spectrum at gain peak (Fig. 17). The maxima of the narrowed spectra at 2400 nm and 2300 nm correspond to the gain maxima of both crystals and are shifted by 100 nm from each other. Threshold pump energy density as low as ∼20 mJ/cm2 could be observed in Cr:ZnSe and a factor of 1.5 higher in Cr:ZnS, which corresponds to the higher threshold of Cr:ZnS in the bulk form [14]. An interesting feature of this new class of midinfrared random lasers is a remarkably low threshold. In fact, the threshold pump intensities in the powder and bulk samples are comparably low (4–6 kW/cm2 in powder vs. 3–4 kW/cm2 in bulk samples), and significantly lower than in such undoped semiconductor random lasers like ZnO, where the threshold pump intensity Ith is ∼80 MW/cm2 [114]. This makes the Cr2+ -doped random lasers very attractive for real-world applications.

249

BROADBAND MID-INFRARED LASERS 0.2

0.4

J/J sat

0.6

Emission intensity (rel.units)

Decay time (µs)

0.0 10

1

0.1

0.0

a)

0.1 0.2 Pump energy (mJ)

0.3

Cr:ZnS Cr:ZnSe (low-loss)

Cr:ZnSe (high loss, largegrain)

Cr:ZnSe (high loss, small grain)

0.0

0.2

0.4 0.6 0.8 1.0 1.2 Incident pump energy (mJ)

1.4

b)

Figure 16. a) Decay time dependence on pump energy in the Cr2+ :ZnSe powder (excitation wavelength 1780 nm, pump spot diameter 0.7 mm). b) Emission intensity vs. pump energy for Cr2+ :ZnSe and Cr2+ :ZnS (excitation wavelength 1780 nm, pump spot diameter 1.1 mm) [113].

Figure 17. Emission spectra of the Cr2+ :ZnSe powder (upper graph) and Cr2+ :ZnS powder (lower graph). The experimental conditions and pump energies are marked on the graphs. [112, 113].

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IRINA T. SOROKINA

Finally, it should be noted that the stimulated emission in Cr2+ :ZnSe and Cr2+ :ZnS powders is eye safe and eye safe-pumped. This opens a broad range of applications of mid-infrared random nanolasers in aero- and space technologies, for marking and identification, search and rescue, etc. The demonstrated extremely low laser threshold in both lasers renders continuous wave operation in these powder materials feasible. A few years ago, a sensitization of induced radiation in these crystals in the presence of charge transfer processes [13, 58] has been observed, allowing to pump the upper laser level of Cr2+ through the charge transfer mechanism. This phenomenon served as the first milestone on the way towards electrically pumped active-ion doped nanocrystalline ZnSe lasers. The following investigations by other authors confirmed this mechanism as described below and in the Chapter II.4 of this book. 3.3.6. On the way towards electrical pumping and opto-optical switching An important feature, distinguishing the Cr2+ -doped materials from all the other solid-state lasers combines the properties of semiconductors with that of the traditionally used in solid-state lasers dielectric materials. As a result, Cr2+ -doped materials possess the excellent laser properties along with the interesting physics as well as optical and nonlinear properties, distinguishing them from the traditionally used dielectric laser media. This opens up an exciting white field of research and new opportunities for the use of these materials in laser- and nonlinear-optical applications, as well as for direct electrical pumping. Here we only briefly touch this topic. For more details on the subject the reader is referred to the following Chapter II.4. Because of the semiconductor nature of II-VI compounds the charge transfer processes play an important role in these materials. For the first time they were studied in application to the Cr2+ -doped lasers in Ref. [115]. In this work it was demonstrated that the lasing of Cr2+ -ions can be achieved by pumping through the charge transfer channels. In the following works other authors observed this phenomenon as well [116,117]. Observation of the manifestation of charge transfer processes in Cr2+ -doped lasers and their understanding was an important milestone, because these processes paved the route to electrical pumping. Let us summarize the most important features of these materials, which distinguish them from other oxide and fluoride laser crystals: 1. Noncentrosymmetric tetrahedral sites for Cr2+ ions. This leads to the partially allowed electric-dipole transitions and large absorption and emission crosssections (∼10−18 cm2 ). 2. Covalent rather than ionic type of bonding leads to the fact that intraionic laser processes are not purely “intracentral” in these materials, which results in high probability of charge-transfer processes and explains multiple


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valency of transition-metal ions, especially in highly concentrated samples (∼1019 cm−3 ), as required for diode-pumping; 3. Semiconductor nature of the crystals implies that charge-transfer processes generate free carriers leading to photorefractive phenomena; it also leads to the high second- and third-order nonlinearity of the host crystal; Indeed, the tetrahedral sites provide lower crystal-field stabilization of the ions than the octahedral sites [118]. Covalent bonding plays larger role in the tetrahedral sites, causing the frequently observed multiple valence states of the transition-metal ions in these sites and the high probability of charge-transfer processes. Whereas in octahedral sites internal e ↔ t2 transitions do not significantly redistribute the charge around the active ion (i.e., both the initial and the final one-electron wave functions are almost equally localized around the impurity, hence the term “internal” transitions), in covalent tetrahedral sites such excitations can redistribute the charge from impurity-centered orbitals (i.e. essentially purely d-like e states) to ligand-centered orbitals (i.e., the p-d hybridized t2 states) [119,120]. They are, therefore, not really “internal” transitions. All this is especially true for tetrahedrally coordinated Cr2+ ions in II–VI compounds. As it has been recently shown, the charge transfer processes in some cases may affect the laser performance of Cr:ZnSe and Cr:ZnS lasers with the active ions in tetrahedral sites [13, 14, 115]. In both these lasers we observed a novel effect of sensitization (modulation) of the induced radiation around 2.5 µm with only a few milliwatt of the visible and near-infared radiation (470–770 nm). The reported phenomenon is of the photorefractive nature and involves charge transfer to Cr ions, similar to the mechanism of photorefraction, which takes place in other transition-metal doped chalcogenides. Typical examples are chromium doped GaAs [121], vanadium-doped CdMnTe [122,123] or CdTe[124]. The details of the experiment on the sensitization of induced radiation can be found in Refs. [13, 14, 58]). Discussing the mechanisms of the observed phenomenon, we notice that it is of photorefractive nature and involves charge transfer to Cr ions [58]. Under the visible excitation, two relevant types of charge-transfer processes are known to occur, described by the following formulas: Cr2+ + hν → Cr1+ + h VB , Cr1+ + hν → [Cr2+ ]∗ + eCB ,

(6) (7)

where h VB and eCB denote a hole in the valence band (VB) and an electron in the conduction band (CB), respectively. The two-step electronic transitions of a free carrier from the valence band to the conduction band were observed at high concentration of chromium (1.0 · 1019 cm−3 ) [125,126]. The positions of Cr1+ and Cr2+ states in Cr:ZnSe are 1.24 and 2.26 eV beneath the conduction band edge respectively [125]. The 532 nm and 633 nm wavelengths coincide well

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IRINA T. SOROKINA

with the rather broad charge transfer band, having a maximum just beneath the fundamental absorption edge around ∼2 eV. The process (6) reduces the number of active Cr2+ ions, causing a drop in efficiency and an increase of the threshold. In the process (7), Cr1+ ions release an electron to the CB under excitation with shorter than ∼1 µm wavelength, resulting in an excited state [Cr2+ ]∗ . The process (7) [125,127] increases the number of active ions and counteracts the process (1). This last process can be used for electrical pumping in the properly optimized crystal. The link between the ionization transition of Cr1+ and Cr2+ ions and the 2.4 µm infrared emission of Cr2+ has been earlier discussed by other authors [128], as well as in Chapter II.4 (see references therein). Summarizing, the described effect of sensitization of induced radiation can be used for both, electrical pumping of Cr2+ -laser, and for opto-optical switching. Indeed, the “zero-to-one” switching was realized in Cr:ZnSe laser by switching on and off the probe beam, whereas the laser changed its condition from the state with “no lasing” to the state with laser operation. This was a proof-of-principle demonstration of using a diode-pumped solid-state laser as an alternative type of switching device. 4. Conclusion and outlook Summarizing, Cr2+ -doped lasers have come of age and already entered several real-world applications, such as gas analysis, ultrasensitive spectroscopy, and quantum optics. They can be diode-pumped and operate in various regimes. The wavelength coverage reached 3.1 µm (CW) and 3.5 µm (pulsed) at room temperature, with output powers ∼2 W (CW) and ∼20 W (pulsed), 400 mW (mode-locked) at sub-ps pulse durations. Crystal field engineering allows extension of operation wavelength and bandwidth (Cr:CdMnTe, Cr:CdZnTe and Cr:ZnSSe). Passive mode-locking of Cr:ZnSe using InAs/GaSb SESAM generated down to 80 fs pulses at 80 mW at 2450 nm, which corresponds to only ten oscillations of electric field! Maybe one of the most exciting developments in Cr2+ -doped lasers recently was the demonstration of the first Cr:ZnSe random nanolaser, based on nanometer (down to 200 nm) sized Cr2+ :ZnSe powder emitting around 2.4 µm. Potentially the semiconductor particle size can be decreased down to 1) and high temperature (kT greater than effective phonon energy), the radiationless transition rate is described by the Mott equation. This process is typical for nonradiative relaxation in optical centers with a strong electronphonon coupling. This approach leads to a fluorescence lifetime and radiationless rate given by the following equations [see for example 117]: −1 τ −1 = τrad + τ N−1R τ N−1R = Wa exp(−E a /kT ),

(2) (3)

where Ea –energy gap between the intersection of the adiabatic potential energy curves and the minimum of the excited state curve (see Fig. 9). The best fit of the data is shown in Fig. 12 and was obtained with parameters Ea = 1900 cm−1 and 1/Wa = 5 ns. The quantum efficiency of luminescence of Fe:ZnSe at RT is too small for effective CW pumping but the luminescence lifetime is still longer than the typical pulse duration of Q-switched lasers (1–100 ns). Hence, there is a possibility to obtain room temperature lasing of Fe:ZnSe in a gain-switched regime with pump pulses shorter than 300 ns. The absorption cross-section spectra was obtained from absorption measurements and using the known absorption cross section at 2.698 µm [96]. Emission

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SERGEY MIROV AND VLADIMIR FEDOROV

Lifetime, µs

100

10

1

0.1 0

100

200

300

Temperature, K

Figure 12. Luminescence lifetime versus temperature for Fe:ZnSe crystals. (♦)-experimental data according to [5], () according to [114].

cross sections at room temperature are determined using either the reciprocity method (RM) or the Fuchtbauer-Landenburg (FL) equation [118, 119]. Using a fundamental relationship between spontaneous and stimulated processes, the FL equation can be written as σem (λ) =

λ5 I (λ) , 8πcn 2 τrad I (λ) λdλ

(4)

where σem (λ) is emission cross section, λ-emission wavelength, n-refractive index, c-speed of light, τrad -radiative emission life-time, and I -energy per area per unit time. The emission cross section can be also obtained from the absorption spectra by the RM. According to this method the absorption and emission cross sections are related as: Zl σem (ν) = σab (ν) exp E zl − hν /kT , (5) Zu where Ezl -is the energy separation between the lowest crystal field components of the upper and lower states, Z u , Z l are partition functions that can be obtained using the energy gap (E i , E j ) from the lowest crystal field level of each manifold and (gi , g j ) energy-level degeneracies by the following equations: Zu = g j exp −E j /kT (6) j

Zl =

gi exp (−E i /kT )

(7)

i

The Z l /Z u factor depends on temperature but does not contain any spectral dependence. The emission cross-section calculated according to RM with factor Zl /Zu = 1.5 is shown in the Fig. 13. The difference in the Zl /Zu factor from

NEW REGIMES OF EXCITATION AND MID-IR

279

Crosssection x1018 cm2,

(iii) 2

(i) 1 (ii) 0 2

3

4 wavelength, µm

5

Figure 13. Room temperature absorption (i) and emission cross-sections (ii) and (iii). Emission cross-section calculated using reciprocity method (ii) and Fuchtbauer-Landenburg equation (iii).

gl /gu ratio is caused by larger upper level splitting (5 T2 ) in comparison to the ground state level (5 E) and thermal energy E = kT . As one can see from Fig. 13, both methods (FL and RM) demonstrate a wide amplification band at RT with a maximum at ∼4.3 µm and a bandwidth of ∼1.1 µm. However, the spectral shapes of the curves are not identical. This difference can be explained by several reasons. First, RM is very sensitive to the accuracy of the absorption measurements for transitions with a large Stocks shift due to an exponential factor. From the other side, the FL method is valid when all the transitions have the same strength regardless of the components involved. However, according to [96], the measured Fe2+ lifetime increases in the 12 K–120 K temperature range and this increase could be a result of very different radiative lifetimes of the components of the 5 E ↔ 5 T2 transition. In addition, measured emission spectra can be of slightly suppressed intensity at the short wavelength tail of the spectrum due to a reabsorption process. In spite of the minor differences, both techniques produce close values for the position of the maximum and linewidth of the amplification band of Fe2+ ions at room temperature. Thus, one can see from this analysis Fe:ZnSe has a large emission crosssection σem = 2–3 × 10−18 cm2 and a 370 ns lifetime at room temperature, hence, lasing of the Fe:ZnSe crystal at room temperature could be feasible in a gain-switch regime. Indeed, RT lasing is shown in subsequent sections. 3.4. Fe2+ :ZnSe LASER CHARACTERISTICS

3.4.1. Low temperature lasing After the pioneering work of Adams et al [96], where laser effect was realized with an output energy of 5 µJ at 150 K, efficient lasing of Fe:ZnSe has been achieved in several different regimes of operation [109, 114, 120, 121]. The lasing characteristics of the Fe2+ :ZnSe laser at low temperatures of the active element

280


were studied in the 85–255 K temperature range. The resonator of the Fe2+ :ZnSe laser was formed by a spherical mirror (with radius of curvature 50 cm) with reflectivity ∼100% and a plane output coupler with reflectivity 70% at around 4 µm. The cavity length was 32 cm. The single crystal active element was mounted at the Brewster angle on a copper heat sink inside a cryostat with CaF2 Brewster windows. A more detailed description of this experimental setup can be found in [120, 121]. The Fe2+ :ZnSe laser was pumped by a flashlamp-pumped free-running Er:YAG laser operating at 2.94 µm with 750 mJ output energy and a 200 µs pulse duration. The pump radiation was linearly polarized. The Fe:ZnSe laser output pulse also consisted of spikes, which at the sufficiently high pump energy followed the pump spikes with a 0.2–0.5 µs delay depending on the excess pump energy over the threshold pump energy. Figure 14 shows the dependences of the output energy of the laser obtained at different temperatures. The slope efficiency and threshold absorbed pump energy were determined from a linear fit to the experimental points using the method of least squares. The maximum slope efficiency of the laser amounting to 43% (the quantum efficiency was 59%) was obtained at T = 85 K. With a pump energy of 733 mJ, the maximum output energy of 187 mJ was obtained (the absorbed pump energy was 470 mJ). One can see from Fig. 14 that the threshold pump energy of the laser is 15 mJ at T = 85 K and the slope efficiency decreases with temperature over the entire temperature range of 85–186 K, however not dramatically. The output spectrum of the Fe2+ :ZnSe laser at T = 85 K was continuously tuned between 3.77 and 4.40 µm in a dispersive resonator with a 70◦ CaF2 prism [120].

Output Energy, mJ

100 80

(ii)

60

(iii)

(i)

40 20 0 0

100

200

300

400

Absorbed Energy, mJ

Figure 14. Output-input characteristics of the Fe2+ :ZnSe laser at different temperatures of the active elements (i-85 K; ii-186 K; iii-220 K obtained with thermoelectric cooler).


281

The dependence of the output energy of the laser obtained by cooling the crystal with the two-stage thermal module [114, 121] is shown in Fig. 14 curve (iii). For an absorbed pump power 370 mJ, the maximum output energy was 91 mJ (the incident pump energy was 718 mJ). The slope efficiency of the laser with respect to the absorbed energy was 30%. To increase the output energy, an additional aluminum mirror, which returned the unused transmitted pump radiation back to the laser crystal was utilized. The more efficient use of the pump radiation resulted in an increase in the output energy of this laser system design using thermoelectric cooling to 142 mJ for incident pump energy of 746 mJ. The slope efficiency of this thermoelectrically cooled laser with respect to the incident pump energy was 21%. Therefore, with further optimization of the laser resonator (selection of the optimal reflectivity of the output mirror, elimination of intracavity losses at chamber windows, better matching of the pump and lasing modes) will provide even higher output energy and better slope efficiency for the Fe2+ :ZnSe laser. 3.4.2. Room temperature Fe2+ :ZnSe microchip lasing Efficient continuous wave and pulse microchip oscillation in Cr:ZnSe and Cr:ZnS crystal were previously demonstrated in [28, 30]. To realize this regime of oscillation, highly doped samples are required. Therefore, in [109, 114] polycrystalline iron doped samples prepared by the thermal diffusion technique were used. The thickness of the crystal plate was h = ∼2 mm. The Fe2+ ion concentration was ∼1019 cm−3 . As a pump source for laser experiments the 2nd Stokes output (2.92 µm) of the Nd3+ :YAG laser in a D2 cell was used. The crystal temperature remained at 300 K during all laser measurements. One of the advantages of the described pump system is short pulse duration (less than 5 ns). This short pulse duration is important for room temperature studies of Fe:ZnSe. In [109, 114] stimulated emission was observed at RT without any coatings on the crystal surfaces and oscillation feedback was due only to Fresnel reflection from the crystal surfaces (R ∼ 17%). As one can see from the Fe:ZnSe emission spectra depicted in Fig. 15, an increase of pump energy density above the threshold level of 170 mJ/cm2 results in Fe stimulated emission at 4.4 µm accompanied by a sharp line narrowing from 1.1 down to 0.2 µm. In spite of the poor feedback due to Fresnel reflection, the required gain may be achieved. Indeed at σem = 2–3 × 10−18 cm2 and a Fe2+ concentration of (6–9) × 1018 cm−3 the gain may be as high as 12–27 cm−1 while the cavity loss is h−1 · ln(1/R) = 10 cm−1 . In subsequent experiments, the laser crystal was set on the surface of gold mirror. The cavity in this case was formed by a gold mirror and Fresnel reflection from the output facet of the Fe2+ :ZnSe crystal. Fig. 16 shows the Fe2+ :ZnSe laser output as a function of pump energy density. A linear approximation of the experimental data estimates the threshold value of the pump energy density to be 50 mJ/cm2 . In this experiment the laser spectral line was centered at 4.35 µm with a linewidth of 0.15 µm. The maximum output energy was estimated to be ∼1 µJ. Obtaining


Intensuty, a.u.

282

iii ii i 4.0

4.5

5.0

wavelength, µm

Figure 15. Emission spectra of Fe:ZnSe crystal versus pump density at RT under pump energy density 40 mJ/cm2 (i); 110 mJ/cm2 (ii); 170 mJ/cm2 (iii).

Output Energy, µJ

1.5

1.0

0.5

0.0 50

100

150

Pump Energy, mJ/cm2

Figure 16.

Output-input dependence of RT microchip Fe:ZnSe laser.

high output energy at RT was not the goal of this initial experiment. The lasing efficiency was small due to the following reasons. First, the low optical density of the crystal resulted in a poor efficiency of pump absorption. Second, the use of an output coupler formed by Fresnel reflection from the crystal facet was not optimal. Later experiments will optimize crystal geometry, doping densities, and the output coupler reflectivity to increase the output energy. 3.4.3. Passively Q-switched Er:YAG laser as a pumping source for a mid-IR Fe:ZnSe RT laser system Passive Q-switching of mid-infrared lasers has attracted much attention in recent years. Q-switching of a 1.54 µm Er:glass laser was demonstrated using Cr2+ :ZnSe and Co2+ :ZnSe crystals [122]. A Cr2+ : Cd0.55 Mn0.45 Te crystal was used for the


283

Q-switching of a 2.09 µm Ho:Tm:Cr:YAG laser [123]. However, effective passive solid-state Q-switches for the 3 µm spectral range are not currently available. A 2.94 µm Er:YAG laser was Q-switched using a rotating mirror as reported in [124], electro-optic Q-switch in [125] and a passive water and ethanol Q-switch in [126]. In [114,127]), passive Q-switching of an Er:YAG laser was demonstrated using a Fe2+ :ZnSe single crystal as the saturable absorber. As one can see from Fig. 13 the absorption cross section of Fe2+ ion in the ZnSe crystal at λ = 2.94 µm is 9.5 × 10−19 cm2 , which is approximately 35 times higher than the cross section for the laser transition in the Er3+ ion in yttriumaluminum garnet. A flashlamp pumped Er:YAG laser was used in [114, 127] for studying the Fe2+ :ZnSe as a passive Q-switch. The input-output characteristics of Er:YAG laser in free-running and passively (Fe2+ :ZnSe with initial transmission 85 %) Q-switched modes are presented in Fig. 17. The threshold pump energy for the Q-switched Er:YAG laser was 19 J. Under the pump energy Ep = 19−21 J the laser produced single 6.5-mJ, 50-ns (FWHM) giant pulses. Under Ep = 21–24 J the laser produced two similar giant pulses with a total energy 13–14 mJ, which followed each other after 30 µs. Under higher pump energies the laser produced three giant pulses separated by intervals of ∼25 µs with the total output energy of 22–23 mJ. The output laser energy in freerunning mode (without the passive Q-switch) was 30 mJ for a pump energy of Ep = 20 J. It means that the conversion efficiency (the ratio of energy of single giant pulse to the respective free-running energy) exceeded 20%. The broad absorption band of Fe2+ :ZnSe crystal (2.5–4.2 µm) makes it a promising material for passive Q-switching of mid-infrared laser cavities. 80

Output Energy, mJ

(iv) 60

40 (iii)

20

(ii) (i)

0 10

15

20

25

30

Pump Energy, J

Figure 17. Output-input characteristics of the free-running Er:YAG laser (iv) and Er:YAG laser passively Q-switched with Fe2+ :ZnSe crystal: (i)-one pulse, (ii)-2 pulses; and (iii)-3 pulses.

284


Output Energy, mJ

0.4

0.3

0.2

0.1

0.0 0

1

2

3

4

5

Absorbed Energy, mJ

Figure 18.

Input-Output characteristics of the gain switched Fe2+ :ZnSe laser at RT.

3.4.4. Tunable room temperature oscillation Efficient room temperature Fe2+ :ZnSe laser oscillation was achieved in [114,121] using a 2.94-µm passively Q-switched Er:YAG laser as a pump source. The nonselective 17-cm-long Fe2+ :ZnSe laser cavity had a 0.5 m radius high reflector and a flat, 90% reflectivity (λ = 4.4 µm) output coupler. Figure 18 shows the room temperature Fe2+ :ZnSe laser output as a function of absorbed pump energy. Maximum output energy and slope efficiency were 0.37 mJ and 13%, respectively. The threshold absorbed pump energy was 1.4 mJ. The 0.1 µm width output spectrum was centered at a wavelength of 4.4 µm. Under the high pump energy, the leading edge of the laser pulse was delayed with respect to the maximum of pump pulse by 20–30 ns, and the laser pulse duration did not exceed 40 ns. The output spectrum of the room temperature Fe2+ :ZnSe laser was continuously tuned using an intracavity dispersive element (70◦ CaF2 prism) placed in front of the high reflector. The tuning curve shown in Fig. 19 covers the spectral range 3.95–5.05 µm and on the short-wavelength edge is probably limited by the output coupler reflectivity, which sharply decreased for wavelengths shorter then 4.2 µm. The output spectrum width was 0.05 µm in this dispersive resonator. As it was mentioned above short pump pulses are required for room temperature operation of a Fe2+ :ZnSe laser because of the high rate of thermally induced nonradiative decay of the upper laser level. Hence, it was demonstrated that Fe2+ :ZnSe laser can efficiently operate in free running regime with a simple thermoelectric cooling. In this case, the slope efficiency of the laser with respect to absorbed energy was 30% and with respect to the incident pump energy can exceed 20%. In gain-switched regime Fe2+ :ZnSe gain materials holds promise to efficiently operate at room temperature in microchip as well as in external cavity configuration, where the

Output Energy, mJ


285

0.3

0.2

0.1

0.0 4.0

4.2

4.4

4.6

4.8

5.0

Wavelength, µm

Figure 19. Tuning curve of room-temperature Fe2+ :ZnSe laser with intracavity prism obtained at absorbed pump energy of 4.5 mJ.

slope efficiency with respect to absorbed pump energy was demonstrated to be up to 13%, which is equivalent to a quantum efficiency of 20%. The output spectrum of the room temperature Fe2+ :ZnSe laser was continuously tuned in the spectral range 3.95–5.05 µm. Thus, the total range of the Fe2+ :ZnSe laser tuning spans from 3.77 to 5.05 µm. 4. En-route to electrically pumped TM doped II–VI mid-IR lasers 4.1. TM-DOPED II–VI THIN FILMS FOR MID-IR APPLICATIONS

The wide-band gap II–VI semiconductors have been regarded as promising materials for blue-green diode lasers. Operation at lower voltages (2.4 V) in comparison to competitor GaN based devices make II–VI based LEDs attractive for numerous applications. The first observation of stimulated emission under optical pumping in Cd1−x Mnx Te-CdTe (764 nm) and ZnSe-Zn1−x Mnx Se (453 nm) multiple quantum well (MQW) structures grown by Molecular Beam Epitaxy (MBE) were reported in [128, 129] (note that, the stimulated emission from ZnSe under optical excitation has been previously investigated in [130]). Lasing effect at 453 nm in ZnSe/ZnSx Se1−x superlattice pumped by electron beam was reported in [131]. Further development of modern growth techniques such as MBE and MOCVD allowed manufacturing the p-n junction structure required for the diode laser. The first semiconductor pulsed blue-green LD at 77K was reported in 1991 [132]. The major technical challenge of II–VI based diode structures relates to the improvement of their operation lifetime. Although the progress in fabrication of reliable II–VI based laser diodes is not as fast as one would wish, the recent growth technology improvements and optimization of the structure of laser diodes

286


has resulted in a very positive outcome. The current record for the continuous operation of ZnSe laser diode fabricated by “Sony” is about 400 hours [133]. In case of light-emitting diodes, the resource of work already exceeds 10000 hours for operational current of 5–10 mA. [134]. Another important application area of the TM doped II–VI devices is a spintronics. The diluted magnetic semiconductors (DMSs) have been intensively investigated for many years. Most of the early papers were devoted to materials doped by Mn, Fe, and Co ions. DMS structures in Zn1−x Mnx Se and Zn1−x Fex Se/ZnSe superlattices were studied in [135–137]. Later possible stability of the ferromagnetic state of the Cr doped II–VI materials was theoretically predicted in [138]. The magnetic and transport properties in Zn1−x Crx Te and Zn1−x Crx Se thin film layers grown by MBE were studied in [139–143]. 4.1.1. Chromium and Iron doped ZnSe thin film Attention to the possible application of TM doped II–VI structures as light sources for the mid-infrared spectral range were simulated by a progress in the bulk lasers. A series of Cr-doped ZnSe epilayers for mid-infrared optical studies were grown in a MBE system on semi-insulating GaAs (001) substrates [144, 145]. Cr incorporation was performed using a crucible based effusion cell containing chromium diphenyl benzol tricarbonyl (CDBT). After cleaning the substrate was cooled to the growth temperature of 310C, the Zn source shutter was opened and 30 seconds later the Se shutter was opened and a 300–700 nm buffer layer of ZnSe was grown. The relationship between the Zn and Se fluxes were sustained at the level of beam equivalent pressure (BEP) (Zn/Se) = 2–2.5 resulting in a growth rate of 0.1 nm/s. Without interruption, the CDBT shutter was then opened and a ∼600–1000 nm layer of Cr:ZnSe was grown. During the growth of undoped ZnSe a 2x1 surface-reconstruction characteristic was observed, which corresponds to the surface enrichment with Se. During the Cr:ZnSe growth (BEP = 1.2x10−9 , 5.0x10−7 , and 1.1x10−6 torr, for CDBT, Zn, and Se, respectively) the transition (2x1) → (1x1) was observed, which is likely to indicate a sufficiently high concentration of CDBT molecules and dissociation products on the substrate. Energy-dispersive X ray (EDX) analysis of the Cr:ZnSe layer shows evidence of chromium in the film. More sensitive and precise laser mass-spectroscopy analysis showed that the chromium concentration was in the range of (2–5)x1019 cm−3 . Incorporation of chromium in the active Cr2+ state in thin MBE grown epilayers was further verified by optical spectroscopy and direct comparison of the PL spectrum of thin film to that of bulk Cr:ZnSe grown for mid-IR laser applications. The optical density of the GaAs/ZnSe/Cr:ZnSe thin film is shown in Fig. 20 A. The film thickness estimated from the oscillation period was d = 1.45 µm. Measurements performed with electron microscopy showed a comparable result: total ZnSe-ZnSe:Cr thickness of 1.36 µm with an active layer thickness of 1.04 µm. The PL signal was collected in 90◦ and 0◦

287

NEW REGIMES OF EXCITATION AND MID-IR T 0.9

A

iii Intensity, a.u.

∆ν=1400 cm−1

0.8 0.7 0.6

B

ii i

0.5 4000

5000

6000

Frequency, cm−1

7000

2.0

2.5

3.0

Wavelength, µm

Figure 20. A-Transmission spectra of the Cr:ZnSe thin film sample at room temperature; B-PL spectra of Cr2+ ions in GaAs/Cr:ZnSe thin film: 90◦ light collection geometry (iii), 0◦ light collection geometry (ii), and Cr2+ :ZnSe bulk crystal (i).

geometries, corresponding to the direction of light collection either normal or parallel to the film interfaces, respectively, and using erbium-doped fiber laser at 1.56 µm as a pumping source. The measured PL spectra of both the bulk Cr:ZnSe and the GaAs/Cr:ZnSe thin film at room temperature are depicted in Fig. 20 B. These spectra are quite similar, indicating that chromium has been successfully incorporated in the MBE grown thin films in the active Cr2+ state. A difference in the emission spectra could be attributed to waveguide effects in the ZnSe films. The PL decays of the studied samples can be fit within the experimental error by a single exponential curve. At room temperature the decay time of the thin film (τ = 3.2 µs) was half that of the bulk crystal (τ = 6.4 µs). This difference could be explained by the enhancement of the spontaneous emission in the thin film as well as concentration quenching beginning in the thin film samples with concentrations larger than 1019 cm−3 . The decay time of thin film fluorescence increases to τ = 5.4 µs with a reduction of crystal temperature to T = 23 K. The excited-state lifetime of the bulk crystal slightly drops to τ = 5.6 µs with temperature of T = 20 K. The changes of the PL lifetime of the bulk crystal can be explained by a lower probability of radiative transitions from the higher-lying components of the excited state sublevels. Mid-IR photoluminescence associated with Fe2+ transitions in Fe-doped ZnSe thin layers was reported in [146]. ZnSe epilayers 100 nm thick were grown by molecular beam epitaxy on GaAs semi insulating substrates. The growth was interrupted after 50 nm and the sample was transferred to a metallization chamber to deposit different [Fe] quantities ranging between 0.01–1 monolayers at room temperature. Each sample was then annealed at two different temperatures (350◦ and 400◦ ) under selenium flow. The study of the influence of different annealing temperatures on the photoluminescence spectra has shown a substantial Fe2+ incorporation. Optimal results were obtained using a doping procedure consisting


Intensity, a.u.

288

3.6

3.7

3.8

3.9

4.0

Wavelength, µm

Figure 21. Mid-IR photoluminescence in Fe-doped ZnSe thin layers at T = 20 K [146]

in five 0.03-monolayer thick Fe layers equally spaced by 200 nm and annealing temperature of 350◦ C. The mid-IR emission spectrum at temperature T = 20 K shows the characteristic luminescence band around 3.7 µm (see Fig. 21) under excitation by He-Cd laser. 4.1.2. Chromium doped ZnS and ZnTe thin film Thin films of Cr:ZnS grown by means of PLD were studied in [147]. Although the concentration of extended defects in PLD grown thin films is typically higher than those reported in Metal Organic Chemical Vapor Deposition and MBE, the simplicity and versatility of PLD renders it ideal for the low-cost, rapid prototyping of thin films in exploratory setting. PLD is a flexible platform for the deposition of homogeneous multilayer and multi-component semiconductor and oxide thin films of uniform thickness and it is believed that PLD could also be used for the fabrication of laser grade active materials. Another important feature of PLD is that being a well-known method for thin film synthesis, it usually provides a good transfer of material stoichiometry from the target to thin films. This is especially important for TM doped II–VI crystals. Cr-doped ZnS nanocrystalline films were synthesized by PLD as follows. The targets were made from the mixture of chromium (or Cr2 S3 ) and ZnS powders. The films are deposited on Si (100) substrate, which is heated at the temperature of 20–670◦ C during the ablation. 248 nm KrF laser with energy density of 1–2.5 J/cm2 and repetition rate of 10–50 Hz is focused on to the rotating target with an exposure time ranging from 5 to 50 minutes. Important parameters for thin film growth are: 1) the substrate temperature; 2) the laser repetition rate; 3) the laser energy; 4) the focal point size; 5) the substrate-target distance; and 6) the gas pressure.

289

NEW REGIMES OF EXCITATION AND MID-IR A

B

C

0.2 µm ZnS Si

2 µm

11.8 µm

ZnS Si

T,%

Cubic (111)

Ln (I)

Figure 22. SEM images of thin ZnS films grown by PLD [147]. A-thin film, grown with the deposition rate of 0.017 nm/pulse; B-thick film, grown with the deposition rate of 0.109 nm/pulse; C-surface SEM image of the thick film.

A

B

15

10

5 30

40

50

2θ, degree

60

1.5

2.0

2.5

Wavelength, µm

Figure 23. (A)- XRD scan of Cr doped ZnS crystalline thin film on Si (100), (B)- transmission spectra of 11.8 µm ZnS thin films.

Cr doped thin films were grown on the silicon (100) substrates at temperature of 550C or 650C. The thickness of the films achieved in our experiments varied from 200 nm to 12 µm, depending on the laser energy density and targetsubstrate (T-S) distance. The cross section and surface images of the ZnS thin films measured by SEM are shown in Fig. 22. Figure 22 A shows the SEM image of thin film obtained after 20-minute of ablation with a deposition rate of 0.017 nm per pulse. A deposition rate of 0.109 nm per pulse was achieved for the second sample (see Fig. 22 B) due to the shorter target-substrate distance. Figure 22 C shows the surface morphology of the 11.8-µm thin film. The surface of the thin film made in high vacuum (2.6 × 10−6 torr) is smooth and has few defects and clusters. The surface of the thin film made at 1.25torr (not shown) is composed of nanocrystalline clusters, and the average of the grain size is roughly less than 50 nm. Energy dispersive X-ray (EDX) characterization of grown Cr doped ZnS films showed that the concentration of chromium in the thin film is about 3.7×1020 cm−3 , which is in a good agreement with Cr concentration (∼3.5 × 1020 cm−3 ) in the initial target material. The phase quality and structure were investigated by thin-film X-ray diffraction. The XRD crystalline phases of the doped ZnS thin film are shown in Fig. 23 A.

290

SERGEY MIROV AND VLADIMIR FEDOROV B Intensity, a.u.

Intensity, a.u.

A (ii) (i)

2.0

2.5 Wavelength, µm

3.0

2.0

2.5

3.0

Wavelength, µm

Figure 24. Fluorescence spectra of (A) Cr2+ :ZnS thin films (i) and bulk crystal (ii) at RT; and (B) Cr-doped ZnTe thin layers at T = 5 K [148].

The film mainly consisted of cubic (111) phase with the FWHM of 0.44◦ in 2θ scan. The characteristic transmittance spectrum of grown Cr2+ :ZnS thin film is depicted in Fig. 23B. The transmittance curve featured an oscillatory character and was nicely fitted by a theoretical transmission characteristic (Airy’s function) of a Fabry-Perot etalon made from ZnS with a thickness of 10.7 µm, which was close to the 11.8 µm thickness measured by the SEM (see Fig. 22 B). The luminescence spectra of Cr2+ :ZnS films measured with 1.55 µm excitation from a CW Er fiber laser are depicted in Fig. 24 A (i). For comparison, the luminescence of the bulk crystal grown by chemical vapor transport technique is shown in Fig. 24 A(ii). Figure 24 A shows that thin film features luminescence band similar to the band in bulk crystal (slightly blue-shifted). The emission lifetime of Cr2+ :ZnS films with Cr2+ concentration of ∼2 × 1019 cm−3 was measured to be ∼3 µs. The emission lifetime was shortened to 1 µs for 1.8×1020 cm−3 and to 0.67 µs for 3.5×1020 cm−3 concentration of chromium. The concentration quenching is probably responsible for the lifetime shortening. The optical study of the chromium doped ZnTe grown by MBE was reported in [148–150]. The undoped ZnTe buffer layers with thickness 0.3–1.0 µm were grown on the GaAs substrate followed by the chromium doped epilayer. The growth rate was 0.7 µm/h. Chromium concentrations in the doped epilayers ranged from 1014 to 1020 cm−3 [149]. Figure 24 (B) shows the Cr2+ emission at 5 K from a sample with a Cr concentration ∼1018 cm−3 under 514.5-nm excitation [148]. In addition to the chromium mid-IR photoluminescence band under visible excitation, several bands were measured in the 1.1–1.8 µm spectral range [144, 147]. These bands were possibly due to internal transitions associated with the vacancies in the II–VI structure.

291

NEW REGIMES OF EXCITATION AND MID-IR 4.2. EXCITATION MECHANISMS OF TM DOPANT IONS IN II–VI BULK SEMICONDUCTORS

4.2.1. Inter-band excitation of Cr2+ and Fe2+ in bulk II–VI semiconductors For decades, the pure and doped (Cu and Mn) wide-bandgap II–VI semiconductors have been called promising materials for the fabrication of light-emitting devices and phosphors for electro-luminescent displays. It has been known for a long time that the inadvertent presence of TM ions such as chromium or iron provides very effective deactivation of visible light emission from donor-acceptor pair (DAP) or intra-shell transitions of Cu and Mn. Cr2+ and Fe2+ ions introduce deep energy levels in the forbidden gap, with 5 T2 being the ground state and 5 E the first excited state for chromium and vice versa for iron [151]. It was determined that in most of the chromium or iron-related recombination processes characteristic intra-center mid-IR emissions of Cr2+ and Fe2+ are induced (5 E → 5 T2 , with the wavelength ∼2 µm for chromium and 5 T2 → 5 E, with the wavelength ∼3.5–5 µm for iron) [152]. The nature of these processes of inter-band excitation and following Cr or Fe recombination can be quite different. It was found that mid-IR intra-shell PL of chromium and iron can be induced due to the following major processes depicted in Fig. 25. The first process relates to the binding of excitons by Cr and Fe ions. For most of the cases excitons bound by TM ions decay nonradiatively and energy can be is transferred from the excitons to states of the impurities, which were binding the exciton (Fig. 25a). Thus, the energy transfer results in intra-shell excitation (Cr2+ )∗ and not in ionization of a TM ion [153]. The second process (see Fig. 25b) relates to TM excitation caused by energy transfer from an adjacent DAP to a TM ion leading to TM intra-shell excitation [154]. As in case a), the energy transfer results in intra-shell excitation and not in ionization of the TM ion. The third process (see Fig. 25c) is due to TM2+ ionization caused by an Augertype process, followed by recapture of the hole or electron by the ionized Cr or Fe and as in case a) leads to mid-IR photoluminescence [153, 155]. a)

c)

b)

d)

e

e De (Cr2+)* h

De

Cr

(Cr2+)*

(Cr2+)* Cr

Cr2+ A h

Cr+

+

Ah h

(Cr2+)*

2+

h

h

Figure 25. Schematic diagram of major mechanisms of inter-band excitation of intra-shell mid-IR emission of Cr2+ and Fe2+ ions via a) energy transfer from the bounded exciton; b) energy transfer (ET) from adjacent DAP; c) TM2+ ionization caused by a three center Auger-type recombination (TCAR) processes; d) carrier trapping by ionized impurity.

292


The fourth process (see Fig. 25d) relates to the fact that carrier trapping by ionized impurities can proceed through one of the highly excited states of the TM2+ impurity, and thus results in intra-shell emission of TM ions [153, 156]. The fifth process is a direct excitation of the Cr2+ centers in ZnSe by the impact of hot carriers. This mechanism is usually observed in Mn:ZnS thin film electroluminescent (TFEL) devices [157, 165]. Another possible mechanism of excitation suggests impact ionization of Cr2+ [158]. Photoionization processes have been successfully utilized by Klein in [159] where the first observation of laser oscillations at 3.53 µm due to intrashell transitions of the Fe2+ centers in n-type InP:Fe under interband optical excitation was reported. 4.2.2. Optical sub-band (532 nm) excitation of Cr2+ in bulk II–VI semiconductors – excitation via photoionization transitions The information discussed in the previous paragraphs clearly states that both chromium and iron belong to the most active centers of interband recombination leading to intracenter excitation and mid-IR emission. It is of significant importance to study the nature of the physical mechanisms of Cr2+ and Fe2+ ions optical interband excitation, to identify the most effective mechanisms and to formulate the conditions necessary for achieving mid-IR lasing. The study of mechanisms of optical sub-band excitation of Cr2+ in ZnSe via photoionization transitions was performed in [160]. These mechanisms are very similar to the processes of Cr2+ excitation via carrier’s recombination and interband optical excitation. Understanding these mechanisms and achieving lasing of Cr2+ ions in ZnSe via its photoionization will be the first important step in demonstrating the feasibility of future Cr2+ :ZnSe mid-IR lasing under direct electrical excitation. Photoinduced EPR studies of Chromium doped ZnSe performed by Dr. Godlevski’s group [152–155, 161] show that the Cr2+ center demonstrates an acceptor nature and under optical excitation with energy in excess of ∼1.9 eV could release a hole in the valence band, with the Cr2+ being ionized into the Cr+ state. On the contrary, it has been shown that Cr+ , in spite of the fact that it is a good trap of holes, could be considered a donor center. Indeed, under optical excitation with energy larger than ∼0.8 eV Cr+ releases an electron in the conduction band forming Cr2+∗ in a highly excited state. Figure 26 a) and b) depicts two possible processes of Cr2+ optical excitation via ionization transitions. As already discussed, the Cr2+ /Cr+ level in ZnSe is located ∼0.8 eV below the conduction and ∼1.9 eV above the valence band of ZnSe, with a bandgap of ∼2.7 eV. According to the notation of Fig. 26 the energy of Cr2+ acceptor center “Eac ” is increased in the downward direction, while energy of the donor Cr+ center “Ed ” is increased in the upward direction.

293

NEW REGIMES OF EXCITATION AND MID-IR Eac ZnSe

CB

Cr2+/Cr+

5

T2 hνos

E

3

T1 3

T2

+ +

Cr2+*

-

ZnSe Cr2+/Cr+

5

hνpump

(b)

Eac

(a)

Cr

VB

Time

D

hνos

5E 3 T1 hνpump> 1.9 eV

2+*

CB

hνpump > 0.8eV 5 T2

2+*

Cr 3

T2

+

A

5 3

T1

5

T2 hνoss

E Cr

2+*

3

T2

VB

Time

Ed

Ed

Figure 26. Diagram of sub-band optical excitation of Cr2+ via ionization transitions: (a) Ionization through single photon interaction. (b) Multi-step ionization utilizing two pump photons and leading to the generation of two mid-IR photons.

In the first process shown in Fig. 26 a) an incident photon with energy 2.33 eV (532 nm) ionizes the Cr2+ ion to the Cr+ state by releasing a hole in the valence band: Cr 2+ + hν → Cr + + e+ VB (8) Subsequently a thermalized hole in the valence band is recombined with the Cr ion leading to formation of Cr2+ ion in a highly excited state Cr2+∗ : +

Cr + + e+ → Cr 2+∗

(9)

Finally this state relaxes to the 5 E first excited energy level of Cr2+ , which radiative decay is then accomplished by the emission of a mid-IR photon: Cr 2+∗ → Cr 2+ + hν MIR

(10)

The second route for Cr2+ excitation via photoionization transitions is depicted in Fig. 26 b). Initially, similar to process (8), a 532 nm photon ionizes the Chromium ion from a 2+ state to a 1+ state with the generation of a hole in the valence band: Cr 2+ + hν → Cr + + e+ VB (11) Next a second pump photon ionizes the Chromium ion from a 1+ state to a 2+ excited state putting an electron in the conduction band: Cr + + hν → Cr 2+∗ + e− CB

(12)

The excited Cr2+∗ , as in equation 10, relaxes to the 5 E first excited energy level of Cr2+ , which radiative decay is again accomplished by emission of mid-IR photon. As one can see, subsequent ionization of Cr2+ and Cr+ by two 532 nm

294


quanta results not only in emission of an mid-IR quantum, but also in the electron hole pair generation. Further recombination of the electron-hole pair could follow one of the routes of Fig. 25 b), c), d) resulting in Cr2+∗ emission of a second mid-IR photon. 4.3. EXPERIMENTAL VERIFICATION OF PHOTOIONIZATION TRANSITIONS

4.3.1. Photoconductance According to Fig. 26, 532 nm sub-band excitation of Cr2+ in ZnSe could lead to photoionization transitions (Eqs. 8–12) accompanied by the formation of either hole (Fig. 26 a) or electron and hole carriers (Fig. 26b). Photoconductance measurements of bulk polycrystalline diffusion doped Cr2+ :ZnSe samples have been performed in [160] to verify photoionization mechanisms and show the existence of photo-current under their 532 nm (2.33 eV) sub-band excitation. Initial photoconduction experiments were performed in [160] using a polycrystalline sample 1 × 4 × 8 mm clamped between conducting layers of indium. The 2nd harmonic (532 nm) of a Nd:YAG laser was incident upon the long edge of the sample and a current was measured using a load resistor of either 1M or 50 . Measurements of photocurrent versus light intensity and bias voltage have been performed. Figure 27 depicts a photocurrent response of the system detected with a 50 load. Comparison of the temporal shape of 532 nm excitation pulse (Fig. 27-i) and photo-conductance voltage on the 50 load resistor (Fig. 27-ii) shows that the detected photocurrent features a sub-nanosecond response time. This experiment demonstrates fast relaxation ( 1010 · cm. In n-type Al-doped samples the dark resistivity at room temperature was decreased down to a value of ρ = 104 –102 · cm. The deviations in the samples conductivity were due to differences in the parameters of the annealing process. The I–V characteristic of the Al-Cr:ZnSe crystal mid-IR electroluminescence is depicted in Fig. 30. As one can see from the Fig. 30 A, the I–V curve

298

SERGEY MIROV AND VLADIMIR FEDOROV µA

mA 10

A

20

B

5 0

0 −5

−20 −40

−10 −1.8 −1.2 −0.6 0.0 V

0.6

1.2

1.8

−15 −120 −90 −60 −30

0

30

60

90 120

V

Figure 30. Conductivity measurements of Cr:Al:ZnSe with In contacts for small (A) and large (B) potential differences across the sample.

features quasi-Ohmic behavior with R ≈ 53 k(ρ = 84 k·cm) for small (0.002) volume fraction of nanoparticles in the host material are the major issues for achieving stimulated emission. The approach to the utilization of II–VI nanocrystals co-activated by TM and dispersed in a conductive matrix for achieving mid-IR lasing under direct electrical excitation is based on three innovative ideas combined in one system. The first key element of the system utilizes the above mentioned principles of electrical excitation of closed pack films of undoped nanocrystals [172] and light emitting diodes (LEDs) designed [174] using semiconductor nanocrystallites (quantum dots) dispersed in a matrix. Using this approach Alivisatos [174] produced LEDs with high conversion efficiencies by utilizing quantum dots embedded in polymer matrices. The second key element relates to the fact that although nanocrystallites have not yet completed their evolution into bulk solids, structural studies indicate that they have the bulk crystal structure and lattice parameter [175]. This fact provides a strong foundation for our hypothesis that similar to the bulk II–VI crystals, tetrahedral coordination of TM2+ centers in II–VI nanocrystallites will provide a small crystal field splitting and place the dopant transitions into the mid-IR. The third key element of the system utilizes the “quantum-confined atoms” approach proposed

302


recently by Bhargava [176]. Because the radii of the excited states of an impurity (0.1 to 1 nm) are significantly smaller than the typical Bohr’s radii of exciton in semiconductors (3–10 nm) the wavelength of the impurity characteristic fluorescence should hardly change, whereas the spectroscopic characteristics such as oscillator strength and intensity of the mid-IR transition can be modulated by quantum confinement. The most interesting results, in the case of the quantum confined impurity, are an efficient energy transfer from the host nanocrystal to the impurity, accompanied by the relaxation of the selection rules for intra-shell transitions of TM2+ ions and corresponding fluorescence enhancement, which was verified for ZnS:Mn2+ nanocrystals by several authors [177, 178]. This is a very attractive approach, especially if combined with simultaneous confinement of carriers and photons, which provides smaller threshold and larger output power. 4.4.3. Electrical excitation of doped II-VI heterostructures For decades, the wide-band-gap II–VI semiconductors, particularly ZnSe, have been called promising materials for the fabrication of visible LEDs and lasers. The lifetime of II–VI based LEDs already exceeds 10,000 hours [179]. It is believed that use of II–VI heterostructures with an active layer co-activated by transition metals is a promising route for achieving broadly tunable mid-IR lasing under direct electrical excitation. The structure of the lasers could be similar to double heterojunction blue-green lasers based on a ZnMgSSe alloy forming a type I heterostructure with ZnCdSe [180, 181], where the active ZnCdSe layer is doped by Cr2+ or Fe2+ ions. The layer should be QW or QD and in addition to simultaneous confinement of carriers and photons the effective (due to phenomena of quantum confinement) energy transfer from the host to the emitting ion is provided. 5. Conclusion remarks There is significant progress in the development of room temperature mid-infrared lasers based on Cr2+ doped chalcogenides (mainly Cr2+ :ZnSe and ZnS). These lasers have already become sources of choice for those who need a compact system with continuous tunability over 2−3.1 µm, output powers up to 2 W, and high (up to 70%) conversion efficiency. This chapter has attempted to focus on the specific regimes of operation of these lasers. The unique blend of ultrabroadband gain bandwidth, high στ product and high absorption coefficients make these materials ideal candidates for the microchip regime of operation. Combined with fiber and/or diode pumping and technologically available polycrystalline material, Cr2+ doped chalcogenides could become practical and cost-effective lasers operating in the mid-infrared. Future improvements in the technology of hot-pressed ceramic Cr:ZnSe and ZnS materials could


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stimulate further cost reduction in the fabrication process and increase the output power and energy. In addition, Cr2+ doped chalcogenide crystals featuring ultrabroadband gain bandwidth are ideal candidates for ultrabroadband and multiline lasing in spatially-dispersive cavities. These lasers can operate at many wavelengths simultaneously, producing any pre-assigned output of desired spectral composition as well as a continuous ultrabroadband spectrum within the 2–3 µm spectral range. These lasers could find important practical application for free space optical communication, information coding, multi-analyte remote sensing, and numerous wavelength specific military applications. This chapter reviews these non-traditional Cr-doped mid-IR lasers as well as describes emerging Fe2+ :ZnSe lasers having the potential to operate at room temperature over the spectral range extended to 3.7–5.1 µm. Recent progress in Fe2+ :ZnSe materials demonstrate that lasers of this type can operate in gainswitched regime at room temperature with efficiencies of dozens of percents, generating output energies from mJ level at RT to hundreds of mJ with thermoelectric cooling of the crystal. Future progress in developing pure cw Fe2+ lasers depends on the success for a search for new, less quenched bulk materials. The use of low-dimensional Fe2+ :ZnSe and ZnS structures with reduced phonon density of states could suppress thermal quenching of Fe2+ ions and make possible RT lasing over the 3–5 µm spectral range with cw optical excitation. In addition to effective RT mid-IR lasing transition-metal doped II–VI media, being wide band semiconductors, hold potential for direct electrical excitation. Further insight into the excitation and deexcitation processes in TM doped bulk and quantum confined structures could open the way for future electrically pumped Cr2+ and Fe2+ doped quantum dot and quantum well structures. This work maps the initial steps towards achieving this goal by studying Cr2+ ion excitation into the upper laser state 5 E via photoionization transitions as well as via direct electrical excitation. It also shows that MBE and PLD provide optically active chromium and iron in different chalcogenides and represent a viable route for the fabrication of future optically and possibly electrically pumped waveguide confinement laser structures, broadly tunable in the mid-IR spectral region. 6. Acknowledgements It is our pleasure to acknowledge the valuable contributions of our colleagues I. Moskalev, A. Gallian, K. Graham, R. Camata, A. Stanishevsky, S. Wang, C. Kim, L. Luke, and V. Badikov. This material is based upon work supported by the National Science Foundation under Grants No. ECS-0424310, EPS-0447675, and BES-0521036. We also acknowledge support from the Nation Science Foundation (NSF)-Research Experience (REU)-site award to the University of Alabama at Birmingham (UAB) under Grant No. DMR-0243640.

