Undersea Fiber Communication Systems (Optics and Photonics)

UNDERSEA FIBER COMMUNICATION SYSTEMS OPTICS AND PHOTONICS (Formerly Quantum Electronics) EDITED BY PAUL L. KELLY Tu...

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UNDERSEA FIBER COMMUNICATION SYSTEMS

OPTICS AND PHOTONICS (Formerly Quantum Electronics)

EDITED BY

PAUL L. KELLY Tufts University Medford, Massachusetts IVAN P. KAMINOW Lucent Technologies Holmdel, New Jersey GOVIND P. AGRAWAL University of Rochester Rochester, New York

Recently Published Books in the Series: Jean-Claude Diels and Wolfgang Rudolph, Ultrashort Laser Pulse Phenomena: Fundamentals, Techniques, and Applications on a Femtosecond Time Scale Eli Kapon, editor, Semiconductor Lasers I: Fundamentals Eli Kapon, editor, Semiconductor Lasers II: Materials and Structures P. C. Becker, N. A. Olsson, and J. R. Simpson, Erbium-Doped Fiber Amplifiers: Fundamentals and Technology Raman Kashyap, Fiber Bragg Gratings Katsunari Okamoto, Fundamentals of Optical Waveguides Govind P. Agrawal, Nonlinear Fiber Optics, Third Edition Govind P. Agrawal, Applications of Nonlinear Fiber Optics Jose´ Chesnoy, Undersea Fiber Communication Systems

A complete list of titles in this series appears at the end of this volume.


Jose´ Chesnoy Alcatel Optics Group Nozay Cedex, France

Amsterdam

Boston

London New York Oxford Paris San Diego San Francisco Singapore Sydney Tokyo

This book is printed on acid-free paper. Copyright 2002, Elsevier Science (USA). All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Requests for permission to make copies of any part of the work should be mailed to: Permissions Department, Harcourt, Inc., 6277 Sea Harbor Drive, Orlando, Florida 32887-6777. ACADEMIC PRESS An imprint of Elsevier Science 525 B Street, Suite 1900, San Diego, California 92101-4495, USA http:==www.academicpress.com Academic Press 84 Theobolds Road, London WC1X 8RR, UK http:==www.academicpress.com Library of Congress Catalog Card Number: 2002100203 International Standard Book Number: 0-12-171408-X PRINTED IN THE UNITED STATES OF AMERICA 02 03 04 05 06 07 MB 9 8 7 6 5 4 3 2 1

CONTENTS

CONTRIBUTORS xv FOREWORD xxiii PREFACE xxv

I

INTRODUCTION 1 Introduction to Submarine Fiber Communication JOSE´ CHESNOY AND JEAN JERPAHAGNON

I. Introduction 3 II. Configuration of a Submarine Communication System III. The Advent of Terabit Optical Technology 6 A. The Birth of Optical Technology 6 B. The First Transoceanic Optical Systems 8 C. Optical Amplification 9 D. WDM Optical Systems 10 IV. Evolution of Submarine Systems in the 2000s 11 V. Objectives and Outline of the Book 11 References 13

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2 Historical Overview of Submarine Communication Systems GE´RARD FOUCHARD

I. Introduction 16 II. The Era of Telegraphy over Submarine Cables 17 A. The Early Age of the Electric Telegraph (1800–1850) 17 B. The British Era of Submarine Cable (1850–1872) 18 C. The Global Network (1872–1920) 22 D. Cable and Radio Competition (1920–1960) 25 E. Technical and Economical Aspects 26 III. The Era of Telephone on Coaxial Cables 30 A. The Earliest Telephonic Submarine Cable Trials 30 B. The First Generation of Coaxial Submarine Cable (1850–1961) 31 C. The Second Generation of Coaxial Submarine Cable (1960–1970) 32 D. Wideband Submarine Cables (1970–1988) 34 E. Technical and Economical Aspects 34 IV. The Era of Fiber Optic Submarine Cables 38 A. From Analog to Digital (1976–1988) 38 B. Regenerated Fiber Optic Cables and the Consortium Era (1986–1995) 39 C. Optical Amplification and WDM Technology (1995–2000) 44 D. Cable Ships and Offshore Works 45 V. Conclusion 47 References 47

II

SUBMARINE SYSTEM DESIGN 3 Basics of Digital Optical Communications PHILIPPE GALLION

I. Optical Channel and the Multiplexed Data 53 A. Optical Bandwidth 53 B. Optical Channel Capacity 53 C. Binary Optical Channel and the Symbol Probabilities 56 II. Modulation Formats and Modulation Bandwidth 57 A. Parameters to Be Modulated 57 B. Spectrum of Digitally Modulated Signals 58 C. Modulation Formats 61 D. Modulation Implementation 65 III. Signal and Noises at the Receiver 67 A. Photodetector Sensitivity and Optical-to-Electrical Signal Conversion 67 B. Noise Generation and Demonstration Mechanisms at the Receiver

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C. Noise Addition in Optical Amplification 74 D. Optical Signal-to-Noise Ratio 78 IV. Receiver Performance Evaluation 79 A. Electrical Signal-to-Noise Ratio Definition 79 B. Bit Error Ratio and Receiver Sensitivity Definitions 79 C. Shot-Noise-Limited Ideal Detection 83 D. Amplifier Less Thermal-Noise-Limited Detection 86 E. Detection of Preamplified Optical Signals 87 References 92

4 Optical Amplification DOMINIQUE BAYART

I. Introduction 96 II. EDFA Amplification Principles 97 A