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ADVANCES IN MID-INFRARED FIBER LASERS Mid-Infrared Fiber Lasers MARKUS POLLNAU1 and STUART D. JACKSON2 Integrated Optical Micro Systems Group MESA + Institute for Nanotechnology Department of Electrical Engineering University of Twente NL-7500 AE Enschede The Netherlands E-mail: [email protected] 1

2

Optical Fibre Technology Centre The University of Sydney 206 National Innovation Centre Australian Technology Park Eveleigh NSW 1430, Australia E-mail: [email protected]

Abstract. The current state of the art in mid-infrared fiber laser research is reviewed. The relevant glass and ceramic fiber host materials and the fiber, pump, and resonator geometries are introduced. Lasers operating on transitions ranging from 1.9 to 4 µm occurring in the rare-earth ions Tm3+ , Ho3+ , Er3+ , and Dy3+ and their population mechanisms are discussed on the basis of the fundamental spectroscopic properties of these ions. Continuous-wave fundamental-mode power levels ranging from a few mW near 4 µm up to 85 W near 2 µm have been demonstrated in recent years. Power-scaling methods and their limitations, the possibilities to optimize the population mechanisms and increase the efficiencies of these lasers, novel concepts, as well as the prospects of future mid-infrared fiber lasers at transitions in the wavelength range beyond 3 µm and extending to 5 µm are described.

1. Introduction Since the introduction of the double-clad fiber more than two decades ago and with the recent technological advances in the fields of fiber fabrication and beamshaped high-power diode lasers, the performance of diode-pumped fiber lasers has dramatically improved. Today, fiber lasers can compete with their corresponding 315 M. Ebrahim-Zadeh and I. T. Sorokina (eds.), Mid-Infrared Coherent Sources and Applications, 315–346. c 2008 Springer.

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bulk crystalline systems in certain applications, especially when fundamentaltransverse-mode, continuous-wave (CW) laser operation at output powers in the milliwatt to the kilowatt range is required. The increased recent interest in fiber lasers emitting at mid-infrared wavelengths between 2 and 3 µm primarily relates to the high application potential in laser micro-surgery. Due to the high absorption of water in the spectral region at 2.7–3.0 µm, high-quality laser cutting or ablation has been demonstrated in biological tissues. In addition, laser wavelengths near 2 µm could be suitable for tissue welding and lithotripsy. A number of other potential laser applications in the mid-infrared spectral region, e.g. environmental trace-gas detection, are becoming increasingly important. In all these applications fiber lasers may find their niches. The high costs of fabricating fibers with sufficiently low losses in the midinfrared region of the spectrum has impeded the necessary research efforts in the field of mid-infrared fiber lasers. The currently available fiber materials that are suitable as host materials for specific rare-earth-doped fiber lasers in the spectral region 2–5 µm will be introduced in Sect. 2. The invention of the double-clad fiber geometry and the holey fiber concept has accelerated the scaling of the output power and hence the success of high power fiber lasers. The various aspects of the fiber, pump, and resonator geometries will be described in Sect. 3. An overview of mid-infrared fiber lasers will be given in Sect. 4. Equipped with this general information, the performance of the most important mid-infrared fiber laser transitions in the wavelength range 2–3 µm will be discussed in detail. Sect. 5 will be devoted to the Tm3+ fiber lasers at 1.9 and 2.3 µm, whereas the Ho3+ fiber lasers at 2.1 and 2.9 µm will be discussed in Sect. 6. An impressive example of the variety of population mechanisms and operational regimes in a single system is the Er3+ 2.7-µm fiber laser transition, which will be investigated in Sect. 7. The latest member of the mid-infrared fiber laser group, the Dy3+ -doped fluoride fiber laser will be discussed in Sect. 8. At wavelengths beyond 3 µm, it becomes increasingly difficult to find suitable host materials for actively doped laser systems. This statement holds true for glass fibers in the same way as for crystalline materials. The prospects of future midinfrared fiber lasers in this wavelength range and novel concepts for mid-infrared fiber lasers will be discussed in Sect. 9. Besides general introductions to the different topics of lasers [1, 2] that include many aspects relevant also to mid-infrared fiber lasers, a comprehensive introduction to the field of rare-earth-doped fiber lasers can be found in [3]. 2. Fiber materials The choice of the fiber material involves a number of considerations: the maximum phonon energy, the environmental durability, the draw ability, the rare-earth solubility, and the purity of the starting materials. The maximum phonon energy

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Figure 1. Calculated and measured multiphonon-relaxation rates as a function of the energy gap between energy levels for glasses with different maximum phonon energies. (Data taken from [4,5]).

of the glass sets the overall infrared transparency range of the fiber and the multiphonon-relaxation rates that influence the quantum efficiency of radiative electronic transitions. The multiphonon-relaxation rates for the common glasses used for optical fibers as a function of the energy gap between energy levels are shown in Fig. 1. The optical transparency window relates to both the position of the band gap at short wavelengths and the infrared absorption cut-off wavelength. The latter position relates to the vibrational frequency ν of the anion-cation bonds of the glass. For an ordered structure, ν = (1/2π) k/M, (1) where M = m 1 m 2 /(m 1 + m 2 ) is the reduced mass for two bodies m 1 , m 2 vibrating with an elastic restoring force k. While for disordered structures like glass, this is not an accurate expression, nevertheless, it does highlight the important contributions to the glass transparency. The relative cation-anion bond strength is intimated by the field strength Z /r 2 , where Z is the valence state of the cation or anion and r is the ionic radius. Generally, glasses composed of large anions and large cations with low field strengths display high transparency in the mid-infrared spectral region. The important physical properties of the popular glasses used for optical fibers are shown in Table 1. 2.1. SILICATES

This glass is perhaps the most important material used for optical fiber production [3, 10], however, the maximum phonon energy is high (∼1100 cm−1 ) and has so far limited the emission wavelength of mid-infrared fiber lasers using

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MARKUS POLLNAU AND STUART D. JACKSON TABLE 1.

Properties of popular fiber materials.

Fiber material

Max. phonon energy (cm−1 )

Infrared transparency (µm)

Propagation losses (λ at minimum) (dB / km)

Thermal conductivity (W / K m)

Silica ZBLAN GLS

1100 [4] 550 [7] 425 [5]

3 µm is at the forefront of current fiber-laser research efforts. As mentioned above, fiber lasers operating on laser transitions that have wavelengths >3 µm will need to use glasses, which have very low phonon energies. While rare-earth-ion-doped heavy-metal oxides [159] have been studied for 2–3-µm mid-infrared emission, up to now, there has been no report of laser action for a fiber laser comprised of such a glass. Heavy-metal oxides do not seem to be suitable for lasers at wavelengths beyond 3 µm, because their maximum phonon energies are comparable to fluoride glasses and are too high for laser transitions beyond 3 µm. The chalcogenide glasses have, by contrast, been doped with a number of rare-earth ions including Ho3+ [160], Tm3+ [161], Tb3+ [161], Dy3+ [162], Pr3+ [163], and Er3+ [164,165] for studies into >3-µm mid-infrared luminescence, see Table 3. Fiber-laser action has been reported, however, only for an Nd3+ -doped GLS glass operating at a wavelength of ∼1 µm [166]. Recent demonstrations of fabricating Bragg gratings [167], single-mode fiber [168] and holey fiber [169] with chalcogenide glass highlight the utility of this glass for fiber-based applications; however, the purity and toxicity of the starting materials and the difficulty of making ultra-low loss fiber currently impede the widespread use of chalcogenide glass for mid-infrared fiber-laser applications. Once these obstacles have been overcome, future >3-µm fiber lasers will most likely involve the rare-earth ions Pr3+ , Nd3+ , Dy3+ , and Ho3+ doped into chalcogenide glass, because most TABLE 3. Examples of luminescent transitions investigated as candidates for mid-infrared lasers in sulfide fibers. Ion Dy3+ Tm3+ Ho3+ Dy3+ Tb3+ Ho3+

λLaser (µm) 3.2 3.8 3.9 4.3 4.8 4.9

Transition

Ref.

6H 6 13/2 → H15/2 3H → 3H 4 5 5I → 5H 5 6 6H 6 11/2 → H13/2 7F → 7F 5 6 5I → 5I 4 5

[162] [161] [160] [162] [161] [160]


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of the important mid-infrared transitions relevant to these ions can be accessed with pump-photon wavenumbers 3-µm output some time in the future. One area of particular interest in the development of Raman fiber lasers for emission at mid-infrared wavelengths. Recently [170], the emission wavelength from Raman fiber lasers has been extended to beyond 2 µm using three and four cascaded germanate-based Raman fiber lasers. To date, the longest wavelength and maximum reported output power from mid-infrared Raman fiber lasers is 2.2 µm and ∼210 mW, respectively [171]. In similar way to rare-earth-ion-doped fiber lasers, future Raman fiber laser systems will most likely involve non-oxide glasses in order to push the emission wavelength further into the mid-infrared. The recent demonstration of a chalcogenide glass Raman fiber laser shows some promise for future developments [172]. 10. Conclusions On our journey through the forest of the various established and yet to be demonstrated mid-infrared fiber lasers, we have found that the shorter the wavelength, the better is the laser performance. When we approach longer wavelengths in the mid-infrared spectrum, we find that the quality and durability of the required lowphonon-energy fibers decline, Stokes and slope efficiencies decrease, whereas the thermal problems increase. The assumption that due to its large surface-to-volume ratio, the fiber geometry might avoid all thermal problems has been questioned by several recent high-power fiber-laser experiments in the near- and mid-infrared spectral region. All the above phenomena are not much different from the situation found in crystalline lasers. Nevertheless, there remain distinct differences between these two host categories. When flexibility of the resonator design, short pulses, and high peak powers are required, the fiber shows some disadvantages. On the other hand, fiber lasers are preferred when high beam quality or low pump threshold combined with medium CW output power are desired. The low pump threshold is an invaluable advantage when cascade-laser operation is required to depopulate the long-lived terminating level of one laser transition by a second laser transition. The comparatively low dopant concentrations that are useful in fiber lasers due to the long interaction lengths can minimize energy dissipation by interionic processes but, equally true, limit the exploitation of these processes as a tool to optimize the population mechanisms of a certain laser system. Although still a great challenge with respect to the fabrication process, chalcogenide-glass fibers have the potential to revolutionize CW mid-infrared lasers in the wavelength range between 3–5 µm.

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MID-INFRARED OPTICAL PARAMETRIC OSCILLATORS AND APPLICATIONS

M. EBRAHIM-ZADEH ICFO-Institut de Ciencies Fotoniques, Mediterranean Technology Park, 08860 Castelldefels, Barcelona, Spain and Institucio Catalana de Recerca I Estudis Avancats (ICREA), Passeig Lluis Companys 23, 08010 Barcelona, Spain

Abstract. The current status of optical parametric oscillator (OPO) device technology and applications in the mid-infrared are reviewed. The discussion provides an overview of the latest developments in continuous-wave and pulsed OPOs at wavelengths between ∼1.5 and ∼12 µm, including innovative design concepts, novel laser pump sources, the most pertinent device characteristics, and new applications of OPO sources in the mid-infrared.

1. Introduction Optical parametric oscillators (OPOs) continue to fulfil their promise as versatile sources of tunable coherent radiation for spectral regions inaccessible to lasers. More than 40 years after demonstration of the first experimental device [1], OPOs have been finally recognised as viable and practical coherent light sources for a wide range of applications. The potential of OPOs derives from their exceptional wavelength versatility, which allows convenient access to substantial portions of the optical spectrum with a single device by suitable selection of nonlinear material and laser pump source. At the same time, because of the instantaneous nature of nonlinear gain, OPOs offer unique temporal flexibility, which permits output generation in all temporal regimes from the continuous-wave (cw) to ultrafast femtosecond time-scales by appropriate choice of pump laser. Such temporal flexibility is also not available to conventional lasers, where the generation of the shortest optical pulses is limited by the lifetime of the laser transition, which is in turn determined by inherent properties of the particular laser gain material. In addition, the OPO offers a practical all-solid-state design, can be configured in compact architectures, is capable of providing high output power and efficiency, and operates at or above room temperature without the need for cryogenic cooling. These 347 M. Ebrahim-Zadeh and I. T. Sorokina (eds.), Mid-Infrared Coherent Sources and Applications, 347–375. c 2008 Springer.

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characteristics make OPOs highly competitive alternatives to conventional lasers and other technologies for the generation of widely tunable coherent radiation in difficult spectral and temporal domains. In the current state of technology, OPO devices can provide spectral access from ∼400 nm in the ultraviolet (UV) to ∼12 µm in the mid-infrared (mid-IR), as well as the terahertz (THz) spectral region. They can also provide temporal output from the cw and long-pulse microsecond regime to nanosecond, picosecond, and ultrafast sub-20 fs time-scales. 2. Mid-infrared optical parametric oscillators The resurgence of interest in OPOs began in the 1980s, with the advent of a new generation of birefringent nonlinear crystals, most notably β-BaB2 O4 (BBO) and LiB3 O5 (LBO), and related materials. The high optical damage threshold, moderate optical nonlinearity, and favourable phase-matching properties of these crystals led to important breakthroughs in OPO devices, particularly in the pulsed high-intensity operating regime, enabling the development of a wide range of practical systems and their deployment in new applications. However, the limited infrared (IR) transparency of BBO and LBO confined the wavelength coverage of the majority of practical OPO devices to the visible and near-IR at wavelengths typically below ∼2 µm. The subsequent development of KTiOPO4 (KTP) and its arsenate isomorphs, namely KTiOAsO4 (KTA) and RbTiOAsO4 (RTA), offering improved effective nonlinearity and deeper transparency to ∼5 µm, provided added impetus for the development of OPOs for the mid-IR. However, the lack of optimal phase-matching conditions, particularly noncritical interaction, similarly confined the development of practical OPO systems based on these materials mainly to the high-intensity pulsed regime. On the other hand, the most important recent advances in OPO device technology over the past decade have arguably been brought about by the advent of quasiphase-matched (QPM) nonlinear crystals, particularly periodically-poled LiNbO3 (PPLN), as well as periodically-poled KTiOPO4 (PPKTP), RbTiOAsO4 (PPRTA), LiTaO3 (PPLT) and related ferroelectrics. The flexibility offered by gratingengineered quasi-phase-matching circumvents the need for optical anisotropy and can in principle permit wavelength conversion throughout the transparency range of the nonlinear material, not attainable under birefringent phase-matching. The technique also facilitates noncritical phase-matching (NCPM), overcoming the effects of beam walkoff, while at the same time offering long interaction lengths and substantially enhanced effective nonlinearities. Combined with a transparency out to ∼5 µm, the development of QPM materials, especially PPLN, has had an unprecedented impact on OPO device technology for the mid-IR. The impact has been particularly widespread in the cw and low-intensity pulsed regimes, where the development of practical OPO devices based on birefringent materials has been challenging. As a result, numerous new OPO devices based on QPM

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materials and using innovative design concepts have been developed over the past decade, offering unprecedented performance with regard to wavelength coverage, output power, pulse energy and repetition rate, conversion efficiency, spectral and spatial coherence, frequency stability, and fine tuning capability. Before the development of orientation-patterned GaAs (OP-GaAs), the mid-IR wavelength range available to OPO systems based on QPM materials was limited to ∼5 µm due to material absorption, but readily covers the important spectral range of 2–5 µm, which is of interest for numerous applications. Many of the developed OPO systems have now been successfully deployed in a variety of new applications including spectroscopy, environmental trace gas detection and monitoring, life sciences, biomedicine, optical frequency metrology and synthesis, safety and security, and imaging. For wavelength generation beyond ∼5 µm, the QPM nonlinear material OPGaAs, alternative birefringent mid-IR materials such as the newly developed LiInS(e)2 , HgGaSe2 , and related compounds, as well as the more established nonlinear crystals of AgGaS2 , AgGaSe2 and ZnGeP2 offer significant promise, with a number of OPO devices successfully demonstrated within the past five years. The deep mid-IR transparency (typically to ∼10 µm and beyond) together with large optical nonlinearities in these materials can permit wavelength generation well beyond the ∼5 µm limit attainable with PPLN or other periodically-pled crystals. However, the short wavelength absorption cutoff well above ∼1 µm precludes the direct use of widespread solid-state Nd pump lasers in many of these crystals, so that successful OPO implementation often requires cascaded two-step pumping arrangements to extend the pumping wavelength into the material transparency. Based on such techniques, successful operation of OPO devices has been achieved in a number of these materials at mid-IR wavelengths to ∼12 µm in the pulsed regime, although cw operation still remains challenging. The goal of this chapter is to provide an overview of the recent advances in OPO device technology for the mid-IR and their applications. The description will focus on cw and pulsed OPOs, since most of the important recent breakthroughs have been in this area. We will confine our discussion mainly to the developments since the year 2000. Other reviews on cw and pulsed OPOs, including synchronously-pumped oscillators, prior to the year 2000 can be found elsewhere [2, 3]. In the present discussion we do not concern ourselves with the background to the origin of the nonlinear optical effects, crystal optics and phase-matching, which can be found in other references [4, 5]. We also avoid detailed description of the fundamental concepts of optical parametric generation and amplification, design criteria and optimization of parametric devices, material and pump laser selection, cavity resonance and pumping architectures, which again can be found in other reviews [5–11]. Instead, we focus on a discussion of the most pertinent device characteristics and applications of mid-IR OPO sources. For the purposes of this chapter, we define the mid-IR spectral range to include devices operating at wavelengths primarily above ∼1.5 µm.

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3. Continuous-wave parametric oscillators Of the different types of OPO devices, the development of practical OPOs in the cw operating regime has been traditionally the most challenging, since the substantially lower nonlinear gains available under cw pumping necessitate the use of high-power cw pump laser or the deployment of multiply-resonant cavities to reach operation threshold. As in a conventional laser oscillator, the OPO is characterised by a threshold condition, defined by the pumping intensity at which the growth of the parametric waves in one round-trip of the optical cavity just balances the total loss in that round-trip. Once threshold has been surpassed, coherent light at macroscopic levels can be extracted from the oscillator. In order to provide feedback in an OPO, a variety of resonance configurations may be deployed by suitable choice of mirrors forming the optical cavity. The mirrors may be highly reflecting at only one of the parametric waves (signal or idler, but not both), in which case the device is known as a singly resonant oscillator (SRO). This configuration is characterised by the highest operation threshold. In order to reduce threshold, alternative resonator schemes may be employed where additional optical waves are resonated in the optical cavity. These include the doubly resonant oscillator (DRO), in which both the signal and idler waves are resonant in the optical cavity, and the pump-resonant or pump-enhanced (PE-) SRO, where the pump as well as one of the generated waves (signal or idler) is resonated. In an alternative scheme, the pump may be resonated together with both parametric waves, in which case the device is known as a triply resonant oscillator (TRO). Such schemes can bring about substantial reductions in threshold from the SRO configuration, with the TRO offering the lowest operation threshold. The comparison of steady-state OPO threshold under different resonance schemes is shown in Fig. 1, where the calculated external cw pump power threshold for the different resonance configurations is plotted as a function of the effective nonlinear coefficient of several materials including LBO, KTA, KTP, KNbO3 , PPLN and PPRTA. From the plot it is clear that for the majority of birefringent materials the attainment of SRO threshold requires pump powers on the order of tens of Watts, well outside the range of the most widely available cw laser sources. However, in the case of PPLN, the SRO threshold is substantially reduced to acceptable levels below ∼1 W, bringing operation of cw SROs within the convenient range of widespread cw solid-state pump lasers. With the PE-SRO, considerably lower thresholds can be achieved, from a few hundred milliwatts to ∼1 W for birefringent materials and below ∼100 mW for PPLN. In the case of DRO, still lower threshold of the order of 100 mW are attainable with birefringent materials, with only a few milliwatts for PPLN, whereas with the TRO thresholds from below 1 mW to a few milliwatts can be obtained in birefringent materials. It is thus clear that practical operation of cw OPOs in SRO configurations is generally beyond the reach of birefringent materials, but requires DRO, TRO,


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Figure 1. Calculated minimum thresholds for different OPO resonance configurations versus the effective nonlinear coefficients in various nonlinear materials. The calculation assumes confocal focusing and loss values that are typically encountered in experimental cw OPOs, the finesses representing round-trip power losses of approximately 2.0%. The plots correspond to a pump wavelength of 800 nm, degenerate operation, a pump refractive index of ∼1.7, a crystal length of 20 mm, signal and idler cavity finesses of ∼300, and a pump enhancement factor of ∼30. In the case of PE-SRO and TRO, the enhancement factor of 30 represents the maximum enhancement attainable with parasitic losses of ∼3% at the pump [12].

and PE-SRO cavities. On the other hand, implementation of cw SROs necessitates the use of PPLN or similar QPM materials, offering enhanced optical nonlinearities and long interaction lengths. However, the threshold reduction from SRO to PE-SRO, DRO, and TRO cavity configurations is often achieved at the expense of increased spectral and power instability in the OPO output arising from the difficulty in maintaining resonance for more than one optical wave in a single cavity. For this reason, the SRO offers the most direct route to the attainment of high output stability and spectral control without stringent demands on the frequency stability of the laser pump source. On the other hand, practical implementation of PE-SRO, DRO, and TRO requires active stabilization techniques to control output power and frequency stability, with the TRO representing the most difficult configuration in practice. In addition, practical operation of OPOs in multiply resonant cavities can only be achieved using stable, single-frequency pump lasers and such devices also require more complex protocols for frequency tuning and control than the SRO. More detailed description of the different resonance and pumping schemes for OPOs and analytical treatment of tuning mechanisms, spectral behaviour, frequency control and stabilisation can be found elsewhere [8].

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3.1. SINGLY-RESONANT OSCILLATORS

The SRO configuration represents the most direct route to the realisation of practical cw OPOs by offering the highest cw output power, convenient broadband wavelength coverage, high frequency stability, and the most simplified fine-tuning protocols. The SRO also offers the widest mode-hop-free tuning capability using standard cavity designs, and often without recourse to active electronic stabilisation and control. On the other hand, as highlighted above, the relatively high pumping intensities necessary to reach SRO threshold limit the use this resonance configuration to high-power cw pump lasers. Even in the case of PPLN, the minimum experimental thresholds for cw SROs still remain above ∼1 W, with typically a few watts of pump power required for reliable operation well above threshold. While the required pumping intensities are readily available to Q-switched and mode-locked pulsed lasers, they are beyond the reach of the most commonly available cw laser sources. Whereas the use of intracavity pumping techniques has enabled cw SRO operation in birefringent materials at practical pump power thresholds [13], the development of cw SROs in conventional external pumping has relied almost entirely on QPM materials, with the vast majority based on PPLN. The material has also been the prime candidate for mid-IR devices, because of its transparency to ∼5 µm, high optical quality and low transmission loss, large effective nonlinearity (deff ∼15 pm/V), long interaction length (up to 60 mm), NCPM capability, and ready availability. Combined with the development of new high-power solid-state pump sources based on crystalline, fiber and semiconductor diode lasers and innovative OPO device concepts, PPLN has led the way to realisation of truly viable cw SROs for the 1–5 µm spectral range with unprecedented performance capabilities, including pump power thresholds in the 1–5 W range, mid-IR output powers up to 10 W, high spectral and spatial beam quality and frequency stability, and mode-hop-free tuning capability in excess of 100 GHz. By using a 10-W cw single-frequency diode-pumped Nd:YAG laser at 1.064 µm, Van Herpen et al. [14] demonstrated a cw SRO based on PPLN with an idler tuning range of 3.0–3.8 µm in the mid-IR. The SRO, configured in a ring cavity and using a 50-mm-long crystal with fanned grating, exhibited a pump power threshold of ∼3 W and could provide a maximum idler output power of 1.5 W for 9 W of pump power at 3.3 µm. The combination of the single-mode pump laser, a ring cavity for the SRO, and the inclusion of an intracavity etalon enabled mod-hop-free tuning of the idler over 12 GHz by tuning the pump frequency over 24 GHz, with the idler mode-hop tuning range limited by mode hopping in the pump laser. Under this condition, 700 mW of single-frequency, smoothly tunable idler power could be provided by the SRO. In a later experiment, using the same PPLN crystal and identical cavity design for the SRO, the authors were able to improve the idler output power in the 3.0–3.8 µm range by


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increasing the available Nd:YAG pump power to 15 W and by optimising pump focusing and the SRO cavity length [15]. The SRO similarly exhibited a cw power threshold of ∼3 W, but could provide 2.2 W of idler power for 10.5 W of input pump power. The coarse and fine tuning properties of this SRO were similar to the earlier device. In a further experiment, using the same pump laser, the authors reported a cw SRO based on a multi-grating PPLN crystal and providing extended idler coverage into the 3.7–4.7 µm spectral range in the mid-IR [16]. The ringcavity SRO exhibited an oscillation threshold of between 5 W and 7.5 W over this spectral range and for an input pump power of 11 W could provide a maximum idler output of 1.2 W at 3.9 µm, decreasing to 120 mW at 4.7 µm. The increase in SRO threshold and corresponding decrease in output power were attributed to the increasing idler absorption in PPLN at longer wavelengths towards 5 µm. With the inclusion of an intracavity etalon to stabilise the resonant signal frequency, continuous mode-hop-free tuning of the idler over 24 GHz was achieved by tuning the pump frequency, but with a reduction in idler power by as much as 50%. Discontinuous mode-hop tuning of the idler output could also be obtained through rotation of the intracavity etalon. Subsequently, the use of a tunable high-power (>20 W) diode-pumped Yb:YAG laser in combination with two PPLN crystals with fanned gratings and two sets of OPO mirrors enabled the generation of widely tunable idler radiation with a total tuning range of 2.6–4.66 µm and at increased cw power levels [17]. With non-optimised mirror and crystal coatings, the SRO could provide 3.0 W of mid-IR idler output at 2.954 µm for 18 W of input pump power. The SRO could provide continuous mode-hop-free tuning over 100 MHz and mode-hop tuning over 25 GHz in the idler by tuning the pump laser. With the continued advances in pump laser technology, the development of cw SROs based on high-power diode-pumped fiber lasers and amplifiers has also become a reality. Fiber lasers are attractive alternatives as pump sources for cw SROs, because they combine the high-power properties of crystalline solid-state laser materials with significant wavelength tuning and excellent spatial beam quality in compact and portable design. The pump tuning capability allows rapid and wide tuning of the SRO output without recourse to temperature or grating period variation, while the high available powers and excellent beam quality allow access to SRO threshold and enable the generation of practical output powers. The use of fiber pump lasers can thus provide a versatile class of cw SROs for the mid-IR that offer the advantages of simplicity, compact all-solid-state design, portability, reduced cost, improved functionality, and high output power and efficiency. Operation of a cw SRO pumped by a fiber laser was first reported by Gross et al. [18] by using a tunable Yb-doped fiber laser. The laser delivered more than 8 W of cw output power in excellent spatial beam quality and was tunable over the wavelength range of 1031–1100 nm. With the use of a 40-mm-long multi-grating PPLN crystal and a ring cavity for the SRO, a cw idler output power of 1.9 W was generated at a wavelength of 3.2 µm in the mid-IR for 8.3 W of fiber pump power,

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Figure 2. (a) Experimental setup of the rapidly tunable fiber-laser-pumped cw SRO. The ring cavity of the fiber laser comprises the ytterbium-doped double-clad fiber pumped by a 976-nm diode laser coupled via a dichroic mirror (DCM), polarization-correcting optics (POL), two Faraday isolators (ISOs), half-wave plates (HWPs), and a polarizing beam splitter (PBS). The fiber-laser wavelength is all-electronically controlled by the AOTF in the laser cavity. The cw SRO consists of a PPLN crystal in a four-mirror ring cavity (M1 -M4 ) and generates rapidly tunable mid-infrared idler radiation. (b) A: Idler output power of the cw SRO as a function of the all-electronically tunable idler wavelength. B: Fiber laser power at the corresponding fiber laser wavelength. At 3.335 µm, a maximum idler power of 1.13 W is generated for a fiber laser power of 6.6 W at 1.074 µm [19].

with a corresponding SRO power threshold of 3.5 W. Idler wavelength tuning over 3.057–3.574 µm could be accomplished by varying the crystal temperature or changing grating period. However, wider and more convenient wavelength tuning was also available by exploiting the tuning capability of the fiber pump laser, where an idler tuning range of more than 700 nm over 2.980-3.700 µm was obtained by varying the pump wavelength between 1.032 µm and 1.095 µm. In a subsequent experiment, Klein et al. [19] demonstrated rapid wavelength tuning of a similar cw SRO by using electronic wavelength control of the Yb-doped fiber pump laser with an acousto-optic tunable filter (AOTF). A schematic of the experimental configuration and SRO output performance is shown in Fig. 2. The SRO, based on a 40-mm-long single-grating PPLN crystal, was arranged in a similar ring cavity and at a fixed crystal temperature and grating period could be rapidly tuned over 3.160–3.500 µm in the idler wavelength by electronically tuning the fiber pump laser from 1060 to 1094 nm. The 340-nm idler tuning could be achieved within a time interval of 330 µs, representing a frequency tuning rate of 28 THz/ms. The overall electronic tuning range of the fiber pump laser over 1.057–1.100 µm resulted in an SRO idler tuning range of 437 nm in the mid-IR from 3.132 µm to 3.569 µm. For the maximum fiber pump power of 6.6 W at 1.074 µm, the SRO generated an idler output of 1.13 W at 3.200 µm. The development of PPLN has also enabled extension of operation of cw SROs to semiconductor diode lasers as the primary pump source. The large effective nonlinearity (deff ∼15 pm/V) and long interaction lengths (up to 60 mm)


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Figure 3. (a) Schematic of experimental arrangement. diode: 3-section DBR diode laser, fiber pump: 25 W fiber-coupled 976 nm diode bar, ISO 1: 60 dB optical isolator, ISO 2: 30 dB optical isolator, Q: quarter wave plate, H: half wave plates, M1 -M4 : OPO cavity mirrors, PPLN: 40 mm PPLN crystal in oven. (b) Variation of OPO output wavelengths (lower plot), and corresponding idler output power (upper plot), during pump tuning by seed laser DBR section alone. PPLN grating period was 29.75 µm and temperature was 180.5◦ C [21].

under NCPM offered by PPLN have led substantial reductions in SRO threshold, compatible the use of high-power semiconductor diode lasers and amplifiers. An important advantage of this approach is the tunability of semiconductor diode laser, which allows rapid and continuous tuning of the SRO at a fixed temperature and grating period through pump tuning. However, to provide the sufficiently high cw pump powers (typically >1 W) and the highest beam quality to reach SRO threshold, it has been necessary to boost the available power from single-mode diode lasers using amplifications schemes. By employing a grating-stabilised, extended-cavity single-stripe InGaAs semiconductor diode laser at 924 nm as a master oscillator and a single-pass tapered amplifier, Klein et al. [20] demonstrated operation of a cw SRO based on 38-mm-long PPLN crystal with a pump power threshold of 1.9 W. For 2.25 W of diode pump power, 200 mW of singlefrequency idler radiation was generated at 2.11 µm. Wavelength tuning was achieved by electronic control of the master oscillator cavity, providing continuous mode-hop-free tuning of the diode pump radiation over 60 GHz from the power amplifier with a corresponding linewidth of 95% in the wavelength range 3200 nm < λ < 3800 nm (but 95% in the wavelength range 2800 nm < λ < 3400 nm. The best device has a threshold of only 10 mW coupled pump power (λp = 1541.5 nm) in cw-operation. A continuous tuning range of 2804 nm < λ < 3379 nm has been demonstrated by tuning the pump wavelength from 1532 nm to 1570 nm; the maximum output power is about 8 mW. The fine tuning behaviour is determined by a sawtooth tuning characteristics of about 180 GHz spectral width as known from bulk OPOs. Also doubly resonant OPOs with dielectric mirrors vacuum-deposited on the waveguide end faces have been developed; their oscillation threshold is somewhat higher than with external mirrors. Using a tuneable mode-locked fiber laser (10 GHz; 6.4 ps; 1545 nm < λ < 1565 nm) as pump source, short MIR-pulses (2850 nm < λs , λi < 3350 nm) have been generated by synchronous pumping of a specially designed 68.05 mm long, doubly resonant structure. The threshold (average) pump power is 300 mW (λp = 1554.75 nm); at 600 mW more than 4 mW of MIR (average) power is emitted. The results of modelling calculations indicate a great potential for further improvements. More complex OPOs with additional intracavity components such as wavelength splitters and phase shifters will be developed in the future to obtain true continuous tuning. References 1. R. Regener, W. Sohler: “Loss in low-finesse Ti:LiNbO3 optical waveguide resonators”, Appl. Phys. B 36, 143–147, 1985. 2. G. Schreiber, D. Hofmann, W. Grundkötter, Y. L. Lee, H. Suche, V. Quiring, R. Ricken, and W. Sohler: “Nonlinear integrated optical frequency converters with periodically poled Ti:LiNbO3 waveguides”, Proc. SPIE, vol. 4277, 144–160 (2001) Photonics West 2001, paper 4277–18 (invited) 3. A. Galvanauskas, M. A. Arbore, M. M. Fejer, M. E. Fermann and D. Harter: “Fiber-laser-based femtosecond parametric generator in bulk periodically poled LiNbO3 ”, Opt. Lett., Vol. 22, No. 2, 105–107 (1997) 4. M. C. Hübner, D. Hofmann and W. Sohler: “Efficient integrated Ti:PPLN MIR-optical parametric generator”, 2002 Technical Digest Nonlinear Guided Waves and their Applications (NLGW ’02), Stresa/Italy, September 2002, paper NLMD19 (post deadline paper)

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5. X. Xie, A. M. Schober, C. Langrock, R. V. Roussev, J. R. Kurz, and M. M. Fejer: “Picojoule threshold, picosecond optical parametric generation in reverse proton-exchanged lithium niobate waveguides”, J. Opt. Soc. Am. B 21, No. 7, 1397–1402 (1994) 6. S. Orlov, I. Kadetov, W. Grundkötter, V. Quiring, R. Ricken, W. Sohler: “MIR-optical parametric fluorescence: from photon pairs to pump depletion”, Proc. European Conference on Integrated Optics (ECIO ’05), Grenoble, April 2005, p. 237–240 7. W. Grundkötter: “Dynamik nichtlinearer Wechselwirkungen zweiter Ordnung in integriert optischen Wellenleitern”, Ph.D. thesis, University of Paderborn, 2006 8. W. Grundkötter: “Quantitative model for high power optical parametric fluorescence in Ti:PPLN channel waveguides” Proc. European Conference on Integrated Optics (ECIO ’05), Grenoble, April 2005, p. 630–633 (poster session) 9. D. Hofmann: “Nichtlineare, integriert optische Frequenzkonverter für das mittlere Infrarot mit periodisch gepolten Ti : LiNbO3 Streifenwellenleitern”, Ph.D. thesis, University of Paderborn, 2001 10. M. A. Arbore and M. M. Fejer: “Singly resonant optical parametric oscillation in periodically poled lithium niobate waveguides”, Opt. Lett. 22, pp 151–153, (1997) 11. S. Orlov, W. Grundkötter, V. Quiring, R. Ricken and W. Sohler: “Synchronously Pumped MidInfrared Ti:PPLN Waveguide Optical Parametric Oscillator”, Proc. Conference on Mid-Infrared Coherent Sources (MICS 2005), Barcelona/Spain, November 2005, paper Mo2

OPTICAL PARAMETRIC GENERATORS AND AMPLIFIERS

VALDAS PASISKEVICIUS∗ and FREDRIK LAURELL Royal Institute of Technology, Roslagstullsbacken 21, 10691 Stockholm, Sweden

Abstract. Mid-infrared parametric generators and amplifiers in quasi-phase-matched and birefirngence phase-matched nonlinear crystals are reviewed. Broadband mid-infrared generation using collinear and noncollinear parametric interactions is discussed. Keywords: Mid-infrared sources; optical parametric generators and amplifiers; quasi-phasematching.

1. Introduction Optical parametric generators (OPG) and amplifiers (OPA) have proven to be practical and reliable sources of tunable or broadband coherent radiation in the spectral regions which are difficult to reach using traditional laser materials. Midinfrared (MIR) is one of those rather inconvenient but very significant spectral regions not yet covered by efficient lasers. There are a number of applications which require pulsed mid-infrared coherent light sources generating pulses with pulse-lengths from nanoseconds to femtoseconds. Femtosecond pulses in this region are of interest primarily for ultrafast spectroscopy. For instance, sub-100 fs pulses in the region between 3 µm and 4 µm are required for investigation of hydrogen-bounded liquids by measuring relaxations of X-H (X = N, O) stretching vibrations [1]. Another example can be stretching vibrations of carbonyl bonds in proteins whose absorption lines fall between 5 µm and 6 µm [1]. Strong electric field within few-cycle optical pulses has been used for highharmonic generation in gases (see Ref. [2] for review). The highest cutoff frequency of the high-harmonics depends largely on the acquired ponderomotive energy, and it is inversely proportional to the fundamental carrier frequency of the excitation pulse. Thus, it would be advantageous to use high-energy, few-cycle pulses in the mid-infrared for high-harmonic generation. Clearly, this is an important motivation to look for broadband gain media which can handle relatively high ∗ To whom correspondence should be addressed.


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energies in MIR. Due to relatively low absorption in the parametric gain media, it can handle high-energy and high-average power pulses. In contrast, energy and power handling capability not easy in MIR lasers, because laser transitions with lower photon energies necessitate the use of low-phonon energy materials, which, as a consequence, have rather low thermal conductivity. Efficiency of THz generation employing optical rectification can be substantially enhanced in periodically structured materials, as discussed in Part II, Chapter 5. Orientation-patterned GaAs (OP-GaAs) [3] seems to be a very promising material in this respect. It is advantageous to use femtosecond pulses in MIR for pumping these structures. The first reason is a possibility to avoid two-photon absorption in the material by using longer pump wavelength; the second reason is related to the potentially higher conversion efficiency due to the fundamental limitations of the Manley-Rowe relations. Compact and efficient femtosecond MIR OPA based on periodically structured ferroelectric can be an excellent pump source for this application. Other applications, such as remote sensing using differential-absorption techniques or countermeasure systems [4], require relatively narrowband but highenergy and robust MIR sources. Optical parametric oscillators (OPO) can offer an efficient solution for these applications. However, the presence of optical resonators increases the complexity of the device and, inevitably, reduces the reliability. As many applications of MIR coherent light sources require deployment and hands-free operation on moving platforms or in environments with large level of vibrations and temperature variations, the reliability of the coherent light source becomes an important issue. OPG and OPA are relatively simple devices which can be operated over extended stretches of time with very few adjustments. In the remainder of this Chapter, following a brief theoretical introduction in the Section 2, we will discuss nonlinear materials employing birefringence phase matching as well as quasi-phase-matched (QPM) structures which have been increasingly used in recent years for MIR OPA and OPG. Section 3 will focus on broadband parametric generation and amplification and consider methods to overcome group-velocity mismatch (GVM). Special attention will be devoted to broadband parametric amplification in QPM structures. 2. Parametric generation and amplification 2.1. THEORETICAL BASIS

Parametric generation has been demonstrated [5, 6] soon after the invention of the laser. Essential theoretical aspects of parametric generators and amplifiers for narrowband pulse interaction have also been developed early on [7, 8]. Here, we consider parametric interactions attributed only to second order susceptibility χ(2) , i.e., the processes in non-centro-symmetric media. Three-waves at frequencies


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ωm (m = 1, 2, 3) interact in second-order nonlinear medium, and this interaction fulfills the energy conservation: ω1 + ω2 = ω3 ,

(1)

k1 + k2 = k3

(2)

and momentum conservation

conditions. Here, km = 2πn m /λm are the wavevectors of the corresponding waves and n m denotes the refractive indices in the nonlinear medium. For definiteness, the waves at the carrier frequencies ω1 ≤ ω2 < ω3 will be called idler, signal, and pump, respectively. When the signal and idler waves have the same frequency, ω1 = ω2 , the parametric interaction reaches degeneracy. For parametric interaction of narrowband signals it is convenient to express the electric field amplitudes of the plane waves by their monochromatic Fourier amplitudes [9, 10]: E(t, z) =

1 Eωm (z) exp(i(ωm t − km · z)) + c.c. , 2 ωm≥0

(3)

where z is the direction of propagation and c.c. signifies complex conjugate. By employing slowly varying envelope approximation, |d 2 E m /dz 2 | |2km d E m /dz|, the narrowband pulse parametric interaction is well described by a system of coupled-wave equations for the Fourier amplitudes: d E1 ω1 de f f ∗ E 2 E 3 exp(−i k · z), = −α1 E 1 − i dz cn 1 d E2 ω2 de f f ∗ E 1 E 3 exp(−i k · z), = −α2 E 2 − i dz cn 2 d E3 ω3 de f f E 1 E 2 exp(i k · z), = −α3 E 3 − i dz cn 3

(4a) (4b) (4c)

where c is the speed of light, de f f is the effective nonlinear coefficient dependent on the material, light polarization, and propagation direction and αm are the absorption coefficients for particular waves. The phase mismatch, defined here as k = k3 − k2 − k1 , plays a crucial role in determining the parametric interaction efficiency and the bandwidth and is the main parameter which can be manipulated either by the parametric interaction geometry and/or by employing artificially structured QPM materials. Optical parametric generation, parametric amplification and difference frequency generation (DFG), in essence, represent the same type of nonlinear interaction where the pump photon is split into two photons, signal and idler, according to the conditions Eq. (1) and Eq. (2). From Eq. (4) it is straightforward to obtain

396


the Manley-Rowe relations, which, in effect, show the detailed balance of the photon flux in the interaction: 1 d I1 1 d I2 1 d I3 = =− . ω1 dz ω2 dz ω3 dz

(5)

Here, Im = 0.5ε0 n m c |E m |2 is the optical intensity. The main difference between OPA, OPG and DFG comes from the initial conditions, namely, the ratio between the intensities of the pump and the signal waves. This ratio is very large in OPA and OPG, while in the DFG process, the pump and the signal have comparable intensities. It should also be noted that the DFG process is often used to reach long wavelengths, beyond 7 µm, in MIR spectral region. In the case of lossless parametric generation (αm = 0), the set of equations Eqs. (4), has well known solutions expressed in terms of Jacobi’s elliptic functions [11]. For most practical cases, an approximate solution (assuming non-depleted pump E 1 (z) ≈ const) gives an adequate description of nanosecond and picosecond OPA and OPG: ⎤ ⎡ sinh2 L 2 − (k/2)2 ⎦, I2 (L) = I2 (0) ⎣1 + 2 (6a) 2 − (k/2)2 2 2 − (k/2)2 sinh L ω1 , (6b) I1 (L) = I2 (0) 2 ω2 2 − (k/2)2 where L is the length of the nonlinear medium and where 2 =

8π 2 de2f f I3 n 1 n 2 n 3 λ1 λ2 0 c

.

In the limit of large gain (L >> 1), the Eqs. (6) simplify to give 2 2 I2 (L) = 0.25I2 (0) exp 2L − (k/2) , ω1 2 2 I1 (L) = I2 (0) exp 2L − (k/2) . 4ω2

(7)

(8a) (8b)

The pump non-depletion approximation is still used here, so the Eqs. (8) are valid when the signal and the idler powers are small compared to that of the pump, i.e., close to OPG threshold or in a first parametric amplifier stage, which can have power gains as large as 50 dB to 60 dB, but where the pump depletion is small. The Eq. (8a) defines the parametric signal gain which, for the perfect phase matching (k = 0), becomes: G = I2 (L)/I2 (0) = 0.25 exp(2L).

(9)


397

The factor in Eqs. (6–9) determines the parametric gain achievable in a given length of a particular nonlinear medium. It is customary to define a figure-of-merit (FM) from Eq. (7) by collecting the material-related parameters and the interaction wavelengths [12–14]: de f f FM = √ . (10) λ1 λ2 n 1 n 2 n 3 The FM is a convenient parameter to compare nonlinear media for a particular spectral range, but it neglects the effects of absorption and group-velocity mismatch. Idler absorption becomes an important issue in designing parametric devices above 2.5 µm in oxide materials such as β-BaB2 O4 (BBO) [15], LiB3 O5 (LBO) [16], and above 4 µm in LiNbO3 , LiTaO3 , and in KTiOPO4 (KTP) isomorphs [17]. Example of a transmission spectrum in 10 mm-thick KTP and RbTiOAsO4 (RTA) for light polarized parallel to the crystal z-axis is shown in Fig. 1. The absorption of the idler reduces the parametric signal gain by a factor [18, 19] G(α) 2[exp(−αL/2) − 1] + αL , (11) = G(0) (αL/2)2 where α is the absorption coefficient at the idler wavelength. For large absorption (αL 1), the gain reduction, Eq. (11), becomes inversely proportional to the crystal length: G(α) 4 = . (12) G(0) αL

Transmission

0.8

RTA KTP 0.4

0.0

0

1

2

3

4

5

6

Wavelength, µm

Figure 1.

Transmission in 10 mm-long KTP and RTA for the light polarized parallel to z-axis

398


Despite a high absorption of α = 70 cm−1 for the idler and the corresponding gain reduction, parametric oscillation has been demonstrated at 7.1 µm in periodicallypoled LiNbO3 [19] (PPLN). Another solution has been suggested which consists of using spatial decoupling of the generated idler wave into a non-absorbing linear waveguide located in proximity with the nonlinear interaction volume [20]. In addition to the gain reduction, the idler absorption has other effects on the operation of the OPG and OPA: (1) temperature gradients can develop along the crystal length which would lead to the broadening of the gain bandwidth, and (2) in the case of large absorption the interaction length reduces to approximately one absorption length L ∼ 1/α, which will also increase the interaction bandwidth. When considering the parametric interaction with broadband signals it is more convenient to use the coupled-wave equations Eq. (4) defined in the time-domain, instead of using them in the frequency-domain. This simplifies the inclusion of material dispersion contributions. By defining real electric field in terms of quasi monochromatic plane-waves and time-dependent envelopes: E(t, z) =

1 Eωm (z, t) exp(i(ωm t − km · z)) + c.c. , 2 ωm≥0

(13)

the lossless coupled-wave equations for the field envelopes become: ∂ 2 E1 ω1 de f f ∗ ∂ E1 1 ∂ E1 i E 2 E 3 exp(−ik · z), (14a) + − β21 2 = −i ∂z v g1 ∂t 2 ∂t cn 1 ∂ 2 E2 ω2 de f f ∗ ∂ E2 1 ∂ E2 i E 1 E 3 exp(−ik · z), (14b) + − β22 2 = −i ∂z v g2 ∂t 2 ∂t cn 2 ω3 de f f ∂ 2 E3 ∂ E3 1 ∂ E3 i E 1 E 2 exp(ik · z), (14c) + − β23 2 = −i ∂z v g3 ∂t 2 ∂t cn 3 where v gm ≡ 1/(∂k/∂ω)ω=ωm is the group velocity and β2m ≡ (∂ 2 k/∂ω2 )ω=ωm is the group-velocity dispersion (GVD) at a particular frequency. Coupled wave equations Eq. (14) are usually solved numerically, for instance, by using Fourier split-step algorithm. 2.2. PHASE MATCHING CONSIDERATIONS

2.2.1. Birefringent phase-matching As can be seen from Eqs. (8), the parametric gain is maximized at the phasematching point (k = 0). In scalar form, Eq. (2) can be written as n 3 ω3 − n 2 ω2 − n 1 ω1 = 0. One method to satisfy the momentum conservation is by employing material birefringence. So, in uniaxial crystals, the extraordinary index of refraction, n e (θ, T ), is a function of the polar angle, θ, between the crystal optic axis z and wavevector k, while the ordinary refractive index, n o (T ), depends only

399


on temperature T for a given wavelength. Thus, angle and temperature tuning can be applied to achieve birefringent phase-matching. Two types of birefringent phase-matching can be broadly defined: type-I corresponds to the process when signal and idler have same polarizations, while type-II phase-matching refers to the parametric process where signal and idler have perpendicular polarizations. Here we define the signal and the idler according to relations: ω3 > ω2 ≥ ω1 . For the type-I phase-matching, the oo → e and the ee → o process can be realized in negative (n e < n o ) and positive (n e > n o ) uniaxial crystals, respectively. For the type-II phase-matching, both eo → o and oe → e processes can be employed. In biaxial crystals, the refractive index ellipsoid lacks rotational symmetry, which makes the refractive indices dependent on both the polar angle θ and the azimuthal angle ϕ between the x-axis of the index ellipsoid and the wavevector projection in the x-y plane. By convention, two optical axes in biaxial crystal are located in the x-z plane. Both type-I and type-II phase-matching can be employed although the analysis is substantially more complicated than in the case of uniaxial crystals. It can, however, be simplified for the phase-matching in the principal planes of the index ellipsoid [21–23]. Any optimization procedure for a nonlinear process has to maximize the interaction efficiency which, apart from the phase-matching considerations should include a maximization of the FM (Eq. 10) and the nonlinear interaction length. It is often possible to phase-match the same signal and idler wavelengths using different types of interactions. One example is shown in Fig. 2, where birefringence phase-matching curves are given for the parametric generation of wavelengths up to 2.5 µm using pumping at 0.75 µm in the X-Z plane of BiB3 O6 (BiBO, see Ref. [24] for the crystal properties). Type-I and type-II processes can provide the same range of wavelengths, however from the FM dependencies, it becomes evident that a type-I process might be more efficient due to the angular dependence of the refractive indices and the effective nonlinear coefficient de f f . In the interactions involving extraordinary-polarized waves, the Poynting vector walk-off has to be taken into account, except for the cases when the interactions

2400

45

e

1600

1200

44

2000 58 1600 e

40

(a) 40

Signal, idler, nm

−1 8

FM x10 , V

Signal, idler, nm

50

o

2000

60 e

1200 48

52

Internal angle, deg

56

FM x108, V −1

55 2400

56

(b)

10.95 11.00 11.05 11.10 11.15 11.20 11.25 Internal angle, deg

Figure 2. Phase matching curves for parametric generation and FM in BiBO for type-II eo → o, (a), and type-I ee → o, (b), processes in X-Z plane. Pump wavelength 750 nm.

400


are phase-matched along the principle axes of the refractive index tensor. The latter case is called noncritical phase-matching and is usually a preferred regime of parametric generation. In general, the Poynting vector walk-off angle measured with respect to the wavevector can be calculated from tan ρ = −

1 dn e . n e dθ

(15)

There are three main effects associated with a Poynting vector walk-off: (1) a reduction of the effective interaction length. The effective interaction length can be defined as L ρ ≡ 2wo / tan ρ, where wo is the beam radius of the ordinarypolarized beam. (2) The interacting beams will become astigmatic. In OPG and OPA, even if only one wave is extraordinary-polarized (e.g. eo → o in Fig. 2(a)), both the signal and the idler will develop astigmatism due to gain guiding [25]. (3) Due to the walk-off and angular dispersion, the pulse front of a broadband extraordinary-polarized beam will be tilted with respect to the phase-front, i.e., the signal and the idler pulses will be angularly dispersed [25]. This is a general consequence of pulse propagation through an optical system with angular dispersion [26, 27]. An example of this effect is shown in Fig. 3, where simulation results are shown for the type-II OPG in 5 mm–long BiBO generating an ordinarypolarized idler at 2.4 µm and an extraordinary-polarized signal at 1.091 µm, with the phase-matching characteristics of Fig. 2(a) and pumped with 1 ps-long pulses at 0.75 µm. The pulse-front tilt has been determined from 3D simulation using a SNLO software package [28].

2

Tilt angle, mrad

1 signal

0 −1

idler −2 −3 −4 −3

−2

−1

0

1

2

3

Frequency, THz

Figure 3. Signal and idler pulse-front tilt angle versus frequency in 5 mm BiBO type-II oe → o OPG. Signal 1.091 µm and idler 2.4 µm. Pump energy 100 µJ, beam diameter 200 µm.


401

Effects of Poynting vector walk-off can be mitigated by employing a multicrystal parametric device consisting of pairs of nonlinear crystals, where the Poynting vector walk-off in the first crystal is offset by a symmetric walk-off in opposite direction in the other crystal [29]. Moreover, pre-tilting of pulse fronts in femtosecond OPA has been proposed as a means to manipulate the effective GVD in nonlinear crystals [30]. Clearly, the latter proposition is not limited to birefringence phase-matched crystals and can also be employed in QPM materials. Finally, it should be mentioned that the list of techniques for engineering the nonlinear interactions in birefringent materials does not end here. The composition of a nonlinear crystal can, in some cases, be adjusted to tune the dispersion parameters and, for instance, achieve noncritical interaction for particular wavelengths. The materials which have been demonstrated in the MIR spectral region, and are especially suitable for this type of tuning, are chalcopyrite semiconductor solid alloys A I B I I I C2V I such as AgGa1−x Inx S2 [31], AgGa1−x Inx Se2 [32], CdGe(As1−x Px )2 [33], AgGa(Se1−x Sx )2 [33], and Cdx Hg1−x Ga2 S4 [34]. In addition to tailoring the refractive index dispersion for noncritical interaction, the composition engineering also allows to choose a composition which would have lower two-photon absorption losses or a lower GVM [34]. Both parameters are of critical importance for generating ultrashort pulses in parametric devices. 2.2.2. Quasi-phase-matching Although the birefringence phase-matching is a powerful and versatile way to achieve efficient second-order interaction, and that it even lends itself to engineering to a certain degree, the technique, however, still limits the wavelengths accessible for the phase-matched interactions. Moreover, some semiconductors ¯ belonging to the 43m symmetry class with very large second-order nonlinear coefficients and high transparency in MIR region such as GaAs, GaP, InAs, InSb, InP, ZnSe, ZnTe are also optically isotropic so the birefringence phase-matching cannot be employed. In ferroelectrics such as LiNbO3 , LiTaO3 , KTiOPO4 isomorphs, the highest nonlinear coefficient corresponds to the diagonal χ(2) tensor element responsible for the nonlinear material reaction to the electric fields parallel to the polar axis. These coefficients can not be exploited by using birefringence phase-matching technique. In 1962 in a seminal paper, Armstrong et al [11] proposed a scheme for QPM by a one-dimensional modulation of the second-order susceptibilities. The modulation period should coincide with the coherence length, lc , of a particular interaction, i.e., the length over which the phase difference, klc = π , and the process reverses direction of the energy flow. This modulation of the second-order susceptibility is equivalent to adding a QPM wavevector, k Q = 2πq/lc , to Eq. (2), so that it now reads: k = k3 − k2 − k1 − k Q , (16)

402


where k Q can be either positive or negative, depending on the particular situation. This, simply, is a manifestation of the fact that Fourier transform of the spatial modulation profile of the χ(2) contains symmetric parts with both positive and negative spatial frequencies. The vector q has a direction along the direction of the χ(2) modulation and the length of |q| = lc /Λ, where Λ is the spatial modulation period. The modulation of the nonlinearity can be accomplished by periodically inverting the sign of the χ(2) susceptibility, utilizing a zigzag optical path in slabs of nonlinear material with total-internal reflection [11, 35, 36] or by modulating the amplitude of the second-order susceptibility by periodically modifying the material properties, for instance, by employing quantum-well intermixing in GaAs-AlAs waveguides [37–39]. The latter two QPM methods have rarely been used so far either because of the relatively high losses as in the case of the totalinternal-reflection geometry, or due to the small thickness of the modulation which mandates a waveguide geometry for the frequency conversion device. However these methods have been successfully demonstrated in semiconductors and, thus, remain of interest for the MIR spectral region. Periodic inversion of the sign of the nonlinearity is at the moment the most promising technique in bulk ferroelectric and semiconductor crystals. The first demonstration of the χ(2) sign-inverted QPM structure was accomplished in LiNbO3 by periodically modifying the crystal growth conditions which resulted in a boule with periodically inverted ferroelectric domains when the crystal was cooled below the Curie temperature [40]. However, the real breakthrough came when the electric-field poling technique was demonstrated in LiNbO3 [41]. The technique enabled periodic structuring of bulk crystals which is important for most applications. Following LiNbO3 , the technologies for structuring other bulk ferroelectric materials, such as LiTaO3 [42] and KTiOPO4 [43] isomorphs [44,45] have been successfully developed. Fig. 4 shows an example of a ferroelectric domain

Figure 4. To the left: selectively etched polar surface of periodically poled KTP with definitions of QPM period and QPM grating vector. To the right: distribution of the optical parametric oscillator (signal 1.72 µm, idler 2.789 µm) output power measured by scanning pump beam across the crystal aperture. Gray coding shows the output power in mW The pump average power is 3 W.


403

arrangement in periodically poled KTiOPO4 (PPKTP) which can be revealed by a selective chemical etching. The picture on the left of Fig. 4 shows the distribution of the MIR power in PPKTP optical parametric oscillator generating 1.5 W of average power in a 1.72 µm signal and a 2.789 µm idler [46]. Recently, this family of oxide ferroelectrics, where QPM structures have been realized and are of interest for the MIR spectral region, was joined by KNbO3 [47] and near-stoichiometric compositions of LiNbO3 [48] and LiTaO3 [49,50]. The latter crystals are substantially easier to pole than their congruent counterparts. Also, there are indications that stoichiometric MgO:LiTaO3 has higher damage threshold as compared to the congruent composition, attributed to a lower susceptibility to photorefraction. As has already been mentioned, the oxide materials have optical transmission cutoff at around 5 µm (see Fig. 1). Thus, recent demonstration of MIR parametric frequency converter with orientation-patterned GaAs [3, 51] is of very high importance for further expansion of the QPM technique to longer wavelengths. The second-order interactions in QPM structures, with any structure of the χ(2) modulation, can be analyzed by summing up the contributions from each domain where χ(2) is uniform. Considering that the change in the wave amplitudes over the domain length is small, and that the pump wave is not depleted, the Eqs. (4) can be written as iωu (e−ikz j − 1) E3 d j E v∗ (z j ) , cn u k j=1 n

E u (z n ) =

u, v = 1, 2;

u = v,

(17)

where d j is the nonlinear coefficient corresponding to each domain. For a rectangular periodic structure with a period Λ, the QPM interaction can be viewed as an interaction in a homogeneous crystal with an effective nonlinear coefficient equal to the Fourier coefficient of the d(z) spatial distribution [52]: de f f = 2d j sin(πm D)/(πm),

(18)

where D is the duty cycle, i.e., the ratio of the domain length with d j > 0 to that where d j < 0; m = Λ/2lc is called the order of quasi-phase-matching. In general, for small-signal interactions, when two out of three interacting waves can be considered constant, we can look at the QPM process as a frequency filter whose properties are given by a Fourier transform of the spatial distribution of the nonlinear coefficient d(z) [53]. For instance, in the case of difference-frequency mixing in the limit of low conversion efficiency and a narrow-band pump, the resulting difference-frequency amplitude spectrum can be expressed as [54]: E 1 (Ω) = d(Ω)E 2∗ (−Ω)E 3 ,

(19)

404


where Ω ≡ ω − ω1 is a detuning frequency and iω1 d(Ω) = − cn 1

∞ d(z) exp [−i (k(Ω)z)] dz.

(20)

−∞

Obviously, the relations, Eq. (19) and Eq. (20), are also valid in the case of birefringent phase-matching. However, only QPM gives the powerful and unique functionality of spectral manipulation due to the spatial modulation of the nonlinear coefficient. Fabrication of the QPM structures is always associated with errors in the domain duty cycle. The effect of these errors has been assessed in Ref. [52]. An extreme case of domain length error is a random distribution of the domain boundaries, i.e., structures with stochastic quasi-phase-matching [55, 56]. It has been shown [56] that even in a stochastic structure, there is a substantial enhancement in the conversion efficiency which grows directly proportionally to the number of domains encountered by the interacting beams. These structures might be of interest in semiconductor materials such as ZnSe, ZnS used for MIR applications, where the periodic structuring technology does not yet exist, but in which the polycrystalline matrix can be processed to give a predetermined average size of the polycrystallites with only a small standard deviation of the size distribution. 3. Broadband optical parametric generation and amplification 3.1. COLLINEAR INTERACTION

Parametric interactions of broadband signals are described by the coupled-wave Eqs. (14). Recasting the equations into a time-frame moving with the group velocity of the pump, it becomes evident that the parametric gain depends on the group-velocity matching between the pump and the parametric waves. It is useful to define a pulse-splitting length, l j3 ≡ τ/ j3 , where j3 ≡ 1/v g j − 1/v g3 , j = 1, 2 and where τ is the pump pulse length. If the signal and the idler pulses are moving in the same direction with respect of the pump, 13 23 > 0, then the splitting length determines the maximum interaction length and, thus, also the maximum nonlinear crystal length and gain. On the other hand, if 13 23 < 0, i.e., the signal and the idler are moving in the opposite directions with respect to the pump, the interaction becomes much more efficient and tends to stay within the frame of the pump pulse over the lengths substantially exceeding the pulse splitting length [14]. The OPA spectral bandwidth is primarily determined by the GVM between the signal and the idler and the GVD at the signal and the idler wavelengths. For collinear parametric interaction, when all interacting waves are propagating in the


405

same direction, the phase mismatch, k, can be expanded in Taylor series around the phase-matching point to give 1 1 1 ∼ ω + [β21 + β22 ] (ω)2 . − (21) k = v g1 v g2 2 In the case of a large gain, the full width at half maximum (FWHM) OPA signal bandwidth can be determined from Eq. (8a) and Eq. (21): √ 2 ln 2 1 . (22) υ ∼ = π L |12 | If the group velocities of the signal and the idler are approximately matched, 12 ≈ 0, as in the case of type-I near-degenerate parametric generation, the FWHM signal bandwidth will be determined by the GVD instead: 2(ln 2)1/4 1/4 1 ∼ . (23) υ = π L |β21 + β22 |1/2 The parametric signal bandwidth also depends weakly on the pump intensity through the parameter . Note that the increase in the gain bandwidth with increasing total gain in parametric amplifiers is opposite to that found in laser amplifiers, where the higher gain normally brings also spectral narrowing which is undesirable for high-energy, ultra-broadband signal generation [57]. The discussion in this chapter provides criteria which are useful for designing broadband collinear OPA. Unfortunately, there is no single parameter which would tell unambiguously which gain material and pump wavelength is best suited for broadband generation in the MIR. First, for choosing optimal material it is worthwhile to investigate the FM (Eq. (10)). The FM might be an adequate parameter for long-pulse OPA, where the GVM effects on the gain can be neglected. In Fig. 5, the FMs for different periodically-poled ferroelectrics: MgO:LiNbO3 (PPMgO:LN) [58], KNbO3 (PPKN) [59], PPKTP [60], RbTiOPO4 (PPRTP) [61], RbTiOAsO4 (PPTRA) [62], stoichiometric LiTaO3 (PPsLT) [63] are compared in the MIR region for 0.82 µm (Fig. 5a) and for 1.064 µm (Fig. 5b) pump wavelengths. The FM values in Fig. 5 correspond to the nonlinear coefficient, d33 , which was considered constant throughout the spectral range. The general trend in Fig. 5 is obvious – from the FM point of view it is beneficial to employ shorter pump wavelengths and a material with higher nonlinear coefficient. The GVM curves, corresponding to an OPA realized with the same QPM crystals and pumped at 0.82 µm and at 1.064 µm, are shown in Fig. 6a and Fig. 6b, respectively. Here, we use the product of the GVM between the pump and the signal, and the pump and the idler, 23 13 , in order to identify the spectral regions where this product is close to zero or slightly negative, i.e., the regions where

406

VALDAS PASISKEVICIUS AND FREDRIK LAURELL 3.2

PPMgO:LN

2.4

PPKN

2.0

PPMgO:LN

2.8

PPKN

2.4

PPKTP

PPKTP 2.0

1.6

PPRTP

PPRTP 1.6

(a)

PPRTA

1.2

(b)

PPRTA

PPsLT

PPsLT

1.2 1.5

2.0

2.5

3.0

3.5

2.0

4.0

2.5

3.0

3.5

4.0

4.5

Wavelength, µm

Wavelength, µm

Figure 5. Figure-of-merit (Eq. 10) plots for different QPM materials for 0.82 µm pumping (a), and for 1.064 µm pumping (b).

8

PPKN PPMgO:LN

PPKN

1 ∆23∆13x10 , ps /µm

2

6

0

PPKTP

8

8

4 PPRTP PPKTP

2

0

PPRTA PPsLT PPRTP

2

PPRTA

2

∆23∆13x10 , ps /µm

2

PPMgO:LN

−1

PPsLT

(a)

(b) −2

1.5

2.0

2.5 3.0 Wavelength, µm

3.5

4.0

2.0

2.5

3.0

3.5

4.0

Wavelength, µm

Figure 6. GVM between the pump and the signal and the pump and the idler in QPM ferroelectrics in the MIR OPA pumped at 0.82 µm (a) and 1.064 µm (b).

the highest broadband gain should be expected. The graphs indicate that PPKTP, PPRTP, and PPsLT should be promising materials for an 0.82 µm-pumped OPA in the spectral region above 3.2 µm, while in an OPA pumped at 1.064 µm, PPKN and PPRTA have low GVM in the region around 4 µm. PPKTP, on the other hand, should have large broadband gain at around 2.8 µm (signal of 1.7 µm) for a 1.064 µm pump. A similar analysis for a collinear OPA, using birefringence phase-matched crystals in the MIR region, have been reported in the literature: for pumping at the Ti:Sapphire amplifier wavelengths of KTP isomorphs [12, 64, 65], BBO [64], KNbO3 [1,5,66], MgO:LiNbO3 [67]; for type-I and type-II parametric interaction in AgGaS2 pumped by Cr:Forsterite (1.25 µm) [68, 69] and by 1.1 µm–1.6 µm OPA [70]; and for ZnGeP2 OPG pumped at near 2 µm and operating in the 2.5 µm – 10 µm wavelength region [71]. Finally, according to Eq. (22), the FWHM bandwidth of the collinear parametric interaction can be assessed by considering the GVM between the signal and the idler. In Fig. 7, the GVM 21 is shown as a function of the idler wavelength in

407

OPTICAL PARAMETRIC GENERATORS AND AMPLIFIERS 0.08 0.0 0.04

PPKN PPRTA −0.1

PPRTA

∆21, ps/mm

∆21, ps/mm

0.00

PPMgO:LN

−0.04

PPsLT

PPKN PPMgO:LN

−0.2

−0.08

PPsLT −0.3

PPRTP −0.12

(a)

PPRTP

(b) PPKTP

PPKTP −0.4

−0.16 1.5

2.0

2.5

3.0

Wavelength, µm

3.5

4.0

2.0

2.5

3.0

3.5

4.0

4.5

5.0

Wavelength, µm

Figure 7. GVM between signal and idler in QPM ferroelectrics in OPA pumped at 0.82 µm (a), and 1.064 µm (b).

an OPA pumped at 0.82 µm (Fig. 7a), and at 1.064 µm (Fig. 7b). First observation is that the GVM in all materials is lower for the 0.82 µm pumping. Consequently, larger bandwidths are expected in the Ti:Sapphire-pumped OPA and OPG as compared to those pumped with Yb3+ or Nd3+ -based lasers. Second, PPKTP, PPsLT and PPRTP should have larger bandwidths for the same gain compared to other QPM materials in the 0.82 µm-pumped devices. On the other hand, PPKTP has the largest GVM in the 1.064 µm-pumped OPA so its gain bandwidth will be strongly limited. Other materials, such as PPRTA and PPKN offer almost three-times smaller GVM in the MIR for this pump wavelength. It should also be mentioned that pumping at 1 µm is preferable because high-peak and high-average power pump sources can be readily made using very efficient diode-pumped Yb3+ -doped laser hosts. Traveling-wave OPA experiment [72] with an 80 fs Ti:Sapphire pumping of PPKTP and a narrowband seeding at 1.064 µm, has confirmed that, indeed, the parametric gain for the MIR idler increased by an order of magnitude as the idler wavelength was tuned from 3.2 µm to 3.8 µm, in accordance with Fig. 6a. The FWHM pulsewidth of 210 fs has been generated. At the same time, experiments on optical parametric chirped pulse amplification in PPKTP [73, 74] and PPsLT [75], using 1.064 µm pumping and a broadband seed at 1.57 µm (3.3 µm idler), have clearly shown the gain-bandwidth limitation, which did not allow the generation of pulses shorter than about 300 fs in 5 mm-long crystals. Similar bandwidth limitation has been observed in PPLN OPG pumped at 0.777 µm [76]. These results are in accordance with the theoretical dependencies shown in Fig. 7. Decreasing the nonlinear crystal length will increase the bandwidth (see Eq. (8), Eq. (22)), but, at the same time, the pump intensity has to be increased to reach the same amplification. Eventually, the gain bandwidth will be limited by the optical damage threshold. In practical devices, where certain reliability in the device performance is required, this method of expanding the amplifier bandwidth has limited value.

408


On the other hand, narrow-bandwidth, tunable sources in the MIR are of interest for spectroscopy applications. Owing to the high-nonlinearity of the QPM materials and a possibility to design QPM structures for specific parametric interaction wavelengths, compact and simple QPM OPG-OPAs can be alternatives to more complex OPOs. Indeed, spectroscopic applications of narrowband, tunable nanosecond OPG-OPA devices have been realized in PPLN using pumping by a compact, Q-switched Nd:YAG microlaser [77, 78]. In broadband picosecond and femtosecond devices, the pump intensities can be very high. In such circumstances, two-photon absorption of the pump becomes a serious problem. Two-photon absorption is especially important for MIR devices which employ semiconductor crystals as gain media. For instance, AgGaS2 , HgGa2 S4 should be pumped at wavelengths longer than 1.1 µm [68, 69, 79], for OP-GaAs, wavelengths above 1.55 µm should be used [51,80], while for ZnGeP2 , pump wavelengths should be longer than 2 µm [71,81]. In oxide materials, including structured ferroelectrics, the fundamental bandgap is in the ultraviolet spectral region. Consequently, two-photon absorption is not a major problem in OPA and OPG pumped in the near-infrared by commercially available laser sources. By considering Eqs. (22) and (23), it becomes evident that the broadest collinear parametric gain bandwidth should be achieved when the parametric degeneracy point is close to the zero-GVD point either for both waves in type-I interaction. In QPM materials, it is possible to realize such broadband interaction by designing a QPM structure which is phase-matched for degenerate parametric generation close to the zero-GVD point. One example of such a structure is PPKTP with a QPM period of 28 µm [82]. The graphs in Fig. 8 display the collinear 0

−20

Power, dB

−10

−30

827 819 , nm p

808 1000

1500

2000

2500

3000

3500

4000

Pu

m

4500

Wavelength, nm

Figure 8. Measured PPKTP collinear OPG spectra for different pump wavelengths. The QPM periodicity of PPKTP 28 µm, crystal length −8 mm.


409

OPG spectra in this structure pumped at several different pump wavelengths by narrow-band (0.8 nm FWHM) picosecond pulses derived from a Ti:Sapphire laser. At a pump wavelength of 0.827 µm, the parametric gain between 1.08 µm and 3.8 µm is realized with the FWHM bandwidth of 115 THz. A similar broadband OPG with spectral span between 4 µm and 9 µm has been reported with the OP-GaAs pumped by 1 ps pulses in the 3.1 µm–3.3 µm wavelength region [83]. 3.2. NONCOLLINEAR PARAMETRIC INTERACTION

The parametric fluorescence generated by a pump beam consists of an angular cone distribution with different output wavelengths radiating in different directions corresponding to the maximum gain [7, 84]. This angular distribution of generated wavelengths, in turn, gives rise to an angular dispersion of the parametric beams, which is similar to the pulse-front tilting, discussed in the subsection 2.2.1 of this chapter. It should be noted, that in contrast to the pulsefront tilting of the extraordinary–polarized beams in birefringent materials, the pulse-front tilting in noncollinear parametric interaction can develop for any beam polarization and is a function of the group velocity matching condition for a particular wavelength. The parametric gain bandwidth, which depends on the GVM between the interacting waves, is a function of the material dispersion and the beam-propagation geometry. Noncollinear parametric interaction was used in birefringence phasematched crystals to better match the group velocities and, thus, enlarge the gain bandwidth in near and mid-infrared OPAs [79, 85]. Noncollinear interaction also allows for easy geometrical separation of the signal and the idler beams, thus simplifying device configuration. A similar approach can also be used in OPAs employing QPM materials. Recently, the noncollinearity-induced modification of the retracing behavior of the parametric tuning curves close to degeneracy has been investigated in PPLN [86, 87] and in PPKTP [82] with the aim of increasing the parametric amplification bandwidth. The bandwidth broadening in noncollinear, nondegenerate MIR OPG has also been experimentally demonstrated in both materials [82, 88, 89]. The group velocity matching in the noncollinear interaction is equivalent to minimizing the angular dispersion in one of the parametric beams. Consider the general noncollinear interaction geometry in a QPM structure as shown in Fig. 9. The phase-matching conditions can now be written: k3 sin α p − k2 sin αs − k1 sin αi = 0,

(24a)

k3 cos α p − k2 cos αs − k1 cos αi − k Q = 0.

(24b)

The bandwidth of the OPA signal generated in a given direction will be inversely proportional to the angular dispersion. The signal angular dispersion can be

410


k3

k1 αsp

αp αs

k2

αi

Seed

kQ

Pump

Figure 9. General noncollinear QPM geometry used in OPA.

derived from Eq. (24) [89]: ∂αs 1 1 cos (αi − αs ) . = − ∂ω2 k2 sin (αi − αs ) v g1 v g2

(25)

Since αi ≡ αs for collinear signal and pump propagation, the signal angular dispersion is comparably large. Thus, the achievable OPA signal bandwidth is limited for the nondegenerate collinear configurations. As in the case of birefringence phase-matching, the angular dispersion is substantially modified by the noncollinear signal propagation with respect to the pump. The signal angular dispersion, given by Eq. (25), will decrease for increasingly noncollinear signal and pump propagation, since the change in the idler phase-matching angle is larger than the change in the signal angle, which is evident from Eq. (24a): |dαi /dαs | = k2 cos αs /k1 cos αi > 1.

(26)

The experimental demonstration of the OPA signal bandwidth broadening with increasing noncollinear angle between the pump and the seed is shown in Fig. 10. Here, the measurements were performed using 10 mm-long PPKTP with a QPM periodicity of 35.4 µm. The OPA was pumped by 5 ns pulses from a Q-switched Nd:YAG laser and the seed was derived from an infrared supercontinuum. The supercontinuum was generated by transmitting nanosecond OPO pulses at 1.54 µm through 5 m of a single-mode optical fiber. An increase in the OPA signal bandwidth from 2.4 THz to about 7 THz for the same signal gain has been obtained by just increasing the noncollinear seed angle by 31 mrad. Finally, the parametric gain bandwidth in the noncollinear QPM interaction can be maximized by using the same recipe as outlined in the subsection 3.1 for collinear QPM interaction, i.e., by choosing the pump wavelength in such a way that the degeneracy point of the parametric generator is close to the zero-GVD point. For instance, in PPKTP utilizing the d33 nonlinear coefficient, this means that pumping of the OPA at Ti:Sapphire wavelengths is required. The reduction of the angular dispersion and the dramatic increase in the signal bandwidth is illustrated in Fig. 11 where the signal detuning from degeneracy is plotted as a function of the external propagation angle. The pump wavelength is at 0.849 µm.


411

Idler (nm) 2750 1.0

2800

2850

2900

2950

3000

3050

3100

αsp=31.1 mrad

Normalised Power

0.8

0.6

αsp= 0 mrad

0.4

0.2

Seed

0.0 1620

1640

1660

1680

1700

1720

1740

Signal (nm) Figure 10. Signal spectra in collinear and noncollinear OPA seeded with infrared continuum

Signal detuning from degeneracy, THz

100

29.5µm

λp = 849 nm

80

60

26.3µm 40

28.5µm 20

0 0.00

28µm 27µm 0.02

0.04

0.06

0.08

0.10

0.12

External angle, rad Figure 11. Picosecond PPKTP OPG signal frequency detuning from degeneracy as a function of external angle for 0.849 µm pump wavelength for different QPM periodicities: 29.5 µm (open circles), 28.5 µm (solid circles), 28 µm (solid triangles), 27 µm (open squares), 26.3 µm (solid squares). Data points – central frequency, error bars mark FWHM of the frequency bandwidth. Lines – theoretical calculation.

412


The data points mark the experimentally measured central frequencies while the error bars show the FWHM of the signal spectrum. For a QPM period of 29.5 µm, the FWHM bandwidth of 64 THz has been obtained for a propagation angle of 31 mrad. It should be noted that this combination of pump wavelength and a QPM period is not unique for broadband noncollinear signal generation. For instance, a similar broadband signal has been obtained at 52 mrad angle for a QPM period of 26.3 µm and at a pump wavelength of 0.8 µm. This broadband noncollinear gain is not unique for PPKTP. Simulations have shown that PPsLT with a period of 22.5 µm would have a similar broadband signal generated at a 52 mrad angle for a pump wavelength of 0.808 µm. As it has been already mentioned, the MIR idler displays a substantially larger angular dispersion in a noncollinear QPM OPA, producing tilted pulses at the output of the crystal. Thus, the achromatic phasematching [90] or, in other words, pre-tilting of the idler would be required in order to obtain broadband amplification in the MIR region. The tilt can subsequently be compensated for by using dispersive elements. There is one caveat, however – in noncollinear OPAs, the effective interaction length becomes shorter due to the geometrical separation of the waves, similarly as in the case of the Poynting vector walk-off in birefringent materials. 4. Conclusions and future outlook This Chapter has attempted to present the status of OPA and OPG technologies and possible choices of gain materials relevant for the MIR spectral region, with a view of generating ultrashort and/or tunable pulses with µJ and higher energies. Unlike in the visible and the near-infrared, where BBO is the nonlinear crystal of choice for ultra-broadband parametric amplification, in the MIR region there is a much larger variety of materials with large nonlinearities and with capability for broadband phase-matching. The largest difficulty in this region is that highly nonlinear semiconductor crystals cannot be pumped with well-established commercial laser sources in the near infrared due to the large absorption in these materials. The notable exception is LiInS2 [91] which has high-transmission region from 0.6 µm to 8 µm and, thus, extends farther into the MIR than for all oxide materials, including the ferroelectrics. However, the nonlinearity in this material is lower than in the structured ferroelectrics. QPM technology has a definite appeal due to a unique possibility to engineer the nonlinear interactions. By using different QPM materials, this additional degree of freedom can now be employed in the spectral regions from the ultraviolet to the MIR extending to approximately 16 µm. OP-GaAs is, so far, the only semiconductor with proven QPM structuring technology, but it should be expected that other semiconductors with even higher nonlinearities, especially


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TUNABLE THz SOURCES BASED ON QUASI-PHASE-MATCHED GALLIUM ARSENIDE Tunable THz Sources KONSTANTIN VODOPYANOV E. L. Ginzton Laboratory, Stanford University, Stanford, CA 94305, USA, [email protected]

Abstract. We report a new highly efficient source of frequency-tunable (0.5–3.5 THz) narrowbandwidth terahertz wave packets with up to 1mW average power, based on parametric downconversion in quasi-phase-matched GaAs. Different lasers were employed as a pump source, including femtosecond OPA/DFG system (wavelength range 2–4 µm), Tm-fiber femtosecond laser (wavelength ∼2 µm), and near-degenerate synchronously-pumped picosecond OPO system with extra- and intracavity THz generation. We prove experimentally that the optical-to-terahertz conversion efficiency is fluence–dependent, with the scaling factor being the same for femtosecond (optical rectification) and picosecond (difference frequency generation) pump pulses, with optical-to-terahertz conversion efficiency on the order of 0.1% per µJ. Keywords: Terahertz wave generation, optical rectification, difference frequency generation, quasiphase-matched, gallium arsenide GaAs.

1. Introduction There is a potential for using terahertz (THz) waves (1 THz = 1012 Hz) for numerous applications including real-time imaging (THz waves have, in many occasions, much smaller scattering than the optical waves and thus can penetrate many materials) and spectroscopy, both in condensed and gaseous phase, because of richness of absorption spectra in the THz range. Parametric frequency down-conversion of optical pulses is an established, but inefficient so far, way of generating terahetz radiation. By this technique, one can generate either monochromatic THz radiation using difference frequency generation (DFG) or broadband THz transients using optical rectification (OR). In the DFG case which was first demonstrated in 1972 in GaAs [1], two optical waves of different frequencies are mixed in a nonlinear crystal to generate monochromatic THz frequency at their beat note. In the case of optical rectification (OR), sufficiently short laser pulses are used as a pump. A broadband THz output 419 M. Ebrahim-Zadeh and I. T. Sorokina (eds.), Mid-Infrared Coherent Sources and Applications, 419–441. c 2008 Springer.

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is produced via difference-frequency mixing between Fourier components of the same optical pulse (self-frequency-mixing). First demonstrated with picosecond (ps) pulses in ZnTe, ZnSe, CdS and quartz [2] and in LiNbO3 [2, 3], optical rectification was later extended to femtosecond (fs) laser pulses [4] which allowed to generate much broader bandwidths in the terahertz region [5], and even reach mid-IR frequencies of 40 to 50 THz [6, 7]. Nonlinear optical frequency conversion is intensity-dependent and it might appear that, from the viewpoint of achieving high optical-to-THz efficiency, OR is more attractive than DFG, because of access to higher peak powers with fs pulses. However, in the OR case, the propagation velocity of the THz wave packet should match that of the optical pulse and this group-velocity walk-off constrain limits the useful length of the crystal, to typically 1mm or less. Another constrain for both OR and DFG is that conventional crystals used for THz generation (LiNbO3 , ZnTe) have high absorption at THz frequencies (characteristically 10–100 cm−1 ). That is why optical-to-THz conversion efficiencies achieved so far are low [8], typically 10−6 –10−9 , even with femtosecond pump pulse energies as high as 10 mJ [9]. In order to enhance the optical-toTHz conversion efficiency, larger interaction lengths with collinear interaction of THz and optical waves is desirable. A way to increase the interaction length by means of using the tilted-front pump pulses was demonstrated recently [10]. The authors reported conversion efficiency of 5 × 10−4 and achieved 240 µW THz average power from a bulk lithium niobate crystal when pumped by optical pulses from a Ti:Sapphire oscillator – regenerative amplifier system with 500 mW of average power at 1 kHz. Another approach to increase the efficiency of OR is to use quasi-phase-matched (QPM) nonlinear materials, as was first demonstrated with periodically-poled lithium niobate crystals (PPLN) [11, 12]. The authors used femtosecond pulses at 800 nm and PPLN crystal with different QPM periods and achieved ∼10−5 conversion efficiency. PPLN was cryogenically cooled (T = 18 K) to reduce THz absorption. Optical rectification with QPM crystals gives rise to a multi-cycle narrow-band terahertz radiation. Each inverted domain of a QPM nonlinear crystal contributes a half-cycle of the THz pulse [10] and thus the THz wave packet has as many oscillation cycles as the number of quasi-phase-matched (QPM) periods over the length of the crystal (Fig. 1). In this Chapter, we report on THz applications QPM GaAs. GaAs is attractive for THz generation because of several reasons: it has (i) small terahertz absorption coefficient, (ii) large coherence length due to small mismatch between the optical group and THz phase velocities, and (iii) high thermal conductivity. THz wave generation in QPM GaAs was first demonstrated in 2005 [13]. To a large extent, the progress in QPM GaAs applications for THz generation became possible due to earlier development at Stanford of technology of growth of GaAs with periodic orientation reversal [14, 15], originally targeting mid-IR applications.

TUNABLE THz SOURCES BASED ON QPM GAAS

421

Figure 1. Illustration of THz generation by optical rectification of femtosecond pulses in an EO crystal with periodically inverted sign of χ (2) .

2. Theory of optical THz generation in QPM media Let us first evaluate maximum optical-to-terahertz conversion efficiency which can be achieved by use of a quasi-phase-matched down conversion process (OR or DFG) and find optimal conditions in terms of pulse format. 2.1. PLANE WAVE ANALYSIS, FEMTOSECOND PULSES

Consider as an optical pump, bandwidth-limited fs laser pulses propagating along z in the form of infinite plane waves, with the gaussian time envelope of the electric field 1 E(t) = E 0 exp −t 2 /τ 2 exp[i(ω0 t)] + c.c., (1) 2 where ω0 is the central frequency and τ is the pulsewidth. Intensity envelope is thus I (t)∼ exp(−2t 2 /τ 2 ) and the pulse duration at full width of half-maximum is τFWHM = (2 ln 2)1/2 τ = 1.18τ. Using Fourier transform pair in the form ∞ f (t) =

f (ω) exp(iωt)dω −∞

1 f (ω) = 2π

(2)

∞ f (t) exp(−iωt)dt,

(3)

−∞

we get (z = 0) a transform of the electric field (1) as 2 τ (ω − ω0 )2 E0τ , E(ω) = √ exp − 4 2 π

(4)

422


and for arbitrary z E(ω, z) = E(ω) exp[−ik(ω)z], (5) where k(ω) is a module of the wave vector. The one-dimensional equation (scalar form) for the Fourier component of the THz field at the angular frequency , E(, z), follows directly from Maxwell’s equations and is given, in the slowly varying envelope approximation and in the limit of no absorption, by [16]: d E(, z) iµ0 c PN L () exp(ikz), (6) =− dz 2n 1 where the Fourier component of nonlinear polarization, PNL (), can be expressed through the material nonlinear susceptibility χ(2) as ∞ (2) E(ω + )E ∗ (ω)dω (7) PN L () = ε0 χ −∞

Here ε0 and µ0 are respectively the permittivity and permeability of free space, c is the speed of light in vacuum, n 1 – THz refractive index. From (4) and (7) it follows that 2 2 2 τ (2) E 0 τ (8) PN L () = ε0 χ √ exp − 8 2 2π and (6) becomes 2 2 χ (2) E 02 τ d E(, z) τ exp(ikz) (9) exp − = −i √ dz 8 4 2πcn 1 The k-vector mismatch k is given by the following relation 2π k = k() + k(ω) − k(ω + ) − (10) Since ω, we can replace k(ω + ) − k(ω) by (∂k/∂ω)opt [17] and obtain k in the form 2π n T H z 2π dk gr n T H z − n opt − k = − − = , (11) c dω opt c gr

where n THz is the phase refractive index for the THz wave, n opt is the optical group velocity refractive index, and is the QPM orientation-reversal period. ∂2k We assumed here that the optical group velocity dispersion ∂ω 2 is negligible (which will be justified later). With the undepleted pump approximation, (9) can be integrated to get the power spectrum of the THz field 2 2 2 de2f f E 04 τ 2 2 τ 2 |E(, L)| = sinc2 (k L/2) L exp − (12) 2 2 4 8πc n 1 Here we assumed χ (2) = 2deff , where deff = (2/π)dOR is an effective QPM nonlinear coefficient; dOR corresponds to the optical rectification process dOR


423

(0 = ω − ω) and is derived from electro-optic coefficient ri jk using the relation [16] djkl = −n 4 /4rjlk , where n is the optical refractive index. In GaAs, for example, r14 = 1.5 pm/V [18], corresponding to nonlinear coefficient dOR = 46 pm/V. If the nonlinear crystal is long enough, terahertz radiation will be emitted in the form of narrow-band spectrum centered at 0 , corresponding to k = 0 condition 2πc 0 = (13) , λT H z = n, n gr where n = n T H z − n opt is the index mismatch. By differentiating (11) we get d(k) = n and the phase-matching acceptance bandwidth based on the condition d c k L/2 = π c 2πc accept = k accept = (14) n Ln We assumed that n THz is nearly constant, which is true for frequencies well below the lowest phonon resonance. For GaAs, this resonance is at 8.1 THz [19], gr n THz ≈ 3.6 [20], n opt = 3.41 (for the 2.1-µm optical pump) [21], n = 0.19, accept and acceptance bandwidth for L = 1 cm crystal is νT H z = 5.3 cm−1 . In the absence of quasi phase-matching, interaction between the optical and THz waves is limited to the coherence length lc = π c/ n,

(15)

corresponding to the klc = π condition. It is worth mentioning that backward emission of THz wave is also possible. In this case, the phase-matching condition becomes 2π gr n T H z + n opt − =0 (16) c Optical-to-THz energy fluence efficiency for plane waves (PW) is Fluence(T H z) (17) ηTP HWz = Fluence( pump) Pump fluence is given by ∞ π cε0 n 2 2 cε0 n 2 2 |E(t, 0)| dt = F pu = (18) E0 τ , 2 2 2 −∞

where n 2 is the optical refractive index. The THz fluence is ∞ ∞ cε0 n 1 cε0 n 1 2 |E T H z (t, L)| dt = |E(, L)|2 d, 2π FT H z = 2 2 −∞

where we used Parseval’s theorem:

−∞

∞ −∞

| f (t)|2 dt = 2π

∞ −∞

| f ()|2 d.

(19)

424


From (12) and (18–19) we get

ηTP HWz

∞

2 de2f f E 02 τ 2 = √ L 2 2πc2 n 1 n 2

−∞

τ 2 2 2 n( − 0 )L sinc d, (20) exp − 4 2c

where we replaced k L/2 with n( − 0 )L/2c. For L lc , which is equivalent to the condition accept 0 , sinc2 function under the integral dominates and we obtain ηTP HWz = g1

230 de2f f

Llc F pu = g1 2

πε0 c3 n 1 n 2

220 de2f f L ε0 c2 n 1 n 22 n

(21)

F pu

where 0 is given by (13). The reduction factor

g1 = exp(−(τ 0 /2)2 ) = exp −(πνT H z τ )2

(22)

reflects the fact that the optical pulse should be short enough, so that its spectrum span is larger than the THz frequency 0 . For very short optical pulses, τ 0 < 1, g1 ≈ 1 and optical-to-THz conversion efficiency depends on pulse fluence only, not intensity. Fig. 2a shows the reduction factor g1 as a function of the product νTHz τ. For example at νTHz τ = 0.1, g1 = 0.91, close to unity, and experiences little change as the pulse duration is further decreased. 2.2. PLANE-WAVE ANALYSIS, PICOSECOND PULSES

Let us now regard as a pump, bandwidth-limited pulses with longer (pico- or nanosecond) duration τ, such that νTHz τ > 1. In this case, the spectrum of a single pulse is narrow and to generate THz output, two different pump pulses need to be mixed to achieve difference frequency generation. Assume that two gaussian bandwidth-limited optical pulses (plane waves) at frequencies ω2 and ω3 with 1 relative THz efficiency

relative THz efficiency

1

0.1

0.1

0.01 0.01

(a)

0.1

νTHzτ

0.1

1

(b)

1

10

l w/L

Figure 2. (a) Reduction factor g1 as a function of νTHz τ for the case of fs pump pulses (νTHz = /2π). (b) Reduction factor g2 as a function of lw /L for the case of ps pump pulses.


425

equal pulse widths propagate collinearly and generate THz wave centered at 0 = ω3 − ω2 , and the electric fields (i = 2, 3) are in the form E i (t) =

1 E i exp −t 2 /τ 2 exp[i(ωi t)] + c.c, 2

(23)

then Fourier transforms are given by 2 τ (ω − ωi )2 Ei τ . E i (ω) = √ exp − 4 2 π

(24)

The Fourier component of nonlinear polarization at THz frequency is PN L () = ε0 χ

(2)

∞

−∞

2 τ ( − 0 )2 E2 E3τ exp − E 3 (ω + )E 2∗ (ω)dω = ε0 χ (2) √ 8 2 2π (25)

Integrating (6) in the limit of no absorption and no pump depletion, we get the power spectrum of the THz field |E(, L)|2 =

2 de2f f E 22 E 32 τ 2 8πc2 n 21

L 2 exp(−

τ 2 ( − 0 )2 )sinc2 (k L/2), 4

(26)

where k is given by (11). Suppose that the QPM orientation-reversal period is such that the sinc2 peak is centered exactly at 0 = ω3 − ω2 . In this case k L/2 can be replaced by ( − 0 )n L/2c. Using Parseval’s theorem, we find the optical-to-THz fluence conversion efficiency with respect to one of the two pump pulses (at ω2 ) W ηTP H z

∞ 2 2 2 de2f f E 32 τ 2 Fluence(T H z) τ n L = L exp − = √ sinc2 d Fluence(ω2 ) 4 2c 2 2π c2 n 1 n 2 −∞

(27) where = − 0 The temporal walk-off length between the optical and THz pulses can be introduced as √ lw = π cτ/n, (28)

which is proportional to the length in a crystal at which the optical pulse walks away in time, with respect to THz wave, by its width τ, due to difference in propagation velocities. It is analogous to the Boyd-Kleinmann’s [22]√birefringent aperture length in the theory of second harmonic generation la = πw0 /ρ

426


(w0 is beam radius, and ρ is the birefringent walk-off angle). Now (27) can be expressed as ηTP HWz

2 de2f f E 32 τ 2 = √ L 2 2πc2 n 1 n 2

∞

−∞

√ π L τ 2 2 2 exp(− )sinc [ ( )τ ]d 4 2 lw

(29)

In the limit of long pulses, lw L, exponential function under the integral dominates and (29) becomes 2 de2f f E 32 L 2 22 de2f f L 2 I3 = ηT H z = √ √ , ε0 c 3 n 1 n 2 n 3 2 2c2 n 1 n 2

(30)

where n 2 and n 3 are refractive indices at ω2 and ω3 and I3 is the peak pump intensity. This formula is similar to the well-know expression [23] for the CW √ difference frequency generation, with I3 / 2 playing the role of time-averaged pump intensity. In the limit of short pulses, lw L, (29) becomes 2 de2f f E 32 L 2 22 de2f f Llw I3 ηT H z = √ = √ , ε0 c 3 n 1 n 2 n 3 2 2c2 n 1 n 2

(31)

Thus, for lw L , L 2 term is replaced by Llw , in full analogy with the case of second harmonic generation with the spatial walk-off [22], where L 2 is replaced by Lla for la L. Also, conversion efficiency can be rewritten in terms of coherence length lc = πc/ n and energy fluence F3 ηT H z =

23 de2f f Llc πε0 c3 n 1 n 2 n 3

F3 ,

(32)

This shows that at lw L, terahertz conversion efficiency is a function of fluence only. Besides, it is equal to the conversion efficiency for the case of a femtosecond pulses with νTHz τ 1. The only difference is that in a two-color picosecond case, in order to get the same energy per THz pulse, one needs to have twice total energy (U0 in each of the beams), as compared to U0 in the femtosecond case. In the case of intermediate pulse durations, we can use (32) with a reduction factor g2 (lw /L), ηT H z = g2

23 de2f f Llc πε0 c3 n 1 n 2 n 3

where 1 g2 (x) = π

F3 = g2

22 de2f f L ε0 c2 n 1 n 2 n 3 n

F3 ,

(33)

∞ exp(−x 2 µ2 /π)sinc2 (µ)dµ. −∞

(34)


427

Fig. 2b is the plot of the reduction factor g2 as a function of lw /L. In many cases, it is desirable to have longer pulses to suppress high-order nonlinear optical effects (e.g. nonlinear refraction and multi-photon absorption), even at the expense of some loss in efficiency. Thus setting lw /L = 1(g2 = 0.69) might be a good compromise between efficiency and pump intensity. For an L = 1 cm GaAs and pump at 2.1 µm, the lw /L = 1 condition corresponds to the pulse duration of 3.6 ps. At longer pulses, the THz efficiency will decline; however it will not be improved dramatically if the pulses are made shorter. As calculations show, [24] for the optimal pump focusing (approximately confocal with respect to the THz wave) the optical-to-THz conversion efficiency for GaAs is ηTHz ∼0.1%/µJ at 1–2 THz, for both fs and ps pulses with optimized pulsewidths. 3. Comparison of nonlinear optical crystals for THz generation Table 2 gives comparison of different electrooptical (EO) crystals suitable for optical THz generation. This table was based on the known EO coefficients [25] as well as relation between EO and nonlinear optical (NLO) coefficients in the THz region dijk (0, −ω, ω) = −n 4 /4 × rikj [16]. While GaAs has a reasonable NLO coefficient, it is superior to conventional THz EO crystals in terms of very low THz loss. The frequency dependence of GaAs absorption coefficient is shown in Fig. 3a. Fig. 3b demonstrates phase and group refractive indices for GaAs at optical frequencies. Dashed line on the same plot represents THz refractive index (at ∼2THz). TABLE 1. THz nonlinear optical coefficients for different materials derived from EO coefficients [25]. Crystal

Optical ref. index

EO coeff. (pm/V)

NLO coeff. (pm/V)

LiNbO3 LiTaO3 KNbO3 KTP LiIO3 ZnTe ZnSe CdTe GaAs GaP InP

2.14 2.12 2.12 1.83 1.72 2.8 2.48 2.84 3.33 3.1 3.2

r33 = 29.4 r33 = 29 r33 = 25 r33 = 35 r33 = 6.4 r14 = 4 r14 = 2 r14 = 4.5 r14 = 1.5 r14 = 1 r14 = 1.6

d33 = 154 d33 = 146 d33 = 126 d33 = 98 d33 = 14 d14 = 61 d14 = 18 d14 = 73 d14 = 46 d14 = 21 d14 = 42

428

KONSTANTIN VODOPYANOV 4.0

8

(a)

(b)

GaAs GaAs ref. index

absorption, cm−1

7 6 5 4 3 2

3.8 n (THz) 3.6

ngroup (optical)

3.4

1

nphase (optical) 3.2

0 0

1

2

THz

3

4

1

2

3

4

5

6

7

8

9

10 11 12

wavelength, µm

Figure 3. (a) GaAs absorption at THz frequencies [26]; and (b) GaAs phase (thin line) and group (thick line) refractive indices at optical frequencies. Dashed line represents THz refractive index (at ν∼2THz).

4. THz generation with fs-pulses from OPA/DFG (λ = 2– 4.4 µm) In our first set of THz experiments, we used as a pump, mid-IR OPA/DFG system. Optical pulses, tunable in the range 2–4.4 µm, were produced using a parametric amplifier (OPerA, Coherent Inc.) pumped by 800-nm Ti:Sapphire pulses after a regenerative amplifier (Legend, Coherent Inc.). To achieve λ > 3 µm wavelengths, an additional difference frequency generation stage was used. Typical pulse durations were ∼100 fs, repetition rate 1 kHz, and pulse energy up to 3 µJ. The >2 µm pump wavelength range was chosen to avoid two-photon absorption (2PA) in GaAs (2PA edge is at ∼1.75 µm), which creates additional losses both at pump wavelength and at terahertz frequencies (in the latter case because of induced absorption due to generated free carriers). We have used [27] two types of QPM GaAs samples: (i) diffusion-bonded GaAs (DB-GaAs) produced by stacking and bonding together alternately rotated (110) GaAs plates [14]; wafer fusion in this case creates a monolithic body with periodic change in the nonlinear coefficient, and (ii) orientation-patterned GaAs (OP-GaAs) grown by a combination of molecular beam epitaxy, photolithography, and hydride vapor phase epitaxy, where periodic inversions of the crystallographic orientation are grown into the material (Fig. 4). While DB-GaAs provides larger apertures, OP-GaAs has more reproducible technology and allows lithographic definition of QPM gratings. The samples were not AR-coated. Their main parameters are listed in Table 2. The optical pump beam with a beam size (1/e2 intensity radius) ranging between w = 300 µm and 1.5 mm, propagated along the [110] direction of GaAs. A Picarin lens was used to collect the THz radiation to the liquid He-cooled silicon bolometer which measured the average power of THz pulses. A black polyethylene filter was used to block optical radiation. To measure the spectral

TUNABLE THz SOURCES BASED ON QPM GAAS TABLE 2.

429

Parameters of the QPM GaAs samples.

Sample

QPM type

Aperture (mm2 )

Length (mm)

QPM period (µm)

DB-77 A3 A10 B5 B10 C5

DB-GaAs OP-GaAs OP-GaAs OP-GaAs OP-GaAs OP-GaAs

10 × 10 0.4 × 3 0.4 × 3 0.4 × 3 0.4 × 3 0.4 × 3

6 3 10 5 10 5

504 1277 1277 759 759 564

0.75 mm air

polished AR-coated 3-rd growth run L=5mm sample (C5) QPM period 704 µm

2-nd growth run 1-st growth run substrate

Figure 4. OP-GaAs sample C5 for the optical THz generation. The inset shows optical transmission obtained with a near-infrared (λ∼1 µm) microscope. There were 3 runs of HVPE thick-film growth, the last one being the most successful, providing the useful thickness of 0.75 mm.

properties of THz radiation, we have used a Michelson interferometer (Fig. 5). We utilized a 25-mm-thick mylar film as a beam splitter and two gold mirrors as end reflectors. One of the mirrors was mounted on a computer-controlled motorized stage. By computing the amplitude of the Fourier transform of the interferograms we extracted the power spectra of the generated THz radiation. Fig. 6 shows both original interferograms and computed spectra for different samples and different pump wavelengths. The spectra were noticeably distorted by water vapor absorption (also shown in Fig. 6). Interestingly, for sample A10 with the largest QPM period, 1277 µm, we observed (Fig. 6d) a second peak

430

KONSTANTIN VODOPYANOV Si bolometer (4K)

QPM-GaAs

Picarin lens f50

Mylar 25 µm THz

Optical pump

Figure 5.

Experimental setup for THz generation and Michelson interferometry.

power spectrum (a.u.)

1.0

0.5 −20 0

(a)

−20 0

20

ps

ps

20

(b)

0.0

1.0

0.5 −20 0

(c)

ps

−20

20

0

20

ps

(d)

0.0 0

1

2

3

4

0

1

2

3

4

frequency (THz) Figure 6. Spectra of THz pulses obtained by Michelson interferometry. (a) Sample DB-77, pump at 2.03 µm (b) sample DB-77, pump at 3.5 µm (c) sample B10, pump at 4.4 µm; (d) sample A10, pump at 4.4 µm. The spectra are distorted by water vapor absorption (HITRAN water transmission spectrum for 10 cm path is shown on top of each plot). Insets show original interferograms.

at ∼2.6 THz which is likely to be the 3-rd order QPM peak, at approximately three times the frequency of the main peak. The amplitudes of both peaks are comparable. Efficiency reduction (1/32 ) due to the 3rd order QPM is offset by the

431


pump 4400 nm

frequency (THz)

frequency (THz)

3

2

1

2

1

(a) 0

pump 2130 nm

3

(b)

500

1000

QPM period (µm)

2000

0 500

1000

2000

QPM period (µm)

Figure 7. THz central frequency as a function of the OP-GaAs QPM period. (a) Pump wavelength at 4.4 µm and (b) at 2.13 µm.

ν2THz factor which appears in the expression for the efficiency of any DFG-like process [23]. The central frequency of terahertz radiation, produced by the QPM optical rectification is given by Eq. (13): νTHz = c/n and corresponds to the zero wave-vector mismatch condition. The spectral width of terahertz wave packets is determined by Eq. (14) : νTHz = c/Ln. Experimentally, we observed central frequencies and bandwidths of THz pulses that are in good agreement gr with these predictions based on known GaAs dispersion relations; for GaAs, n opt varies [28] between 3.43(λ = 2 µm) and 3.33 (4.4 µm). By changing the pump wavelength or GaAs QPM period, we generated THz wave packets with central frequencies between 0.9 and 3 THz. The tuning curves for two different optical pump wavelengths is shown in Fig. 7 and matches the theory pretty well. We found that the THz beam propagated collinearly with respect to the optical pump and was close to diffraction-limited (a pinhole method was used to measure the far-field THz beam size). Fig. 8. shows optical-to-terahertz conversion efficiency, ηTHz , as a function of peak pump intensity, I0 , inside the sample, at λ = 3.5–4.4 µm pump wavelength. The pump beam size varied in this case between 810 µm (open circles), 520 µm (closed circles), and 300 µm (crossed circles). One can see that the linear dependence (sample DB-77) of ηTHz , expected by theory, rolls off for I0 > 2GW/cm2 . This roll-off behavior was also observed at similar intensities at shorter, λ∼2 µm pump. The onset of saturation is most likely due to nonlinear refraction (n 2 ) in GaAs which induces self-phase modulation and selffocusing of the optical pulses. Indeed, we have measured n 2I ≈ 1.5·10−4 cm2 /GW for GaAs at 3.5 µm and estimated that at I0 = 2GW/cm2 and L(GaAs) = 6 mm, the nonlinear phase shift at beam center reaches ∼π. Terahertz conversion efficiencies for the OP-GaAs samples A3 and B5 are very similar to each other and are smaller, by a factor of ∼3.5, than that of the DB-77 sample (in both cases the pump was at 3.5 µm, central frequencies at 1.5

432

optical-to-THz efficiency


1x10−4

DB-77

A3 1x10−5

0.1

1

peak pump intensity,

10

GW/cm2

Figure 8. Optical-to-terahertz conversion efficiency as a function of peak pump intensity for the sample DB-77 (central frequency ∼2.2 THz, circles) and A3 (central frequency ∼1.5 THz, triangles). The average pump beam size was 810 µm (open circles), 520 µm (closed circles), 590 µm (triangles), and 300 µm (crossed circles). The pump wavelength was 3.5 µm (open circles and triangles) and 4.4 µm (filled and crossed circles). Dashed lines – linear fits.

and 1.76 THz, correspondingly). We attribute smaller THz outputs in A3 and B5 to the beam clipping: their limiting dimension (height) is only 0.4 mm, comparable to THz wavelengths (∼200 µm). Also, for the sample DB-77, pump polarization was aligned along [111], while for A3 and B5 it√was along [110]; in the former case, the nonlinear optical coefficient was larger: 4/3d14 vs. d14 . In the DB-77 sample, we generated 0.66 nJ of output at 2.2 THz, with 2.3 µJ of pump pulse energy (w = 300 µm), which corresponds to optical-to-terahertz conversion efficiency of 2.9 × 10−4 , internal efficiency 8.7 × 10−4 (the samples were un-coated) and photon conversion efficiency of 1.1% (internal photon efficiency 3.3%). These efficiencies are in accord with the calculated values [24], based on the known nonlinear optical coefficient for optical rectification deff = 2/π × d14 = 2/π × 46 pm/V (see Table 1). We note that the measured conversion efficiency can be affected by water vapor absorption along the beam path (∼30 cm). 5. THz generation using OP-GaAs pumped by a fiber laser In our second set of THz experiments [29], we used as a pump, a recently developed compact all-fiber source that generates femtosecond pulses at the wavelength near 2 µm. Fiber-based sources of short optical pulses have well-known benefits of compactness and environmental reliability compared to their bulk counterparts, as particularly advantageous for practical applications. The demonstrated

433

TUNABLE THz SOURCES BASED ON QPM GAAS Raman shifting fiber amplified Er fiber oscillator

Dispertion control fiber

OP-GaAs

picarin lens

Tm fiber amplifier

100 MHz

1980 nm 120 fs

beam splitter Si bolometer

Figure 9.

Schematic of the THz experiment with a fs-Tm-fiber laser.

combination of fiber laser and OP-GaAs technologies promises a truly practical source of THz radiation. The experimental setup for THz generation and characterization is shown in Fig. 9. The optical pump source was an all-fiber laser that produced 120-fs pulses at 100 MHz repetition rate with the average power of 3 W (30 nJ pulse energy) at the wavelength of 1980 nm. Briefly, output of a mode-locked Er-fiber oscillator at 1557 nm was amplified in an Er/Yb-doped fiber amplifier, then Raman-shifted to 1980 nm, and finally amplified a large-mode-area Tm-doped fiber amplifier. The details of the system architecture and the performance achieved are reported in ref. [30]. We used two OP-GaAs samples (A3 and B3) grown by epitaxy [14]. Both samples were 0.4-mm-thick and 3-mm-long, and had lithographically-defined QPM periods of 1277 mm (sample A3) and 759 mm (sample B3). The pump beam was propagating along the [110] direction of GaAs and was polarized along [111] to maximize the effective nonlinear optical coefficient. The focusing of the pump beam was optimized to produce the maximum THz power. The resulting optimal spot size was found to be w0 = 65 µm which in agreement with theoretical predictions. [24] The generated THz beam was collimated with a Picarin plastic lens that had a focal length of 50 mm. THz power was measured with a Si bolometer. In order to measure spectral properties of the generated THz radiation we used a Michelson interferometer (Fig. 9), described above. For the sample A3, the spectrum was centered at 1.78 THz and has a width of 0.3 THz, while for the sample B3 the spectrum was centered at 2.49 THz and has a width of 0.25 THz, in good agreement with predicted QPM peak position and width. Fig. 10 shows the measured THz power versus the incident optical power at 1980 nm. Both samples show very similar power-curve behavior: at the highest optical power of 2.1 W available at the samples we obtained ∼3.3 µW of THz average power. The THz output power is quadratic with respect to the incident pump

434

THZ power, uW


slope = 2

1

0.1

sample A3 sample B3

0.01 0.1

1 pump power, W

Figure 10. THz average power versus average pump power for the OP-GaAs samples A3 (filled circles) and B3 (open circles). Straight line is the best fit to the sample A3 data.

power and does not show any saturation effects, up to the maximum pump power of 2.1 W at the samples (peak intensity inside the samples of 1.85 GW/cm2 ). The maximum optical-to-THz efficiency achieved was 1.6 × 10−6 . Here we note that the OP-GaAs samples were not antireflection-coated and the Fresnel losses at optical and terahertz frequencies exceeded 30% per surface. Thus, the internal THz efficiency was calculated as 4.7×10−6 , corresponding to the internal normalized efficiency of 2.24×10−4 µJ−1 . The conversion efficiencies achieved in these experiments are about 25% of the ideal calculated values [24]. The discrepancy can be accounted for by several factors, namely, clipping of the generated THz beam because the wavelength of the THz wavelength is comparable to the sample thickness (0.4 mm); attenuation of THz radiation in air due to water vapor absorption; the pump pulses being about twice the transform limit and not having the ideal Gaussian shape as was used in the theoretical calculations. Although we have used OP-GaAs samples with the fixed QPM periods, however the lithographic nature of fabrication readily allows to fabricate multiple QPM grating segments or even a fan-out QPM gratings, so that continuous THz frequency tuning can be achieved by transverse translation of the sample. 6. THz generation with a near-degenerate synchronously-pumped ps OPO With the femtosecond excitation, the limit for THz efficiency is set by parasitic high-order nonlinear effects (e.g. nonlinear refraction). The optical-to-THz efficiency can be improved by using a two-color DFG scheme with longer (ps) pulses [24]. To explore ps pump pulse format for THz generation, we have used a near – degenerate type-II PPLN OPO, synchronously pumped by a CW mode-locked

435

TUNABLE THz SOURCES BASED ON QPM GAAS M1

M2 Type-II PPLN

M3

M4

Pump : 1.06µm, 9W, 6ps, 50MHz

M5

M6 pol.

M7

120 W of resonating 2 µm ‘signal’ 71% of 1.06 µm pump laser depletion

OPO far field

idler wave

OPO spectral output

OPO tuning 2160

λs

1.0

λi

Wavelength (nm)

spectral intensity (a.u.)

1.5

0.5

0.0

Y-pol wave Z-pol wave

2150 2140 2130 2120 2110 2100

2080

2100

2120

2140

2160

wavelength (nm)

2180

80

90

100

110

120

130

PPLN Temperature (C)

Figure 11. Near – degenerate type-II PPLN OPO, synchronously pumped by ps pulses at 1.06 µm. Insets: ‘signal’ wave far field intensity distribution, spectral output of the OPO at two different PPLN temperatures, and OPO tuning curve with respect to PPLN temperature.

N d : Y V O4 -laser at 1.06 µm (High Q Laser, Austria). The laser had repetition rate 50 MHz, pulse duration 6.5 ps, average power up to 10W in a TEM00 mode. The PPLN crystal (HC Photonics) served as an OPO gain medium and was 10-mm-long, 3-mm-wide and 1-mm-thick and had a QPM period of 14.1 µm. It was designed for the type-II QPM three-wave interaction (Y-YZ), so that the signal and the idler had orthogonal polarizations. The PPLN was AR-coated for both 1.06 and 2.1–2.16 µm. The high-finesse standing-wave OPO cavity (Fig. 11) was 3-m-long and consisted of 7 mirrors, all of which were highly transmissive at 1.06 µm and highly reflective (>99.9%) in the vicinity of the 2.13 µm degeneracy wavelength. Mirrors M1 -M2 , and M7 were flat, mirrors M3 -M4 had ROC of 200mm, and mirrors M5 -M6 - ROC of 500 mm. A polarizer inside the cavity served as a 100% idler-wave outcoupler, thus the OPO in this case was singly resonant (SRO). Insets to Fig. 11 show (i) the signal-wave far field intensity distribution, (ii) spectral output of the OPO at two different PPLN temperatures, and (iii) OPO tuning curve with respect to the PPLN temperature. The OPO linewidth (Fig. 11) is preserved even when the OPO crosses the degeneracy point (at ∼106◦ C) and is close to the time-bandwidth limit ν∼3 cm−1 . In general, any frequency spacing, from 0 to 125 cm−1 (0–3.75 THz)

436


between the OPO signal and the idler waves, can be achieved by changing the PPLN temperature. At the measured pump beamsize w = 31 µm and the resonating signal eigenmode beamsize of w = 51 µm, the OPO threshold was ∼2 W and, at the full average pump power of 9 W available at the PPLN crystal, the idler output reached 3W with the pump depletion of 71%. By measuring the signal-wave power leaking through one of the OPO mirrors, we have measured that the intracavity resonating average signal power was as high as 120 W. Thus, there was a substantial resonant – field enhancement of the signal wave, due to low-loss cavity (the total round-trop loss was estimated to be 3%). 6.1. EXTRACAVITY THZ GENERATION

In our extracavity THz generation experiments, we used the signal and the idler waves of the OPO output (Fig. 12) to generate monochromatic THz output at their difference frequency. The two beams were collinearly focused into the GaAs crystal, to a beamsize of ∼80 µm. The inset shows THz efficiency vs. frequency curves for three OP-GaAs samples with QPM periods of 932, 759 and 564 µm. For each sample, THz output is maximized when the THz frequency determined by the beat note between the two optical frequencies ωTHz = ω3 − ω2 , matches the

Figure 12. Experimental set-up for THz extracavity generation in QPM GaAs via DFG. A picosecond near – degenerate synchronously-pumped type-II PPLN OPO is used as a pump source. The inset shows THz output curves, as a function of THz frequency, for three GaAs samples with QPM periods (lengths): (a) 932 µm (L = 3 mm), (b) 759 µm (L = 10 mm), and 564 µm (L = 5 mm).


437

Figure 13. THz average power versus average pump power for a 5-mm-long OP-GaAs sample with the QPM period 704 mm and the central frequency of 2.2 THz. Straight line is the best fit.

QPM condition. Here ω3 and ω2 are angular frequencies of the OPO signal and the idler. THz tuning curves obtained in this experiment (THz peak frequency vs. GaAs QPM period) are in excellent agreement with the results of fs experiments (Fig. 7b). Fig. 13 is a log-log plot of THz average power versus average pump power for a 5-mm-long OP-GaAs sample with the QPM period 704 µm and the central frequency of 2.2 THz. In fact, the powers at the two pump beams (the OPO signal and the idler) were unequal and we assigned the ‘pump power’ to a geometric mean of the powers of the two beams. The best fit is a straight line with a slope of 2, which indicates that the THz output is linear with respect to the product of the powers of the two pump beams. The conversion efficiency was about 40% of theoretical [24]; again, the discrepancy can be accounted for by the beam clipping, water vapor absorption at THz frequencies, and possible uncertainty in THz detector calibration. Overall, experiments with ps pulses are in good accord with theory and confirm predictions of theory that one can get the same THz efficiency per µJ of pump pulse energy for both ps and fs pulses. 6.2. INTRACAVITY THZ GENERATION

By placing the QPM GaAs inside the OPO cavity, one can take the advantage of resonant enhancement of pump optical power near 2-µm wavelength. As we have shown experimentally, this enhancement can be a factor of 10–40. In the case of single resonant OPO (SRO), only one wave is enhanced, while in the doubly resonant OPO (DRO), both waves are enhanced and the total THz efficiency can be boosted by a factor of >100. With the AR-coated 6-mm-long DB-GaAs crystal (QPM period 504 µm) inside the SRO cavity and optical beamsize at the DB-GaAs crystal of ∼200 µm, we generated 50 µW of THz output at 2.9 THz. To extract the THz output

438

KONSTANTIN VODOPYANOV 1.5

THz output (a.u.)

1-order QPM

1.0 3-order QPM

0.5 5-order QPM

0.0 0

1

2

3

4

frequency (THz) Figure 14. THz output as a function of frequency, in the case of intracavity THz generation using a GaAs stack consisting of four 1-mm < 110 > optically-contacted plates. The peaks correspond to the 1-st, 3-rd and 5-th –order QPM in GaAs. Solid curves are sinc2 best fits.

radiation, we used an off-axis parabolic mirror with a hole inside, to transmit resonating optical beam. We also used another type of QPM GaAs, namely optically-contacted GaAs (OC-GaAs). Similar to DB-GaAs [14] technology, (110)-GaAs plates were alternately rotated and stacked together, however without bonding at high temperature. A stack consisting of four 2-inch-diameter 1-mm-thick optically-contacted plates was mechanically robust and had optical transmission of 99% at λ = 2 µm after AR coating. The THz output as a function of the beat note frequency (tuned by changing the PPLN temperature) for the SRO case with the QPM GaAs inside the cavity is shown on Fig. 14. The three peaks correspond to the 1-st, 3-rd and 5-th –order QPM in GaAs. Solid curves are sinc2 best fits with the values for the peak position (FWHM) of 0.66 (0.39), 2.29 (0.33) and 3.38 (0.76) THz correspondingly. Potentially, such a 3-color THz source can be a useful tool for spectrally-selective THz imaging. Schematic of the setup for THz generation using a QPM GaAs inside the cavity of a doubly-resonant type-II PPLN OPO (DRO) is shown on Fig. 15. Two separate sets of end mirrors (and two polarizers) were used to resonate simultaneously the signal and the idler wave. The DRO configuration employed a special linear cavity design which avoided back-conversion of the signal and idler in the PPLN (arm lengths between polarizers and end mirrors were made unequal for ‘s’ and ‘p’ polarizations). For intracavity THz generation, we used an AR-coated 6-mm-long DB-GaAs crystal with a QPM period of 504 µm. Off-axis parabolic mirror with a hole inside was used to extract the THz output radiation. As a


439

Figure 15. Setup for THz generation using a QPM GaAs inside the cavity of a near – degenerate synchronously-pumped doubly-resonant type-II PPLN OPO. Off-axis parabolic mirror with a hole inside is used to extract the THz output radiation.

THz filter, we have used black polyethylene, and as a THz detector – a room temperature DLaTGS pyroelectric detector from Bruker. The average THz power at 2.9 THz was measured to be 1 mW, in a diffraction-limited beam. In this case, we took the full advantage of resonant enhancement of both signal and the idler waves. However, special stabilization of one of DRO mirrors was needed for locking the cavity modes. To accomplish that, we have used the ‘dither-and-lock’ technique consisting of a piezo actuator at one of the end mirrors, a 2-µm photodetector and a feedback electronics. 7. Conclusion We demonstrate a new source of frequency-tunable narrow-bandwidth (∼100 GHz) THz wave packets based on parametric down-conversion process in quasi-phase-matched GaAs. As a pump, we used a variety of laser sources with different wavelengths, pulse durations and repetition rates. We consider intracavity THz wave generation to be the most efficient way of producing THz output. This allowed us to achieve 1 mW of THz average power at room temperature, with ∼10−4 optical-to-THz conversion efficiency and potential scalability to 100 mW. I would like to acknowledge my collaborators at Stanford: Joe Schaar, Paulina Kuo, Xiaojun Yu, Dmitri Simanovskii, Martin Fejer, James Harris. Also special thanks to Vladimir Kozlov from Microtech Instruments, Yun-Shik Lee from Oregon State University, Gennady Imeshev and Martin Fermann from IMRA America. David Bliss and Candace Lynch (US AFRL, Hanscom, MA) are acknowledged for doing thick-film HVPE growth of the OP-GaAs samples. This work was sponsored by DARPA under AFOSR Grant FA9550-04-1-046.

440


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SEMICONDUCTOR WAVEGUIDES FOR NONLINEAR FREQUENCY CONVERSION

L. LANCO1 , M. RAVARO1 , J.P. LIKFORMAN1 , P. FILLOUX1 X. MARCADET2 , S. DUCCI1 , G. LEO1 , and V. BERGER1 1 Laboratoire Matériaux et Phénomènes Quantiques, UMR 7162, Université Paris 7 – Denis Diderot, 2, Place Jussieu, Case 7021, 75251 Paris France 2 Alcatel-Thales III-V Lab, TR&T, Route Départementale 128, 91767 Palaiseau, France

Abstract. We describe the utilisation of semiconductor waveguides for nonlinear frequency conversion. Different phase matching schemes are presented: form birefringence, modal phase matching and counterpropagating phase matching. The characteristics and the performances of these three solutions are discussed and compared for different kinds of applications. The emergence of these compact and integrated devices would be en important technological breakthrough in spectroscopy, telecommunications and quantum optics applications.

1. Introduction The development of new optical sources in the near- and mid-infrared has attracted a growing attention for potential applications in telecommunication systems [1], spectroscopy [2, 3], gas sensing [4], quantum information sources [5–7]. In this regard, nonlinear frequency conversion is an interesting process due to its relative simplicity and to the tunability of the output wavelength. In this process three coherent waves are coupled in a nonlinear medium; the relation between their frequencies verify energy conservation and, in order to have a high efficiency, the phase velocity mismatch between the interacting waves has to be cancelled (phase matching condition). The first kind of materials used to realize this last condition were birefringent nonlinear crystals for which the refractive index depends on the polarisation of the beam traversing the medium. In particular, one of the two indices (called ‘extraordinary’) depends on the propagation angle of the beam with respect to the optical axis. A convenient orientation of the crystal allows the realization of the phase matching condition. 443 M. Ebrahim-Zadeh and I. T. Sorokina (eds.), Mid-Infrared Coherent Sources and Applications, 443–463. c 2008 Springer.

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However, to satisfy the criteria of integration, robustness and stability which are very attractive for the realization of original devices, waveguides are preferred to bulk materials. So far, the fabrication of periodically poled lithium niobate waveguides [8] has permitted to reach conversion efficiencies up to 10−6 , but their use in practical applications could be limited by the difficulty of integration of the pump source and the nonlinear waveguide. Such a limitation could be overcome by using semiconductor hétérostructures: by carefully designing the thickness and the composition of the different layers, the band structure and the optical properties of the device can be engineered to meet particular requirements. GaAs-based devices are particularly attractive due to their huge nonlinearities, room temperature operation, well-mastered growth and processing techniques and the possibility of integration with a laser source. However GaAs is optically isotropic and the usual birefringence phase matching scheme can not be implemented. Quasi-phase matching has led to interesting results, and an optical parametric oscillator has recently been obtained [9]. However, the complexity of this technology still makes the realization of low loss waveguides a difficult task for the moment. In this chapter we focus on three alternatives routes for perfect phase matching in semiconductor waveguides: in sections 2–4 we report on form birefringence phase matching, modal phase matching, and counterpropagating phase matching respectively. In section 5 we discuss and compare the characteristics of these three solutions for different kinds of applications. 2. Form birefringence phase matching Sample design Form birefringence phase matching is obtained by using the artificial birefringence of a composite multilayer material: the isotropy of bulk GaAs is broken by inserting thin oxidized AlAs (Alox) layers. The idea has been proposed in a pioneering paper of Van de Ziel in 1975 [10], but the experimental realization of form birefringence phase matching has been achieved only in 1997, when the development of oxidation techniques [11] has permitted the realization of a well suited couple of materials having a high nonlinear coefficient and a high enough refractive index contrast [12]. The principle of form birefringence can be understood by making some symmetry considerations on the crystalline structure of this new artificial material. The presence of thin Alox layers grown on a (100) GaAs substrate breaks the symmetry of 3-fold rotation axes of the GaAs and the point group of the composite ¯ material becomes 42m, the same as KDP. In this way we obtain a material with the same nonlinear properties as GaAs (the small zero contribution of the thin Alox

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Figure 1. Refractive index profile (2.128 µm) and intensity distribution of the modes TE0 (solid line) at 2.128 µm and TM0 (dashed line) at 1.064 µm. The epitaxial structure of the waveguide is described in the text.

layers can be neglected), and the linear optical properties of KDP. For a periodic layered medium and a propagation direction, it can be shown that: h1 2 h2 2 n1 + n2 h1 1 h2 1 = + n12 n22

n 2T E = 1 n 2T M

with the period and hi (ni ) the thickness (refractive index) of the ith repeated layer (i = 1, 2; h1 + h2 = λ). Form birefringence (nTE − nTM ) occurs due to different boundary conditions for ETE and ETM : in the TM polarization, the continuity of the electric displacement forces the electric field to have a large value in the low-index material. This is illustrated on Figure 1, which presents a heterostructure having the following epitaxial structure: 1000 nm Al0.92 Ga0.08 As/1000 nm Al0.7 Ga0.3 As/4 × (37 nm AlAs/273 nm GaAs)/37 nm AlAs/1000 nm Al0.7 Ga0.3 As/30 nm. Such a structure is designed to be phase matched, after the oxidation process, for a degenerate three wave mixing process between a TM-polarized photon at 1.064 µm and two TE-polarized photons at 2.128 µm. All the heterostructures presented in this chapter are grown by molecular beam epitaxy on GaAs (001) substrates. Experimental results and perspectives The first achievement of perfect phase matching in an Alox-based heterostructure has been demonstrated through mid-infrared generation from two near-infrared waves [12, 13]. Two CW pump lasers (a TE polarized Nd:Yag laser at 1.32µm and a tunable Ti:Sa laser TM polarized) were end-fire coupled in a GaAs/Alox

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Figure 2. Mid-infrared DFG signal measured by an InSb detector, as a function of the wavelength of the Ti:Sa laser.

waveguide; by tuning the Ti:Sa wavelength a DFG process occurred. The infrared signal is shown in Figure 2 as a function of the tunable laser wavelength: the observed sinc2 curve is a clear signature of a phase matched process. The maximum efficiency is obtained for the following three wave mixing process: (1.035 µm, TM) − (1.32 µm, TE) → (4.8 µm, TE). Parametric fluorescence (PF) has also been obtained in the same kind of structure. [14] A CW Ti:Sa laser tunable from 950 to 1070 nm, was coupled into a 3.2 mm-long waveguide and the PF signal was detected with a InSb detector, the pump being completely absorbed by a germanium filter. The wavelengths of the down-converted beams are reported in Figure 3 as a function of the pump wavelength. As expected from the selections rules imposed by the crystal symmetry and by the phase matching condition, signal and idler are TE polarized for a TM polarized pump. Due to the spectral broadening at degeneracy, typical of type I process, we expect that the spectrally integrated PF output increases rapidly as the degeneracy is approached, whereas at longer pump wavelength almost no photons are generated because phase matched down-conversion is forbidden. The corresponding measurement is shown in Figure 4, where the PF peak appears clearly and its shape is asymmetric with a sharp fall on the right-hand side. It has also been shown that the output signal power depends linearly on the pump power, as expected in the low-gain limit of a PF process. The measurement of the normalized PF efficiency, defined as the amount of power carried by the signal wave divided by the waveguided pump power and normalized to the square of the sample length L, has given ηPF = 6 × 10−6 W/W/cm−2 .


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Figure 3. Signal and idler wavelengths as a function of the pump wavelength. Solid line: calculated parametric tuning curve; circles: experimental data. Experimental twin points correspond to a single measurement: one wavelength has been measured, and the other one has been reported considering energy conservation. Another example, together with a very simple and synthetic formula fitting this tuning curve, can be found in ref. 32.

Figure 4.

Parametric fluorescence signal as a function of the Ti:Sa pump wavelength.

The demonstration of efficient parametric fluorescence opens the perspective to the realization of a micro optical parametric oscillator [14] around 2 µm. As the semiconductor laser sources that could be used to pump this device are usually poorly tunable, the large opening of the tuning curve results in a great advantage: small variations of the pump wavelength are sufficient to provide a very wide tunability of the output wavelengths, between 1.4 and 3.5 microns. The realization of a compact mid-infrared OPO would find a great application to environmental problems (in particular gas sensing). With comparison to traditional chemical probes, absorption spectroscopy has the advantages of weak maintenance costs, rapid responses, and teledetection. By taking into account the measured efficiency of parametric emission and the value of optical losses [15], a doubly resonant system provided with 90% dielectric mirrors would have a pump threshold of 100 mW. A technological study

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is in progress to acquire a deeper comprehension of the oxidation process and to improve the reflectivity of the mirror deposited onto the waveguide facet. This will hopefully allow the reduction of optical losses and consequently the value of oscillation threshold. The heterostructure described in this section doesn’t make use of one of the principal advantages of semiconductor materials with respect to the other nonlinear materials : the possibility of integration of an internal quantum well laser pump in the core of the waveguide. The will to exploit all the possibilities of GaAs/AlGaAs systems lead us to the conception of a very compact device in which laser effect (by electrical pumping) and nonlinear effects occur in the same chip. The insulating nature of the oxidized layers makes difficult electrical transport in the structure, and form birefringence is thus incompatible with this kind of structure. A high degree of compactness is possible with another kind of heterostructure, based on modal phase matching, which is described in the next section. 3. Modal phase matching Sample Design In the modal phase matching scheme, phase velocity mismatch is compensated by multimode waveguide dispersion. An important advantage of this scheme, as compared to form birefringence, is that the index contrast provided by AlGaAs materials is high enough to allow for the realization of multimode waveguides phase matched in the telecom range, without requiring any oxidation process. Thus, this scheme is compatible with a highly-compact, electrically-pumped device. The realization of such an active component would lead to integrated nonlinear devices controlled by electrical injection: frequency converters for telecommunications or, even more challenging, twin-photons micro-sources for quantum cryptography. To achieve this, laser emission and nonlinear effects must be integrated in the same waveguide; electrical pumping has to induce a laser emission on a mode which is phase-matched with others guided modes of the structure. An illustration of a twin-emitting-diode based on this principle is shown on Figure 5. Our device is designed such that the effective index of the third order guided mode (TE20 ) at 775 nm is the same as that of the fundamental modes (TE00 and TM00 ) at 1.55 µm (Figure 6). This configuration allows the parametric generation of twin photons at 1.55 µm, starting from photons at 775 nm in the third-order mode. [16] A quantum well is inserted inside the waveguide in order to provide laser action at the latter wavelength.


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Figure 5. Schematic view of a twin-photons emitting diode for quantum cryptography. The internal source for the parametric down-conversion endows these devices with several advantages: a high degree of compactness, simple electric control of the device, and the absence of pump coupling losses.

Figure 6. Dispersion curves of the effective indices of the modes involved in the intracavity parametric down-conversion. The lines joining the effective index of the mode TE20 at 775 nm and those of the modes TE00 and TM00 at 1.55 µm illustrate the phase matching condition.

The design of this heterostructure is the result of a subtle trade-off between several constraints. 1) It is necessary to optimize the nonlinear overlap integral to obtain a good conversion efficiency. 2) It is necessary to insert inside the structure a quantum well emitting on the third order mode; this means that the third order mode has a strong overlap with the quantum well, whereas the fundamental mode has to be weak. This condition is satisfied thanks to the presence of the ‘barrier layers B’ (see Fig. 7) which further the third order mode with respect to the fundamental one at the quantum well location. 3) Too high energy barriers at the hetero-interfaces must be avoided, as these could block the carrier transport towards the quantum well, thus hindering the necessary radiative recombination.

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Figure 7. band gap profile and intensity distribution of the guided modes TE20 and TE00 at 775nm. The intensity distribution shows that the third order mode has a larger overlap with the quantum well than the fundamental mode. In the band gap profile are shown the cladding and the waveguide core, entailing the ‘generation G’ layers, the ‘barrier B’ layers and the quantum well.

4) It is also necessary to accurately optimize the refractive indices of the heterostructure layers to obtain phase matching and to improve mode confinement, thus reducing optical losses. All these constraints imply several conditions on the composition of the layers, their thickness and the doping of the structure. As an example, the choice of the Aluminum content in each layer is dictated by the following inequalities: %AlQW < %AlG < %AlB < %Alclad . The first inequality is dictated by the necessity of lasing action in the quantum well, the second one by the necessity to optimize the overlap integral between the quantum well and the third order mode, the third one by the necessity of good confinement of the guided modes. Experimental results and perspectives The first demonstration of the third order mode laser has been done in 2002, with the realization of an optically pumped device [16]. Optical pumping with a 532 nm laser has led to the observation of laser emission at the required wavelength, with a far field intensity distribution characteristic of the third order mode. More recently, an electric device has been obtained, after a careful engineering of a heterostructure adapted to electrical pumping. The epitaxial structure used is the following: 1200 nmAl0.98 Ga0.02 As (cladding)/152 nm Al0.25 Ga0.75 As (generation layer)/138 nm Al0.50 Ga0.50 As (barrier layer)/10 nm Al0.11 Ga0.89 As (quantum well)/138 nm Al0.50 Ga0.50 As (barrier layer)/152 nm Al0.25 Ga0.75 As (generation layer)/1200 nm Al0.98 Ga0.02 As (cladding). The waveguide core is uniformly doped at 2 × 1017 cm−3 ; the cladding layers are gradually doped from 2 × 1017 to 1018 cm−3 . The device is processed for gain-guided operation: the current aperture is realized by proton implantation into the upper cladding layer and ohmic contacts are deposited afterwards. Figure 8 shows an image of the laser diode on


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Figure 8. Image of the laser diode on its mount and projection of the far field of the emitted light onto a screen.

its mount and the projection of the far field onto a screen: the emission on the third order mode is evident. In order to demonstrate the presence of nonlinear effects inside the waveguide, a second harmonic generation (SHG) experiment has been realized on a sample having the same structure but without quantum well (in order to avoid the absorption of the second-harmonic frequency) [17]. The light of a CW laser, tunable from 1.5 to 1.6 µm and with a spectral width of 2 kHz, is end-fire coupled into the waveguide via a 40× objective. The SHG signal is collected by a second 40× objective and detected with a silicon photodiode. The input beam is linearly polarized at 45◦ in order to couple TE and TM modes simultaneously; the generated signal is TE polarized, which demonstrates that the observed SHG corresponds to the required type II nonlinear process. Figure 9 shows the intensity of the generated signal as a function of the pump wavelength. The envelope of the signal has the classic sinc2 shape; in our case the signal is also modulated by a Fabry-Perot transmission function, as the fundamental beam is submitted to multiple reflections from the waveguide facets. The internal SHG efficiency has been estimated to η = 30% ± 5% W−1 cm−2 . This value is smaller than the one obtained in section 2 for two main reasons: firstly, the nonlinear overlap is smaller in the present modal phase-matching scheme (where the interacting modes are the third- and the first-order modes); secondly, the third-order mode may present important optical losses (which are not taken into account in the efficiency estimation) due to a bad confinement or to the presence of defects in the cladding layer.

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Figure 9. Typical SHG spectrum as a function of the fundamental wavelength. Solid line: experimental data. Dashed line: fitting curve resulting from the product if a (sinc x)2 with an Airy transmission function. Inset: second harmonic integrated power as a function of the fundamental power on a log-log scale. Circles: experimental data. Solid line: power law fitting function y ∝ x1.99 .

Two applications based on this type of structures are envisaged: the first one is wavelength conversion in telecommunication networks. In such a process, a wavelength λ1 in the telecom band is shifted to another channel λ2 via a difference frequency generation process involving a pump beam at λ3 ∼ 770 nm [18]. The efficiency of this process, close to a degenerate parametric process, is equal to the efficiency of the SHG process under study in this paper, since the two processes are simply reverse. The second application is the realization of an integrated source of twin photons by an intra-cavity parametric down-conversion. The expected generated power for the parametric fluorescence PPF is given by the formula PPF = PP ηP0 , where PP is the laser internal power and P0 is the vacuum fluctuation power, depending on the bandwidth of the process which in our case is estimated to be 15 THz [19]. For a laser peak power PP = 100 mW a pair production rate of 300 pairs per 200 ns pulse is expected. We notice that the observation of a PF signal requires that the laser emission wavelength (λem ) corresponds to the phase-matching wavelength (λPM ). This condition can be possibly satisfied by using temperature as a parameter to tune the two wavelengths. Unfortunately, for the sample described in this section, it is not possible to satisfy the condition λem = λPM for a temperature value which allows a good laser operation, and for this reason we have not measured a PF signal yet. It is clear that an important point for our devices is their sensitivity to the variations of the structure parameters. In particular, as shown in Section V, form birefringent and mode-matched devices are quite sensitive to the layer thicknesses. A much more stable device, based on a counterpropagating signal/idler geometry, is presented in the next section.


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Figure 10. Schematic diagram of an AlGaAs waveguide with a pump beam at an angle of incidence θ. The “signal” (resp. “idler”) beam is the one copropagating (resp. counterpropagating) with respect to the longitudinal (z) component of the pump beam.

4. Counterpropagating phase matching Sample design In this scheme, two counterpropagating orthogonally-polarized guided modes interact with a transverse pump beam propagating across the heterostructure. [20–22] This geometry allows phase matching in the longitudinal (z) direction; for each angle of incidence θ of the pump beam, the z component of the pump wavevector compensates the wavevector mismatch, ks −ki , between the signal and idler beams: k = k p sin θ+ki −ks = 0. In the epitaxial (x) direction quasi-phasematching is implemented – through an alternation of λ p /2 layers with nonlinear coefficients d14 as different as possible – in order to maximize the efficiency of the nonlinear process [23]. The most attractive application of such heterostructure is the parametric generation of counterpropagating twin photons from a pump beam which transversely illuminates the waveguide. Important advantages of this scheme, in the aim of realizing quantum communication devices, result from this geometry: easy separation and coupling of the down-converted photons into optical fibres, narrow spectral bandwidth due to counterpropagation, and tunability through the angle of the pump beam. Three kinds of semiconductor materials are currently studied in our group: AlGaAs for down-converted photons around 1.55 µm [23] (for fibered experiments), GaN and ZnSe for an emission around 800 nm [24] (for free-space experiments). All these materials lead to type-II parametric interactions, where one of the down-converted photon is TE polarized, and the other one is TM polarized. This implies that there are two ways to cancel the phase-mismatch in the z direction: either the signal is TE polarized and the idler is TM polarized (which we shall refer to as “interaction 1”), or the signal is TM polarized and the idler is TE polarized (“interaction 2”).

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The central frequencies for the signal and the idler are determined through the conservation of energy and of momentum in the z direction, leading to the following equations: ω P = ωS + ω I (interaction 1) ω P sin θ = ω S n TE (ω S ) − ω I n TM (ω I ) ω P = ωS + ω I (interaction 2) ω P sin θ = ω S n TM (ω S ) − ω I n TE (ω I ) These central frequencies obviously depend on the incidence angle θ of the pump beam, which provides a very convenient mean to tune them. Figure 11 reports the dependency of the signal and idler wavelengths on θ, for a structure having the following epitaxial structure: 1081 nm Al0.94 Ga0.06 As (cladding) / 110 nm Al0.25 Ga0.75 As/4 × [128 nm AlAs/110 nm Al0.25 Ga0.75 As] (core) / 1081 nm Al0.94 Ga0.06 As (upper cladding). We observe that X-shaped tuning curves occur, as expected in type-II interactions; the difference between the

Figure 11. signal and idler wavelengths versus angle of incidence for the structure reported in the text. The values obtained for both interactions 1 and 2 are reported.


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degeneration angles relative to interactions 1 and 2 is due to modal birefringence in the waveguide. The spectrum of the down-converted photons is given by the usual function sinc2 (k L/2), where L is the waveguide length. One of the main advantages of counter-propagating geometry arises from the rapid increase of k when one moves off from perfect phase-matching, which leads to a very narrow bandwidth for the down-converted photons. This is a favourable issue for this device, as chromatic dispersion can cause problems for some application. For example, quantum cryptography schemes implementing phase or phase-and-time coding rely on photons arriving at well-defined times, i.e. well localized in space. In dispersive media, like optical fibers, different group velocities are a source of noise for the localization of photons; for this reason the broadening of photon bandwidth must be circumvented or controlled [5]. In our device the spectral width of signal and idler is given by 1 ω = 5.57 1 v gS + v1g I L where v gS and v g I are the signal and idler group velocities at perfect phasematching. For the above AlGaAs structure, we obtain a bandwidth of about 0.3 nm. We notice that, in copropagating geometry, the sum of the group velocities is replaced by their difference in the previous expression, thus increasing the spectral width. Furthermore, an interesting advantage of this scheme is that the combination of type-II phase-matching with counter-propagation for the signal and the idler leads naturally to polarization entanglement, as in the polarization-entangled photon pairs source of Kwiat et al. [25]. The photon pair is generated in a superposition of the states produced by interaction 1 and 2. The weight of each of those states in the total state vector is related to the efficiency of the corresponding interaction. Namely, after removal of the vacuum component, it can be written as : |ent =

η2 ω¯ S,1 , TE ω¯ I,1 , TM + ω¯ S,2 , TM ω¯ I,2 , TE |η1 |2 + |η2 |2 |η1 |2 + |η2 |2 η1

where |ηi |2 may be regarded as the efficiency of interaction i expressed in photon pairs per pump photon [18]. Actually, it appeared from numerical simulations that for any incidence angle the pair state should remain close to a maximally entangled state, i.e. |η1 |2 ≈ |η2 |2 [22]. It is interesting to stress that in this geometry, the entanglement can be obtained for three variables : energy, momentum and polarization. More complex experimental setups (e.g. the illumination of the sample through an appropriate diffraction grating) allow to directly obtain the Bell states [17]; this would allow to perform Bell’s inequality tests on the photons emitted by this source.

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Experimental results and perspectives The demonstration of the efficiency of the nonlinear process has been realized by a measurement of surface emitting second harmonic generation (SESHG). SESHG, which was first demonstrated in 1979 [26], is the reverse of spontaneous parametric down conversion at degeneracy (ω S = ω I = ω P /2): two crosspolarized counterpropagating guided modes at ω P /2 (fundamental frequency, FF) generate a second harmonic field radiating from the surface of the waveguide. The emission angle is given by the phase matching condition, which simplifies to θ = sin−1 (n T E − n T M )/2 at degeneracy. The measurements were performed employing one end-fire coupled FF beam relying on Fresnel reflection at the opposite facet to obtain back propagating modes. The fundamental frequency was linearly polarized at 45◦ relative to the substrate so that the input power was equally divided between TE and TM eigenmodes. The input beam was supplied by a continuous-wave DFB laser diode at λ = 1.55 µm. The SH field was acquired by an optical system mounted over the waveguide, perpendicularly to its plane. This optical system consist of a high resolution charge-coupled device (CCD) and either a lens for far-field images (Fig. 12) or a microscope for near-field images (Fig. 13). Under these excitation conditions, and considering beam reflection on the waveguide facets, two nonlinear processes occur at the same time, one where

Figure 12. SESHG far-field pattern at 1.55 µm.


Figure 13.

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SESHG near-field pattern at 1.55 µm.

Figure 14. SESHG versus fundamental frequency. Horizontal axes report guided FF power, for wave-front unit and total; vertical axes report SH power and intensity.

the TE beam interacts with the reflected part of the TM beam, the other where the TM beam interacts with the reflected part of the TE beam. This configuration leads to the generation of two second harmonic waves, with comparable amplitudes, which radiate respectively with angles θ and −θ. At the waveguide surface (near-field) an interference pattern can thus be observed. Its period is a direct measure of θ through the relation |sin θ| = λ S H /2. A 41 microns period is found with Figure 13: this gives a 0.54◦ angle which corresponds to a birefringence nTE -nTM = 0.019, in agreement with the predicted value. Figure 14 reports the detected SESHG power and intensity (the latter normalized to the top surface of the ridge) versus the guided FF power: SESHG power data are in good agreement with the parabolic fit curve, as expected for a quadratic nonlinear process. SESHG measurements has permitted to obtain as much information as possible on the “reverse” process of parametric down conversion. In fact we exploited them to verify the phase-matching angles, to test the positive impact of the vertical quasi-phase-matching structure, and to single out the most performing sample.

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We also want to emphasize that if SESHG and parametric down-conversion were truly reciprocal effects, it would be a great advantage to quantitatively predict the down-conversion efficiency from our experimental knowledge of the SESHG efficiency. Since this is unfortunately not the case, we have thus implemented a numerical model in order to evaluate the propagation of the pump beam through the structure and the corresponding efficiency of the down-conversion process. A conversion efficiency value of 4 × 10−13 (down-converted pair/pump photon) is found: shining a 775 nm pulsed pump (peak power 1 W, pulse duration 100 ns), we predict a 0.15 pair/pulse production rate [23]. Another perspective of counterpropagating phase matching is the possible realization of a cavityless optical parametric oscillator [20, 27]. Indeed, for a strong enough level of pumping, the two generated counterpropagating beams, coupled through the nonlinear interaction, create a distributed feedback: the presence of the signal enhances the amplitude of the idler, and reciprocally. This mechanism can lead to the threshold for oscillation without mirrors as predicted . By writing the classical coupled equations governing the amplitudes of the counterpropagating fields (in the absence of optical losses and in the case of a pump illuminating the whole waveguide of length L), we obtain the following solutions at threshold: As (z) = a sin(gz) Ai (z) = −i a ∗ ωs n i /ωi n s cos(gz) gL = π/2 with g the parametric gain g = χ A p ωs ωi /c2 n s n i . Ap,s,i denote the pump, signal, and idler amplitudes respectively, χ is the nonlinear overlap (in pm/V) and a is a complex constant. Boundary conditions As (0) = 0 and Ai (L) = 0 have been used: they express the absence of any mirror to reflect the signal and the idler beam. The field amplitudes are reported in Fig. 15.b : for z = 0 no signal beam is present and, consequently, the idler amplitude is not varying at this point; for z = L a macroscopic signal amplitude is found, leading to an important growth of the idler beam amplitude. For comparison the field amplitudes below threshold are given in Fig. 2.a : in this case no classical beams are present in the waveguide and the parametric down-conversion process relies on the amplification of vacuum fluctuations. The relation gL = π/2 gives the oscillation threshold value of the pump √ πc n s n i field A Pth : A Pth = 2χ L √ωs ωi . By considering a 1 cm-long and 10-µm-wide ridge waveguide pumped by a beam at 5 µm, we calculate χ = 30pm/V and a threshold pump power of 130 kW is obtained. This corresponds to a 130 MW/cm2 intensity, which is lower than the damage threshold of the material (∼200MW/cm2 ): parametric oscillation without any mirror or cavity should thus be possible.


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Figure 15. Field amplitudes Ai and As , as a function of the position inside the waveguide, in the case of parametric fluorescence (a) and at the oscillation threshold (b).

Note that the above expression can be simplified. At degeneracy (s = i), prefering wavelength to frequency, this expression becomes A Pthv = n/4χ ·λ/L, which is of the order of A Pthv = 1/χ · λ/L. The field reaches the threshold when it is equal to the inverse of the nonlinear susceptibility (expressed in m/V) times the ratio between the wavelength and the length of the waveguide. This remarkable expression can be understood with the following argument : using the classical coupled equations describing the nonlinear three wave coupling, it appears that the ratio Aχ/λ is the growth rate of the signal, when multiplied by the idler field : ∂ As A p χ Ai = ∂z λs,0 The expression A Pthv = 1/χ .λ/L thus means that when the threshold is reached, the growth rate of the signal is equal to the idler field divided by the length of the waveguide. The idler field at the waveguide facet is simply taken equal to the vacuum fluctuations, in a parametric fluorescence process. As a result, this means that at threshold, the signal needs a length L to grow typically by one photon (the order of vacuum fluctuations). This very simple result is perfetly analogous to the lasing threshold as defined in the context of cavity quantum electrodynamics : the threshold is reached when the cavity is filled by more than one photon (see ref. 33). Comparative analysis Although all the above–mentioned solutions to obtain phase matching are quite different, we want to discuss and compare the characteristics and performances of the devices presented in the previous sections. A summary of this discussion is given in Table 1.

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L. LANCO ET AL. Synopsis of the characteristics and performances of the devices presented in this

Type of phase matching

Form birefringence

Modal phase matching

Counterpropagating signal and idler phase matching

Active/passive device Twin photons wavelength (realized) Signal spectral width at degeneracy

passive (end fire coupling) 2.1 µm (exp.)

active 1.55 µm (exp.)

passive (easy top coupling) 1.55 µm (exp.)

∼150 nm (exp. for a waveguide of length 3.2 mm)) ∼6 × 10−6 W/W/cm2 (exp.) 1 cm−1 (4dB/cm) (exp. at 2.1 µm) Thickness of GaAs layer Refractive index of Alox (th.)

∼120 nm (th for a waveguide of length 1 mm.) ∼6 × 10−7 W/W/cm2 (th.) 0.1 cm−1 (0.4 dB/cm) (exp. at 1.55 µm) Thickness of Al0.25 Ga0.75 As layers (th.)

PF efficiency Optical losses (TE polarization) Sensitive parameter for phase matching wavelength

∼0.3 nm (exp. for a waveguide of length 1 mm) ∼1 × 10−13 W/W (exp.) 0.25 cm−1 (1dB/cm) (exp. at 1.55 µm) Very stable and easy tunable (th.)

The first characteristic we want to point out is whether the device is active or passive. In the case of form birefringence, the need of a pair of materials with a sufficient index contrast leads to the oxidation of the AlAs layers; therefore, due to the insulating nature of the oxide, an electrical transport within the structure would be difficult. We can possibly consider the option of an optical pumping, but a deep investigation is necessary to ensure that the proximity of the Alox is not a problem for the radiative efficiency of the emitters. For these reasons, the form-birefringent device presented in this paper is passive. The whole design of our mode-matched device is conceived such to result in an active structure: laser emission and nonlinear conversion occur on the same chip. Our actual studies on counterpropagating signal and idler geometry, conversely, involve an external laser pump; a development of this device, including a VCSEL on the top of the waveguide, can be envisaged [28]. In this case the emitted photons will have a fixed wavelength as the angle of incidence would be fixed. The frequency conversion range of the three devices described is linked to the transparency window for the used materials, the availability of pump source wavelength and the phase matching condition. The transparency range for AlGaAs is very broad: the limits are given by the phononic resonance (around 30 µm) and by the band-gap energy. The direct band-gap energy at room temperature goes from


461

1.42 eV(∼870 nm) for GaAs to 2.8 eV(∼443 nm) for AlAs [29]. In the domain of twin-photon applications the devices realized up to now are thus well suited to the production of twin photons in the telecom range, for fiber transmissions. In the case of counterpropagating geometry we have also investigated the feasibility of a source for the Silicon absorption band, for line-of-sight experiments in quantum key distribution. Numerical simulations show that a ZnSe/ZnMgSe structure would have the same overall efficiency than the AlGaAs structure. Concerning the parametric efficiency of the three devices, a few remarks are in order: in the two cases of copropagating signal and idler (form birefringence and modal phase matching) the efficiency depends quadratically on the sample length L, which explains why the efficiency is normalized to L2 in the Table 1. In the case of counterpropagating signal and idler, on the contrary, the efficiency does not depend on L (of course in this reasoning optical losses are not taken into account). Another discriminating issue is the bandwidth of the generated signal; the counterpropagating geometry allows to generate a spectrally narrow signal, which we emphasize as an important advantage compared with what is obtained in the copropagating geometry. We notice that the greater refractive index dispersion of semiconductor materials with respect to usual nonlinear crystals makes the phase matching resonance narrower in the semiconductor case. The bandwidth values obtained in this paper for the three configurations are in the same range as those obtained in [22] for PPLN. Optical losses are another crucial characteristic our devices: the method we generally use to measure propagation losses in waveguides is based on Fabry-Perot transmission fringes, and is well established for single-mode optical waveguides. We have recently proposed an extension of this technique to the case of multimode and tightly confining semiconductor waveguides [30]. This procedure involves Fabry-Perot measurements on a large spectral range, in order to find an interval where multimode effects do not alter the loss measurements. The validity domain of this method does not include form-birefringent samples; the loss measurement reported in Table 1 was obtained with a scattering technique using femtosecond pulses [31]. For the three kinds of devices, optical ridges are defined by chemical etching; the heterostructures based on modal phase matching and counterpropagating geometries presents a relatively low losses value. In form-birefringent samples, optical losses (1 cm−1 ) have two main origins: scattering (especially at the interface with the oxide) and two-photon absorption. A material science investigation is in progress in order to study the oxide interface under different growth and oxidation conditions; this will lead to a deeper knowledge of AlOx and to a reduction of optical losses. Finally, another important point for our devices is an analysis of how parameter variations in the structure (layer thicknesses, alloy composition, refractive indexes) influence the parametric tuning curves. This analysis is important for any

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practical design, in order to asses the tolerances in growth step and knowledge of the refractive indexes. The results given here are obtained by performing numerical simulations in the planar waveguide approximation, which is quite satisfactory as far as the ridge is wider than 5 µm. For each of the three devices, we have looked for the most sensitive parameter for frequency conversion. In the case of form-birefringent structures the thickness of GaAs layers has to be controlled most homogeneously: a 1% relative variation of the thickness induces a 6 nm shift of the pump wavelength at degeneracy [32]. Another crucial point for these structures is the precise knowledge of the Alox refractive index, which depends on the oxidation conditions (oxidation time and temperature, thickness of AlAs layers,..). A variation of 0.03 of this index can induce a shift of 10 nm from the degenerate pump wavelength. The modal phasematched structures are grown by realizing a super lattice; the MBE cells contain GaAs, AlAs and Al0.25 Ga0.75 As: all the alloys of the structure are blended by conveniently adjusting the flux of these cells. We have thus investigated the sensitivity of the structure to relative variations of thickness and concentrations of the different layers, finding that the most critical parameter is the thickness of Al0.25 Ga0.75 As layers: a 1% variation of this parameter induces a 2.5 nm shift of the degenerate pump wavelength. Concerning the counterpropagating geometry our calculations show that the structure is very stable with respect to the variation of both thickness and composition of the layers; the most sensitive parameter is Aluminium concentration: as en example, a relative variation of 5% induces a variation in the signal wavelength of 0.1 %, for an angle of incidence of 20◦ . In conclusion, in this paper we have illustrated our recent advances in the realization of semiconductor devices for nonlinear frequency conversion. Three kind of sources have been presented and compared; their different characteristics allow to choose the most adapted device, according to the application envisaged. Acknowledgments This work was funded by the European Union through the Projects OFCORSE, OFCORSE II, QUCOMM and RAMBOQ. References 1. S. J. B. Yoo, IEEE J. LigthwaveTechnol. 14, 955 (1996). 2. W. D. Chen, J. Burie, and D. Boucher, Spectrochim. Acta A 55, 2057 (1999). 3. A. Arie, K Fradkin-Kashi, and Y. Shreberk, Opt. Laser Eng. 37, 159 (2002). 4. D. G. Lancaster, D. Richter, and F. K. Tittel, Appl. Phys. B 69, 459 (1999).


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5. N. Gisin, G. Ribordy, W. Tittel, and H. Zbinden, Rev. Mod. Phys. 74, 145 (2002). 6. A. V. Sergienko and G. S. Jaeger, Contemp. Phys. 44, 341 (2003). 7. D. Bouwmeester, A. Ekert, and A. Zeilinger, The physics of quantum information, (Springer, Berlin, 2000). 8. S. Tanzilli, W. Tittel, H. De Riedmatten, H. Zbinden, P. Baldi, M. De Micheli, D. B. Ostrowsky, and N. Gisin, Eur. Phys. J. D 18, 155 (2002). 9. K. L. Vodopianov, O. Levi, P. S. Kuo, T. J. Pinguet, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, Opt. Lett. 29, 1912 (2004) 10. J. Van der Ziel, Appl. Phys. Lett. 26, 60 (1975). 11. J. M. Dellesasse, J. N. Holonyak, A. R. Sugg, T. A. Richard, and N. El-Zein, Appl. Phys. Lett. 57, 2844 (1990). 12. A. Fiore, V. Berger, E. Rosencher, P. Bravetti, and J. Nagle, Nature 39, 463 (1998). 13. A. Fiore, V. Berger, E. Rosencher, P. Bravetti, N. Laurent, and J. Nagle, Appl. Phys. Lett. 71, 3622 (1997). 14. A. De Rossi, V. Berger, M. Calligaro, G. Leo, V. Ortiz, and X. Marcadet, Appl. Phys. Lett. 79, 3758 (2001). 15. S. Venugopal Rao, K. Moutzouris, M. Ebrahimzadeh, A. De Rossi, G. Gintz, M. Calligaro, V. Ortiz, and V. Berger, Optics Commun. 213, 223 (2002). 16. A. De Rossi, N. Semaltianos, V. Berger, E. Chirlias, B. Vinter, and V. Ortiz, Appl. Phys. Lett. 80, 4690 (2002). 17. S. Ducci, L. Lanco, V. Berger, A. De Rossi, V. Ortiz, and M. Calligaro, Appl. Phys. Lett. 84, 2974 (2004). 18. M. H. Chou, J. Hauden, M. A. Arbore, and M. M. Fejer, Optics Lett. 23, 1004 (1998). 19. A. De Rossi, V. Berger, M. Calligaro, G. Leo, V. Ortiz, and X. Marcadet, Appl. Phys. Lett. 79, 3758 (2001). 20. Y. J. Ding, S. J. Lee, and J. B. Khurgin, Phys. Rev. Lett. 75, 429 (1995). 21. A. De Rossi and V. Berger, Phys. Rev. Lett. 88, 043901 (2002). 22. M. C. Booth, A. Atatüre, G. Di Giuseppe, B. E. A. Saleh, A. V. Sergienko, and M. Teich, Phys. Rev. A 66, 023815 (2002). 23. M. Ravaro, Y. Seurin, S. Ducci, G. Leo, V. Berger, A. De Rossi, and G. Assanto, J. Appl. Phys. 98, 063103 (2005). 24. S. Ducci, G. Leo, V. Berger, A. De Rossi, and G. Assanto, Journ. Opt. Soc. A 22, 2331 (2005) 25. P. G. Kwiat at al., Phys. Rev. Lett. 75, 4337 (1995). 26. R. Normandin and G. I. Stegeman, Opt. Lett. 4, 58 (1979). 27. E. Harris, Appl. Phys. Lett. 9, 116 (1966). 28. Y. J. Ding, J. B. Khurgin, and S. J. Lee, IEEE J. of Quantum Electron. 31, 1648 (1995). 29. S. Adachi, in Properties of Gallium Arsenide, edited by S. Adachi (INSPEC, London, 1993) 30. A. De Rossi, V. Ortiz, M. Calligaro, L. Lanco, S. Ducci, V. Berger, and I. Sagnes, to J. of Appl. Phys. 97, 073105 (2005). 31. S. Venugopal Rao, K. Moutzouris, M. Ebrahimzadeh, A. De Rossi, G. Gintz, M. Calligaro, V. Ortiz, and V. Berger, Optics Commun. 213, 223 (2002). 32. A. De Rossi, V. Berger, G. Leo, and G. Assanto, IEEE J. Quantum Electronics, 41, 1293 (2005). 33. C. Weisbuch, E. Burstein, Confined Electrons and Photons, Plenum (1994).


Part III

Applications

SEMICONDUCTOR LASER BASED TRACE GAS SENSOR TECHNOLOGY: RECENT ADVANCES AND APPLICATIONS Laser Based Trace Gas Sensor Technology FRANK K. TITTEL∗ , GERARD WYSOCKI, ANATOLIY KOSTEREV, and YURY BAKHIRKIN Rice University, 6100 Main Street, Electrical and Computer Engineering Department – MS 366, Houston, TX, 77005, USA

Abstract. Recent advances in the development of sensors based on infrared diode and quantum cascade lasers for the detection of trace gas species is reported. Several examples of applications in environmental and industrial process monitoring as well as in medical diagnostics using quartz enhanced photoacoustic spectroscopy and laser absorption spectroscopy will be described. Keywords: Trace gas detection, near infrared diode lasers, mid infrared quantum and interband cascade lasers, quartz enhanced photoacoustic spectroscopy, laser absorption spectroscopy.

1. Introduction Infrared laser absorption spectroscopy is an extremely effective tool for the detection and quantification of molecular trace gases. The demonstrated sensitivity of this technique ranges from parts per million by volume (ppmv) to the parts per trillion (pptv) level depending on the specific gas species and the detection method employed [1,2]. The spectral region of fundamental vibrational molecular absorption bands from 3 to 24 µm is the most suitable for high sensitivity trace gas detection. However the usefulness of the laser spectroscopy in this region has been limited by the availability of convenient tunable laser sources. Real world applications (see Table 1) require the laser source to be compact, efficient, reliable and operating at near room-temperatures. Existing options include lead salt diode lasers, coherent sources based on difference frequency generation (DFG) described in Part IV-2, optical parametric oscillators (see Parts II-8 and IV-3), tunable solid state lasers (see Part II-5), quantum and interband cascade lasers. Sensors based upon lead salt diode lasers are typically large in size and require ∗ [email protected]


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FRANK K. TITTEL ET AL. TABLE 1. Wide Range of Gas Sensing Applications.

Urban and Industrial Emission Measurements Industrial Plants Combustion Sources and Processes (e.g. early fire detection) Automobile and Aircraft Emissions Rural Emission Measurements Agriculture and Animal Facilities Environmental Gas Monitoring Atmospheric Chemistry (e.g. ecosystems and airborne) Volcanic Emissions Chemical Analysis and Industrial Process Control Chemical, Pharmaceutical, Food & Semiconductor Industry Toxic Industrial Chemical Detection Spacecraft and Planetary Surface Monitoring Crew Health Maintenance & Advanced Human Life Support Technology Biomedical and Clinical Diagnostics (e.g. breath analysis) Forensic Science and Security Fundamental Science and Photochemistry

cryogenic cooling because these lasers operate at temperatures of 100 cm−1 per device ∼0.5–1 µm

1 W cw (pulsed)

Fiber Laserb OPO DFGc

∼2.7 3–6 3–16

RT operation (Cryogenic cooling) RT operation RT operation RT operation

>100 nm ∼µm for specific setup ∼µm for specific setup

Watts 1W µW to mW

a Examples: Cr2+ :ZnSe laser / (Fe2+ :ZnSe laser), etc. b Example: Erbium-doped ZBLAN c Examples: PPLN (periodically poled lithium niobate), AgGaSe , LiInS , LiInSe , etc. 2 2 2

optical sources (OPOs and DFG systems) employing different kinds of nonlinear crystals such as periodically poled LiNbO3 (PPLN), yet on the cost of complexity. The wavelength range of CO2 lasers can be extended by using CO2 isotopomers. Furthermore, the wavelength coverage can be drastically improved by operating the laser at multiatmospheric pressure. At 10 bars, continuous tuning is achieved, yet only in a pulsed mode [2]. Frequency doubling into the 5 µm range has also been demonstrated using quasi-phase-matched GaAs [3]. With the recent progress in orientation-patterning [4], GaAs is becoming an important, efficient nonlinear optical material for frequency conversion processes. Most recent developments with quantum cascade lasers (QCLs) equipped with external cavities are very promising, as a tuning range around 10% of the central wavelength has been demonstrated [5, 6]. Such devices are becoming commercially available now. The availability of QCL wavelengths, however, is still limited. A further new development concerns Er:ZBLAN fiber lasers emitting in the 2.6 to 2.9 µm wavelength range with CW powers up to 10 W [7]. The broadest tuning

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range and best wavelength coverage is apparently achieved with novel solid state lasers and with nonlinear optical systems [8]. As example, a CW OPO system with PPLN as nonlinear optical medium with a tuning range from 3.7 to 4.7 µm and a power of up to 1.2 W has been reported [9]. For further, detailed and up-todate information on tunable mid- infrared laser sources the reader is referred to the corresponding contributions in this volume, particularly in parts I & II. 3. Detection schemes Most detection schemes employed in mid-infrared gas sensing are based on absorption. They involve direct absorption/transmission [1, 10–12] (e.g. in multipass arrangements), also in combination with wavelength-modulation techniques [13–15], cavity ringdown (in various modifications) [16–18], optogalvanic [19], as well as photoacoustic and photothermal methods [20–23]. Each of these techniques has its advantages and drawbacks and the choice of the preferred scheme is also influenced by the actual application. One key parameter concerns the ultimate detection sensitivity, often given in minimum detectable absorption coefficient obtained per time interval of observation. A typical number is 10−9 cm−1 Hz−1/2 . This sensitivity enables the detection of concentrations in the ppb to sub-ppb range. However, it should be noted that detection selectivity is often equally important as sensitivity as in most cases one deals with multi-component mixtures. Further important issues to be addressed are calibration procedures, data acquisition, the implementation of algorithms for multi-component analyses, and – if available – comparison with independent measurements. 4. Applications in trace gas sensing The performance of mid-infrared spectrometers in point monitoring has been widely discussed in the literature. Detection limits at the sub-ppb and even ppt concentration level and applications in the field have been demonstrated. As examples from our own research activity we recently reported on in situ measurement campaigns in fruit storage and on street traffic emissions. Both studies were performed with a mobile, automated CO2 -laser based photoacoustic system. The former was devoted to time-resolved recordings of fermentation processes in fruit storage. Gaseous emissions of ethene (ethylene, C2 H4 ), methanol (CH3 OH) and ethanol (C2 H5 OH) were simultaneously monitored in the presence of strong CO2 emission [24]. The traffic emissions were recorded at the exit of a street tunnel. They involved the simultaneous monitoring of ethene, ammonia (NH3 ) and CO2 during weeks with the unattended system. This field campaign demonstrated that photoacoustic measurements are feasible even under harsh conditions with high noise levels [25]. The resulting ammonia concentrations were compared with time-averaged data obtained by alternative methods,

ISOTOPIC SELECTIVITY USING DFG-SOURCES

499

yielding good agreement [26]. With the knowledge of traffic flow data, emission factors for various species could be derived, an important parameter for the evaluation of the traffic-related load by a specific compound. More recent developments concern the implementation and spectroscopic applications of novel solid state laser sources such as a Cr2+ :ZnSe laser pumped with a Er+ - fiber laser [27, 28] or the use of new nonlinear optical materials like LiInS2 [29] and LiInSe2 in DFG sources. These systems enable the extension of the wavelength range, either towards shorter wavelengths in the first case or longer wavelengths in the latter case. This enhances the accessibility of molecular absorption spectra. A current research project aims at laser spectroscopic analyses of doping agents used by athletes in sports. In a first step vapors of doping compounds were investigated using a broadband optical parametric generation (OPG) source comprising a pulsed Nd:YAG laser pumped PPLN crystal operated between 2800 and 3100 cm−1 and a small photoacoustic cell. The vapor of the doping compound under investigation was introduced into the cell heated to 60◦ C and operated at an acoustic resonance of 5.7 kHz corresponding to the pulse repetition rate of the Nd:YAG pump laser. Examples included stimulants (e.g. ephedrine), betablockers, diuretica and anabolica [30, 31]. Many of these agents have been investigated for the first time in the vapor phase. 5. Studies on isotopic compositions of trace gases In the following we focus on studies devoted to isotope ratio measurements. Isotopic compositions of trace gases are of interest in such diverse fields as ecological CO2 exchange, volcanic emission, medical diagnostics, extraterrestrial atmospheres, etc. In ecosystem research isotopic ratios of CO2 , H2 O, N2 O, NO and NO2 [32–35] are of interest as they enable to determine the source of, e.g., CO2 (soil, plants, or combustion during energy conversion as a result of anthropogenic activity). In volcanic research, the forecast of eruptions attracts a lot of interest. In addition to seismic sensors the gaseous emissions of CO2 , HCl and SO2 and of ratios of concentrations like CO2 /SO2 or HCl/SO2 may be used for interpreting magmatic processes at depth. Even more interesting are, however, isotopic ratios such as H35 Cl/H37 Cl or 13 CO2 /12 CO2 as magmatic gases may react with rocks and other fluids on their path to the earth surface. Hence, changes of isotopic ratios in emitted gases can serve as indicators of increased volcanic activity, especially for sensing the progress towards eruption [36–40]. A further area of trace gas monitoring, particularly also with isotopic selectivity, is in non-invasive medical diagnostics [17, 22, 41]. Exhaled human breath has been shown to contain hundreds of different species. Some of them have been identified as being characteristic for certain diseases. Isotope ratios of CO2 have

500


been identified as being indicators for the presence of Helicobacter pylori (Nobel prize for medicine in 2005), the bacteria associated with peptic ulcers and gastric cancer. A further research field concerns isotope ratio measurements in extraterrestrial atmospheres. A very recent preliminary investigation is devoted to the development of a near-IR tunable diode-laser based instrument for future in-situ measurements of H2 O and CO2 isotopomers in the Martian atmosphere [42]. These four (and many more) areas illustrate the importance of precise isotope ratio determinations. However, the detection of individual isotopomers and of isotope ratios impose an additional challenge onto the selectivity and the dynamic range of the detection scheme because isotopomers are chemically identical and often their ratios of abundance are rather small, e.g. 13 CO2 only accounts for ca. 1% of the natural CO2 and the ratio between the stable nitrogen isotopes 15 N/14 N is only ca. 0.3%. The current state-of-the-art technique for the isotopic measurements of CO2 is to sample air in glass or steel flasks, transport them to the lab, where the CO2 is cryogenically separated and purified and then analyzed with an isotope ratio mass spectrometer (IRMS). This spectrometer yields a high accuracy of δ = 0.1 or better where δ is defined as 13 Csample /12 Csample δ() = − 1 × 1000 (1) 13 C /12 C std std with the reference standard “Vienna Pee Dee Belemnite” (VPDB) given as Cstd /12 Cstd = 0.0112372 [43]. However, the procedure is very laborious and allows only a limited number of samples (at best 40 per day) to be analyzed [34, 44]. Accordingly, the reliability of the information is somewhat limited. Therefore, a direct on-site measurement technique, which allows a high frequency of measurements (ideally a sampling rate in the 10 Hz range) of the 13 C/12 C and 18 O/16 O isotopic ratio and with high precision (ideally δ = ±0.1), would be a real breakthrough in the field of flux measurements and partitioning. Until recently, the best precision δ = 0.2 and 0.3 for air samples was obtained by Uehara et al. [45] and McManus et al. [46], respectively. Both groups used the method of balancing path length to match the different absorption strengths resulting from the large difference in abundance of the isotopes. They used a near-IR laser [45] or a cryogenically cooled lead salt laser [46]. In both cases their results were limited to two isotopomers of either CH4 [45] or CO2 [46]. McManus et al. [46] extended their studies to the determination of the 13 C/12 C ratio in CO2 of exhaled human breath and of automobile exhaust. In a new study they replaced the lead salt diode laser by a near roomtemperature pulsed quantum cascade laser and achieved a precision of 0.18 for the 13 CO2 /12 CO2 determination in atmospheric air, again using balanced path length and an averaging time of 30 seconds [12]. The advantage of this system 13


501

is its near room-temperature operation (except for the cryogenically cooled IR detector but that may be replaced by a Peltier-cooled detector in the future). However the drawback is the comparatively large QCL line width which exceeds the molecular absorption line width and hence complicates the data evaluation and in some cases of other isotopomers may even impede an accurate isotopic analysis particularly in the presence of other interfering compounds. Castrillo et al. [38] performed the only field measurement of the δ13 C in volcanic CO2 with a 2 µm diode laser spectrometer with precision and accuracy levels of about δ = 0.5. It is evident that there is a great potential in laser-based spectroscopic methods that has not been fully exploited yet. Hitherto, all studies have addressed isotopomers of one or a maximum of two molecules at a time and have been performed at rather high concentrations in the percent to ppm-range. For many real-world applications, however, concentrations are much lower, e.g. typically 300 ppb for ambient N2 O. Furthermore, the required precision of δ < 1 and sufficient reproducibility are often not achieved. This is crucial as the changes in isotopic composition are usually very small, e.g. δ-values are typically of the order of a few . 6. DFG-studies on CO, CO2 and N2 O isotopomers 6.1. DFG-SOURCE

We designed and built a new continuous-wave (cw) DFG-system based on a diode-pumped cw Nd:YAG laser (Innolight Mephisto, 2 Watt, 1064.5 nm) and a tunable cw external cavity diode laser (Sacher TEC-120-850-150, 150 mW, 820 nm-875 nm) mixed in an AR-coated periodically poled MgO-doped LiNbO3 (MgO:PPLN) crystal (HC-Photonics). This source has a continuous tuning range from 4.3 µm to 4.7 µm by using only one crystal grating with a period of 23.1 µm. The grating period is matched to the wavelength by changing the crystal temperature between 30◦ C and 130◦ C. The idler beam has a line width of 1 MHz and a cw power between 23 µW and 5 µW, depending on the wavelength. Since the crystal has an absorption band at 5 µm, the power decreases strongly with increasing wavelength. At 4.3 µm the absorption coefficient α of the crystal is 0.25 cm−1 , at 4.7 µm it amounts to 0.75 cm−1 [47]. With longer crystal length more midinfrared light is generated but also more is absorbed, therefore there is an optimal crystal length with the highest conversion efficiency. The idler power Pi is given by the following formula in SI units [18, 48, 49]: Pi = Pp Ps

32π 2 de2f f L ε0 cn i λi2 (n s λ p + n p λs )

h(ξ, σ, µ, α, L),

(2)

where de f f is the effective nonlinear coefficient, L is the crystal length, c is the speed of light, P is the laser power, λ is the wavelength, n is the refractive index

502


with the subscripts p, s and i referring to pump, signal and idler, respectively. The focusing function h(ξ, σ, µ, α, L) for diffraction limited Gaussian beams is given by: ⎛ ⎞ ξ ξ −iσ (τ −τ )+ αL − αL 4ξ (τ +τ ) 2 e e ⎠ , (3) h (ξ, σ, µ, α, L) = Re ⎝ dτ dτ 1+µ2 4ξ −ξ −ξ 1 + ττ − i 2 (τ − τ ) 1−µ

where L ξ= , b

ns λ p ks = , µ= kp n p λs

np ns ni 1 . σ = −π b − − − λp λs λi

(4)

Here Λ is the grating period, and b is the confocal parameter of both pump and signal laser and is given by the minimal beam waist b = k p ω2p = ks ωs2 . These equations are valid for both bulk and periodically poled crystals, only de f f changes by a factor 2/π compared to the case of a bulk crystal. Our calculations have shown that a crystal length of 5 cm is optimal. The generated idler power is about four to ten times lower than calculated, most probably because of imperfections in the crystal and its grating quality and because of the non-Gaussian beam shape of the external cavity diode laser. 6.2. ISOTOPOMER ABUNDANCES AND LINE STRENGTHS

One problem by measuring isotopomers is that the concentration of the main isotope is often considerably higher than that of the less abundant isotope (e.g. 13 CO2 /12 CO2 = 1.1%). There are two possibilities to overcome this problem, either to measure two lines of similar strength (resulting in a strong temperature sensitivity of the measurement), or by choosing two lines with about the same lower energy level but with very different line strength. The temperature dependence of the isotopic ratio δ/T is proportional to the difference of the ground-state energies E of the corresponding transitions [50] δ E ≈ T kT 2

(7)

where k is the Boltzmann constant, T is the absolute temperature and δ has been defined in Eq. (1) above. As an example the temperature dependence ∆δ 13 C/∆T of CO2 can be calculated taking the 13 CO2 -line at 2310.347 cm−1 (line strength: 6.447 · 10−21 cm−1 /(molecule · cm−2 ), corrected with the natural abundance) paired with the 12 CO2 -line at 2310.002 cm−1 (line strength: 4.664 · 10−21 cm−1 /(molecule·cm−2 ), weak line) or, alternatively, paired with the 12 CO2 line at 2311.106 cm−1 (line strength: 4.731·10−19 cm−1 /(molecule·cm−2 ), strong line) [51]. The lower energy level of the 13 CO2 -line is E 13 = 639.6309 cm−1 and


503

Figure 1. Absorption line strengths for three different isotopomers of CO [51].

the one of the weak 12 CO2 -line is E 12 = 1454.9687 cm−1 . This line pair has similar line strength but the temperature dependence ∆δ 13 C/∆T = 13.5 K−1 is very large. When using a balanced path length setup the strong 12 CO2 -line can be used instead with a lower energy level E 12 = 704.3005 cm−1 , resulting in a temperature dependence of only ∆δ 13 C/∆T = 1.1 K−1 . For most applications the required precision is δ = 1 or less, so either the gas cell needs to be very well temperature stabilized or a balanced path length setup should be used. The wavelength range of 4.3 µm to 4.7 µm contains useful absorption lines of CO2 , CO and N2 O for isotopomer measurements. As example, Fig. 1 shows the absorption spectrum of three isotopomers of CO in this range according to Hitran data [51]. 6.3. MEASUREMENTS AND RESULTS

In our setup we use an astigmatic multipass Herriot cell (New Focus) because it offers the possibility to enter the cell at another angle than usual, so that the beam leaves the cell after only two passes [12]. Hence, there are two different path lengths of 10 m and 40 cm, respectively. This makes it possible to measure two lines of very different line strength. Before the cell a beamsplitter directs part of the light to a reference detector to record the DFG power. After the multipass cell there is another detector to record the transmitted light. We use indium antimonide detectors with liquid nitrogen cooling (Judson Technologies J10D-M204-R04M60) with an active area of 4×4 mm2 . The light is modulated with a chopper at a frequency of 2 kHz. The detector signals are measured with lock-in amplifiers with a time constant of 100 ms. For analyzing the measurements a Voigt function is fitted to the absorption lines. The concentration is determined by using the area under the Voigt line and the known line strength. By comparing the concentrations of the main and the less abundant isotope the isotopic ratio can be calculated.

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HELEN WAECHTER AND MARKUS W. SIGRIST a) 12 16

C O

Figure 2. a) A 12 C16 O absorption line was measured (dotted line) with the short path length of 40 cm. A Voigt curve is fitted (solid line) and from the area under the curve the concentration is calculated. The gas sample was taken from a scooter exhaust containing 200 ppm of CO. b) The 13 C16 O absorption line of the same gas sample was measured with the long path length of 10 m. Again a Voigt curve is fitted to obtain the concentration. By comparing the concentrations between the two isotopomers, the isotopic ratio can be calculated.

The isotope ratios 13 C/12 C and 18 O/16 O of 450 ppm CO2 in ambient air were measured with balanced path lengths (40 cm and 10 m) and single path length (only 10 m). The measurements were made at a pressure of 50 mbar to avoid overlapping of the absorption lines. We also determined the isotope ratios 13 C/12 C and 18 O/16 O of CO in a sample collected from the exhaust of a scooter. The CO concentration amounted to 200 ppm and the results are shown in Fig. 2. The background noise is dominated by detector noise and is the same for both path lengths, but because the absorption of the 12 C16 O line is stronger, the signal-to-noise ratio is four times better for this line. Finally, the isotopic ratio 15 N/14 N of N2 O (2040 ppm in synthetic air) was determined. Our results for the various CO2 , CO and N2 O isotopomers are listed in Table 2. They are in good agreement with the natural abundance (13 CO2 /12 CO2 = 1.1%, 16 O12 C18 O/12 C16 O2 = 0.39%, 13 C16 O/12 C16 O = 1.1%, 12 C18 C/12 C16 O = 0.20%, 14 N15 N16 O/14 N2 16 O = 15 N14 N16 O/14 N2 16 O = 0.36%) [51], but the precision still needs to be improved. The concentrations of the gases were in the ppm range which is sufficient for measurements of CO2 in ambient air, yet not for N2 O and CO. Nevertheless these concentrations are lower than for most other previous studies. First measurements were performed on isotopomers of N2 O using absorption spectroscopy combined with wavelength modulation and first harmonic detection. The isotopic composition of the gas in the multipass cell is compared to a reference gas in a reference single pass cell that is placed in front of the reference detector. The reference cell is 10 cm long and is filled with 5% N2 O diluted in


505

TABLE 2. Measurements of isotopic ratios and δ-values in different trace gases with our DFG system and multipass cell. Gas

Concentration

Isotope ratio: single path length

Isotope ratio: path length

CO2

Laboratory air: 450 ppm CO2

13 C/12 C: 1.3% ± 0.2% 18 O/16 O:

13 C/12 C: 1.4% ± 0.3% 18 O/16 O:

0.44% ± 0.06%

0.47% ± 0.11%

N2 O

2040 ppm N2 O in synth. air

14 N15 N16 O/14 N14 N16 O: 14 N15 N16 O/14 N14 N16 O:

0.30% ± 0.01%

balanced

0.35% ± 0.08%

15 N14 N16 O/14 N14 N16 O: 15 N14 N16 O/14 N14 N16 O:

CO

Scooter exhaust: 200 ppm CO

0.34% ± 0.02%

0.39% ± 0.08%

—

13 C/12 C: 1.1% ± 0.2% 18 O/16 O: 0.16% ± 0.03%

Wavelength δ- value

modulation:

—

14 N15 N16 O/14 N14 N16 O: δ15 N = −44.3 ± 3.5 15 N14 N16 O/14 N14 N16 O: δ15 N = −57.4 ± 4.5

—

synthetic air. The wavelength of the external cavity diode laser is modulated with a frequency of 1 kHz and with an amplitude of 0.6 pm. From these measurements the δ-value can be obtained by taking the ratio of the measured signals of the sample and the reference gas for both isotopomers and compare these ratios for the main and the less abundant isotope lines. To evaluate the data from our measurements we did not take the ratios mentioned above directly but plotted the detector signal I Ssample recorded after the sample gas versus the detector signal I Sr e f er ence recorded after the reference cell and fitted a line I Ssample = I a · I Sr e f er ence + I b for each isotopomer I . By comparing the slopes I a of these curves of the main and the less abundant isotopomer, the difference of the isotopic composition between the sample and the reference gas can be calculated [11]: minor Csample /main Csample δ = − 1 · 1000 minor C main C Std / Std minor Csample /minor C Std − 1 · 1000 (8) = main C main C sample / Std minor minor ratio a δ = main − 1 · 1000 = main − 1 · 1000. ratio a Here main C Std,sample and minor C Std,sample are the concentrations of the main and the less abundant (minor) isotopomer of the standard and the sample gas, respectively, and the ratios are given by main ratio = main Csample /main C Std and minor ratio = minor Csample /minor C Std . The advantage of this method is that there is no need for correcting constant backgrounds.

506


These results, although not directly comparable to the isotopic ratios in Table 2, are also included in the table in the right column. These data have a better precision than the ones with absorption spectroscopy, we are able to measure the δ-value with a precision of δ = 3.5 for a single measurement, but the reproducibility needs to be improved. The main problems are the limited response time of the detectors in combination with the preamplifiers as well as a leaking of the multipass cell. A further problem may be related to the polarity of the N2 O molecule which favors its adhesion to the cell walls and thus may cause variations of the concentration during the measurements. A more detailed study with improved measurement conditions yielding higher precision will be published elsewhere. 7. Conclusions and outlook Laser-based trace gas sensing has attracted considerable attention in recent years. Laser spectroscopy offers some distinct advantages like multi-component capability and lack of sample pretreatment in comparison with more conventional techniques such as chemiluminescence, FTIR or gas chromatography combined with mass spectrometry (GC-MS). The success of laser- based devices in terms of high sensitivity and selectivity in multi-component gas mixtures mainly depends on the availability of broadly tunable narrowband room-temperature mid-IR laser sources. In this respect further developments of nonlinear optical devices (DFG and OPOs), of novel solid state laser materials, and – last but not least – of external cavity quantum cascade lasers play a pivotal role. It should be kept in mind, however, that cost-effective near-IR telecom diode lasers may also be employed in some cases when ultimate detection sensitivity is not a primary issue. A special area of applications are spectroscopic studies with isotopic selectivity of isotopomers as currently pursued in various laboratories as well as in the field because the isotopic signature often contains additional information on the origin of the species. We discuss first studies with a cw narrowband DFG system whose wavelength range enables to record all isotopomers of the important molecules CO2 , CO or N2 O. The compound N2 O is of special interest as 15 N14 NO can easily be distinguished spectroscopically from 14 N15 NO with identical mass. Using DFG combined with wavelength modulation as well as balanced absorption path lengths we achieved a reasonable measurement precision in the - range with respect to the δ-value, even at the ppm-concentration level. Further system improvements are required before the laser-based systems can replace the commonly used isotope ratio mass spectrometry (IRMS) technique which is rather sophisticated and time-consuming.


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PHOTOACOUSTIC SPECTROSCOPY USING CONTINUOUS WAVE OPTICAL PARAMETRIC OSCILLATORS OPO Spectroscopy ANTHONY K. Y. NGAI, STEFAN T. PERSIJN, MAARTEN M. J. W. VAN HERPEN, SIMONA M. CRISTESCU, and FRANS J. M. HARREN∗ Life Science Trace Gas Facility, Molecular and Laser Physics, Radboud University, Toernooiveld 1, 6525 ED Nijmegen, The Netherlands

Abstract. Nowadays, worldwide developments of new cw OPO devices realize widely tunable, cw radiation with high power and narrow linewidth. Here, the versatility and sensitivity of continuous wave, singly resonant OPO’s combined with photoacoustic and cavity ring-down spectroscopy are discussed for trace gas sensing. Keywords: Optical parametric oscillator, continuous wave, infrared radiation, photoacoustic spectroscopy, cavity ring-down spectroscopy, trace gas sensing.

1. Introduction Gas phase spectroscopy is nowadays very common in a wide variety of applications within chemistry, physics, biology, and medicine. From research involving living organisms to air pollution monitoring, spectroscopic gas sensors have proven to be indispensable tools. There are various ways of utilizing gas sensors and each application puts different demands. Some applications require a very high sensitivity for one specific gas compound, while others benefit more from a sensor that has the ability to measure a wide range of gases. A high timeresolution is also desirable, as well as selectivity, robustness, and little or no need for sample preparation. To some extent, these characteristics can be combined in a single device but often a compromise has to be made. Established methods of gas detection such as chemiluminescence and gas chromatography meet some, but not all of these requirements. For example, gas chromatography includes the need for sample preparation while another disadvantage is the sometimes-limited sensitivity. In particular, the sample gas needs to be concentrated on a solid sorbent, which prohibits online measurement. ∗ To whom correspondence should be addressed.


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Laser based absorption spectroscopy performs well in terms of sensitivity and selectivity, and it does feature the ability to measure on-line. The high sensitivity and selectivity it provides are due to several important factors. Firstly, the narrow linewidth of lasers gives a high spectral power density as compared to broadband light sources. Especially for continuous wave (cw) lasers this linewidth is typically much narrower than the molecular absorption lines. This causes the total laser emission to be attenuated by the gas sample under investigation, instead of only a small fraction, as is the case in broadband absorption. Thus, the absorption signal increases strongly due to its narrow linewidth. In addition, the selectivity improves because it enables a wavelength scan over an absorption feature. This helps to distinguish the target molecule from interfering compounds and background signals. Selectivity enhances further by the unique spectral absorption spectrum of each molecule, which corresponds to different ro-vibrational transitions of the molecule. Spectroscopic gas detection probes the internal structure of the molecule, whereas other techniques such as mass spectrometry only assess a global property of the investigated compound. In the infrared wavelength region between 2.5 and 25 µm absorption spectroscopy has the additional advantage of accessing the fundamental ro-vibrational transitions of many molecules. This yields numerous characteristic strong absorption lines available for use with laser-based detection. For this reason, this part of the electromagnetic spectrum is called the ‘fingerprint’ region (Figure 1). The sensitivity, speed and selectivity of mid-infrared laser based absorption spectroscopy make it a very suitable method of gas sensing. The mid-infrared region between 2.5 and 5 µm is of particular interest because the fundamental vibrational transitions of many molecules present strong absorptions (Table 1), making highly sensitive detection possible. Since many of these molecules are involved in industrial process control, air pollution, agriculture, biology, medicine, but also modern themes such as security at public places, there is an increased demand for novel monitoring techniques of all kinds of molecular gas species. At present, no commercial widely tunable laser sources are available in this wavelength range. Direct generation of tunable mid-infrared radiation using solid-state lasers such as quantum cascade lasers and lead salt diode lasers suffer especially from limited tuning properties [1, 2]. Difference frequency generation (DFG) is capable of on-line absorption measurements [1, 3]. However, it is inherently restricted to only lowest mid-infrared powers (nanoWatt to microWatt range) and consequently suffers from long detection times if the sensitivity has to be in the ppbv (part per billion volume; 1:109 ) level. A relatively broad continuous tuning range is provided by optical parametric oscillators (OPO’s) based on quasi-phase matched materials such as periodically poled lithium-niobate (PPLN) crystals. Since they combine relative high power levels (1 W cw) and narrow linewidth with wide tunability (over hundreds wavenumbers with continuous

PHOTOACOUSTIC SPECTROSCOPY USING CONTINUOUS WAVE OPO’S 513

CO2 laser CO laser

Lasers OPO

C2H6

CH4

CH4

Gases

C2H4

NO2

Atmospheric transmission over 300 m

C2H6

100 %

C2H4

C2H4

H2O CO2

0

0

1

2

3

4

5

6

7

8

9

10 11 12 13 14 15

Infrared wavelength in micrometer Figure 1. The atmospheric transmission window in the infrared wavelength region. The lower panel shows the transmission over a 300 m path length and the strong absorptions due to the presence of high CO2 and water concentrations. The middle panel shows the absorption regions of some smaller hydrocarbons, while the upper panel shows the wavelength coverage of the OPO, CO and CO2 laser. The latter two lasers are line tunable lasers while the OPO has continuous wavelength coverage. TABLE 1. Some molecular (end) groups and their characteristic absorbing wavelength regions in the 2.5–5 µm range (2000–4000 cm−1 ). [4] Molecular end group

Spectral range (cm−1 )

Molecular end group

Spectral range (cm−1 )

>CH2 /–CH3 –CHO >O–CH3 –O–CH2 –O >N–CH3 –C≡CH >C=CH2 >C=C–H –OH >NH/=NH –S–H

2960–2850 2900–2700 2850–2810 2790–2770 2820–2780 ∼3300 3095–3075 3040–3010 3650–3590 3500–3300 2600–2550

>P–H –POOH –C≡C– –C≡N –N=C=O –N3 –N=C=N– >C=C=O –N=C=S R–S–C≡N

2440–2350 2700–2560 2260–2150 2260–2200 2275–2250 2160–2120 2155–2130 ∼2150 2140–1990 2175–2140

514


tuning over typically 1 cm−1 ), OPO’s represent an excellent source for sensitive spectroscopic gas analysis. Within laser-based spectroscopy, there are many possible experimental detection schemes for trace gas detection, each with their own advantage and disadvantages. In this work, a number of these schemes are demonstrated and evaluated, and some applications in medical and life sciences are presented. 2. Physical basics of optical parametric oscillators In the optical parametric process of the OPO the pump photon is split in two parts, forming two new photons with different energies. The generated photon with the highest energy is termed the signal, and the other photon is termed the idler. The generated photons cannot be of any frequency due to energy conservation. In addition to that, destructive interference between the photons needs prevention. This gives rise to a second restriction, the phase matching condition [5,6]. Changing the signal and idler frequencies is difficult, but can be done if the refractive indices nidler , nsignal and npump are changed, for instance by rotating or heating the crystal. With quasi phase matching a special crystal is used, which has a characteristic poling period in the crystal axis. This gives rise to an extra term in the phase-matching condition. By poling the crystal with the right value for , the phase-matching condition can always be met for any combination of pump and signal photons. 2.1. QUASI PHASE MATCHING IN PERIODICALLY POLED CRYSTALS

Quasi phase matching (QPM) was devised independently by Armstrong and Franken in 1962 and 1963, respectively [5, 6]. The invention removes the effect of the destructive interference by resetting the phase difference between the generated polarization wave and the idler wave after an odd number of coherence lengths. This can be achieved by periodically inverting the generated polarization wave, which is done by changing the sign of the nonlinear coefficient (Figure 2). By applying locally a high voltage, regions of periodically reversed spontaneous polarization domains (with length ) are formed in ferroelectric crystals like LiNbO3 [7]. The greatest conversion efficiency can be reached when the sign of the polarization is flipped every coherence length. This is called first order QPM. QPM is less efficient than birefringent phase matching. However, this does not mean that QPM will have a lower conversion efficiency. In contrast, it generally has a much higher efficiency. Using QPM the idler, signal and pump waves propagate collinearly. With birefringent phase-matching, the three waves often will have different paths inside the crystal, limiting the range in which the beams overlap. With QPM the waves can have normal incidence on the nonlinear crystal, giving collinear propagation with maximum overlap between the waves.


Df

0

p/2

phase shift p

0

p/2

Lcoh 0

Crystal axis phase shift p

0

p/2

phase shift p

Figure 2. The polarization wave (P) generated by the nonlinear processes in the crystal radiates idler waves (E) at all positions inside the crystal. The polarization wave (thick line) changes its sign (phase shift π) every coherence length Lcoh , thus allowing constructive interference.

In addition, this means that very long crystals can be used, since the full length can be used as effective interaction zone. An additional advantage of QPM is that very high nonlinear coefficients can be used. With birefringent phase-matching, the propagation direction through the crystal is determined by the angle required for phase-matching. Generally this means that the crystal direction with the highest nonlinear coefficient cannot be used. With QPM this problem doesn’t exist, resulting in the use of much higher nonlinear coefficients. Furthermore, with QPM it is also possible to use nonlinear crystals that are not birefringent, but have a very high nonlinear coefficient, such as for example GaAs and ZnSe. 2.2. PERIODICALLY POLED LITHIUM NIOBATE

In 1965, the first large boules of Lithium Niobate were grown at Bell Laboratories and in that same year, the first birefringent phase-matched OPO was reported using a 5-mm long Lithium Niobate crystal [8]. Even though the principle of QPM was already known at this time, [5, 6] it took almost 30 years after this, before Bosenberg et al. built the first continuous wave, quasi phase matched, singly resonant OPO in 1996, [9, 10] using a Periodically Poled Lithium Niobate (PPLN) crystal with a single poling period. PPLN is a good material to use for quasi phase matching due to its high nonlinear coefficient (Table 2) combined with a wide transparency range. The poled structure of PPLN can be engineered with a photolithographic mask, which makes it easy to produce a single crystal with several poling periods. Currently crystals with as many as eight different poling regions are available. To take full advantage of this novel way to engineer PPLN crystals, one could use a fan-out grating design as was demonstrated at Sandia National Laboratories [11]. When such multiple grating crystals are used in an OPO, the operation range can be

516


TABLE 2. Approximate values of the effective nonlinear coefficients and transparency ranges of several types of periodically poled/oriented crystals. Type

PPLN PPKTP PPRTA OPGaAs PPLT

Nonlinear coefficient deff (pm/V)

Transparency wavelength range (µm)

16 10 10 66 9

0.3–5 0.3–5 0.3–5 0.9–12 0.3–5

increased significantly by selecting the poling period of the crystal with translation of the PPLN through the laser beam. Even though PPLN has many advantages, it also exhibits several undesirable properties such as thermal lensing, which makes the OPO very sensitive to air currents, and the need for elevated operation temperatures (typically >100◦ C) to prevent photorefractive degradation. This latter property limits miniaturization of a practical device and restricts the obtainable wavelength range using temperature tuning. Some of the limitations of PPLN can be overcome by the use of other kinds of ferroelectric materials such as LiTaO3 , and RbTiOAsO4 , while orientation patterned GaAs has recently gained a lot of interest [12, 13]. Alternatively, (near-) stoichiometric crystals instead of congruent crystals can be used. Nearly stoichiometric crystals doped with more than 1.8 mol% of MgO showed no measurable photorefractive damage to intensities of as much as 8 MW/cm2 at 532 nm [14]. Dopants like Mg, In or Zn increase the photoconductivity of the crystal. Doping renders several advantages such as three orders of magnitude higher threshold damage, reduced thermal lensing resulting in better power and temperature stability, reduced photorefractive damage and room temperature operation of the crystal [15, 16]. This latter property extends the temperature tuning range within a single period considerably as compared to undoped PPLN (Figure 3). 3. OPO cavity design There are several issues to take into account when designing the OPO cavity. One of the first considerations is for which wavelengths the cavity should be resonant. The simplest OPO cavity setup is the singly resonant OPO (SRO). In this design, the OPO cavity mirrors are only reflective for the signal wavelength and have a high transmission for the pump and idler frequencies. The advantage of this setup is that it is easy to tune, relatively simple to set up, and it can cover a wide


Figure 3. Signal (1475–1739 nm) and idler (2746–3829 nm) wavelengths of the OPO vs. temperature of a MgO-doped PPLN crystal for poling periods 29.0–31.5 µm. The solid lines are the calculated values from SNLO [17].

emission range without the need to change optics. The drawback is that an SRO has a higher oscillation threshold, which means that it requires high pump powers to start oscillation. A typical oscillation threshold for such devices is 3 Watts of pump power. However, some groups demonstrated considerably lower thresholds. For instance, Klein et al. could reduce this threshold to 1.6 W using a 925 nm diode laser as pump source [18]. Doubly resonant OPO’s have a reduced oscillation threshold; as such, next to the signal frequency the OPO cavity is resonant for the idler or pump frequency. An example is a 20 MHz line-width, doubly resonant OPO with 18 mW idler output power covering the 2.2–3.7 µm wavelength region [19]. The advantage of these systems is that they have a very low oscillation threshold (for the last example it could be as low as 135 mW), but the idler output power is rather low compared to an SRO setup, mainly because low power pump sources are used. When a pump resonant OPO is pump-tuned, the length of the cavity needs to be adjusted to keep the cavity resonant for the pump frequency. Therefore a doubly resonant design does not allow very wide continuous pump tuning, since both the signal and pump wavelengths need to be kept in resonance. However, this problem can be solved by using two different cavities for the signal and pump wavelengths. When the pump source is now tuned, both cavities can be adjusted independently in order to keep both the pump and signal frequencies resonant. An example of a

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pump resonant SRO is a 30 MHz linewidth OPO, with 100 mW output power at idler frequencies between 3.1 and 3.9 µm [20]. When an OPO system is constructed, the next consideration is to build a linear cavity or a ring cavity. Bosenberg et al. compared idler output power versus the pump power of both a linear and a ring cavity [9]. They found that the linear cavity had a higher oscillation threshold of 6.0 W compared to 3.6 Watts for the ring cavity. However, the conversion efficiency of the linear cavity went up faster and at 13.5 Watts of pump power both cavities produced the same power (3.6 W). They also found that the linear cavity tended to run with linewidths of about 2 cm−1 . A bowtie ring-cavity design is preferable, because better frequency stability is expected for this type of cavity. 3.1. OSCILLATION THRESHOLD FOR SINGLY RESONANT OPO

The oscillation threshold PT for a singly resonant OPO is given by: [7] PT = A

λ p λs λi de f f 2 L c

(1)

in which λp , λs and λi represent the wavelength of the pump, signal and idler waves, respectively, Lc the crystal length and deff the effective nonlinear coefficient. ‘A’ takes into account factors, such as round-trip losses at the signal wavelength, pump power transmission through the set-up, and the waist of the pump beam. Important to note is that deff (Table 2) is the most determining factor for the threshold power. Longer OPO crystals will reduce the threshold for the SRO. Nowadays, typical crystal lengths are 50 mm. Henderson and Stafford used an 80 mm crystal pumped by a 1083 nm fiber source, which resulted in a record-low threshold of 780 mW for generating 2.8-µm idler [21]. The effect of λp , λs and λi is interesting when generating longer wavelengths, because it turns out that the best performance can be gained with a short pump wavelength. For example, the value for (λp λs λi ) can be compared for generating 10 µm light using a 1 µm, 3 µm and 5 µm source. The oscillation threshold will increase from 11 to 129 up to 500, respectively. The difference between 1 and 5 µm pump wavelengths is roughly a factor of 50. However, this does not mean that the output power will also be 50 times lower. Due to the Manley Rowe relations, the ratio between the idler output power and the pump power is better for longer wavelengths [22]. 4. Frequency tuning with OPO’s One of the main advantages of OPO’s compared to other laser systems is their wide tunability, which means that they can cover a wide range of molecular absorptions. Here, we will distinguish two categories of tuning ranges, namely


total tuning range and continuous tuning range. The total tuning range is the total range of available wavelengths that the OPO can generate. However, if the total tuning range of a laser system is said to be from 3.0 to 3.5 µm, this does not necessarily mean that it is able to generate any wavelength within this range. Good examples of this are the line-tunable CO and CO2 lasers, which can only generate specific wavelengths within their operation range. For the OPO the total tuning range is achieved by tuning of the poling periods and temperature of the crystal (Figure 3), but also pump tuning can be used for this, depending on the pump source that is used. The continuous tuning range is the wavelength range in which the OPO is able to generate any wavelength without any mode hops. This range is important for high-resolution spectroscopy; a continuous tuning range is necessary over multiple ro-vibrational absorption lines of a molecular compound. This can be achieved using pump tuning, tuning of intracavity elements, or changing the length of the cavity. Normally, at standard temperature and pressure molecular atmospheric absorption lines in the infrared wavelength region are dominated by pressure broadening. This means that absorption lines will have a FWHM of 6–10 GHz. In order to measure such an absorption line accurately, it is not necessary to be able to continuously tune the OPO, but it is sufficient to mode-hop tune the OPO [23]. The steps will be small enough to get a good resolution of the scan. 4.1. TUNING BY CHANGING THE POLING PERIOD AND TEMPERATURE

For a particular crystal grating period and temperature of the crystal the idler wavelength can be calculated from the Sellmeier equations using the SNLO software program that has been developed at Sandia National Laboratories [17]. Tuning by changing the grating period means that the crystal needs to be translated through the OPO cavity. Translation needs to be done very carefully to prevent the crystal from breaking when the pump beam hits a potentially damaged spot. An additional problem with this tuning method is that sometimes the OPO cavity might need to be re-aligned. Due to this, it is also difficult to automate translation with a stepper motor. Small variations in the temperature can be used to fine-tune the OPO system; a 1◦ C temperature change yields typically a change in idler frequency of a few cm−1 ’s. However, this method of tuning will not result in continuous tuning, because the signal frequency will be mode hopping over the free spectral range of the OPO cavity. When there are unwanted fluctuations in the temperature of the PPLN crystal, the generated idler wavelength will also tune and thus become unstable. Therefore, it is important to have a very good temperature stability of the crystal oven. It has been shown that temperature fluctuations in the crystal oven can cause instabilities in the idler frequency [24].

520


4.2. TUNING WITH INTRACAVITY ELEMENTS

An OPO consists of various optical elements, including an intracavity etalon to stabilize and tune the OPO frequency. Figure 4 demonstrates the use of an intracavity etalon in the OPO. The OPO cavity consists of mirrors with a high reflectivity for the signal wavelength, so it is also a high-finesse interferometer. This restricts the signal frequencies of the OPO to a certain set of frequencies (cavity modes), given by the transmission peaks of the cavity (Figure 4C). Combined with the QPM gain curve (Figure 4A) one cavity mode will be selected for OPO oscillation. However, if the restriction on the cavity modes is not strong enough, the signal frequency is able to hop from one cavity mode to another. In contrast to a laser cavity with a gain medium inside, an OPO cavity will normally not oscillate simultaneously on several cavity modes. There is mode competition, A) QPM gain

1

Etalon modes

C)

1

Cavity modes

B)

1

QPM gain

0

1

0

0

D)

0 3003

3006

3009

3012

Wavelength (nm) Figure 4. Contributions to the total gain curve of the OPO due to: Panel A the QPM phase-mismatch, Panel B the modes of the intracavity etalon within the OPO cavity and Panel C the cavity modes of the OPO. Panel D shows all contributions multiplied, with the highest transmission is indicated by a thick solid line. The transmission of the cavity modes has been adjusted for better visibility. In reality they are closer together and very narrow.


but once a cavity mode has reached threshold other cavity modes are suppressed, as in a homogeneously broadened laser. Figure 4D shows how the combined contributions of the cavity modes, etalon modes and QPM gain curve select one mode with the highest transmission. Solid etalons have found wide use in OPO’s to restrict the cavity modes enough to let the OPO operate at a single frequency. Typically, etalons with a low reflectivity (∼10%) and hence low finesse etalons are used as high finesse etalons result in too much loss inside the cavity. By rotating the etalon, the OPO can be mode-hop tuned over the cavity modes. In a power enhanced SRO configuration, Stothard et al. used a low-finesse 1 mm thick YAG etalon with a FSR of 83 GHz with 10% reflectivity coating for the signal and antireflection coated at the pump wavelength [25]. They demonstrated a systematic hopping from one mode to its adjacent mode over nearly the entire FSR of the etalon. In total in excess of 100 hops were observed. In our SRO configuration an uncoated YAG etalon with a FSR of 207 GHZ and a reflectivity of 8% was selective enough to stabilize the OPO cavity to a single mode. The maximum output reduces slightly from 1.6 to 1.5 W due to insertion of the etalon [24]. In contrast to solid etalons, air-spaced etalons have found limited use, as these are much more difficult to align than solid etalons and lead to a considerable increase in oscillation threshold. In addition, for high-resolution spectroscopy length fluctuations of the air-gap should be minimized to prevent frequency drifts. Bisson and co-workers using a combination of an air-spaced intracavity etalon and a fan-out grating demonstrated 14 cm−1 mode hop tuning with a single hop ranging typically between 0.02 and 0.1 cm−1 [23]. Van Herpen et al. achieved 100 GHz of mode hop tuning using an air-spaced etalon with a 20% reflectivity coating. They observed an unexpectedly strong dependence of the idler output power on the steering voltage of the piezo probably due to walk-off losses [24]. 4.3. PUMP TUNING

Due to energy conservation, the generated signal and idler frequencies are widely tunable if the pump frequency is widely tunable as well. With pump-tuning, very wide tuning ranges can be obtained, because well-developed tuning methods for the pump sources can be transferred to the generated idler frequency. Klein and coworkers developed a single-frequency SRO directly pumped by a tunable InGaAs diode laser [18]. Tuning the pump output from 924 to 925.4 nm resulted in coarse tuning of signal and the idler wavelengths from 1.55 to 1.70 µm and from 2.03 to 2.29 µm, respectively. They achieved 56 GHz continuous pump-tuning for the idler wave [26]. A drawback of this system was that the power of the amplified diode laser radiation varied with frequency resulting in a one order of magnitude change in idler power within the tuning range. Van Herpen et al. combined wide pump tuning with a high power SRO OPO [27]. Tuning of the idler frequency was

522


achieved by longitudinal mode-hop tuning of the pump source (FSR 100 MHz). In this way an idler frequency scan of 100–150 GHz could be obtained, after which the signal frequency hops ahead over the Free Spectral Range of the intracavity etalon of the OPO (207 GHz). Recent advances show that fiber lasers are very promising for wide pump tuning. Lindsay and co-workers obtained a record-high 110 GHz continuous tuning using a fiber-amplified DBR laser [28]. In addition, using a fiber-based source Henderson and Stafford achieved 60 GHz of continuous mode-hop-free tuning by applying a voltage to a piezo electric transducer attached to the fiber [21]. 4.4. TUNING BY CHANGING THE CAVITY LENGTH

By synchronously changing the cavity length of the SRO and angle-tuning the etalon, both signal and idler waves can be continuously tuned. Normally, this is achieved by mounting one cavity mirror on a piezo and using electronics to control the etalon angle or spacing. Stroessner et al. achieved 38 GHz tuning using this approach [29]. In a bowtie cavity, the tuning range is limited due to misalignment at large mirror displacements. To extend the tuning range a skewed bowtie has also been used. A 14 cm−1 idler tuning was achieved using a low-finesse air-spaced intracavity etalon [23]. 4.5. FREQUENCY TUNING BY USING A COMBINATION OF TUNING TECHNIQUES

Combining two or more tuning techniques, complete coverage over extended wavelength ranges is feasible. Bisson et al. already demonstrated a 14 cm−1 mode hop tuning by changing an intracavity etalon and translating a fan-out grating in the OPO cavity [23]. We combined pump, etalon, and temperature tuning to cover an extended wavelength range with high resolution. At a fixed etalon angle the pump is scanned continuously over maximum 48 GHz (with mode hops of the pump source every 12 GHz). After that, the etalon is rotated by a galvo driver over a small angle and the pump is again scanned. This procedure is repeated until one free spectral range of the etalon (207 GHz) is covered (Figure 5). Subsequently, the crystal temperature is changed by 2–5◦ C and the entire procedure is repeated. In this way wavelength scans up to several hundred of wavenumbers at a single crystal period are feasible. Note that a similar scan could be performed without changing the etalon angle; this process would be significantly slower due to the increased number of temperature changes. As compared to temperature tuning, varying the etalon angle also offers a more reproducible way of selecting a wavelength. The complete scanning process was fully automated and computer controlled, so that long wavelength scans and sensing of multiple gases over long periods could be achieved.

PHOTOACOUSTIC SPECTROSCOPY USING CONTINUOUS WAVE OPO’S 523 3585.2

3586

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Frequency (cm-1)

3584.8

3585 3584.4

3584

12

14

16

18

3583 3582 3581 0

10

20 30 Time (minutes)

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50 8

Photoacousitc spectrum Calculated spectrum

Photoacoustic signal (A.U.)

B

-

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-

3580

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0 2790

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Figure 5. Panel A. Combined scanning of the pump wavelength and etalon angle, resulting in high resolution (99.98%) over a wider spectral range and very precise alignment of the cavity to the coherent source for good mode-matching are issues which need attention.

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Figure 7. For a period of 20 minutes the CO2 production of an ant (upper panel) and fruit fly (lower panel) are monitored. Clearly is seen that the ant can keep his breath for several minutes, while the fruit fly is continuously respiring.

The setup in Figure 8 for cw CRDS consists of a germanium acousto-optic modulator (AOM, 100 MHz), a ring-down cavity (L = 59.4 cm) and a fast photo detector (Figure 8) [16]. The AOM deflects a part of the idler beam (∼10%, under an angle of 15◦ ) towards the ring-down cavity. The ring-down cavity itself has two high reflective mirrors (R = 99.98% at 3.3 µm). To bring the cavity into resonance with the OPO wavelength, the length of the cavity was swept continuously at a rate of 30 Hz by means of a piezo-electric transducer (PZT). In Figure 9 the cavity transmission modes are shown as function of the piezo voltage. In Figure 10 the horizontal scale is expanded as compared to the previous figure. It can clearly be seen that, when the OPO is not switched off, the high finesse cavity and the


Figure 8.

The OPO and cw CRDS setup. (HWP: half wave plate, PBS: polarizing beam splitter)

Figure 9.

Mode spectrum of the ring-down cavity.

coherent OPO light produce a beating signal. This beating signal occurs when the linewidth of the cavity and the OPO are comparable. This is earlier described and explained by Müller et al. [49] From this, we estimate an extremely narrow linewidth of our OPO of 7 kHz over 20 µs without any form of active stabilization. To perform CRDS, the AOM switches off as soon as the intensity build-up in the cavity has reached a pre-determined threshold. The subsequent exponential decay of the radiation in the cavity can be determined with the fast detector and calculated using a fitting algorithm [50].

530


Figure 10. Beating of the high finesse cavity transfer field with the idler field of the OPO.

Figure 11.

Methane isotopes measured with Cavity Ring-Down Spectroscopy.

To determine the sensitivity of the OPO CRDS system, methane and ethane are used at different concentrations in the ppbv range at 100 mbar pressure. A noiseequivalent detection limit of 0.07 ppbv over 60 seconds was determined, which corresponds to a minimum detectable absorption coefficient of 1.4 × 10−9 cm−1 . Figure 11 shows a spectrum of 12 CH4 and 13 CH4 isotopes of methane in lab air recorded with continuous wave cavity ring-down spectroscopy. The spectral


region around 3.2 µm was chosen because of the relative strengths of the absorption peaks of 12 CH4 and 13 CH4 . Since the abundance of 13 CH4 is a factor 100 lower in the atmosphere than of 12 CH4 , the ratio in absorption strengths for the two isotopes was chosen such that the absorption would be similar. Because the absorption strengths of 13 CH4 are of the same order of magnitude as for 12 CH4, , enriched mixtures of 13 CH4 can be detected with the same sensitivity. References 1. F. K. Tittel, D. Richter, and A. Fried, “Mid-infrared laser applications in spectroscopy” in Solid-State Mid-Infrared Laser Sources (SPRINGER-VERLAG BERLIN, Berlin, 2003), Vol. 89, pp. 445–510. 2. P. Werle, F. Slemr, K. Maurer, R. Kormann, R. Mucke, and B. Janker, Opt. Lasers Eng. 37(2–3), 101–114 (2002). 3. C. Fischer and M. W. Sigrist, “Mid-IR difference frequency generation” in Solid-State MidInfrared Laser Sources (Springer-Verlag Berlin, Berlin, 2003), Vol. 89, pp. 97–140. 4. M. Hesse, H. Meier, and Bernd Zeeh, Spectroscopic methods in organic chemistry. (G. Thieme, Stuttgart ; New York, 1996). 5. J. A. Armstrong, N. Bloembergen, J. Ducuing, and P. S. Pershan, Physical Review 127(6), 1918–1939 (1962). 6. P. A. Franken and J. F. Ward, Rev. Mod. Phys. 35(1), 23–39 (1963). 7. M. M. Fejer, G. A. Magel, D. H. Jundt, and R. L. Byer, IEEE J. Quantum Electron. 28(11), 2631–2654 (1992). 8. J. A. Giordmaine and R. C. Miller, Phys. Rev. Lett. 14(24), 973–976 (1965). 9. W. R. Bosenberg, A. Drobshoff, J. I. Alexander, L. E. Myers, and R. L. Byer, Opt. Lett. 21(17), 1336–1338 (1996). 10. W. R. Bosenberg, A. Drobshoff, J. I. Alexander, L. E. Myers, and R. L. Byer, Opt. Lett. 21(10), 713–715 (1996). 11. P. E. Powers, T. J. Kulp, and S. E. Bisson, Opt. Lett. 23(3), 159–161 (1998). 12. K. L. Vodopyanov, O. Levi, P. S. Kuo, T. J. Pinguet, J. S. Harris, M. M. Fejer, B. Gerard, L. Becouarn, and E. Lallier, Opt. Lett. 29(16), 1912–1914 (2004). 13. O. Levi, T. J. Pinguet, T. Skauli, L. A. Eyres, K. R. Parameswaran, J. S. Harris, M. M. Fejer, T. J. Kulp, S. E. Bisson, B. Gerard, E. Lallier, and L. Becouarn, Opt. Lett. 27(23), 2091–2093 (2002). 14. Y. Furukawa, K. Kitamura, S. Takekawa, K. Niwa, and H. Hatano, Opt. Lett. 23(24), 1892– 1894 (1998). 15. T. Andres, P. Haag, S. Zelt, J. P. Meyn, A. Borsutzky, R. Beigang, and R. Wallenstein, Appl. Phys. B-Lasers Opt. 76(3), 241–244 (2003). 16. A. K. Y. Ngai, S. T. Persijn, G. von Basum, and F. J. M. Harren, Appl. Phys. B-Lasers Opt. Special Issue (2006), accepted. 17. A.V. Smith, SNLO software (2005).

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18. M. E. Klein, D. H. Lee, J. P. Meyn, K. J. Boller, and R. Wallenstein, Opt. Lett. 24(16), 1142– 1144 (1999). 19. A. J. Henderson, P. M. Roper, L. A. Borschowa, and R. D. Mead, Opt. Lett. 25(17), 1264–1266 (2000). 20. F. Müller, A. Popp, F. Kühnemann, and S. Schiller, Opt. Express 11(22), 2820–2825 (2003). 21. A. Henderson and R. Stafford, Opt. Express 14(2), 767–772 (2006). 22. A. Yariv, Quantum electronics, 3rd ed. (Wiley, New York, 1989), pp.xx, 676 p. 23. S. E. Bisson, K. M. Armstrong, T. J. Kulp, and M. Hartings, Appl. Optics 40(33), 6049–6055 (2001). 24. M. M. J. W. van Herpen, S. Li, S. E. Bisson, S. te Lintel Hekkert, and F. J. M. Harren, Appl. Phys. B-Lasers Opt. 75(2–3), 329–333 (2002). 25. D. J. M. Stothard, I. D. Lindsay, and M. H. Dunn, Opt. Express 12(3), 502–511 (2004). 26. M. E. Klein, C. K. Laue, D. H. Lee, K. J. Boller, and R. Wallenstein, Opt. Lett. 25(7), 490–492 (2000). 27. M. M. J. W. van Herpen, S. E. Bisson, A. K. Y. Ngai, and F. J. M. Harren, Appl. Phys. B-Lasers Opt. 78(3–4), 281–286 (2004). 28. I. D. Lindsay, B. Adhimoolam, P. Gross, M. E. Klein, and K. J. Boller, Opt. Express 13(4), 1234–1239 (2005). 29. U. Strössner, J. P. Meyn, R. Wallenstein, P. Urenski, A. Arie, G. Rosenman, J. Mlynek, S. Schiller, and A. Peters, J. Opt. Soc. Am. B-Opt. Phys. 19(6), 1419–1424 (2002). 30. D. D. Lowenthal, IEEE J. Quantum Electron. 34(8), 1356–1366 (1998). 31. H. Su, Y. Q. Qin, H. C. Guo, and S. H. Tang, J. Appl. Phys. 97(11), 113105 (2005). 32. G. A. Turnbull, D. McGloin, I. D. Lindsay, M. Ebrahimzadeh, and M. H. Dunn, Opt. Lett. 25(5), 341–343 (2000). 33. E. V. Kovalchuk, D. Dekorsy, A. I. Lvovsky, C. Braxmaier, J. Mlynek, A. Peters, and S. Schiller, Opt. Lett. 26(18), 1430–1432 (2001). 34. C. M. Lindsay, W. K. Lewis, and R. E. Miller, J. Chem. Phys. 121(12), 6095–6096 (2004). 35. A. Terasaki and T. Kondow, J. Opt. Soc. Am. B-Opt. Phys. 22(3), 675–686 (2005). 36. Y. Bai, J. Yu, N. P. Barnes, H. R. Lee, M. Petros, and S. Chen, presented at the Proceedings of SPIE – The International Society for Optical Engineering, 2003 (unpublished). 37. M. W. Sigrist, “Air Monitoring by Laser Photoacoustic Spectroscopy” in Air monitoring by spectroscopic techniques, edited by Markus W. Sigrist (Wiley, New York, 1994), Vol. 127. 38. F. J. M. Harren and J. Reuss, “Photoacoustic spectroscopy” in Encyclopedia of applied physics, edited by G.L. Trigg (VCH, Weinheim, 1997), Vol. 19, pp. 413–435. 39. A. Miklos, P. Hess, and Z. Bozoki, Rev. Sci. Instrum. 72(4), 1937–1955 (2001). 40. M. W. Sigrist, Rev. Sci. Instrum. 74(1 II), 486–490 (2003). 41. F. J. M. Harren, R. Berkelmans, K. Kuiper, S. te Lintel. Hekkert, P. Scheepers, R. Dekhuijzen, P. Hollander, and D. H. Parker, Appl. Phys. Lett. 74(12), 1761–1763 (1999). 42. H. Zuckermann, F. J. M. Harren, J. Reuss, and D. H. Parker, Plant Physiol. 113(3), 925–932 (1997).

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ONLINE MONITORING OF EXHALED BREATH USING MID-INFRARED LASER SPECTROSCOPY Laser Spectroscopic Breath Monitoring ∗ ¨ and PETER HERING MANFRED MURTZ University of Düsseldorf, Institute for Laser Medicine, Universitätsstr. 1, D-40225 Düsseldorf, Germany

Abstract. This review describes the merits of laser-assisted analytical instrumentation for biomedical diagnostics. In particular, we present an overview of the recent progress on spectroscopic online monitoring of exhaled breath with mid-infrared coherent sources. The current detection limits of laser spectroscopic approaches are in the picomolar to nanomolar range, depending on the molecular compound. The time resolution of the measurements is down to the sub-second range. This very high sensitivity and time resolution open up exciting perspectives for novel analytical tasks in biomedical research and clinical diagnosis. Keywords: laser absorption spectroscopy; trace gas monitoring; cavity ring-down; exhaled breath

1. Introduction Modern infrared lasers get more and more useful for analytical purposes in biomedical research. In the past decade, an increasing number of publications dealt with the investigation of biogenic trace gases. In particular, the role of volatile disease markers released by the human body have gained growing interest. The quantitative trace analysis of exhaled breath provides important information about the health status of a living subject. Sampling and analysis of breath is preferable to a direct measurement of the metabolites from blood samples because it is non-invasive, and the measurements are much simpler in the gas phase than in a complex biologic fluid. Current breath tests involve, e. g., the analysis of exhaled nitric oxide (diagnosis of airway inflammations) and the analysis of 13 C carbon dioxide (diagnosis of Helicobacter Pylori infection of the gastric mucosa). Besides the major components, like carbon dioxide and water, exhaled human breath contains several hundred volatile species of endogenous origin. Most of

∗ To whom correspondence should be addressed.



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¨ MANFRED MURTZ AND PETER HERING

them are present in volume fractions on the order of one part per billion (ppb, 1:109 ) or even below. A few years ago, it has been found that small molecules like nitric oxide, carbon monoxide and volatile hydrocarbons are formed in the human organism. Some of these exhaled compounds are considered to be disease markers. For example, ethane and pentane are potential markers of lipid peroxidation, whereas nitric oxide is considered to be an important marker for inflammations in the respiratory tract. There is strong evidence that the analysis of these and other trace constituents in exhaled breath could provide a new way of non-invasive monitoring of inflammation, oxidative stress and other processes in the airways and lungs. On the other hand, various exhaled volatiles which have been found in exhaled breath after inhalation of polluted air are interesting markers for exposition to toxic compounds. The non-invasive nature of the measurement of exhaled markers makes breath tests ideally suited for serial monitoring of patients or people that have recently been exposed to hazardous agents. The development of rapid and sensitive analytical techniques for measurements of relevant volatile compounds released, e. g., in exhaled breath or from the skin, is still a challenge. In the past 15 years, the performance of laser spectroscopic methods for analytical purposes has made significant progress. The excellent properties of laser radiation – like spectrally narrow emission and low intensity fluctuations – enabled the development of analytical techniques with ultra-high sensitivity and specificity. A major advantage of laser spectroscopic breath analysis is the capability of online measurements. Online measurement means, that the exhaled breath is analyzed during exhalation in real-time whereas with offline techniques the breath is collected in a bag or a sorbent trap. The potential problems of off-line methods, like reproducibility of breath sample collection, contamination during sample storage and the inability to allow for instantaneous feedback, can be avoided with online methods. Additionally, information about the concentration during different exhalation phases is directly accessible via fast online measurements, whereas offline methods integrate over a complete exhalation or require an extra effort to separate exhaled gas coming out of the lungs from gas that originates from the upper airways (dead space air). This review is organized as follows: In Section 2, a brief introduction to the role of trace gases in medicine and biology is given. In Section 3, a number of laser spectroscopic approaches, suitable for online trace gas analysis are described. In Section 4, we describe recent progress on laser-based monitoring of the disease markers nitric oxide, carbon monoxide, and ethane in exhaled breath. Finally, in Section 5 we outline some perspectives for laser spectroscopic breath monitoring.

LASER SPECTROSCOPIC BREATH MONITORING

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2. The role of trace gases in medicine and biology 2.1. TRACE CONSTITUENTS OF EXHALED HUMAN BREATH

Besides the main constituents nitrogen, oxygen, and water, exhaled human breath contains various volatile metabolites formed in the organism. The major metabolite in breath is carbon dioxide (CO2 ) which is exhaled in volume fractions of about four percent. Though CO2 is not a disease marker itself it plays an important role for breath testing when 13 C-labelled pharmaceuticals are applied (Ghoos et al., 2002,Mansfield et al., 2002). A prominent example of isotopic breath testing based on carbon dioxide is the non-invasive verification of a Helicobacter pylori infection in the gastro-intestinal tract by means of a 13 CO2 /12 CO2 breath test. This is one of the few diagnostic breath tests which have been approved by the US Food and Drug Administration (FDA) up to date. A selection of important endogenous trace gases found in exhaled breath is summarized in Table 2.1. Many other compounds, in particular volatile organic compounds (VOCs), have been identified up to now; however, many of these VOCs which are detectable in exhaled air are of exogenous origin and have just been inhaled with polluted ambient air or ingested (prominent example: ethanol). The presence of such volatiles in breath does not indicate a disease but may act as an indicator of recent exposure to these compounds. It is hypothesized since more than ten years that some of the endogenous breath VOCs may be markers of disease (Phillips, 1992). Since then, this research field has made only slow progress. The main reason is that it is extremely difficult TABLE 1. Selection of endogenous trace gases found in exhaled breath and their average fraction in the breath of healthy humans. (Kharitonov and Barnes, 2001, Risby and Sehnert, 1999). Breath constituent Methane (CH4 ) Ethane (C2 H6 ) Pentane (C5 H12 ) Nitric Oxide (NO) Carbon Monoxide (CO) Carbonyl Sulfide (OCS) Nitrous Oxide (N2 O) Isoprene (C5 H8 ) Ammonia (NH3 ) Acetone ((CH3 )2 CO)

Average fraction 0 – 20 ppm 0 – 5 ppb 0 – 5 ppb 10 – 30 ppb 1 – 10 ppm 0 – 10 ppb 0 – 20 ppb 50 – 200 ppb 0 – 1 ppm 0 – 1 ppm

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to reliably analyze those ultra-low concentrations with conventional instrumentation. Another reason is that there is only little knowledge about the synthesis pathways of the volatile metabolites. There are a number of exhaled trace compounds however, which have been studied quite thoroughly. For example, the group of branched alkanes in breath has been evaluated as tumor marker in lung cancer (Phillips et al., 1999). Alkanes and monomethylated alkanes are oxidative stress products that are excreted in the breath, the catabolism of which may be accelerated by polymorphic cytochrome p450-mixed oxidase enzymes that are induced in patients with lung cancer. Compared to healthy volunteers, patients with primary lung cancer had abnormal breath test findings that were consistent with the accelerated catabolism of alkanes and monomethylated alkanes (Phillips et al., 2003). Next to these and other hydrocarbons, one of the most prominent disease marker in exhaled human breath is nitric oxide (NO). Until the 1980’s, nitric oxide was mainly regarded as a noxious gaseous component of air pollution. The presence of endogenous NO in exhaled breath of animals and humans was first described by (Gustafsson et al., 1991). Nitric oxide is the most extensively studied exhaled marker and abnormalities in eNO have been documented in several lung diseases, particularly in asthma (Kharitonov, 1999). Apart from NO, there are a number of other diatomics and triatomic, which have been identified as endogenous trace constituents of breath, e.g., CO, OCS, H2 S, N2 O, etc. There is no doubt, that the analysis of exhaled breath will provide a new way of non-invasive monitoring of disease in the future, though clinical breath analysis is still in its infancy (Miekisch et al., 2004). In order to achieve reliable and reproducible breath measurements, real time breath monitors need to be developed which are capable to perform online measurements, i. e., which respond to the concentration of the biomarker during a normal breath cycle. Offline sampling methods, mostly in combination with accumulation or preconcentration of the breath sample, are not only much more time consuming but also prone to systematic errors (Knutson et al., 1999). Moreover, online measurements with suitable time resolution can directly quantify the alveolar concentration which appears in the final part of each exhalation. There are a number of clinical applications where real-time breath analysis would have an immediate application such as: monitoring the progress of hemodialysis therapy for patients with end-stage renal disease, identifying pulmonary infections (bacteria, fungus or virus) in patients suffering from cystic fibrosis, identifying pulmonary infections (bacteria, fungus or virus) or acute tissue rejection in patients who are immunocompromised due to receiving lung transplants and for identifying gastrointestinal dysfunction (Risby, 2005).


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2.2. OTHER BIOLOGICAL SOURCES OF VOLATILE MARKERS

Emissions of volatile compounds can be found in a wide variety of biological systems. For example, it is well-known that the gastro-intestinal tract of animals and humans is a rich source of volatiles, mostly originating from metabolization of the food and from the colonic flora. Predominant compounds are methane and sulfur compounds. The analysis of exhaled breath is a potentially useful method for application in veterinary diagnostics (Wyse et al., 2004). Breath samples can be easily collected from animals by means of a face mask or collection chamber with minimal disturbance to the animal. Measurements of exhaled ethane, carbon monoxide and hydrogen peroxide by horses with respiratory inflammation has been reported (Wyse et al., 2005). Plants emit a large number of volatile compounds; these emissions provide an interesting insight into several physiological processes of plants. For example, ethylene is an important plant hormone which plays an major role during fruit ripening, etc.. Also, fermentation of fruits, yielding in particular ethanol and acetaldehyde emissions, has been studied (Harren et al., 1998). Other plant emissions of recent interest are ethane (Santosa et al., 2003) and isoprene (Dahnke et al., 2001). Very recently, the breath of small insects has been monitored using infrared laser spectroscopy. Although quantifying of the gas exchange in small insect species is of great biological interest, the low emission rates from these insects is a challenge for the gas sensor. Firstly, loss of water by the minute Western Flower thrips was recorded by means of photoacoustic spectroscopy (Persijn et al., 2006). Furthermore, real-time measuring of the fluctuations of the CO2 concentration in the breath of a single ant and individual fruit flies was reported (van Herpen et al., 2006). Apart from the in-vivo measurements, numerous studies investigated volatile emissions from biological samples in vitro. For example, the biogenic carbon monoxide production rate above cultures of vascular cells has been observed (Morimoto et al., 2001, Kosterev et al., 2002c). In that work, an extractive technique was used with gas samples taken from the flask containing the cell culture. It should be noted that volatile metabolites from animals or humans are also excreted across the skin. For example, Harren and co-workers observed elevated ethylene emissions from the skin after application of UV radiation (Harren et al., 1999). All of the above mentioned biological sources of trace gases have in common that the gas production rates are extremely low. Typical release rates are in the order of picomol per second. This means, that only ultra-sensitive measurement methods are capable to quantify these emissions.

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3. Suitable laser spectroscopic approaches for online analysis Among the great variety of laser spectroscopic techniques there are a number of methods which have been successfully applied to the analysis of gas samples in life sciences. Most techniques are based on the principle of absorption spectroscopy and many of them have been originally developed for the sensitive in-situ detection of atmospheric trace gases. The gas sample of interest is transferred into an absorption cell and the wavelength-dependent attenuation (or in some cases the dispersion) of the laser light which passes the cell is measured (Fig. 1). The concentration of a particular compound can then be obtained from the absorption measurement on specific spectral lines according to the Beer-Lambert law. Spectroscopy in the mid-infrared spectral region is most advantageous since most of the gaseous compounds of biomedical interest are molecular gases that have characteristic, strong ro-vibrational absorption bands in this spectral region. For example, nitric oxide and carbon monoxide have strong fundamental absorption bands in the wavelength region near λ = 5 µm; for hydrocarbons the most interesting wavelength region is around λ = 3 µm where strong absorption lines according to the CH stretching vibration are located (see Fig. 2). Infrared spectroscopy of these fingerprint spectra allows sensitive, specific and rapid monitoring of gas mixtures. In the past decade the performance of laser spectroscopic methods for analytical purposes has made significant progress. For example, photoacoustic spectroscopy and cavity-enhanced spectroscopy have been developed towards ultra-high sensitivity; detection limits in the picomolar region have been demonstrated. Additionally, considerable progress in laser technology has been made, enabling the development of compact and high-performance infrared laser sources with outstanding spectral properties, i. e., narrow linewidth, wide wavelength tunability and smooth beam profile. Suitable coherent light sources for mid-infrared spectroscopy include semiconductor lasers, like tunable lead-salt diode lasers (TDL) and quantum cascade lasers (QCL) – cf. chapter of J. Faist in this book –, as

Figure 1. Illustration of laser-spectroscopic human breath monitoring,


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Figure 2. Mid-infrared absorption spectra of selected volatiles. TABLE 2. Tunable mid-infrared lasers sources that have been used for analysis of exhaled breath and other biogenic gases in our laboratory. Laser

Wavelength [µm]

Power [mW]

Linewidth [MHz]

Set-up

Laboratory, cryo cooling Laboratory, cryo cooling Portable, room temperature Portable, room temperature Portable, Peltier-cooling

CO(v = 2) sideband CO(v = 1) Sideband DFG

2.6 – 4.0

0.15

0.1

4.8 – 7.8

0.3

0.1

3.0 – 3.6

0.3

1

OPO

3.0 – 4.0

100

5

QCL

5.1 – 9.4

3

2

well as all-solid-state pumped nonlinear conversion devices based upon difference frequency generation (DFG) – cf. chapter of M. Sigrist in this book –, or optical parametric oscillation (OPO) – cf. chapter of A. Ngai et al. in this book. Table 2 summarizes mid-infrared laser sources that have been used for analysis of exhaled breath and other biogenic gases in our laboratory.

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3.1. MULTI-PASS ABSORPTION

In order to achieve a high detection sensitivity, most laser absorption spectrometers take advantage of a multi-pass absorption cell, where the optical pathlength is increased in order to improve the absorption signal and thus the detection sensitivity. This has been implemented mostly with multi-pass cells either of the White type or the Herriott type. Such cells allow multiple passes (in the order of 100) of the laser beam through the gas sample volume and thus extend the path of interaction between laser beam and molecules to the order of 100 m. The minimum detectable absorption using multi-pass cells and wavelength modulation techniques is typically on the order of 10−8 /cm, corresponding to ppb sensitivity for many molecular compounds. In particular, tunable diode lasers (TDL) have been combined with multi-pass cells for the measurement of various exhaled trace gases (Lee et al., 1991, Lee et al., 1994, Stepanov and Moskalenko, 1993, Moskalenko et al., 1996, Giubileo et al., 2001, Roller et al., 2002, Skeldon et al., 2005a, 2005b). Also, difference frequency generation has been widely used in combination with multi-pass cells (Chen et al., 1998, Petrov et al., 1998, Lancaster et al., 1998, 1999, 2000; Richter et al., 2002, 2006; Pesce et al., 2003, Rusciano et al., 2003). These systems are generally based on periodically poled lithium niobate (PPLN) which restricts the usable wavelengths to the region from 2 to 5 µm. For longer wavelengths, quantum cascade lasers are the more and more used for sensitive trace gas detection with multi-pass cells (Weidman et al., 2004a, 2004b; Wysocki et al., 2004, Moeskops et al., 2006a, 2006b).

3.2. CAVITY-ENHANCED TECHNIQUES

A versatile technique, which takes advantage of the increased optical path length in optical cavities, is called cavity-enhanced spectroscopy. High-finesse cavities are capable to considerably improve the detection sensitivity as compared to multi-pass cells. There are several different schemes that make use of the enhancement of the absorption pathlength in an optical cavity: Cavity ring-down spectroscopy (CRDS) has revolutionized the sensitivity and speed of trace gas analysis in the past ten years. CRDS is based upon the optical excitation of a high-finesse cavity which encloses the gas sample to be analyzed. The absorption measurement is carried out via monitoring the decay rate of the light leaking through one of the cavity mirrors. Because of its ultra-high sensitivity and extraordinary specificity, CRDS is perfectly suited to measure the trace levels of volatile biomarkers that are present in exhaled human breath. Due to the large effective absorption pathlengths (typ. 1 to 10 km), this technique offers considerably better detection limits than is obtainable in conventional


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absorption spectroscopy. Our group has recently demonstrated real-time monitoring of ethane in exhaled human breath by using cavity leak-out spectroscopy (CALOS), a cw variant of cavity ring-down spectroscopy. The use of cw lasers with a long coherence length is advantageous particularly in the midinfrared since the cw ring-down approach provides higher spectral resolution and requires only relativ low laser powers (Romanini et al., 1997, Mürtz et al., 1999a, Paldus et al., 2000, Kosterev et al., 2001, Dahnke et al., 2001). Our spectrometer is based on a high-finesse cavity (length: 50 cm) which provides an optical absorption pathlength of 3.6 km (Stry et al., 2002, Popp et al., 2002). A minimum detectable absorption of 10−10 /cm with a 1 s integration time has been reported (von Basum et al., 2004). This corresponds to sub-ppb fractions of ethane and other relevant trace gases. Moreover, this technique allows for time resolution in the sub-second regime, for example enabling online breath ethane detection in single exhalations (von Basum et al., 2003). Another method to exploit a high finesse optical cavity for increasing the detection sensitivity is called integrated cavity output spectroscopy (ICOS). Here, the laser light is coupled into a high-finesse cavity with dense mode spectrum. Most recently, off-axis cavity alignments similar to the mirror configuration in astigmatic Herriott cells are used (Bakhirkin et al., 2004, 2006; Silva et al., 2005, Provencal et al., 2005, Malara et al., 2006). The time-integrated intensity leaking out of such a cavity, averaged over many cavity modes, is used to determine the intra-cavity absorption. This provides an effective optical pathlength of several kilometers. The sensitivities demonstrated so far are up to 5.7 × 10−9 cm−1 Hz−1/2 (Malara et al., 2006). Though this reach the sensitivity of the cw ring-down technique, ICOS is advantageous in terms of robustness and ease of use.

3.3. PHOTOACOUSTICS

Photoacoustic spectroscopy (PAS) is an indirect absorption technique. The gas sample is transferred into an acoustic cavity in which a transient temperature rise in the absorbing medium is periodically induced by the absorbed light. This translates into periodic pressure changes via non-radiative relaxation and the induced sound is recorded via a microphone. The strength of the recorded acoustic signal is proportional to the concentration of the absorbing molecules. The chapter by A. Ngai et al. in this book describes the PAS technique in more detail. Trace gas detection by means of laser-based photoacoustic spectroscopy has proven to be a versatile tool for environmental, biological, and medical trace gas sensing, mostly using powerful CO or CO2 lasers (Martis et al., 1998, Hekkert et al., 1998, Dahnke et al., 2000, Nägele and Sigrist, 2000, Sigrist et al., 2001, Santosa et al., 2003, Persijn et al., 2006). Since PAS is a background-free

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technique, the detection sensitivity is comparable to cavity-enhanced absorption spectroscopy. For example, the plant hormone ethylene (C2 H4 ) can be detected at ppt levels with a intra-cavity CO2 laser PAS (Fink et al., 1996). A continuous flowthrough system at atmospheric pressure transfers the trace gases released from the plant chamber to the photoacoustic resonator cells at flow rates where various physiological processes can be studied with medium time resolution. Typical response times of PAS analyzers are in the order of one minute. In recent years, photoacoustic laser spectroscopy was more and more performed utilizing OPOs (Kühnemann et al., 1998, Miklos et al., 2002, van Herpen et al., 2002, Müller et al., 2003, van Herpen et al., 2006), difference frequency generation (Fischer et al., 2001, Fischer and Sigrist, 2002; chapter of M. Sigrist in this book) and QCLs (Paldus et al., 1999, Hofstetter et al., 2001, Nägele et al., 2001,Elia et al., 2005). Few years ago, a novel variant of PAS called quartzenhanced PAS has been developed (Kosterev et al., 2002b; chapter of F.K. Tittel in this book). Instead of using a gas-filled resonant acoustic cavity, the sound energy is accumulated in a high-Q crystal element. Feasibility experiments utilizing a quartz watch tuning fork demonstrated a sensitivity in the low ppb regime for N2 O detection (Kosterev et al., 2005) and formaldehyde detection (Horstjann et al., 2005).

3.4. MAGNETIC RESONANCE

Laser magnetic resonance spectroscopy (LMRS) is a sensitive technique which exploits the property of magnetic molecules to rotate light polarization when an external magnetic field is present. It can be applied to all molecules exhibiting a permanent magnetic moment, i.e., radicals with an open shell structure. In breath analysis, the only important long-living radical is nitric oxide (NO). Originally, the magnetic tuning via the Zeeman effect was the key feature of LMRS which allows to tune the radical transition to the frequency of a laser with restricted tuning capabilities (for example line-tunable gas lasers). Apart from this, magnetic modulation of the transition frequency provides a most powerful means for specific detection of the magnetic species by lock-in techniques. In this way it is possible to discriminate the magnetic molecules from any non-magnetic background absorptions. The magnetic modulation amplitude, necessary to produce a modulation depth comparable to the molecular line width for sensitive detection, is in the order of 100 Gauss. Since LMRS is a background-free technique, the detection sensitivity is typically below 10−9 cm−1 Hz−1/2 (Urban et al., 2004). Even more sensitive is a polarization dependent variant of LMRS, called Faraday LMRS. This method allows to determine very low concentrations of gaseous free radicals with high time resolution. Faraday LMRS has been reported


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to be useful for online NO detection in exhaled breath in the sub-ppb regime (Mürtz et al., 1999b, Menzel et al., 2005). Furthermore, this technique has been successfully utilized for lung function tests (Heller et al., 2002, 2004, 2005), where the stable nitric oxide isotopes 14 NO and 15 NO were used for the determination of the pulmonary diffusing capacity. Faraday magnetic modulation spectroscopy has also been demonstrated with continuously tunable lasers (Ganser et al., 2003, 2004). In this case, there is no need for a strong magnetic field since only magnetic modulations is applied. Thus, very compact spectroscopy cells with a simple solenoid can be used. Utilizing a cw QCL near 5.2 µm, online sensing of of nitric oxide traces was reported by Ganser et al. (2004). The minimum detectable NO concentration was found to be 4 ppb (sampling time: 10 s). Continuous monitoring of the NO release from biological liquids is described, and the detectable NO release rates are down to 10 pmol/s.

4. Monitoring of exhaled diseasemarkers Non-invasive breath monitoring may assist in differential diagnosis of various diseases, assessment of disease severity and response to treatment. Because these techniques are completely non-invasive, they can be used repeatedly (to give information about kinetics), they can be used to monitor patients with severe disease and children, including neonates. In this section, we present some examples, where the benefits of laser spectroscopy for breath analysis has been demonstrated in the past five years. 4.1. NITRIC OXIDE (NO)

Nitric oxide is known to be a central mediator in biological systems. The presence of endogenous NO in exhaled breath of animals and humans was first described by Gustafsson et al. (1991). The average fraction of exhaled nitric oxide (eNO) is generally in the low nanomolar region and can be analyzed by means of a chemiluminescence technique. Abnormalities in eNO have been reported in several lung diseases, particularly in asthma (Kharitonov, 1999). When the airways are inflamed, such as occurs in patients with asthma, NO concentrations in exhaled air are significantly increased. The NO breath test has been recently achieved FDA approval as a diagnostic tool to monitor inflammation in asthma. Most of the recent publications on laser-based NO detection either report the use of multi-pass cells or cavity-enhanced techniques (Kosterev et al., 2001,Menzel et al., 2001, Roller et al., 2002a, 2002b; Halmer et al., 2005, Silva et al., 2005, Moeskops et al., 2006a, Bakhirkin et al., 2006). Online analysis of NO in exhaled breath has also been demonstrated using LMRS (Mürtz et al., 1999b,Menzel et al.,

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Figure 3. Suitable spectral window for simultaneous spectroscopic detection of 14 NO and 15 NO. The detection limit with an CO-laser based CALOS set-up using these absorption lines is 800 ppt for 14 NO and 40 ppt for 15 NO, respectively (Halmer et al., 2005).

2005). These approaches take advantage of the strong fundamental absorption band of NO near 5.2 µm. Detection limits are typically in the low ppb range. A particular advantage of laser-based NO analysis is the capability to distinguish between different isotopologues, for example 14 NO and 15 NO. For the investigation of a specific metabolic reaction it is advantageous to apply substances that are labeled with a rare isotope. By monitoring the increase of metabolites that contain an isotopic label one can draw conclusions about the metabolic reaction rate etc. Such investigations are called tracer investigations. Our group has recently demonstrated that simultaneous online detection of 14 NO and 15 NO is feasible with ring-down spectroscopy (Halmer et al., 2005). Fig. 3 shows a suitable spectral window for simultaneous spectroscopic detection of 14 NO and 15 NO. For continuous online monitoring of biogenic NO release rates, for example from blood or sweat samples, it is essential that there are no cross interferences to other molecular compounds which are present in the complex biological gas sample, like carbon dioxide or water. In this case, a spectroscopic sensor based on Faraday modulation spectroscopy has proven to be a powerful device (Suschek et al., 2003, Ganser et al., 2004, Paunel et al., 2005). 4.2. CARBON MONOXIDE (CO)

Carbon monoxide (CO) is produced endogenously from heme catabolism by the enzyme heme oxygenase and exhaled via the lungs. Over the last 20 years, exhaled carbon monoxide (eCO) has been measured to identify current and passive smokers, to monitor patients after CO poisoning, to determine bilirubin production, including hyperbilirubinemia in newborns, and in the assessment of the lung diffusion capacity (Kharitonov and Barnes, 2001). Moreover, CO appears to be


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an important signalling molecule which may be useful for the assessment of different diseases, in a similar way like NO. Elevated eCO levels have been found in pediatric asthma (Zayasu et al., 1997) and have also been reported in diabetes and correlated with glucose concentration in blood (Paredi et al., 1999). eCO has been measured by a number of different techniques. Most of the measurements in humans have been made using electro-chemical or near-infrared (NDIR) sensors, as used for continuous monitoring of atmospheric carbon monoxide. These devices do not allow for fast, breath-resolved CO measurements. Infrared laser absorption spectroscopy has been successfully used for detection of biogenic CO at the ppb level in real time. Previously, endogenous CO production from vascular cells using a mid-IR laser based on a difference frequency generation laser (Morimoto et al., 2001) and a quantum cascade laser (Kosterev et al., 2002a, 2002c). The CO absorption was detected in the fundamental vibration band near 4.6 µm. A noise-equivalent detection limit of 12 ppbv was experimentally demonstrated with a 1 m optical pathlength. Very recently, online measurements of exhaled carbon monoxide and with a CRDS approach (von Basum et al., 2005) and with a QCL-based sensor (Moeskops et al., 2006b) were reported. 4.3. ETHANE

Among the various volatile hydrocarbons found in breath, the alkanes ethane (C2 H6 ) and pentane (C5 H12 ) have been extensively studied since they were identified as end-products of the oxidative degradation (lipid peroxidation) of polyunsaturated fatty acids. The process of lipid peroxidation has gained interest as one of the important features of free-radical-induced damage in biology and medicine. During peroxidation of omega-3 and omega-6 fatty acids, ethane and pentane, respectively, are formed which are excreted via the lungs and thus can be detected in exhaled breath. Enhanced free-radical-induced damage is called oxidative stress and has been related to a variety of diseases, including diabetes mellitus, rheumatoid arthritis, and chronic obstructive pulmonary disease (Pryor and Godber, 1991, Sies, 1997). Since lipid peroxidation is considered as the major, probably the only endogenous source of pentane and ethane, these volatile compounds may serve as specific markers for oxidative damage. Several studies provide evidence that ethane and pentane in exhaled air are useful markers of in-vivo lipid peroxidation (Andreoni et al., 1999, Risby and Sehnert, 1999, Paredi et al., 2000, Risby, 2005). Despite the growing number of reports on breath ethane the development of rapid and sensitive analysis techniques for measurements of these markers in exhaled breath remains still a challenge. Ethane concentrations in expired air are in the parts per billion (ppb, 1:109 ) range which is below the detection limit of most analytical methods. The technique usually applied for quantifying these hydrocarbons in exhaled breath is gas chromatography (Knutson et al., 1999, Risby

548


and Sehnert, 1999). To detect ppb levels the breath samples must be accumulated and preconcentrated up to hundred-fold, e.g., by means of a sorbent trap, before subsequent desorption and analysis. This procedure plus the GC analysis is time consuming and under several circumstances such measurements are prone to errors. Ethane exhibits a very nice fingerprint spectrum in the mid-infrared (see Fig. 4). Our group has recently demonstrated that CRDS is capable of online quantifying ethane traces in exhaled human breath down to 500 ppt (parts per trillion) with a time resolution better than 800 ms (von Basum et al., 2003). One aspect of this work was to measure the profile of a single exhalation. With our cavity ringdown approach in the 3 µm wavelength region, we were able to record ethane expirograms of single exhalations where recorded concentrations were plotted against the exhaled volume. Furthermore, an analysis of the alveolar plateau of the ethane exhalations was performed for the first time. Other groups published laser spectroscopic ethane detection in exhaled breath using multi-pass cells (Puiu et al., 2005, Skeldon et al., 2005a, Skeldon et al., 2005b). Very recently, a clinical study on lung cancer patients was reported by (Skeldon et al., 2006), utilizing lead-

Figure 4. Fingerprint spectrum of ethane near 3000 cm−1 . The largest peak near 2983.4 cm−1 is used for real-time analysis of ethane in exhaled breath. The detection limit for ethane with an OPO based CALOS set-up is 0.4 ppt for 1 second integration time (von Basum et al., 2004).


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salt diode laser absorption spectroscopy to measure the concentration of ethane in a single exhaled breath sample. 5. Perspectives for laser spectroscopic breath monitoring It is obvious that the analysis of breath metabolites opens new diagnostic windows in clinical medicine. Breath analysis is very attractive because this is a literally non-invasive way to monitor a patient’s physiological status. However, the clinical value of exhaled biomarkers will depend on the availability of reliable and inexpensive analyzers. Since the exhaled concentrations are extremely low, the technical problems of breath testing are still severe. Laser-based breath analysis is an exciting way to improve this situation. Laser spectroscopy is currently the only technique that allows for single-breath resolved real-time measurements of exhaled traces gases with picomolar sensitivity. For example, the sensitivity and specificity for breath ethane monitoring is unprecedented. Laser spectroscopic online monitoring of breath ethane could become a promising approach for non-invasive acquisition of the oxidative stress status in various pathophysiological situations. Future progress in this field will depend on the availability of tunable, roomtemperature MIR laser sources that are compact, cheap, and robust. The most promising candidates for this purpose are semiconductor lasers (quantum cascade lasers, interband cascade lasers) and direct solid-state lasers (e.g. ZnSe crystalline lasers, cf. chapter of I. Sorokina in this book). In combination with the spectroscopic techniques that have been discussed in this chapter, portable real-time breath analyzers seem feasible in the near to mid-range future. Advances in optical technologies will definitely result very soon in smaller devices that are cheaper and easier to use. In particular, the use of optical fiber technology will lead to more compact and finally portable analyzers. As soon as portable breath sensors are available for bedside monitoring the range of applications will increase. 6. Acknowledgements The authors acknowledge long-standing financial support by the Deutsche Forschungsgemeinschaft. We would like to thank Sandra Stry, Daniel Kleine, Hannes Dahnke, Golo von Basum, Heiko Ganser, Daniel Halmer, and Markus Horstjann for their contributions to the work on breath monitoring. References Andreoni K. A., Kazui M., Cameron D. E., Nyhan D., Sehnert S. S., Rohde C. A., Bulkley G. B., and Risby T. H., 1999, Ethane: a marker of lipid peroxidation during cardiopulmonary bypass in humans, Free Radic.Biol.Med. 26:439–445.

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ULTRABROADBAND SOLID-STATE LASERS IN TRACE GAS SENSING

EVGENI SOROKIN∗ Photonics Institute, Technische Universitä Wien, Gusshausstr. 27/387, A-1040 Vienna, Austria

Abstract. Application of ultrabroadband Cr2+ -doped mid-infrared lasers to sensitive molecular spectroscopy in the 2–3 µm wavelength range is demonstrated using two different techniques: scanning photoacoustic spectroscopy and intracavity absorption spectroscopy. It is shown, that the broad gain bandwidth is a crucial parameter, allowing multicomponent analysis and extreme sensitivity down to 10−5 mbar of partial pressure (H2 O vapor). A number of previously unknown combination bands in CO2 , N2 O and C2 H2 have been observed. The demonstrated spectral resolution reached 0.1 cm−1 for the photoacoustic technique, which is sufficient for multicomponent analysis. For intracavity technique the demonstrated resolution was 0.006 cm−1 , which is below the Doppler-limited linewidth. The laser devices are application-ready and allow directly diode-pumped self-contained implementation.

1. Introduction The room-temperature solid-state lasers have made a significant advance into the mid-IR domain. In addition to long-known rare-earth ion based crystalline media, there exist nowadays also the broadband transition-metal ion doped crystals. These lasers matured from demonstration objects to versatile application-ready tools, notably the optically pumped Cr2+ -doped II-VI semiconductors. In this chapter, the recent applications of Cr2+ :ZnSe and Cr2+ :ZnS in trace gas sensing will be reviewed. In order to fully exploit the advantages of mid-infrared lasers in applications, they should be used in a different way, as compared to shorter-wavelength lasers, e.g. in the visible. The scaling rules of the nonlinear-optical interactions favor in most cases shorter wavelengths, this is especially true for scattering-based techniques, like Raman, CARS etc. The exact value of the laser wavelength in such techniques does not play immediate role, since it is only the frequency shift that matters. Much more important is the fact, that scattering efficiency scales strongly with inverse wavelength, so that visible lasers are by far more useful for these types of measurement. ∗ [email protected]



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To the contrary, for direct absorption measurements, the light source should come as close as possible to the transition wavelengths. In case of the molecular absorption, like e.g. in gases, the fundamental transitions lie in the mid-infrared from 2.3 to about 10 µm. While it is possible to interact also with obertones or combination bands, the absorption cross-section for such bands rapidly decreases with wavelength. The long-wavelength lasers, approaching the fundamental vibrations of molecules and solids are much better candidates for such measurements. For this reason the first applications tackled by the Cr2+ -based lasers lie within the field of trace gas sensing and ultrasensitive spectroscopy described in this chapter. The availability of the possibly broadest gain bandwidth is another critical issue for spectroscopic and sensing applications, as will be shown below. 2. Cr2+ -based mid-IR lasers From this point of view, the Cr2+ :ZnSe and other Cr2+ -chalcogenide laser materials appear promising: they offer very broad gain bands, centered in the mid-IR regions between 2 and 3.5 µm [1]. Additionally, they operate at room temperature and can be pumped with available solid-state, fiber, and diode lasers. The key specific properties of the lasers, based on Cr2+ -doped II-VI compounds are as follows: – room-temperature and directly diode-pumped operation; – continuous tuning over an extremely broad wavelength range (e.g. 2000– 3100 nm for continuous-wave Cr:ZnSe [2]); – average output power >1 W in continuous-wave operation; – average power >10 W in pulse regime at kHz repetition rate; – extremely narrowband operation (down to single-frequency), and – modelocked ultrashort-pulsed operation. For more information the reader is referred to the chapter II.3 in this volume. It should be noted, that there exist competing technologies for obtaining radiation with high degree of transversal coherence in this wavelength range. Notably, the semiconductor lasers have by now made a tremendous advances towards the mid-IR, reaching 3.26 µm [3]. Other successful techniques are based on nonlinear-optical methods and include optical parametric oscillators (OPO) and difference frequency generators (DFG). In comparison with these techniques solid-state lasers offer convenient ultraboradband tuning at high average power power. From semiconductor lasers, they are distinguished by orders of magnitude broader tuning range, and from nonlinear-optical techniques by much lower cost and complexity. One of the spectroscopic techniques, that especially benefits from high output power is photoacoustic spectroscopy. The solid-state lasers can also

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be operated in unique regimes, such as femtosecond or non-stationary operation. The latter can be used for ultrasensitive intracavity absorption spectroscopy, as will be discussed below. In the experiments described further in this chapter, we have been using laser setups, all being built according to the generic scheme, shown in Fig. 1. This scheme follows the astigmatically compensated four-mirror design, featuring maximum of flexibility: free choice of cavity length and beam size inside the crystal, and two arms with collimated beams for placing the intracavity elements and output couplers. For broadest tuning range it is important, that all surfaces, e.g. the active element itself, prisms, etc. use only Brewster-oriented surfaces. Without the tuning elements the main wavelength-dependent losses originate from the mirror coatings and reabsorption in the crystal at the blue side of the gain spectrum. For experiments described in this chapter, we were using different kinds of mirrors, as shown in Fig. 2. It is important to note, that the gain bandwidth of the Cr2+:ZnSe Cr2+:ZnS

Output 2.0-3.1µm

Pumping 1.6-1.9 µm

OC

Figure 1. The generic four-mirror cavity design for Cr:ZnSe and Cr:ZnS lasers. The mirror radii of curvature varied from 75 to 150 mm, and pump lens focusing distance from 40 to 100 mm. All mirrors except the output coupler (OC) are dichroic high reflectors.

Figure 2. Reflection curves of the high-reflection mirror coatings. The coatings a) and b) use the high index contrast dielectric layers and follow the conventional quarterwave-stack design. The coating c) uses the 51-layer chirped-mirror design, allowing to cover the entire operation range with a single set of mirror, at the expense of increased losses. All coatings are dichroic, with low reflectivity in the 1.6–1.9 µm range for pump radiation. Filled area shows the gain cross-section of Cr:ZnSe.

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EVGENI SOROKIN

Cr2+ -based active media is so broad, that one would need at least two different mirror sets to cover it, if the coating are made using the traditional quarterwave stack design and dielectric materials with the highest index contrast. To cover the whole gain range of the Cr:ZnSe or Cr:ZnS laser with a single mirror is a very challenging task, requiring the special broadband mirror designs. With such mirrors, designed according to the “chirped mirror” technique [4] it was possible to operate the laser in almost the entire tuning range (Fig. 4), although losses in these mirrors are far from optimal (Fig. 2c). 3. Trace gas analysis in the atmosphere The monitoring and analysis of gases at low concentration has become an essential environmental, medical, industrial, and chemical issue. Numerous techniques and instruments have been invented, reaching extremes in sensitivity for certain components. The optical techniques possess some important advantages, e.g. they can be performed without intrusion, in real time, and on a number of components simultaneously, etc. One of the optical techniques based on direct absorption spectroscopy is the photoacoustic (PA) spectroscopy. It requires a tunable narrow linewidth light source and a detection scheme based on photoacoustic effect, e.e. generation of sound waves in the medium by nonradiative decay of molecules, excited by modulated radiation. Being specimen- and wavelength-independent, the PA detection scheme is quite universal. This property is especially important if the measurement is supposed to include different gases, as it is normally the case in typical applications. The PA signal is directly proportional to the absorption cross-section σ (λ) and the power of the exciting radiation [5, 6]: S(λ) = qσ (λ)N P(λ),

(1)

where N is the concentration of the molecules, and P(λ) the wavelengthdependent power of the exciting beam. The sensitivity coefficient q in the equatuion (1) depends on the construction of the cell and microphones, and can be further enhanced by utilizing the acoustic or mechanical resonance. The resonance signal enhancement is typically of the order of ∼10–100 for multimicrophone cells with acoustic resonance but can reach values up to ∼104 –105 using the electromechanical resonances [7]. The equation shows another advantage of the photoacoustic technique. In comparison with many other absorption measurement schemes, where the absorption signal is derived as a ratio between the absorbing and non-absorbing (baseline) spectra, the signal S(λ) is directly proportional to the absorption of the specimen. When the measurement is aimed at detecting the very low absorption, this property strongly lowers the

561

TRACE GAS SENSING

necessary signal-to-noise figure, allowing measurement of absorption of down to 10−8 cm−1 Hz−1/2 despite the much lower sensitivity of the PA technique as compared to, e.g., optical detectors. To fully exploit this advantages of the PA scheme, the excitation laser source should demonstrate broad tunability in the wavelength range of potential specimens, sufficiently narrow oscillation linewidth for good selectivity, and high output power for more sensitivity. Currently available alternatives include systems, based on nonlinear optical conversion techniques and include optical parametric oscillators, difference frequency generators, and tunable semiconductor lasers [6, 8, 9]. The latter are probably most user-friendly, but so far they provide only relatively narrow tuning ranges, making every setup suitable to just one-two species. The tunable broadband solid-state laser, directly covering thousands of wavenumbers provide a really multicomponent ability. The main absorption features of many relevant gases lie in the midinfrared (2–15 µm) region with overtones and combination vibrational-rotational bands in the near-IR (0.8–2 µm) spectral range. The atmospheric window between 2–5 µm is especially interesting, because it is characterized by the presence of the strong fundamental vibrational absorption lines of atmospheric constituents, vapors and other gases. Those include water vapour (H2 O), filling the whole range between 2.4 and 3 µm with maximum around 2.7 µm, carbon monoxide (CO) with strong features around 2.3–2.4 µm, carbon dioxide (CO2 ) absorbing around 2.7–2.8 µm, nitrous oxide (N2 O), having several absorption features all through the 2–4 µm range, as well as many other species. In what follows, the application of the tunable Cr2+ :ZnSe laser source to PA-based trace gas measurement is described. The measurement scheme is shown in Fig. 3. The laser source was the tunable Cr2+ :ZnSe laser, as described in the previous section, pumped by an Er3+ -fibre laser at 1607 nm. In continuous-wave operation, this type of active medium acts

Er:fiber laser (1607 nm)

Cr2+:ZnSe

Lock-in

FS, CaF2 prisms OC Resonant PA cell

Chopper 5 KHz

HR

Tuning

Figure 3. Experimental setup for the photoacoustic measurements. The resonator section of the PA cell had opening diameter of 3 mm and resonance enhancement factor of 4.2 at 5.7 kHz [11].

562

EVGENI SOROKIN

as a homogeneously broadened one [10] so that narrowband tunable operation can be achieved without efficiency penalty. This allows higher output power, which translates into better signal-to-noise ratio according to the expression (1). The tuning has been achieved by a tandem of prisms by rotating the end mirror. Depending on the required spectral resolution and spectral region, CaF2 or dry fused silica prisms have been used. The relative acceptance bandwidth (full-width at half-maximum) of the tuning arrangement in this case is given by the formula λ 1 = λ 8πw0

dn dλ

−1

,

(2)

where w0 is the beam waist radius. The final oscillation linewidth also depends on the cavity arrangement, saturation, and loss level, but in any case it scales with the acceptance bandwidth, i.e. inversely proportional to the prism material dispersion. Table 1 gives dispersion data for some common materials. Fused silica provides the highest dispersion over the whole tuning range, but it suffers OH-related losses beyond 2.5 µm. This is a common problem for many oxide materials, which should be substituted by fluorides or chalcogenides at longer wavelengths. Interestingly, we found that ZnSe does not have any advantages over CaF2 beyond 2.5 µm, despite its much higher refractive index. In the experiments, both dry fused silica and calcium fluoride for tuning and PA measurements. With a single broadband mirror set, a wavelength range between 2000–2937 nm (3400–5000 cm−1 ) can be covered (Fig. 4). With special infrared optics, it is possible to extend the tuning range to 3100 nm. (Fig. 4). The typical experimental results are presented in Fig. 5. Using the same source it was possible to perform measurements from 2.3 µm to 2.9 µm. The laser output power of 100–500 mW is orders of magnitude higher than the powers achieved with difference frequency generation in the same wavelength range. This allows sensitive measurement using even the relatively weak absorption lines in the spectrum. Using the certified gas mixtures, one can calibrate the sensitivity of the whole setup and perform quantitative measurements [11]. The minimum detectable absorbance at a power level of 300 mW was 1.6 × 10−5 . The resulting TABLE 1. Material dispersion dn/dλ (×10−6 nm−1 ) for some common prism materials: zinc selenide, calcium fluoride, and fused silica. The wavelengths correspond to the tuning range of the the Cr:ZnSe laser. Material

λ = 2100 nm

λ = 2500 nm

ZnSe CaF2 SiO2

−12.3 −5.23 −15.4

−7.9 −6.0 −18.7

λ = 3000 nm −5.4 −7.05 −23.7

563

TRACE GAS SENSING

Cross-section (x10-19 cm2)

Fluorescence Absorption

600

10

Gain 400

5 200

0 1800

2000

2200

2400

2600

2800

3000

Output power (mW)

Infrared set

Broadband set

0 3200

Wavelength (nm) Figure 4. Continuous-wave tuning of a Cr:ZnSe laser, using a broadband mirror set (circles) and an infrared mirror set (squares). The effective gain curve is computed from the fluorescence and absorption cross-sections at real ion concentration Nt and threshold inversion n th [2].

minimum detectable concentrations for a number of gases are plotted in Fig. 6, [11, 12]. For many important molecules the detection limit lies well in the ppb (part-per-billion) region. The linewidth of the laser is also an important factor, as it defines the selectivity of the technique. It was measured using the gas lines themselves and was found to be ∼0.2 cm−1 with fused silica prisms (Fig. 5c) and ∼1.2 cm−1 with CaF2 prisms Fig. 5d), due to their lower dispersion [12]. This linewidth is still dominated by the thermal and mechanical instability of the used laser setup, because the short-term linewidth in the comparable setup was measured to be less than 0.02 cm−1 [1]. Nevertheless, for atmospheric measurements the resolution of the current setup with CaF2 prisms is in most cases sufficient for measurements of vibrational-rotational absorption bands, and fused-silica prisms allow resolution of single absorption lines. 4. Intracavity laser spectroscopy Another method of ultrasensitive spectroscopic absorption measurements, where the gain bandwidth plays a crucial role, is the time-resolved intracavity laser spectroscopy (ICLAS) [13]. The principle of ICLAS can be summarized as follows: after a fast switching on of the pumping, the broadband laser will initially start its oscillation from the amplified spontaneous emission, which is effectively a gain spectrum of the active medium. Along with the settlement of the continuous-wave operation, the oscillation spectrum will implode to its stationary value. During this time any narrowband loss inside the cavity (e.g. an absorption line in the air) will appear as a dip in the spectrum. It can be shown, that the form and the depth

564

EVGENI SOROKIN

4288.0

3450

1.9 ppmV methane 0.3 ppm V CO Measured data

1.0.10−6

0.0 2332

2334 2335 Wavelength in nm

4.0.10−4

a) 4326.0 0.012 0.010

Wavenumber in cm−1 4325.0

3420

3410

2.5..10 -6 2.0.10 -6 1.5.10 -6 -6 1.0.10 -7 5.0 .10 0 0.0 10 4282 4284 4286 4288

2.0.10−4

2336

3430

98% CO2 (HITRAN) 2% Water vapour (HITRAN) Measured data

0.0

2333

3440

6.0.10−4

Absorbance

Absorbance

2.0.10−6

Wavenumber in cm−1

Wavenumber in cm -1 4286.0 4284.0 4282.0

2900


2930

b) Wavenumber in cm−1 4324.0

Measured data single CH4 absorption line single CO absorption line

3708 30

0.008

3704

3700

Measured data CO2 (HITRAN) Water vapour (HITRAN) Multiple Lorentzian

20

0.006 0.004

10

0.002 0.0

2311.6

2312.0 2312.4 Wavelength in nm

c)

2312.8

0

2696


2702

d)

Figure 5. Gas absorption spectra using the tunable Cr:ZnSe laser. a) Methane and carbon monoxide in air (1 bar) around 2.3 µm [11]. b) Overview scan of CO2 (1 bar, contaminated with 2% water) around 2.9 µm [12]. c) Methane (500 mbar), single narrow line for resolution estimation [11]. d) CO2 (1 bar, contaminated with 2% water) around 2.7 µm [12]. All measurements performed at room temperature. Spectra a) and c) recorded with fused silica tuning prisms, spectra b) and d) used calcium fluoride prisms.

of the absorption line relative to the broadband spectrum follows the exponential Bouguer-Beer law with an effective propagation distance equal to leff = c(t − t0 ), where t0 denotes the onset of laser oscillation. In properly designed low-loss lasers, the spectrum collapse may take tens and hundreds of microseconds, resulting in effective absorption lengths of tens and even hundreds of kilometers, allowing measurement of absorption as small as 10−9 cm−1 and better. This explains the enormous potential of the ICLAS measurement for detection of weak narrowband absorbers. At the same time, the initially broad spectrum continues to narrow during the laser evolution, so that the maximum effective absorption length can be reached only near the gain maximum. More precisely, it can be shown that the laser bandwidth at a time t after the onset of oscillation follows the rule [13]

565

TRACE GAS SENSING 4500

4000

HF

Water

0.01

CO2

2

cm )

CH4 HCl

HF

100 10

-20

3000 1E-3

1000

σabs (x10

cm−1

3500

NH3

N2O

CH4 CO

0.1 1

1

Cr:ZnSe

0.1

10

Detection limit (ppmV)

5000

Cr:CdSe 2000

2200

2400

2600

2800

3000

3200

3400

Wavelength (nm) Figure 6. Minimum detectable concentrations for a number of gases using the photoacoustic registration. The horizontal bars show the tuning ranges of Cr:ZnSe and Cr:CdSe lasers [2].

λ ∝ λ0 ·

τc , (t − t0 )

(3)

i.e. it is proportional to the initial bandwidth λ0 of the gain spectrum. In the expression (3) τc is the lifetime of the photon in the resonator, depending on the resonator round-trip time TR and the round-trip loss L: τc = TR /L. The optimal laser for the ICLAS experiment should thus exhibit low loss and have possibly long resonator, since the effective absorption path is proportional to the length of the resonator and inversely scales with losses. Reversing the relation (3) makes also clear, that the laser bandwidth is an even more important factor: for a given final bandwidth the effective absorption path length scales quadratically with the initial bandwidth: leff = c(t − t0 ) ∝ λ20 . The material bandwidth becomes thus a most crucial parameter in the intracavity spectroscopy. For detailed description of ICLAS using the solid-state lasers the reader is referred to Refs. [13–15]. With respect to the above discussion, Cr2+ :ZnSe and Cr2+ :ZnS lasers fit extremely well for the ICLAS spectroscopy: the lasers allow convenient operation at room temperature in a very interesting wavelength range, and possess the broadest gain bandwidth of all known solid-state laser materials [10]. The gain peaks of the two lasers are shifted by about 100 nm (Fig. 7), so that they can be seen as complementary in coverage of the 2.2–2.7 µm region. These media also represent a much broader family of Cr2+ -doped II-VI materials with a potential of extending the wavelength coverage to and beyond 3 µm [1, 10]. Only a few experiments with ICLAS using broadband sources in the infrared were performed: atmospheric spectra were obtained in the 2636–2640 nm region using the KCl:Li F A (II) color center laser [16], in the 2035–2055 nm region using

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EVGENI SOROKIN

Figure 7. Comparison of the normalized gain spectra of Cr:ZnSe and Cr:ZnS laser materials.

the Co:MgF2 laser [17], and in the 1770–1950 nm region using the Tm-doped fiber laser [18]. Quite recently, the Cr:ZnSe laser has been used for the intracavity absorption experiment in the 2410–2460 nm region [19], and a Cr4+ :YAG laser has been applied in the 1350–1610 nm range [20]. However, the extreme sensitivity of the intracavity spectroscopy becomes a problem, if it is used in the infrared region, were air constituents possess fundamental and combination absorption lines. As a result, in most of the above quoted experiments the spectra were completely oversaturated by the atmosphere, predominantly water vapor and CO2 . Equally, even the slightest back-reflection from any surface inside or outside of the resonator creates a weak loss modulation in form of parasitic Fabry-Perot resonance, which act in the same way as a comb of absorption lines. The laser must therefore be carefully optimized with respect to spurious reflections and contain no plan-parallel mirror substrates. Equally detrimental could be residual birefringence in the laser material, when the active element might acts as a shallow Lyot filter, also resulting in spectral loss modulation. In order to make use of the full ICLAS sensitivity in the mid-IR range, we have put the Cr:ZnSe (Cr:ZnS) laser setup into the sealed chamber [21–23]. With an Er:fiber laser pumping, the pumping head was positioned outside the chamber (Fig. 8). For sufficiently fast (few microseconds) turning on of the pump, an acousto-optical modulator was used. The box was then evacuated and filled with a gas of interest at pressures between 0.1–70 mbar, to avoid the collisional broadening. The output of the laser from the output coupler with an average power of tens of mW is atttenuated and examined outside of the evacuated chamber using the Fourier-transform spectrometer in the step-scan mode [24]. In this regime, the complete time sequence is recorded at every position of the FT interferometer. The Fourier transform is performed after the full acquisition, resulting in a complete set of spectra Fig. 10 with high temporal and spectral resolution. The typical

567

TRACE GAS SENSING Er:fiber laser

AOM Cr2+:ZnSe

TRFT spectrometer

HR

OC

Figure 8. Schematic diagram of the time-resolved FT spectrometer. The dashed rectangle shows the evacuated chamber [21].

Cr:ZnSe fluorescence

Transmission (%)

HR

10

10 5 OC

0

Cross-section (10−19 cm2)

20

0 2200

2400

2600

2800

Wavelength (nm)

Figure 9. Fluorescence spectrum of Cr:ZnSe (gray) and spectral losses due to the output coupler (OC) and 5 high reflectors (HRs) on a round trip. A typical output spectrum at 8.9-µs delay (2.6-km effective propagation distance) is shown in black, with the CO2 absorption lines [21].

parameters were: pulse repetition rate up to 1–3 kHz, temporal resolution 0.3–3 µs, spectral resolution 0.006–0.02 cm−1 . Fig. 9 shows the laser gain curve, as well as the reflection curves of the mirrors in the cavity. One single ICLAS spectrum of CO2 is shown, spanning over 100 nm bandwidth, at a 2.6-km effective propagation distance. Fig. 10 shows the complete time resolved ICLAS spectrum of CO2 at 66 mbar. Besides the CO2 , residual water lines can be seen, corresponding to contamination level of the CO2 of about 4 · 10−5 or 2.5 · 10−3 mbar partial pressure of H2 O vapor. Fig. 11 shows a high-resolution portion of the CO2 spectrum, corresponding to 4.9 km of effective propagation distance. The effective absorption is as high as 90% for the strongest lines, corresponding to a sensitivity of 6 × 10−8 cm−1 . The explored spectral domain is the location of the two weak vibration-rotation combination bands 2ν3 −ν2 (Fig. 11) and 2ν3 +ν2 −2ν2 . The maximum absorption of the line profiles reaches 100% with a pressure-absorption path conditions equal to 66 mbar and 30 km, respectively. It is worth noting that previously, these spectra

568

EVGENI SOROKIN CO2

H2O 7.6

Time (µs)

26.5

7.6 Time (µs) 26.5 2450

2500

λ (nm) 2550

Figure 10. Time-resolved ICLAS spectrum of CO2 . The 64 consecutive time components are 0.32 µs apart. This corresponds to a 96 m increase of the equivalent absorbing path Ieff between each spectrum. The upper right-hand enclosure gives the total laser intensity versus time [22]. Wavelength (nm) 2484.0

2483.5

2483.0

2482.5

2482.0

Transmission (%)

100

50

CO2 at L = 4.9 km 2ν2−ν3, R-branch

0 4026.0

4026.5

4027.0

4027.5

4028.0

4028.5

4029.0

Frequency (cm−1)

Figure 11.

Doppler-limited spectrum of CO2 at 4.9-km propagation distance [21].

could only be detected by astronomic measurements in the atmosphere of Venus [25, 26] which is 96.5% CO2 . The sensitivity values obtained with the above setup can be further improved by reducing the intracavity losses. In particular, the output coupler can be replaced with a high reflector with transmission of the order of 0.05%. This allows longer effective path lengths and/or broader spectral coverage, according to the expression (3). The output power of the laser is of the order of few mW (from every mirror). However, since this is a diffraction-limited beam, it can be effectively delivered to the spectrometer and the signal is more than sufficient for recording the spectra. With this setup, effective path length increased up to 30

569

TRACE GAS SENSING

km, resulting in even higher sensitivity, reaching 10−8 cm−1 . This allowed to observe for the first time the previously unknown combination bands of acetylene C2 H2 [27] and nitrous oxide N2 O [28] around 2.5 µm. As already mentioned, using of the Cr:ZnS laser crystal instead of Cr:ZnSe allows shifting of the operation range of the technique by about 100 nm towards shorter waves (Fig. 7). Given the broad bandwidth of the high reflective mirrors (Fig. 9) and the fact that the Cr:ZnS crystal allows efficient pumping at 1607 nm, the experimental setup could be immediately adapted from the previous one (Fig. 8) by simple exchange of the active medium. In addition to that, the cavity length was doubled, enabling even longer effective absorption paths as described above. Fig. 12 shows a representative set of 20 Torr N2 O spectra around 2.4 µm with absorption path up to 110 km, while Fig. 13 shows a high-resolution part of the spectrum at 10.5 km effective absorption path. The broad spectrum modulation, that is seen on the long-propagation distance spectra in Fig. 12 comes most probably from the incomplete birefringence compensation in the Cr:ZnS crystal, which contains some percentage of the wurtzite phase [1]. The crystal acts in this case as a very weak Lyot filter. This modulation can be suppressed by careful orientation of the crystal or by using a material with addition of the small amount of ZnSe for cubic phase stabilization. The mixed Cr:ZnSSe crystals have shown to be good laser crystals with even broader gain bandwidth [2].

N2O

Time (µs) 367

P = 20 Torr

leff = 110 km

319 271 223 175 127 79 31

leff = 9.3 km 4130

4140

Figure 12.

4150

4160

4170

4180

Intracavity absorption spectra of N2 O [29].

4190

(cm -1)

570

EVGENI SOROKIN

Figure 13. Intracavity absorption spectrum of N2 O at 10.5 km of absorption length. The spectral lines below show the absorption of water vapor (not to the scale). [29].

Figure 14. A self-contained sealed diode-pumped setup for intracavity absorption spectroscopy using the Cr:ZnS laser. HR: high reflector. [30].

In order to bring the mid-IR ICLAS technique closer to the applications, it should be made less complex, self-contained and user-friendly. In the case of solid-state lasers this can be achieved by direct diode-pumping. As shown in Fig. 14, the diode laser including collimation optics can be positioned inside the chamber (footprint of the laser assembly is 60 cm by 40 cm). No special light modulation is required, since the diode laser can be conveniently switched on and off with microsecond accuracy by the driving current. The price for the convenience of the diode-pumped setup is the increased pump spot in the crystal. Therefore, the laser length had to be halved with respect to the previous arrangement. The usable effective absorption path reduces correspondingly (compare Figs. 12 and 15). The estimated minimum detectable absorption (assuming signal-to-noise ratio 3 or better) is 1 · 10−8 cm−1 versus 2 · 10−9 cm−1 in the Er-fiber pumped system. Nevertheless, it is extremely good in comparison with other techniques in the same spectral region.

TRACE GAS SENSING

571

Figure 15. Intracavity absorption spectra of N2 O at different absorption lengths recorded with a diode-pumped setup. The spectral lines marked with an asterix correspond to the residual water absorption lines. [30].

5. Conclusions The broadband mid-infrared solid-state lasers, represented by the Cr2+ -doped ZnSe and ZnS have come of age and are suitable for real-world applications. In praticular, detection of trace gases can be performed with extreme sensitivity and over a broad wavelength range. In this chapter, two different approaches for spectral recordings have been demonstrated: narrowband tuning over the absorbing spectral line of interest and broadband spectrum generation using the intracavity laser spectroscopy. The registration of the absorption line in the first case has been performed using the photoacoustic technique. Obviously, any other technique, including some described in the other chapters in this book, can be applied as well. Equally, the spectrum recording by the means of Fourier-transform technique is in no way obligatory for the intracavity absorption experiments, and any other approach can be used for registration depending on the requirements of the application. The extreme bandwidth of the solid-state lasers plays a crucial role in both demonstrated application examples. As an immediate advantage, the broad

572

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bandwidth allows covering of a large wavelength area, thus enabling true multicomponent sensitivity and selectivity using one and the same setup. In the case of intracavity spectroscopy, the broad bandwidth also translates into the highest sensitivity of the measurement, which duly reached levels of 10−9 cm−1 in terms of absorption coefficient. Such sensitivity allows recognition of gases with partial pressure of ∼10−5 mbar and less or recording of previously unknown very weak spectral bands. Further improvement of both techniques are possible, and should include direct diode-pumping of the lasers in order to make them truly transportable and self-contained devices. As shown on example of intracavity measurement, this can be readily achieved with minimal trade-offs in the performance of the setup. Acknowledgements The experiments described in this chapter have been performed in collaboration with C. Fischer and M. Sigrist form ETH Zurich as well as with N. Picqué and G. Guelachvili form University Paris Sud, Orsay, all of whom deserve special thanks for generous sharing their expertise and equipment. I am also grateful to Dr. I. T. Sorokina from the Photonics Institute, TU Vienna, who initiated and actively participated in all the works. The work have been supported by the Austrian National Science Fund (FWF) under grant Nr. P17973 and by the Austrian-French program Amadeus. References 1. I. T. Sorokina: Cr2+ -doped II-VI materials for lasers and nonlinear optics, Optical Materials 26, 395–412 (2004). 2. E. Sorokin, S. Naumov, I. T. Sorokina, Ultrabroadband infrared solid-state lasers, IEEE JSTQE 11, 690–712 (2005). 3. M. Rattunde, M. T. Kelemen, N. Schulz, C. Pfahler, C. Manz, J. Schmitz, G. Kaufel J. Wagner, High-brightness 2.×µm semiconductor lasers, Chapter in this book. 4. R. Szipöcs, K. Ferencz, C. Spielmann, F. Krausz, Chirped multilayer coatings for broadband dispersion control in femtosecond lasers, Opt. Lett. 19, 201 (1994). 5. M. W. Sigrist, ed. Air monitoring by spectroscopic techniques. Chemical analysis series, vol. 127. New York: Wiley; 1994 [chapter 4]. 6. M. Seiter, M. W.Sigrist: Trace-gas sensor based on mid-IR difference-frequency generation in PPLN with saturated output power, Infrared Phys. Technol., 41, 259–269 (2000). 7. A. A. Kosterev, Y. A. Bakhirkin, F. K. Tittel, Ultrasensitive gas detection by quartzenhanced photoacoustic spectroscopy in the fundamental molecular absorption bands region, Appl. Phys. B 80, 133 (2005). 8. F. K. Tittel, D. Richter, A. Fried: Mid-Infrared Laser Applications in Spectroscopy in Solid-state mid-infrared laser sources, Topics Appl. Phys. vol. 89, (Springer, Berlin, 2003) pp 445–516.

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9. F. K. Tittel, G. Wysocki, A. Kosterev, Yu. Bakhirkin, Semiconductor laser based trace gas sensor technology: recent advances and applications, chapter in this book. 10. E. Sorokin, Solid-State Materials for Few-Cycle Pulse Generation and Amplification, in FewCycle Laser Pulse Generation and Its Applications, Topics Appl. Phys. 95, pp. 3–73 (Springer, Berlin, 2004) 11. C. Fischer, E. Sorokin, I. T. Sorokina, M. W. Sigrist: Photoacoustic monitoring of gases using a novel laser source tunable around 2.5 µm, Optics and Lasers in Engineering, doi:10.1016/j.optlaseng.2004.03.015. 12. E. Sorokin, I. T. Sorokina, C. Fischer, M. W. Sigrist: Widely tunable Cr2+ :ZnSe laser source for trace-gas sensing, paper MD4 at Adv. Solid-State Photonics 2005. 13. V. M. Baev, T. Latz, P. E. Toschek: Laser Intracavity absorption spectroscopy, Appl. Phys. B 69, 171–202 (1999). 14. A. Kachanov, A. Charvat, F. Stoeckel, Intracavity laser spectroscopy with vibronic solid-state lasers. I. Spectrotemporal transient behavior of a Ti:sapphire laser, JOSA B 11, 2412 (1994). 15. A. Kachanov, A. Charvat, F. Stoeckel, Intracavity laser spectroscopy with vibronic solid-state lasers: II. Influence of the nonlinear mode coupling on the maximum sensitivity of a Ti:sapphire laser, JOSA B 12, 970 (1995). 16. V. M. Baev, V. P. Dubov, A. N. Kireev, E. A. Sviridenkov, D. D. Toptygin, O. I. Yushchuk, Application of lasers with Fa(II) color centers in KCl:Li crystals in intracavity laser spectroscopy, Sov. J. Quantum Electron. 16, 1121–1123 (1986). 17. M. P. Frolov, Yu. P. Podmar’kov: Intracavity laser spectroscopy with a Co:MgF2 laser, Opt. Comm. 155, 313–316 (1998). 18. A. Stark, L. Correia, M. Teichmann, S. Salewski, C. Larsen, V. M. Baev, P. E. Toschek: Intracavity absorption spectroscopy with thulium-doped fibre laser, Opt. Comm. 215, 113–123 (2003). 19. V. A. Akimov, V. I. Kozlovsky, Yu. V. Korostelin, A. I. Landman, Yu. P. Podmar’kov, M. P. Frolov, Intracavity laser spectroscopy using a Cr2+ :ZnSe laser, Quantum Electron. 34, 185–188 (2004). 20. F. Gueye, E. Safari, M. Chenevier, G. Guelachvili, N. Picqué, Intracavity Cr4+ :YAG laser absorption analyzed by time-resolved Fourier transforms pectroscopy, Appl. Phys. B 81, 1143 (2005). 21. E. Sorokin, I. T. Sorokina, N. Picqué, F. Gueye, G. Guelachvili, Mid-IR High-Resolution Intracavity Cr2+ :ZnSe Laser-Based Spectrometer, paper MD3 at Adv. Solid-State Photonics 2005. 22. N. Picqué, F. Gueye, G. Guelashvili, E. Sorokin, I. T. Sorokina, Time-resolved Fourier transform intracavity spectroscopy with a Cr2+ :ZnSe laser, Opt. Lett., 30, 3410 (2005). 23. E. Sorokin, I. T. Sorokina, G. Guelachvili, M. Jacquemet, N. Picqué, Diode-pumped mid-IR Cr2+ :ZnS-laser-based spectrometer, paper SyB4 at 2nd EPS-QEOD Europhoton Conference, Pisa, Sept. 10–15, (2006). 24. N. Picqué, G. Guelachvili: High-information time-resolved Fourier transform spectroscopy at work, Appl. Opt. 39, 3984–3990, 2000. 25. P. Connes, G. Michel, High-resolution Fourier spectra of stars and planets, Astrophysical Journal. Letters to the Editor 190, L29-32 (1974).

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26. J.-Y. Mandin, Interpretation of the CO2 absorption bands observed in the Venus infrared spectrum between 1 and 2.5 µm, J. Mol. Spectrosc. 67, 304–321 (1977). 27. V. Girard, R. Farrenq, E. Sorokin, I. T. Sorokina, G. Guelachvili, N. Picqué, Acetylene weak band spectroscopy at 2.5 µm from time-resolved Fourier transform intracavity Cr2+ :ZnSe laser absorption, Chem. Phys. Lett. 419, 584 (2006). 28. H. Herbin, N. Picqué, G. Guelachvili, E. Sorokin, I. T. Sorokina, N2 O weak lines observed between 3900 and 4050 cm−1 from long path absorption spectra, J. Mol. Spectroscopy 238, 256 (2006) 29. E. Sorokin, I. T. Sorokina, G. Guelachvili, M. Jacquemet, N. Picqué, Sensitive Broadband MidIR Cr2+ :ZnS-Laser-Based Spectrometer, CLEO/QELS May 21-26, Long Beach, CA, USA, Technical Digest on CD, paper CFL5 (2006). 30. E. Sorokin, I. T. Sorokina, G. Guelachvili, M. Jacquemet, N. Picqué, Diode-pumped mid-IR Cr2+ :ZnS-laser-based spectrometer, paper SyB4 at 2nd EPS-QEOD Europhoton Conference, Pisa, Sept. 10-15, (2006).

MEDICAL APPLICATIONS OF MID-IR SOLID-STATE LASERS Medical Applications RUDOLF STEINER Institut für Lasertechnologien in der Medizin und Messtechnik an der Universität Ulm, Helmholtzstrasse 12, 89081 Ulm, Germany

Abstract. The potential of medical applications of Mid-IR lasers is still not at its end. Continuous research of laser-tissue interactions steadily opened new fields of medical applications for the Er:YAG laser at 2,94 nm wavelength, due to the high absorption of this wavelength in water, biological soft and hard tissue. Lasers with emission at 2 µm had no routine medical application for a long time due to side effects of the pulsed irradiation with large cavitation bubbles. Only recently, with new laser technology, these lasers in cw and pulsed mode seem to be useful for certain medical treatments, complementary to standard procedures. Absolute medical indications for Mid-IR lasers are still rare but will increase in the near future. With new transmission systems on the basis of fibre technology for the 2 µm and 3 µm spectral region endoscopical applications will become possible and help that lasers will be accepted as alternative tools for minimal invasive treatments. Keywords: Medical laser applications; holmium laser; Er:YAG laser; thulium laser; lasers in dentistry.

1. Introduction Solid state MID-IR lasers for medical applications are rather new compared to CO2 lasers, ion-lasers, dye lasers and the Nd:YAG (cw and q-switch) laser. While the Er:YAG laser, after eight years of research and development, became an accepted instrument in dentistry and dermatology, the 2 µm lasers Ho:YAG and Tm:YAG only recently try to find useful applications specially in urology. The reason is that cavitation and acoustic side effects discriminated early applications in orthopedics for smoothing cartilage. It is also surprising that after strong research efforts in using pulsed Nd:YAG lasers and dye lasers for lithotripsy in the 1980s and beginning 1990s, now the technology appears again in form of pulsed holmium laser and much more efficient. Still the endoscopic instrumentation must be adapted to the laser application but stone fragmentation seems to become a domain of the Ho:YAG laser. The potential of these lasers in medicine is not finally


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explored. The understanding of specific laser reaction mechanisms with biological tissue and simulation procedures help to assess selective laser applications in the future. 2. Laser-tissue-interaction The reaction mechanisms of laser light with biological tissue are determined by the optical constants of the tissue to be treated and the laser parameters. The optical constants are the absorption coefficient α[cm−1 ] dependent on the wavelength, the scattering coefficient µs [cm−1 ] and the g-factor describing the unisotropic scattering. With these coefficients the light perfusion into the tissue can be simulated efficiently with Monte Carlo procedures. [1–3] Laser radiation in the MID-IR region of the optical spectrum is highly absorbed by water (Figure 1) and the biological tissue. Therefore, scattering plays a minor role and absorption dominates the reaction kinetics of thermal effects and ablation. The penetration depth of the 2, 94 µm radiation of the Er:YAG laser is about 1–3 µm in biological tissue due to the high absorption of 104 cm−1 . Lasers

Figure 1. Absorption of water, hemoglobin and melanin over the wavelength. Water absorption in the MID-IR region is rather high with maximum at 3000 nm wavelength and a corresponding penetration depth of 1 µm.

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with emission of radiation near 2 µm wavelength (Ho:YAG: 2, 12 µm; Tm:YAG: 2, 01 µm) have a penetration depth which is 100 times larger. Therefore, more energy per pulse is needed for the ablation of tissue and the side effects like cavitation and zone of necrosis are more prominent. Recently, laser diodes for pumping Ho and Tm ions very efficiently at 785 nm were available. Such Tm:YAG lasers at 2,01 µm wavelength are now on the market and can also be used for medical applications (LISA laser products OHG, Germany) with 50 W and 70 W laser power. The advantage compared to CO2 lasers is that the radiation can be guided through water free quartz fibers. Endoscopic laser applications for tissue resection in ENT and urology become possible. The higher penetration depth of the laser light at 2 µm into the tissue has the advantage that smaller blood vessels are coagulated during cutting, but the disadvantage is the larger zone of necrosis retarding the healing process. Studies which will show the benefit of such lasers are in progress. Continuous wave 3 µm lasers are still an object of research and development. With Er:YLF, Er:YSGG and Er:YAG crystals only several hundred mW output power could be achieved. [4] Dinerman and Moulton [5] reported the realization meanwhile of several Watts, but no commercial systems are available. They would be very useful for micro-surgery with 100 µm fibers in diameter. Most of the MID-IR medical laser systems operate flashlamp pumped in the pulsed mode with pulse durations between 50 µs and 800 µs. The repetition rate is up to 20 Hz and the mean power varies from 20 Watt to 50 Watt. Applications under water differ between the 2 µm and 3 µm radiation according to the absorption conditions. The Ho:YAG laser creates a large cavitation bubble at the fiber tip by vaporization and expansion of the water. A review paper by Vogel [9] describes this reaction mechanism in detail. After that the beam hits the tissue through the bubble and ablates the material. Due to the high absorption of the 3 µm wavelength the Er:YAG laser shoots a channel through the water in form of the intensity profile of the laser radiation which can be formed by the structure of the fiber tip. Therefore, thermal and acoustic side effects are much less pronounced than using the Ho:YAG laser. The different behavior is demonstrated in Figure 2. Such laser effects have also been studied for transmyocardial revascularisation, [6] but without any chance to become a routine medical application. Pulsed MID-IR and UV lasers were used to smooth cartilage in the joints. However, probably due to thermal side effects, cells within the cartilage are damaged and die after the Excimer laser application at 308 nm [7] and the use of the Ho:YAG laser. More successful for this indication will be the Er:YAG laser [8] and when some technical difficulties are solved, then this can be a hopeful application in the future. For medical application, the zone of necrosis is important for the wound healing. High laser power applied in short time reduces the necrotic zone to a minimum determined by the wavelength specific penetration depth. As mentioned

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Figure 2. Cavitation bubbles created by a Ho:YAG and Er:YAG laser pulse at 240 µs after begin of the pulse.

already, the Er:YAG laser light at 2, 94 µm has the highest absorption coefficient and a penetration depth into the tissue of about 1 µm. The necrotic zone is only several microns. There was a discussion whether the Er:YSGG laser with a wavelength of 2, 8 µm, slightly off the absorption peak, would not be as good as the Er:YAG because it could be operated with higher repetition rate. But Figure 3 demonstrates clearly that the physics behind laser interaction with tissue cannot be duped. The necrotic zones created with one pulse of equal energy with both lasers reflects the penetration depth of the corresponding wavelengths. For tissue ablation, the Er:YAG laser is the optimum device. However, it happens during operation that blood capillaries will be opened and the bleeding should be stopped. The Er:YAG laser normally cannot do it, the reaction is only superficial. But one can operate the laser in such a way that it will coagulate the blood. The key to this problem is that ablation of tissue is a threshold phenomenon. The energy of the laser pulse must be above threshold for tissue removal. Sub-threshold pulses will only heat the surface. Calculations and simulations in Figure 4 show that with higher repetition rates of sub-threshold pulses in between the ablating pulses keep a certain temperature at the surface, sufficient for coagulation. With the number of such pulses, the zone of necrosis is adjustable to the need of the surgeon. Laser devices with this operation mode are now available (Wavelight AG, Erlangen). Histology in Figure 5 demonstrates this effect. The Er:YAG laser with programs for modulation of the necrotic zone is very well accepted by operating dermatologists, even better than the CO2 laser.


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Figure 3. Zone of necrosis created with an Er:YAG (3a) and Er:YSGG (3b) laser reflecting exactly the penetration depth into the tissue for the corresponding wavelengths.

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Figure 4. Simulation of the temperature profile of sub-threshold Er:YAG laser pulses demonstrate the continuous heating of tissue and coagulation.

The precise operation by ablation with the Er:YAG laser is accompanied by acoustic effects. The fast heating of the tissue, explosive vaporization of the water content in the tissue matrix and ablation of tissue fragments consumes less energy than vaporization of the tissue. During the laser pulse a crater is formed into the tissue until the power drops below the ablation threshold. The remaining energy in the pulse is transformed into heat and is responsible for the necrotic zone. However, this fast heating generates strong acoustic signals. In most applications this is of no importance, except when applied to fragile structures as in the middle ear. [10, 11] Here side effects are reported. In Figure 6 the ablative effect with acoustic waves is demonstrated. 3. Transmission systems For transmission of the 2 µm wavelength of the Ho:YAG and Tm:YAG lasers water free quartz fibers are the standard systems. The diameters vary from 200 to 1000 µm to transmit pulse energies of several Watts at frequencies up to 20 Hz. The disadvantage is the rigidity of the fibers with larger diameters from 600 to 1000 µm, specially for endoscopic applications in the urinary tract. Most applications use the bare fiber end. The optical threshold of destruction of the quartz fibers is at laser irradiation of about 3∗ 1011 W/cm2 . In contact with the tissue it


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Figure 5. Histology of the necrotic zone created by sub-threshold Er:YAG laser pulses, (5a) with one pulse and (5b) with seven pulses.

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Figure 6. pulse.

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Laser ablation of tissue. The process is imaged 10 µs and 40 µs after start of the laser

drops to 30∗ 109 W/cm2 and when the surface of the fiber tip is already rough or slightly damaged then the damage threshold is very low at 1, 25∗ 108 W/cm2 . Higher laser irradiation will cause burn off of the fiber end with quartz debris on the tissue. Prolongation of the laser pulse prevents this fiber damage. The 3 µm laser radiation can not be transmitted with water free quartz fibers, special IR-fibers are needed. GeO2 glass fibers (Infrared Fiber Systems, Inc.) have proven to resist clinical routine application in dentistry. Losses at 2.94 µm are 0.7 dB/m and mean power transmission of 20 Watts at 10 Hz pulse rate is possible. Fibers have an excellent flexibility and strength and are non toxic. Available core sizes are 100–700 µm. If higher radiant exposures are needed, e.g. in dermatology, then articulated transmission arms must be installed in the laser systems.


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4. Medical applications 4.1. HOLMIUM AND THULIUM LASER

There is nearly no laser type which had not been tried for some medical applications. The Ho-YAG laser had its debut in orthopedy but failed due to the side effects. Now with much higher radiant exposures there is a renaissance specially in urology. Stone fragmentation has become a routine application (e.g. WaveLight, AURIGA). Ablation of prostate tissue to treat benign prostate hyperplasia (BPH) is still under investigation also the enucleation of larger prostates. Endoscopic instrumentation in combination with fiber technology must still be optimised for this indication. With side fire catheters one can use the method of laser induced thermo therapy (LITT) for larger amount of tissue coagulation. The future will show what else could be treated with the Ho:YAG laser, studies are under way. The development of laser diodes (785 nm) for pumping directly Thulium ions was necessary to build cw Tm:YAG laser operating at room temperature. High power medical laser systems (e.g. LISA laser procucts OHG) with emission at 2.01 µm and 50 Watt are on the market. Meanwhile single mode fiber lasers have even more power up to 150 Watts (IPG Photonics). With cw irradiation tissue can be cut and vaporised. First medical applications are constriction of the urethra and BPH. Lasers are not yet widly spread and typical applications for the Tm:YAG laser must still be elaborated. 4.2. ER:YAG LASER

4.2.1. Soft tissue The Er:YAG laser is well accepted in dermatology for controlled and gentle removal of delicate skin lesions or ablation of large surfaces for skin resurfacing. Aesthetic and medical indications are reviewed by Kaufmann and Beier. [12] First experiments and clinical trials [13,14] started as soon as Er:YAG lasers were commercially available. Comparing the results of skin resurfacing with the CO2 laser, the Er:YAG laser on a longer time scale will give the same clinical outcome. The advantage, however, is that due to the small zone of necrosis healing occurs much faster. Furthermore, when treating perioral or periorbital skin the precision of the Er:YAG laser is unique compared to dermabrasion or CO2 laser treatment. In Figure 7 the precision of skin ablation is demonstrated removing a tattoo. One thin layer after the other is removed until the first blood capillaries appear. There is no damage of the underlying tissue. The Er:YAG laser is also well suited for removal of superficial epithelial and dermal lesions. Xantelasms around the eye, a very delicate location are easily ablated with excellent cosmetic outcome. Er:YAG laser tissue ablation may be also useful in combination with other surgical techniques like removal of osteoma cutis, the treatment of rhinophyma, grafting of vitiligo lesions or removal of the nail plate.

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Figure 7. Laser ablation of thin layers (7a) of the skin when removing a tattoo, not to be treated by other procedures. The ablation process continues until the pigments are removed or the first blood capillaries appear (7b).

4.2.2. Hard tissue In the late 80s, when pulsed Er:YAG lasers became available, experiments showed that also hard tissue, bones and dental materials [15], can be ablated very efficiently because the material itself, hydroxylapatite, absorbs in the 3 µm spectral region as well. Also thermal side effects have been discussed in the beginning


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Figure 8. Er:YAG laser ablation of enamel (left) and dentin (right) with the corresponding electron microscope pictures demonstrating no thermal effect and open dentin channels.

[16]. It turned out, that with a fine water spray onto the surface during the ablation process no thermal cracks occur in the enamel or dentin (Figure 8). First experiments and applications concentrated on caries removal. The advantage of Er:YAG laser caries removal is much less pain compared to drilling. Also without anesthesia caries ablation near the pulp is tolerable [17]. Meanwhile caries removal is no longer the focus of laser applications in stomatology. Endodontic and periodontal application are even more important, because alternative and standard methods are less effective and more time consuming than laser treatment. A complete set of interchangeable handpieces are ready for the different indications (KaVo, KEYIII dental laser). Root channel disinfection by the Er:YAG laser pulses with a fiber mounted handpiece, soft tissue corrections by ablation and periodontal applications with removal of the infected plaques are new indications. A special handpiece for the periodontal use with a tapered crystalline tip was developed which directs the beam at low angle to the tooth surface producing a clean and smooth surface. Treatment of periimplantitis is the latest application where no mechanical alternative exists. Er:YAG laser pulses ablate the infected bone around the implant with additional sterilisation effect on the surface of the structured implant. Implants can be saved because the growing bone will fix them again.

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Figure 9. Scheme of the principle of caries detection by red light excitation and NIR fluorescence detection.

Figure 10. Smart Er:YAG laser system (KaVo KEYIII) with automatic laser control by caries fluorescence detection integrated into the same handpiece.

A breakthrough in dental laser systems on the market happened after the realisation of a small device (KaVo, DiagnoDent) for caries detection by NIR fluorescence after excitation with red light and the incorporation of caries diagnosis into the laser handpiece. The scheme of the caries detection is shown in Figure 9. Spectral contrast of the fluorescence is used to discriminate between infected and sound tissue. Also caries in the depth, not visible by normal inspection, can be detected with the pencil-like handpiece. The tip contains a central fibre for excitation and a ring of fibres detects the fluorescence which is evaluated by the electronic part. In the third generation of the KEY laser detection and therapy are combined. There are many locations in the mouth where the dentist cannot see the field of operation. In such a case it is a big advantage when the laser itself detects caries and automatically removes it (Figure 10). This is important in parodontology when plaques have to be removed without visual contact by the doctor.


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5. Conclusions and future aspects MID-IR lasers in the 2 µm and 3 µm spectral range have already useful medical indications. The medical Er:YAG laser systems for dental and dermatological applications are well accepted but the potential of new applications and developments is still not exploited. New field could be orthopaedic applications and also in dentistry innovations will be elaborated. With the realisation of the combination of on-line diagnosis and therapeutic intervention future applications will be possible, for example the key hole caries preparation when caries has developed in the dentin under the enamel. Then, through a small hole to save sound enamel, a fibre will enter and remove the caries by scanning the angle and at the same time detecting where infected material is to be ablated. This might become reality soon, when also new filling material has been adapted to this procedure. In the early days of medical laser applications trials with the CO2 laser were reported to make the tooth material more resistant against caries bacteria. The trials failed because thermal side effects damaged the enamel. Now the idea has a renaissance with new lasers and a more adequate pulse regime. Medical applications with the 2 µm lasers, Ho:YAG and Tm:YAG, in pulsed or cw mode are still in the beginning to find their niche of minimal invasive surgical interventions, specially in urology. It always takes time until a new technology or method is introduced into clinical routine and accepted by the medical community. For micro-surgery 3 µm cw lasers with a good beam profile would be beneficial. Such lasers (see Part II, chapter 7) could be coupled into thin fibres for operations in the eye or in small joints when they reach output power of several watts. References 1. A. Kienle and R. Hibst, Light Guiding in Biological Tissue due to Scattering, Phys. Rev. Lett. 97(1), 018104 (2006). 2. A. Kienle and M. S. Patterson, Improved solutions of the steady-state and the time-resolved diffusion equations for reflectance from a semi-infinite turbid medium, J. Opt. Soc. Am. A 14, 246–254 (1997). 3. A. Kienle, L. Lilge, M. S. Patterson, R. Hibst, R. Steiner and B. C. Wilson, Spatially Resolved Absolute Diffuse Reflectance Measurements for Noninvasive Determination of the Optical Scattering and Absorption Coefficients of Biological Tissue, Appl. Opt. 35, 2304–2314 (1996). 4. M. Edelmann, Th. Meier and R. Steiner, Infrared Laser System for Irradiation of Cell Monolayers, Laser Physics, 13(1), 35–40 (2003). 5. B. J. Dinerman and P.F. Moulton, 3 MUM CW Laser Operations in Erbium Doped YSGG, GGG and YAG, Opt. lett., 19(15), 1143–1145 (1994). 6. H. P. Weber et al., CO2, Ho:YAG and Er :YAG lasers for transmyocardial laser revascularisation, Laser Physics, 9(2), 602–609 (1999). 7. R. Fischer, R. Hibst, D. Schröder, W. Puhl and R. Steiner, Thermal side effects of fiber guided XeCl-Eximer-laser drilling of cartilage, Lasers Surg Med. 14(3), 278–286 (1994).

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8. B. J. Züger, M. Frenz, T. Schaffer, J.-F. Clémence and H. P. Weber, Thermal and Mechanical Damage in Articular Cartilage induced by Er:YAG Laser and Conventional Surgical Instruments, Laser Physics, 13(1), 58–64 (2003). 9. A. Vogel and V. Venugopalan, Mechanismsof pulsed laser ablation of biological tissues, Chem. Rev., 103, 577–644 (2003). 10. D. Nagel, The Er:YAG Laser in Ear Surgery – First Clinical Results, Lasers in Surgery and Medicine, 21,79–87 (1997), 11. A. Huber, T. Lindner and U. Fisch, Is the Er:YAG Laser Damaging to Inner Ear Function?, Otology & Neurotology, 22, 311–315 (2001). 12. R. Kaufmann and Ch. Beier, Laser Skin Ablation: An Update on Aesthetic and Medical Indications, Med. Laser Appl. 19, 212–222 (2004). 13. R. Kaufmann and R. Hibst, Pulsed 2.94 µm erbium-YAG laser skin ablation: experimental results and first clinical application, Clin. Exp. Dermatol. 15, 389–93 (1990). 14. R. Hibst and R. Kaufmann, Effects of laser parameters on pulsed Erbium:YAG laser skin ablation, Lasers Med. Sci., 6, 391–397 (1991). 15. R. Hibst and U. Keller, Experimental Studies of the Application of the Er:YAG Laser on Dental Hard Substances: I. Measurement of the Ablation Rate, Lasers Surg Med, 9, 338–344 (1989). 16. U. Keller and R. Hibst, Experimental Studies of the Application of the Er:YAG Laser on Dental Hard Substances: II. Light Microscopic and SEM Investigations,Lasers Surg Med, 9, 345–351 (1989). 17. U. Keller and R. Hibst, Effects of Er:YAG Laser in Caries Treatment. A Clinical Pilot Study, Lasers Surg Med, 20(1), 32–38 (1997). 18. R. Hibst, Lasers for Caries Removal and Cavity Preparation. State of the Art and Future Directions, J Oral Appl, 2, 203–212 (2002).

OPPORTUNITIES FOR MID-IR SOURCES IN INTENSE-FIELD AND ATTOSECOND PHYSICS

MISHA IVANOV1 , VLAD YAKOVLEV2 , and FERENC KRAUSZ2 1 NRC Canada, 100 Sussex Drive, Ottawa, Ontario K1A 0R6 Canada 2 Max-Planck-Institut for Quantenoptik, Hans-Kopfermann-Strasse 1, D–85748 Garching, Germany

Abstract. Intense near-infrared pulses comprising a few wave cycles centred around 800 nm had became routinely available by the turn of the millennium. They have been instrumental in controlled generation of atto-second pulses of extreme ultraviolet light, both single and pulse trains, opening the door to real-time observation of atomic-scale electron dynamics. Attosecond pulses of light are generated by first producing attosecond electron pulses during strong-field ionization of atoms or molecules. These electron pulses offer new opportunities for imaging structures with femtosecond temporal and sub-Angstrom spatial resolution. In this article we look at how these new opportunities might be influenced by the new generation of intense, few-cycle mid-infrared sources with wavelengths in 2 to 3 µm range.

This article addresses the connection between attosecond physics, specifically the generation and some applications of attosecond electron and photons pulses, and the development of mid-infrared sources. We briefly touch upon the main physical principles of the generation of attosecond pulses and their possible applications, and point out unique opportunities that the development of mid-IR sources will open in this new area of research. The turn of this century has witnessed major breakthrough in ultrafast technology – the generation of single XUV pulses and their trains with duration below 1 fsec [1, 2]. Today, the shortest XUV pulses generated in the laboratory are about 250 atto-seconds (1 asec = 10−18 sec) long [1, 2]. These pulses can be used to trigger and time-resolve multi-electron dynamics in the atomic core such as Auger processes [3], including different stages of Auger cascades. The same physical principles that lead to the generation of attosecond pulses and pulse trains can be used to image molecular structures and molecular orbitals [4–9], resolving the motion of protons down to sub-fsec time scale [8]. What does infrared laser technology have to do with it? Everything. 589 M. Ebrahim-Zadeh and I. T. Sorokina (eds.), Mid-Infrared Coherent Sources and Applications, 589–598. c 2008 Springer.

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E coswt V(x)−xE coswt

+

X0

Figure 1. Strong-field ionization (optical tunnelling) in oscillating electric field of the IR laser. Electron escapes from the binding potential well through the barrier created by the laser field and the binding potential. Oscillating electric field brings the electron wavepacket back to the parent ion where it can recombine into initial state and emit a high-energy photon.

The physics of generating attosecond pulses begins with using strong IR laser field to ionize an atom (or a molecule) by optical tunnelling, see Fig. 1. Superposition of the binding potential of the parent atom and the oscillating electric field of the laser create an oscillating potential barrier. Twice every laser cycle, near the peaks of the instantaneous electric field, the electron has a chance to tunnel through the barrier (this quasistatic picture is adequate in the IR fields). When the electronic wavepacket emerges on the other side of the tunnelling barrier at x0 (Fig. 1), it is pulled far away within a small fraction of the oscillation cycle. A quarter-cycle later, the oscillating electric field reverses its direction and can bring the electron back to the parent ion. It is this collision between the liberated electron and the parent ion, termed re-collision, which forms the physical basis of generating attosecond photon pulses. Recollision lasts only a fraction of the driving laser cycle. Attosecond pulses are generated if the returning electron recombines to the same state of the atom which it was liberated from by the strong laser field. The same recombination, as well as elastic scattering on the parent ion (i.e. diffraction), carry spatial information about the structure of the parent ion taken in a fraction of the laser cycle. Let us look at these processes in more detail. Once the electron is freed and is pulled away by the laser field, attraction to the parent ion quickly becomes a small perturbation. Ignoring the ionic potential, the center of mass motion of the liberated electronic wavepacket can be described classically as x¨ = −E L (t) (1) When the electron appears at the “exit’ of the barrier x0 at some instant t0 , its velocity is equal to zero (Fig. 1). Then Eq. (1) yields electron momentum (in atomic units) p(t, t0 ) = A L (t) − A L (t0 ) =

EL [ f (t0 ) sin(ω L t0 + ϕ) − f (t) sin(ω L t + ϕ)] (2) ωL

MID-IR SOURCES IN INTENSE-FIELD AND ATTOSECOND PHYSICS 591

where AL (t) is the vector-potential of the laser field (E L (t) = −dAL /dt), f(t) is the pulse envelope and ϕ – the phase of the carrier relative to the envelope – is crucially important for modern ultrashort pulses with only one-two cycle duration. The electron trajectory along the laser polarization is x(t) ≈ x0 +

EL ω2L

[ f (t) cos(ω L t + ϕ) − f (t0 ) cos(ω L t0 + ϕ)] +

EL f (t0 ) sin(ω L t0 + ϕ)(t − t0 ) ωL

(3) where φ0 = ω L t0 + ϕ is the phase of ionization. For strong IR laser fields the initial offset x0 is negligible since the electron oscillation amplitude α = E 0 /ω2 exceeds the Bohr radius by a couple of orders of magnitude. As for the motion perpendicular to laser polarization, the electron wavepacket spreads transversally 1/2 1/4 with characteristic velocity v ⊥ ∼ E 0 /I p [10]. The first term in Eq. (2) describes electron drift velocity, which changes sign near the maximum of the electric field, at φ0 = ω L t0 + ϕ = 0. Electrons released after the peak of the field, φ0 > 0, return to the core. The return time tr can be obtained by setting x(tr ) = 0 in Eq. (3) for tr > t0 . For each moment of return tr , there is a unique moment of ionization t0 (tr ) associated with it, see Fig. 2(a). The electron energy at the moment of recollision W (tr ) =

p 2 [tr , t0 (tr )] [A L (tr ) − A L (t0 )]2 = 2 2

(4)

is shown in Fig. 2(b). It depends strongly on the phase of ionization and the corresponding phase of return, with maximum reaching 3.17 Up where Up =

E L2 4ω2L

(5)

(a) start

Energy /Up

start

finish 0

(b)

finish

0.5

1

1.5

Time, cycles

2

3.5 3.0 2.5 2.0 1.5 1.0 0.5 0.0 0.0

0.2

0.4

0.6

0.8

1.0

Treturn, cycle

Figure 2. Panel (a) shows that there is one-to-one correspondence between the moment of ionization and the moment of recollision. Panel (b) shows the kinetic energy of the recolliding electron as a function of the return (recollision) time.

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is the cycle-averaged energy of electron oscillations in the laser field, also referred to as the ponderomotive energy. The highest energy electrons return approximately around 3/4 cycle after the peak of the oscillating electric field, close to the moment of time when the field goes through zero. As the electron wavepacket revisits the parent ion, it can re-combine to the state it left from. During recombination, it will emit a photon with energy determined by the energy conservation law: (tr ) = W (tr ) + I p =

[A L (tr ) − A L (t0 )]2 + Ip 2

(6)

where Ip is the binding energy (ionization potential) of the initial (ground) state. The maximum photon energy – the emission spectrum cutoff – is given by cuto f f = Wmax + I p = 3.17U p + I p

(7)

Since ionization occurs periodically every half-cycle of the laser field, every half-cycle a new fraction of the bound electron wavefunction is promoted to the continuum and recollides with the parent ion. The emission process is periodic, and the spectrum contains odd harmonics of the driving field. Typically, the spectrum has a plateau where harmonics have similar intensity, extending all the way to Ip + 3.17Up . The plateau is followed by rapid exponential decrease in harmonic efficiency beyond the cutoff. Quantum-mechanically, high-harmonic generation results from the interference of the “continuum” electron wavepacket ψc upon its return to the core with the portion of the wavefunction left behind in the ground atomic state, ψg . The expectation value of the total dipole moment (polarization) induced in an atom or a molecule by the laser field, d(t) = ψ| d |ψ, includes interference term: dh (t) = ψg d |ψc + c.c. (8) As the returning electron zooms by the parent ion, its wavefunction ψc contains fast-oscillating phase reflecting the fast motion. Its overlap with the ground-state wavefunction creates fast moving volumes of constructive and destructive interference, giving rise to a fast-oscillating component, dh (t), in the total dipole moment, d(t). Simultaneously, Eq. (8) is also a transition matrix element describing recombination from the continuum state to the initial (ground) state during the overlap of the two components of the wavefunction. Rapid variation of the dipole moment means that radiation is emitted, with the emission power Ph (t) ∝ |d¨ h (t)|2

(9)


The time-derivative is dominated by the derivative of fast oscillating phase of the dipole moment. According to Eq. (8), this phase is the difference between the phases of ψg and ψc , and the time derivative of wavefunction’s phase is energy. Thus, the instantaneous oscillation frequency of the dipole Eq. (8) is the difference between the energies of the bound and continuum wavepackets ψg and ψc , (t) = Wr (t) + Ip , just as we have expected from the classical analysis. Looking at the dependence of the ponderomotive potential Up on the intensity and wavelength of the driving laser field, we see that, apart from the ionization potential, cutoff scales as Iλ2 where I is the laser intensity and λ is the laser wavelength. What prevents us from increasing the cutoff energy by increasing either I or λ, or both? Today, harmonics are typically generated using near-IR radiation of the Ti:Sapph laser with λ = 800 nm, and the cutoff energies in most experiments range from few tens to few hundreds of electron-Volts. Why don’t we use mid-IR radiation, say around 3 µm, to increase the cutoff by a factor (3/0.8)2 = 14 and generate few-KeV photons with a table-top setup? And why not use CO2 laser to push the cutoff even further? Why can’t we crank up the intensity of the driving IR field? Let us begin with intensity. The upper limit on the intensity of the IR laser field is set by ionization. According to Eq. (8), we need to have population both in the continuum and in the ground state. Increasing intensity will saturate ionization, deplete the ground state and reduce dh to zero. Of course, one can also use ions as the generating medium, but the presence of many free electrons leads to plasmainduced dispersion. The latter is detrimental to phase matching between highfrequency radiation and fundamental field. It is also detrimental to the propagation of the fundamental pulse, which is destroyed by plasma dispersion. As for the wavelength of the driving field, the main problem is efficiency of harmonic generation. Let us take a closer look at the scaling of harmonic generation efficiency with wavelength. Single-atom emission energy at frequency , per laser cycle, is given by the ¨ square of the Fourier transform of d(t) at the frequency , which is equal to 2 d(). Relevant wavelength-dependent factors in the single-atom response can be found using Ref. [10]: 1 1 4 dg2 () [v ⊥ τtravel ]2 (v || )τtravel |dW (tr )/dt| (10) In this equation, wi is the tunnel ionization rate, τtun = 2I p /E is the tunneling time during which the recolliding electron trajectory leading to the emission of a photon is populated, [v ⊥ τtravel ]2 describes transverse spreading during the 1/4 travel time between ionization and recollision, with v ⊥ ∼ E 1/2 /I p the transverse W S A () ∝ |2 d()|2 ∝ wi τtun

1

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spreading velocity. The factor (v || )τtravel describes longitudinal stretching of the wavepacket due to the velocity chirp v || = Eτtun induced by the laser field when populating the trajectory. Finally, dW (tr )/dt is the energy chirp of the returning electron, which limits the time during which a particular harmonic is emitted, dW (tr )/dt = v(tr )dv(tr )/dt ∝ 2( − I p )E (11) Near the maximum of recollision energy (i.e. at the cutoff of harmonic radiation spectrum) dW (tr )/dt = 0. There it has to be replaced with [d 2 W (tr )/dt 2 ]2/3 which scales as [ 2( − I p )Eω L ]2/3 . Finally, dg2 () in Eq. (10) is the square of recombination matrix element. Taking into account that travel time τtravel scales as 1/ωL we see that singleatom emission per laser cycle scales as ω3L E3

(12)

1 ω3L 2 E [Eω L ]2/3

(13)

W S A () ∝ wi (E) in the plateau region or as W S A () ∝ wi (E)

at the cutoff. Thus, increasing the wavelength (decreasing the frequency) of the driving field will strongly reduce the efficiency of harmonic emission. Let us now turn to the coherent response of the medium. Macroscopic polarization P induced in the medium is P = NA d, where NA is the number density of neutral atoms and d is the induced atomic dipole (ionization, which is the integral part of recollision-induced emission, enters via d). The overall harmonic photon yield Fh in the medium scales as P2 and is proportional to Nh2 W (), where Nh ∝ N A L pm S is the total number of dipoles radiating in phase, with L pm ∝ λ /|n(ω L ) − n()| the phase matching length and S the focal area, n(ω) is the refractive index. For ionizing dilute gas the refractive index is n(ω) = 1 − ω2pl /2ω2 , where ω2pl ∝ Ne ∝ wi τ L ∝ wi ω−1 L Ncycles is the plasma frequency and Ne is the number density of free electrons produced by the laser pulse with duration τ L ∝ ω−1 L Ncycles . Keeping the number of cycles in the laser pulse (i.e. its relative bandwidth) constant at all wavelengths, we find that Nh scales as Nh ∝ Ncycles ω3L /wi . In the absence of any phase-matching scheme which could extend the coherent propagation length beyond Lpm , for the harmonic yield at frequency we get Fh ∝ Nh2 W S A () ∝

ω9L E L3 wi (E L )

(14)

At first glance, this result looks devastating for using mid-IR sources to generate high harmonics. Increasing the wavelength from 800 nm to, say, 2.4 µm while


keeping the laser intensity fixed will reduce the harmonic yield by factor 39 ≈ 2.105 . If we want to use mid-IR sources to push the 3Up cutoff into the KeV range, this is the price we will have to pay in the absence of phase-matching schemes. However, the situation is not nearly as grim as it might look at first glance. We should not forget exponential sensitivity of the ionization rate wi to the laser field strength EL . The rate wi stands in the denominator of Eq. (14). If we want to use mid-IR sources to routinely generate harmonics around 200 eV, we can significantly reduce intensity compared to I ∼ 1015 W/cm2 that is required when using Ti:Sapph laser. Reducing the intensity will dramatically reduce wi (EL ), reduce plasma dispersion associated with ionization and the generation of free electrons, and ultimately increase the total harmonic output from the medium due to improved propagation. Keeping the 3Up cutoff of the harmonic spectrum at the same energy, we can reduce the field strength as EMIR /ENIR = ωMIR /ωNIR . Using this relationship in Eq. (14), we see that the scaling becomes ω6 L /wi (EL ). Even if the ionization rate were given by the power law corresponding to n-photon ionization, wi ∼ EL 2n , for n > 3 the scaling would have been favourable with decreasing the laser frequency. In practice, ionization in MIR fields will proceed via optical tunnelling, which makes wi (EL ) even more nonlinear, suggesting that lower frequencies are better for harmonic generation! Of course, our estimate is not valid when plasma density is so low that the dispersion is dominated by neutral atoms. Thus, one should not extrapolate our result to very long wavelengths and very low plasma densities. To summarize the discussion, it appears that even in the absence of any phasematching schemes, one might benefit from using mid-IR radiation to produce harmonics in the few hundred eV window, which in the case of near-IR Ti:Sapph laser requires very high intensities and thus very high ionization rates. Generation of single attosecond pulses, as opposed to attosecond pulse trains, places two additional requirements onto the driving IR pulses. Firstly, the pulse should be very short – ideally, only one or two cycles long (Fig. 3). In this case the number of high-energy ionization/recollision events is minimized. Indeed, ionization rate is exponentially sensitive to the electric field strength which becomes sufficiently intense only a few times during the pulse. Secondly, the number of highest energy recollision events is also sensitive to the phase of the carrier oscillation relative to the envelope of the pulse – the socalled carrier-envelope phase, CEP. For cosine form, there is only one recollision event which produces the highest energy photons, as shown in Fig. 3. On the other hand, the sin-form of the pulse will result in two attosecond pulses. Thus, it is essential to control the CE phase. Stabilization of the CE phase, which is now routinely done for the Ti:Sapph laser, is a major building block of attosecond technology. Extension of IR-based attosecond technology into the range of 2–3 µm driving field will definitely benefit from CE phase stabilization. It will be a pre-requisite for the generation of single

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Figure 3. Schematic of a carrier-envelope (CE) phase stabilized pulse for two values of the CE phase, φ = 0 and φ = 90 degrees. The carrier wavelength in this schematic is 800 nm. Shaded elliptic areas show moments of ionization which result in the highest-energy recollision electrons. Corresponding recollision windows are shown with open elliptic areas. These are moments of time which correspond to high-energy attosecond bursts in emission of radiation.

Imaging zone

kL (trec)

Outgoing recollision electron

Ω

Incoming recollision

electron High-frequency emission

Figure 4. Strong-field imaging of parent molecule during recollision. Elastic scattering of the returning electron leads to diffraction which maps the structure of the scattering potential onto the angular distribution of the outgoing electron. Recombination of the electron maps the structure of the state it recombines to onto the spectrum of high-frequency emission.

attosecond pulses. As for the energy requirements, the key parameter for strongfield experiments is peak intensity. Once amplified and focused, mid-IR pulses should be able to deliver intensities in the range of mid-1013 W/cm2 to mid1014 W/cm2 , at the very least. This is the range of electric field strengths where highly nonlinear response of matter to few-cycle mid-IR pulses would take place. Application of IR radiation in the range of 2–3 µm should not only benefit the generation of ultrahigh harmonics in 100–200 eV range. It is also a very convenient wavelength for novel approaches to imaging molecular structures and dynamics with simultaneous sub-fsec temporal and sub-A spatial resolution. These approaches are based on using recollision electron. Let us briefly address this issue (Fig. 4).


As seen by parent atomic or molecular ion, recolliding electron creates an ultrashort electron pulse which lasts a fraction of the laser cycle. In a “singlecycle” driving pulse, the number of such recollision pulses is limited to one-two. As the electron pulse scatters of the molecule, its will diffract. Therefore, angle and energy-resolved spectra of the electrons produced during strong-field ionization will carry structural information: the snap-shot of the scattering potential taken by the ultrashort electron pulse [9]. With driving fields that last only onetwo cycles, it might be possible to recover structural information from angle- and energy-resolved electron spectra [9]. If, instead of elastic scattering (diffraction), the returning electron recombines into the ground state of the molecule, emitted high-frequency radiation will also carry structural information, this time reflecting the spatial structure of the bound state wavefunction [4–8]. Indeed, if we approximate the coordinate part of the continuum wavefunction of the electron returning with momentum kL (t) by the plane wave, the recombination matrix element Eq. (8) becomes a Fourier transform of the ground state wavefunction (up to the dipole operator). Harmonic emitted at frequency (t) = k L2 (t)/2+ I p is therefore related to the spatial Fourier transform of the bound state. Taken at all frequencies, harmonic spectrum contains sufficient structural information to reconstruct molecular orbitals [5]. Duration of the electron pulse – a fraction of the cycle of the driving IR field – determines temporal resolution of this measurement. Using 2–3 µm radiation does not compromise it significantly: nuclei in a molecule do not move much on a few-fsec time scale. On the other hand, spatial resolution is determined by the de Broglie wavelength of the recolliding electron. Increasing wavelength of the driving field increases maximum energy of the returning electron 3Up ; spatial √ resolution improves as λ D B ∝ 3U p ∝ λ L . Efficiency of the measurement is related to the probability of recollision, which decreases as 1/λ2L due to transverse spreading of the electron pulse between the moments of ionization and recollision. Selecting the appropriate wavelength of the driving field is a compromise between (i) spatial resolution on the one hand and (ii) temporal resolution and efficiency on the other hand. Compared to Ti:Sapph laser, strong field imaging experiments should benefit from using 2–3 µm radiation: order of magnitude loss in recollision efficiency is offset by factor three improvement in spatial resolution. Moreover, ionization in 2–3 µm spectral range is much more gentle, avoiding complications related to non-adiabatic multielectron excitation [11] which will strongly affect imaging. To summarize, we see important applications of mid-IR sources in attosecond technology and strong-field time and space-resolved imaging. For the generation of attosecond pulses (single or trains) in the range of few hundred eV, mid-IR sources might turn out even more efficient than Ti:Sapph laser. The key reason is very high intensity of the Ti:Sapph laser required to generate few hundred eV

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photons. High intensity leads to very fast ionization, and plasma dispersion in the nonlinear medium restricts efficiency of harmonic generation. Using midIR sources would allow one to significantly decrease plasma-related problems in generating high-energy radiation with compact table-top setup. M. Ivanov acknowledges fruitful discussions with I. Sorokina and E. Sorokin, and partial financial support of the Bessel prize of the A.von Humboldt foundation, NSERC SRO grant, and of the Max Planck Institute for Quantum Optics. References 1. E. Goulielmakis, M. Uiberacker, R. Kienberger, A. Baltuska, V. Yakovlev, A. Scrinzi, Th.Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, F. Krausz, Science 305, 1267 (2004) 2. R. Kienberger, E. Goulielmakis, M. Uiberacker, A. Baltuska, V. Yakovlev, F. Bammer, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, M. Drescher, F. Krausz, Nature, 427, 817 (2004). 3. M. Drescher, M. Hentschel, R. Kienberger, M. Uiberacker, V. Yakovlev, A. Scrinzi, Th. Westerwalbesloh, U. Kleineberg, U. Heinzmann, and F. Krausz, Nature, 419, 803 (2002) 4. M. Lein, N. Hay, R. Velotta, J. Marangos, and P. Knight, Phys. Rev. Lett., 88, 183903 (2002) 5. J. Itatani, J. Levesque, D. Zeidler, H. Niikura, H. Pepin, J. C. Kieffer, P. B. Corkum and D. M. Villeneuve, Nature, 432, 867 (2004) 6. T. Kanai, S. Minemoto and H. Sakai, Nature, 435, 470, (2005) 7. C. Vozzi, F. Calegari, E. Benedetti, J.-P. Caumes, G. Sansone, S. Stagira, M. Nisoli, R. Torres, E. Heesel, N. Kajumba, J. P. Marangos, C. Altucci and R. Velotta, Phys. Rev. Lett., 95, 153902, (2005) 8. S. Baker, J. S. Robinson, C. A. Haworth, H. Teng, R. A. Smith, C. C. Chirila, M. Lein, J. W. G. Tisch, and J. P. Marangos, Science, 312, 424 (2006) 9. M. Spanner, O. Smirnova, P. B. Corkum, and M. Yu. Ivanov, J. Phys. B, 37, L243 (2004) 10. M. Yu. Ivanov, T. Brabec, and N. H. Burnett, Phys. Rev. A., 54, 742 (1996) 11. M. Lezius, V. Blanchet, D. M. Rayner, D.M. Villeneuve, Albert Stolow, and M. Yu. Ivanov, Phys. Rev. Lett, 86, 51 (2001)

ULTRAWIDEBAND MID-INFRARED SPECTROSCOPY OF SEMICONDUCTOR NANOSTRUCTURES

∗ ¨ and KARL UNTERRAINER THOMAS MULLER Institute of Photonics & Center for Micro and Nanostructures, Vienna University of Technology, Gußhausstraße 27–29, 1040 Vienna, Austria

Abstract. We present time- and energy-resolved measurements of intraband absorption in GaAs/AlGaAs quantum wells and InAs/GaAs self-assembled quantum dots by means of midinfrared time-domain spectroscopy. Keywords: Infrared radiation; submillimetre wave generation; III-V semiconductors; quantum wells; quantum dots; carrier relaxation; quantum interference.

1. Introduction Since its first demonstration almost two decades ago, [1, 2] terahertz time-domain spectroscopy has become a well established technique for the investigation of semiconductor properties in the frequency range below ≈10 THz. [3] In recent years, the record bandwidth has been pushed to higher and higher frequencies, extending time-domain spectroscopy into the mid-infrared (mid-IR), i.e., in the frequency region between ≈10 and ≈100 THz. Frequency components beyond 120 THz have been observed with field resolved detection, advancing this technology toward the near-IR. [4] Important semiconductor properties, such as intraband transitions in nanostructures, lead to resonances in the mid-IR spectral regime, making mid-IR time-domain spectroscopy a powerful tool for the investigation of equilibrium and non-equilibrium properties of semiconductors. The purpose of this article is to review coherent mid-IR generation and detection schemes, and to present applications of mid-IR time-domain spectroscopy for the investigation of carrier dynamics in nanostructures. For equilibrium systems, the main application is the determination of the complex refractive index. In time-domain spectroscopy, the electric fields of femtosecond pulses of mid-IR radiation are measured after propagation through a sample and an identical length of free space. The time domain-data are converted to the frequency-domain by a numerical Fourier transform. By dividing the sample ∗ To whom correspondence should be addressed.


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Figure 1. Autocorrelation functions (a) and power spectra (b) of an ultrawideband mid-IR pulse before (dashed line) and after (solid line) transmission through a semiconductor QW.

spectrum by the reference spectrum it is possible to remove the system response of the experiment. This ratio gives the change in amplitude and phase of the midIR beam caused by the sample from which the complex refractive index can be determined. Figure 1(a) shows the interferometric autocorrelation of an ultrawideband mid-IR pulse generated by phasematched difference frequency mixing in a GaSe crystal (dashed line). The correlation function of the mid-IR pulse after transmission through a modulation-doped GaAs/AlGaAs quantum well (QW) sample is shown as solid line. The corresponding power spectra are shown in Figure 1(b). By dividing the sample spectrum (solid line) by the reference spectrum (dashed line) we obtain the transmission spectrum, shown in the inset (symbols). The same transmission spectrum is obtained by conventional Fourier transform spectroscopy using a black-body light source (solid line in the inset). The advantage of time-domain spectroscopy over Fourier transform spectroscopy, however, is that it can be combined with pulsed excitation for the investigation of non-equilibrium dynamics on sub-picosecond timescales. 2. Generation and detection of ultrawideband mid-infrared pulses 2.1. SOURCES OF ULTRAWIDEBAND MID-INFRARED PULSES

2.1.1. Optical rectification in second-order nonlinear materials If an optical pulse of complex amplitude E propagates in a second-order nonlinear crystal, the nonlinear polarization at the difference frequency ω is given by [5] (2) (2) E(ω )E ∗ (ω − ω)dω , (1) P (ω) = ε0 χ or, in the time-domain, P (2) (t) = ε0 χ (2) E(t)E ∗ (t),

(2)

ULTRAWIDEBAND MID-INFRARED SPECTROSCOPY

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Figure 2. Spectrum of the mid-IR emission from GaAs. The dashed line shows the calculated spectrum when using 15-fs Gaussian pulses and a pure non-resonant rectification process.

where χ (2) is the second-order susceptibility. Frequencies can be generated in the mid-IR domain only if in Equation (1) extreme spectral components within the single-pulse spectrum are sufficiently apart. This implies that the spectrum must extend over tens of THz, but as also seen from (2), all the spectral components have to be in phase. This can only be achieved by using femtosecond lasers pulses having less than ≈20 fs duration. Such pulses can be obtained from modelocked Ti:sapphire lasers. Figure 2 shows the emission spectrum obtained from 100-µm-thick [110] GaAs at normal incidence excitation. [5] The spectrum extends up to 50 THz (6 µm). The cut-off at 22 THz is due to the limited spectral response of the detector. The dashed line shows the calculated emission obtained from a pure non-resonant rectification process using a 15-fs incident pulse. The conversion efficiency is typically 2 × 10−7 . GaAs is an absorbing material at the pump wavelength (780 nm) and not phasematchable. Only the ≈1 µm absorption depth at the entrance interface contributes to the mid-IR signal. Since the GaAs bandgap is smaller than the energy of the pump photons, real carriers are generated which get accelerated in the surface depletion field. Under normal incidence, however, the emission from these carriers cannot be measured in the forward direction since no radiation is emitted along the current flow direction. Similar results are obtained for a GaSe crystal. The conversion efficiency is slightly higher (7 × 10−7 ). In contrast to GaAs, the incident optical spectrum is clearly below the bandgap of GaSe and therefore no real charges are created. However, in transparent media both the entrance and exit interface emit mid-IR pulses shifted in time, [6] which may be a drawback for applications. 2.1.2. Phasematched difference frequency mixing Since a sub-picosecond mid-IR pulse has a spatial length comparable to its center wavelength, it travels through a material at its phase-velocity. Therefore, for

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Figure 3. (a) Phasematched difference frequency mixing of 10-fs laser pulses. Mid-IR pulses are generated by mixing of spectral components within the ultrawide spectrum of the near-IR 10-fs laser pulse. (b) Polarization geometry and orientation of the GaSe crystal.

optimum conversion from near- to mid-IR wavelengths, one has to match the group-velocity of the visible pulse with the phase-velocity of the mid-IR pulse. This has been achieved in GaSe by Kaindl et al. [7,8] The concept is illustrated in Figure 3(a). Type-I phasematching is applied, which means that an ordinary wave with frequency ω and an extraordinary wave with frequency ω + ω are mixed to generate an ordinary wave with the difference frequency ω. Efficient energy conversation is achieved at frequencies where the phase mismatch k = c−1 n e (ω + ω, θ)(ω + ω) − n o (ω)ω − n o (ω)ω (3) is zero. Here, n o and n e are the frequency dependent indices of refraction of GaSe for the ordinary and the extraordinary wave, respectively. The incident beam propagates in the y-z-plane of the GaSe crystal, as shown in Figure 3(b). By rotating the crystal around the x-axis the phasematching angle θ is adjusted. The polarization of the input pulse is rotated such that the pulse provides both polarization components – ordinary and extraordinary – for a type-I process. In this way mid-IR pulses are generated via difference frequency mixing within the broad spectrum of a near-IR laser pulse. GaSe is chosen because of its strong nonlinearity and favorable transparency properties in the near- and mid-IR spectral range. Figure 4(a) shows mid-IR spectra for different phasematching angles θ. The spectra exhibit bandwidths in the order of 4–5 THz and demonstrate broad tunability with pulse durations between ≈100 and ≈200 fs. The conversion efficiency is about 100 times larger than that obtained from optical rectification. A key point in the generation of even shorter (sub-50-fs) mid-IR pulses is to apply extremely thin GaSe emitter crystals. [4, 9] In this way, the transparency range is enhanced and dispersion is minimized. In addition, reduction of the interaction length renders the phasematching condition less critical, resulting in broader spectra and shorter pulses. Figure 4(b) shows the electric field of a midIR transient emitted from the 30 µm-thick GaSe crystal. A pulse duration of only 36 fs is obtained. Fourier transform of the electric field gives the emission spectrum, presented in Figure 4(c).


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Figure 4. (a) Spectra of mid-IR pulses generated in 500-µm-thick GaSe at phasematching angles of θ = 55◦ (dotted line), 60◦ , 65◦ , and 70◦ (sold line). Electric field (b), and spectrum (c) of an ultrawideband mid-IR pulse emitted from a 30-µm-thick GaSe crystal.

Figure 5. Interferometric autocorrelation, as measured in the collinear (upper curve) and non-collinear (lower curve) configuration.

2.2. TIME-DOMAIN DETECTION OF MID-INFRARED PULSES

2.2.1. Interferometric correlation measurements Interferometric auto-correlation relies on the generation of two identical mid-IR pulses by use of a sequence of two near-IR laser pulses separated by a variable time delay τ . The interference signal recorded as a function of τ then provides the power spectrum through Fourier transform. Figure 5 shows the interference signal obtained when the output of a Michelson interferometer is focused onto a 500-µm GaSe crystal (upper curve). Although ringing with the expected mid-IR frequency appears in the wings, the signal exhibits high-frequency fringes near τ = 0. The failure of this collinear geometry setup occurs because the two near-IR pump pulses interact in the nonlinear crystal, yielding an additional term E X,τ (t) due to difference frequency mixing between the two incident beams. The total electric field radiated by the crystal then reads E(t) = E M I R (t)+ E M I R (t +τ )+ E X,τ (t). A method to eliminate the crossed term E X,τ (t) is to use the non-collinear configuration, [10] shown in the inset. In this scheme the two incident pulses generate mid-IR radiation propagating in directions k1 and k2 , respectively. In contrast, the crossed term propagates in

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directions k1 − k2 and k2 − k1 . As a consequence, the crossed term component is emitted under a certain angle which allows eliminating it geometrically. Because the diffraction-limited divergence is larger in the mid-IR, it is possible to make the two incident pulses non-collinear while having the two emitted mid-IR pulses nearly collinear. Interferometric cross-correlation allows a direct measurement of the electric field emitted from a mid-IR pulse source. [11, 12] For this purpose, the beam delivered by a femtosecond laser is divided into two parts. The first beam is focused on the sample to generate mid-IR pulses. The emission is then collected using a parabolic mirror and focused on a mid-IR detector. The other part of the laser beam is sent through a variable delay stage, and is then focused on a [110] GaAs sample, where the near-IR pulses undergo optical rectification. This results in the emission of quasi-single-cycle mid-IR pulses, whose spectrum accordingly covers a large part of the mid-IR spectral domain. Finally, the analysis beam interferes on the detector with the emission from the sample. The total mid-IR power falling on the integrating detector is given by S(τ ) = (E MIR (t) + E A (t + τ ))2 dt, (4) where E MIR and E A describe the electric fields at the detector from the unknown mid-IR pulse and the analysis pulse, and τ is the delay between the pulses. The term which varies with delay is the cross-correlation signal: X (τ ) = 2 E MIR (t)E A (t + τ )dt ∝ E MIR (τ ). (5) If the analysis pulse is much shorter than the unknown mid-IR pulse, the crosscorrelation signal (5) is proportional to the electric field of the mid-IR pulse. 2.2.2. Electrooptic sampling The electro-optic detection [3, 13–15] is based on the linear electro-optic effect (Pockels effect) and allows a direct measurement of the electric field emitted from a mid-IR pulse source. The electric mid-IR field strength modifies the refractive index ellipsoid of an electrooptic crystal (ZnTe, GaP). A linearly polarized probe beam co-propagates inside the crystal with the mid-IR beam, and its phase is modulated by the refractive index change induced by the electric field of the midIR pulse. This phase change is converted into an intensity change by a polarization analyzer. A pair of balanced detectors is used to suppress the common laser noise. The setup is shown in Figure 6(a). Apart from the dispersive propagation, absorption and the frequencydependent reflection of the mid-IR pulse, the electro-optic sampling trace will be additionally distorted as a result of phasematching effects. Using a sensor crystal


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Figure 6. (a) Electrooptic sampling setup (BS. . . beamsplitter, P. . . polarizer, WP. . . Wollaston prism, λ/4. . .quarter-waveplate). (b) Normalized frequency response of a ZnTe crystal [14].

with proper thickness is a crucial condition for the optimization of the mid-IR pulse detection. [14] Phasematching requires that [15] n(ωNIR ) + ωNIR ∂n/∂ω|ωNIR = n(ωMIR ),

(6)

which implies that the group velocity at the near-IR frequency should match the phase velocity at the mid-IR frequency. This can be understood in the way that the electro-optic sampling process is most efficient when the intensity profile of the optical pulse travels through the crystal at exactly the same speed as the electric field of the mid-IR pulse. When these velocities differ, the probe pulse averages over several oscillations of the mid-IR field, which leads to a strong reduction of the electro-optic signal. After the mid-IR wave and the optical pulse have copropagated through a sensor of thickness d, the resulting electro-optic modulation of the optical pulse induced by the mid-IR wave is proportional to d as well as the time average of the electric field across the group-velocity mismatch time δ(ω MIR ): [15] G(ωMIR ) =

exp [i2πωMIR δ(ωMIR ) − 1] , n(ωMIR ) + 1 i2πωMIR δ(ωMIR ) 2

(7)

G(ωMIR ) thus determines the frequency response function for the electro-optic crystal. As shown in Figure 6(b), a trade-off clearly exists between broadband response and long interaction length. 3. Intersubband carrier dynamics in quantum wells 3.1. INTERSUBBAND ELECTRON RELAXATION IN QUANTUM WELLS

3.1.1. Time-resolved intersubband absorption spectroscopy Time-resolved mid-IR spectroscopy is a powerful tool for the study of dynamical processes in semiconductor nanostructures because it offers an ultrafast probe on the energy scale of quantized transitions (≈100 meV). As a representative example we present measurements of the time-resolved intersubband (ISB) absorption

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Figure 7. (a) Energy band diagram of a double QW and (b) corresponding ISB absorption spectrum. (c) Schematic drawing of the sample geometry and pump/probe configuration.

in a double QW structure. [16] In this experiment an interband pump pulse injects electrons into the first and second subband of an undoped double QW with a |1 ↔ |2 level spacing smaller than the LO phonon energy. The time evolution of the electron population in these two subbands is monitored by probing the mid-IR ISB transitions to a third (empty) level, as shown in Figure 7(a). Ultrawideband mid-IR pulses are generated by phasematched difference frequency mixing in 30-µm-thick GaSe and detected by using an interferometric crosscorrelation setup. The resulting time-dependent ISB absorption spectrum, shown schematically in Figure 7(b), exhibits two absorption lines, corresponding to the |2 → |3 and |1 → |3 ISB transitions, respectively. On basis of the absorption spectra we determine the relaxation time between states |1 and |2. Figure 7(c) shows the experimental geometry. A mid-IR waveguide is used to enhance the ISB absorption. The near-infrared pump pulse excites the sample from the surface. 3.1.2. Intersubband absorption spectra – low excitation density Time-resolved ISB absorption spectra, recorded at an extremely low photo-excited sheet carrier density of n S = 1 × 1010 cm−2 , are shown in Figure 8. The spectra exhibit absorption peaks at energies of E 32 = 112 meV and E 31 = 126 meV, corresponding to the |2 → |3 and |1 → |3 ISB absorption, respectively. These values are in good agreement with the transition energies obtained by solving the single-particle Schrödinger equation in the envelope function formalism. The amplitude of the low-energy peak decreases with the time-delay after excitation due to ISB relaxation. The amplitude of the second peak, however, rises slightly in the beginning and afterwards decays due to carrier recombination. Since the spectrally integrated absorption |i → |3 (i = 1, 2) is directly proportional to the subband population Ni (t), it is possible to determine the population dynamics in the QW on the basis of the time-resolved ISB absorption spectra. About 40% of the photo-excited electrons are injected into the second subband, while the remaining 60% are injected into the first subband at higher k-value. The population in the second subband shows exponential decay. The electrons which relax down add to the population in the ground level. Subsequently, the population in the ground level drops because of carrier recombination. By fitting the results from


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Figure 8. ISB absorption spectra at different time delays after the pump pulse. The solid line in the inset shows the intensity spectrum of the mid-IR probe pulse generated by phase-matched difference frequency mixing in a 30-µm-thick GaSe crystal. 100 ps after excitation the data (symbols) can be fitted by a single Gaussian (dashed line).

Figure 9. (a) ISB absorption spectra at different time delays after the interband pump pulse for an excitation density of 3 × 1011 cm−2 . (b) Excitation density dependence of the ISB relaxation (symbols). The calculation (dashed line) confirms the experimental results.

a phenomenological rate-equation model to the experimental data, we deduce an ISB relaxation time of T21 = 14 ps and a recombination time of Tr ec ≈ 0.5 ns. 3.1.3. Intersubband absorption spectra – high excitation density At higher excitation densities ISB transitions reveal their collective nature. [17] Figure 9(a) shows absorption spectra taken at an excitation density of n S = 3 × 1011 cm−2 . Compared to the low excitation density spectra, shown in Figure 8, we find two differences: First, the |2 → |3 absorption decays much faster, and we extract an ISB relaxation time of only T21 = 5.9 ps. Second, we observe a spectral blue-shift of the |1 → |3 ISB absorption as the time evolves, i.e., as the electrons in the second subband relax into the QW ground level. Similar results have been obtained by Shtrichman et al. who measured the time-dependent ISB absorption

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in a rectangular QW after photo-excitation. [18] They observed a time-dependent shift of the |1 → |2 ISB resonance as the density of carriers decayed due to recombination. This was explained by a density functional model accounting for static and dynamic many-body effects. Although in our experiment the total sheet carrier density n S in the QW does not alter significantly during the relaxation, it is plausible that the redistribution of carriers in the two lowest subbands due to ISB relaxation can lead to energetic shifts of the ISB resonances. Qualitatively, these shifts can be understood as follows: The depolarization shift of a transition from subband |1 to |3, for example, is proportional to N1 , the population in the first subband. Thus, as the population in |1 increases, one would expect an energetic shift of the resonance to higher energy. Other many-body effects, such as exchange and correlation, will also contribute. A detailed analysis of the individual contributions of the different many-body corrections to the |1 → |3 ISB resonance E 31 with respect to the single-particle energy splitting shows that the blue-shift is manly due to the depolarization effect. The static Hartree term, which often dominates the many-body corrections in modulation-doped nanostructures, is minimized due to the presence of holes in the valence band. In Figure 9(b) we present the excitation density dependence of the ISB relaxation time T21 when varying the photo-excited sheet carrier density from n S = 1 × 1010 cm−2 to more than 1 × 1012 cm−2 . With increasing density we observe a significant shortening of the relaxation time. In the high density regime we observe a steep increase of T21 . In order to find the physical mechanism behind the ISB relaxation we will now discuss possible scattering mechanisms and compare numerical estimates of scattering times with the experimental results. Since the energy spacing between the two lowest subbands of our QW structure is smaller than the LO phonon energy, the electrons in the second subband do not possess sufficient energy to emit LO phonons and ISB relaxation can only be due to acoustic phonon emission and carrier-carrier scattering. Using the model described in Ref. [19] we calculated the acoustic phonon scattering time to be T21 ≈ 0.3 ns for our structure. This time is much too long to explain the experimental findings. Former time-resolved photoluminescence experiments [20] and calculations, [21] however, have shown that the ISB carrier-carrier scattering rates can be very high, almost approaching in some circumstances the ISB scattering rate due to LO phonon emission. We calculated the carrier-carrier scattering rates in the Born-approximation using static single subband screening within the random phase approximation. [22] In this calculation, Pauli-blocking of the final states was not taken into account. We find that the most prominent scattering processes are labeled 2211 and 2221, where ijfg describes an interaction, where an electron in subband |i scatters to | f under collision with a second electron, which scatters from | j to |g. When working out the total population transfer rate between the first and second subbands, both scattering processes and


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the number of electrons which are transferred by each process were taken into account: T21 = (2 · W2211 + W2221 )−1 . The result of this calculation is shown in Figure 9(b) as dashed line. At an excitation density of approximately 1×1012 cm−2 the Fermi-level in the ground state approaches the bottom of the second subband and the ISB relaxation drastically slows down due to Pauli-blocking. This is illustrated by the vertical dashed line. Although we cannot completely exclude the contribution of LO phonon scattering of hot electrons in the second subband of the QW to the relaxation, the strong dependence of the ISB relaxation time T21 on the carrier density and the good agreement with the calculation suggest that the main relaxation mechanism is carrier-carrier scattering. 3.2. QUANTUM INTERFERENCE OF INTERSUBBAND TRANSITIONS

The character of band gap transitions in semiconductors is determined by the joint-density of electrons and holes, causing step-function like absorption coefficients and very short dephasing times. In contrast to that, transitions between quantized states in low-dimensional semiconductors, such as QWs, exhibit Lorentzian absorption lines and the dephasing times are expected to increase with decreasing dimensionality. The atom-like character of these transitions allows translating the atomic concepts of quantum coherence and interference to the solid state. Rabi oscillations have been reported for ISB transitions in modulation-doped QWs. [23] Electromagnetically induced transparency has been observed in a ladder-type QW system, [24] and tunneling induced transparency has been reported for ISB transitions in coupled double QW structures. [25, 26] An inversion-less quantum cascade laser has also been proposed. [27] 3.2.1. Pulse-induced quantum interference The coupled QW, described above, is a very promising solid state system for observing interference phenomena since it resembles a typical Λ-system, which has been studied extensively in atomic quantum optics. A Λ-system is formed by an upper level |3 connected to lower levels |1 and |2 through interaction with an electromagnetic field. The physical reason for cancelling absorption in this system is the uncertainty in optical transitions |1 → |3 and |2 → |3 which can result in destructive interference between them. Since both of these transitions are directed to the same state |3, it is impossible to find out along which path, |1 → |3 or |2 → |3, such a transition is made. This situation is similar to Young’s double-slit problem, where interference is a consequence of uncertainty in determining through which of the two slits the photon passed. The absorption probability will be equal to the squared sum of the probability amplitudes corresponding to |1 → |3 and |2 → |3 transitions. When there is a correlation between these probability amplitudes, it will lead to an interference term which, under appropriate phase conditions, can make the total absorption probability

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equal to zero. However, for the observation of these effects it is necessary to establish coherence between the subbands. We will now discuss an experiment where coherence between the two lowest tunnel-split levels in a double QW is induced by an ultrashort interband laser pulse. [28] The experiment is divided in two steps: In a first step an interband pump pulse of sufficient bandwidth excites electrons into a coherent superposition of the |1 and |2 subband eigenstates. Subsequently, the eigenstates evolve at different rates, leading to a wavepacket oscillation described by the state vector |Ψ ∝ |1 + |2 exp(−iφ), where φ = E 21 t/h¯ , with E 21 being the level splitting. In a second step, after a delay time τ , an ultrashort mid-IR pulse probes the linear absorption from state |Ψ (τ ) to |3. Since the bandwidth of this pulse is larger than the energy splitting the field interacts with both the |1 → |3 and |2 ↔ |3 transitions. The states |1 and |2 are coherently excited and transitions to |3 will occur through two coherent paths, whose transition probability amplitudes can interfere. Depending on the phase φ, the absorption will periodically either be cancelled or enhanced, due to destructive or constructive interference between the contributions of the two levels. The periodicity can be associated with the energy difference E 21 . 3.2.2. Density matrix model Using the density-matrix formalism we will now show how a pulse-induced coherence between |1 and |2 can lead to suppression of ISB absorption in a QW -system. For such a coherent preparation the initial condition on the density matrix is ⎛ ⎞ ∗ ρ11 ρ21 0 ρ = ⎝ ρ21 ρ22 0 ⎠ , (8) 0 0 0 and the time evolution of the upper state coherences can be written ρ˙31 = − (iω31 + γ31 ) ρ31 + i31 ρ11 + i32 ρ21 , ∗ ρ˙32 = − (iω32 + γ32 ) ρ32 + i32 ρ22 + i31 ρ21 ,

(9)

where we have used the notation nm = µnm E(t)/h¯ (with µnm being the ISB dipole matrix element between states |n and |m) for the probe pulse envelope E(t) expressed as a Rabi frequency. γ31 and γ32 denote the total coherence relaxation d ph d ph rates, given by γnm = (γn + γm )/2 + γnm , where γnm is the dephasing rate of the coherence of the |n → |m transition and γn denotes the decay of the population in state |n. When the probe pulse arrives at time-delay τ , the populations ρ11 ∝ µ201 + µ202 [1 − exp(−t/T21 )] and ρ22 ∝ µ202 exp(−t/T21 ) and the oscillating coherence ρ21 = ρ˜21 exp(−iφ), where ρ˜21 ∝ µ01 µ02 exp(−γ21 t), have been given initial values by the pump pulse. The amount of electrons injected into the two subbands is about the same, so that initially ρ11 ≈ ρ22 (see above), and thus, we


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Figure 10. Temporal evolution of the ISB absorption (calculation). In the region between the absorption lines the spectra exhibit typical quantum interference features, i.e., reduced or enhanced absorption. Inset: Coupled double QW.

set µ01 = µ02 . The absorption will be time-dependent and we use a δ–like probe pulse to obtain the absorption spectrum at time-delay τ . From Equation (9) we calculate an expression for the time-dependent absorption spectrum given by the imaginary part of the linear susceptibility: γ31 31 2 Im(χ) ∝ 2 µ13 ρ11 + µ13 µ23 ρ˜21 cos φ − sin φ + 2 γ31 31 + γ31 32 γ32 2 µ cos φ + + 2 ρ + µ µ ρ ˜ sin φ . (10) 13 23 21 23 22 2 γ32 32 + γ32 31 = ω31 − ω and 32 = ω32 − ω are the energy detunings from the upper state. The absorption is made up of two contributions: The first corresponds to the intuitive understanding of a pump-probe experiment: the pump pulse creates populations which modify the transmission of the probe pulse at frequencies ω31 and ω32 . The second contribution is due to the |1 ↔ |2 coherence. Its impact on the absorption spectrum is twofold: First, it leads to a modulation of the absorption proportional to cos φ. This beating can also be observed in the integrated absorption or in terahertz emission experiments. [11] The second term, which is proportional to sin φ, does not contribute to the integrated absorption since it is anti-symmetric with respect to the detunings 31 and 32 . It leads to reduced (enhanced) absorption in between the lines at the expense of enhanced (reduced) absorption in the wings. The calculated time-resolved absorption spectrum for the sample described below is plotted in Figure 10. 3.2.3. Time-resolved intersubband absorption spectra Figure 11(a) shows the ISB absorption 1 ps after excitation. At that delay time the coherence between |1 and |2 is already damped out (ρ˜21 = 0) and according to

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Figure 11. (a) Measured (symbols) and calculated (solid line) ISB absorption spectrum recorded 1 ps after the pump. (b) 2D contour plot of the time-resolved absorption in the coherent regime. The experimental results are represented by grayscale; dashed lines represent the results of the calculation.

Equation (10) only the population term contributes to the absorption. We estimate the total density of photoexcited carriers to be n S ≈ 5 × 1010 cm−2 . The spectra clearly exhibit two Gaussian absorption peaks at energies of ≈ 114 meV and ≈ 130 meV, which we attribute to the |2 → |3 and |1 → |3 ISB transitions, with amplitudes being proportional to the diagonal elements ρ22 and ρ11 of the density operator. On a time-scale of several picoseconds the amplitude of the |2 → |3 absorption decreases due to ISB relaxation. At the same time the amplitude of the |1 → |3 transition rises since the electrons which relax down from subband |2 add to the carriers in the ground level |1. This behavior of the ISB absorption has already been discussed above. Now, we concentrate on the very early times after excitation where the relative phase of the excited states is not yet randomized (ρ˜21 = 0). Figure 11(b) shows a 2D plot of the time-resolved ISB absorption in the coherent regime. It exhibits two contributions: (i) a step-like increase of the absorption which rises within the time resolution of the experiment and shows either a slow decay (around ≈114 meV) or an increase (around ≈130 meV) at later times, and (ii) a superimposed oscillatory signal. As already discussed, the first signal represents the time-dependent electron population in the first and second subband after excitation. The oscillatory signal (ii) is due to quantum interference. The period of the oscillation is ≈250 fs which is consistent with the value obtained from the level splitting. Phase relaxation destroys the |1 ↔ |2 coherence and the photoexcited wave-packet decays into an incoherent subband population. Since the energy spacing between the two lowest subbands is smaller than the LO phonon energy, electron-electron and interface roughness scattering are the dominant dephasing


613

mechanisms. In addition, LO phonon emission by carriers in the high energy tail of the hot carrier distribution in the second subband contributes to the dephasing of the |1 ↔ |2 coherence. A dephasing time of ≈0.6 ps is extracted from the damping of the wave-packet oscillation. Furthermore, in the calculation we set γ31 = γ32 = 170 fs, corresponding to the dephasing time of the |1 ↔ |3 and |2 ↔ |3 transition. [11] Note, that transition energies to the third subband are larger than the LO phonon energy, leading to a fast dephasing of these coherences. Inhomogeneous broadening inh in QW structures is mainly determined by well-width fluctuations. It is taken into account by modeling the structure by an ensemble of independent -systems with a distribution of center frequencies ω31 and ω32 . The distribution function is chosen as a Gaussian (inh = 7 meV half width at half maximum) that reproduces the absorption profile at pump-probe delays >1 ps. Further evidence for the involvement of quantum coherence comes from the lineshape of the absorption spectrum. As it is evident from Equation (10), the coherence between state |1 and |2 not only modulates the strength of the ISB absorption, but it also changes its shape. In order to demonstrate that, we plot in Figure 12 normalized absorption spectra at pump-probe delays of 100 fs and 200 fs, corresponding to phase factors φ ≈ π/2 and φ ≈ 3π/2, respectively. Experimental curves are shown together with results obtained from the density matrix model. The experimental data (symbols) exhibit two transitions with either enhanced (a) or reduced (b) absorption in between the peaks. Such modifications of the absorption profile are typical for quantum interference. As shown in Figure 12 the model (solid line) shows exactly the same behavior and we find perfect agreement with the experimental points. The absorption profile cannot be fitted with two independent (non-interfering) absorption lines. In order to illustrate that, we plot in the same figures results obtained from our model when we set ρ˜21 = 0 (dashed line). It is obvious that in that case the calculation overestimates

Figure 12. Measured (symbols) and calculated (solid lines) ISB absorption spectra (normalized) at pump-probe delays of (a) 100 fs and (b) 200 fs. The absorption between the peaks is either reduced or enhanced due to quantum interference. The dashed lines denote calculated absorption spectra without taking the coherence between states 1 and 2 into account.

614


or underestimates the absorption (depending on φ) at energies between the peaks. For both time-delays the absorption between the two lines is changed by roughly 20% compared to the sum of the two non-interfering lines. 4. Intraband carrier dynamics in quantum dots 4.1. ELECTRONIC STATES AND OPTICAL INTRABAND TRANSITIONS

Optical transitions between confined states in the conduction band of InAs/GaAs quantum dots (QDs) can be observed in the mid-IR spectral regime. These transitions are referred to as intraband or intersublevel transitions, by analogy with ISB transitions in QWs. Figure 13 illustrates the two types of optical transitions in the conduction band (or valence band) of a QD: (a) transitions from the confined QD states to the two-dimensional wetting layer (WL) states or to the three-dimensional continuum originating from the surrounding GaAs matrix [29,30] – so-called intraband transitions, and (b) transitions between confined QD states [31] – so-called intersublevel transitions. Figure 14(a) shows room-temperature photoluminescence (PL) spectra of a QD sample, consisting of 30 layers of InAs QDs separated by 50 nm thick GaAs barriers. The dot density was estimated to be ≈ 2 × 1010 cm−2 per layer. At low excitation density (25 W/cm2 ) we observe two transitions corresponding to e1h1 luminescence at 1.081 eV and e2h2 luminescence at 1.137 eV. At higher excitation

Figure 13. Optical transitions within the conduction band of a QD: (a) intraband transitions, (b) intersublevel transitions. (c) QD density of states.

Figure 14. (a) PL spectra of a QD sample at room-temperature. (b) Photoinduced intraband absorption spectrum at T = 5 K.


615

(1 kW/cm2 ) the QD states are filled up and luminescence corresponding to the e3h3 transition at 1.194 eV is also observable, as well as luminescence at 1.333 eV from the underlying InAs WL. The inhomogeneous broadening of the transitions (≈50 meV full width at half maximum) mainly reflects the size distribution of the QDs. At T = 5 K the PL shifts by ≈90 meV towards higher energy which is due to the temperature-dependence of the GaAs and InAs bandgaps. The energy differences between the QD states, however, are not affected. From the PL we determine an energetic difference of 252 meV between the QD ground state e1h1 and the WL. Approximately two thirds of this energetic difference occur between the conduction band offsets. Thus, we estimate the intraband transition energy between the QD ground state e1 and the WL to be ≈160 meV. Accordingly, we expect intraband transitions from the excited states e2 and e3 to the WL at energies of ≈105 meV and ≈50 meV, respectively (the quantization energy of the holes can roughly be neglected due to their high effective mass). In addition to the PL spectrum, we recorded the photoinduced intraband midIR absorption spectrum of the QD sample at T = 5 K, whereby interband optical excitation was provided by a HeNe-laser. In order to enhance the intraband absorption signal, the sample was polished to form a single-pass waveguide for the mid-IR radiation. The observed intraband absorption, shown in Figure 14(b), is polarized in growth direction and it is maximum at ≈160 meV with an inhomogeneous broadening comparable to the PL linewidth. This value is in perfect agreement with the e1-WL transition energy deduced from the PL measurement and we conclude that the intraband transitions occur between the bound QD states and the WL. In addition to the intraband resonance we observe a monotonous absorption which increases towards low energy. This is attributed to absorption by free carriers in the substrate and barriers, which are not transferred into the QDs. The intraband absorption at probe energies of 160, 105 and 50 meV can be interpreted in terms of e1, e2, and e3 QD level electron populations, respectively. 4.2. ELECTRON CAPTURE AND RELAXATION IN QUANTUM DOTS

A drastic slow-down of the carrier relaxation in QDs compared to higherdimensional structures has been predicted because of the so-called phonon bottleneck effect. However, it has turned out that a number of scattering processes, including multi-phonon emission, [32, 33] electron-electron scattering [34] and electron-hole scattering, [35] can circumvent the phonon bottleneck, leading to capture and relaxation times from approximately one to several tens of picoseconds. Most of the experiments have been performed by using interband techniques, such as time-resolved PL and differential transmission spectroscopy, where the signal reflects the combined electron-hole dynamics. An interband pump – intraband mid-IR probe experiment, however, is sensitive to the capture and relaxation of electrons only. The pump excites electrons and

616


holes in the GaAs matrix surrounding the QDs, while the mid-IR probe is tuned into resonance with electronic intraband transitions between the bound QD states and continuum states in the WL. [36] For time-resolved probing of the intraband transitions a mode-locked Ti:sapphire laser that delivers 10-fs pulses centered at a wavelength of 780 nm is used. Half of the laser intensity serves as an interband pump to inject electrons and holes in the GaAs barriers. The other part is used to generate the linear polarized mid-IR probe pulses by phase-matched difference frequency mixing in a 500-µm-thick GaSe crystal. A double modulation technique is used in which the pump and probe beams are mechanically chopped at frequencies of 1.67 and 2 kHz, respectively, and lock-in detection is performed at the difference frequency. This allows eliminating the background signal arising from the mid-IR radiation which is generated by the pump pulse (for example on the surface of the sample) 4.2.1. Electron capture Figure 15 shows typical pump-probe signals (E pr = 155 meV, Ip = 25 W/cm2 ) at room-temperature when the probe is tuned into resonance with the e1-WL transition. Absorption signals measured at two different mid-IR probe beam polarizations are presented: When the probe is polarized perpendicular to the growth direction (s-polarization) we observe a step-like increase of the absorption, which rises within the time resolution of the experiment and decays within several hundred picoseconds. This signal is attributed to free-carrier absorption in the substrate and barriers and its decay to free-carrier recombination. In accordance with the Fourier spectrometer measurement the free-carrier absorption increases when the probe is tuned to lower energy. When the probe is polarized in growth direction (p-polarization) a slowly rising absorption superimposed on the free-carrier signal is observed. Relaxation and thermalization in the GaAs barriers and the InAs WL occur on a time scale

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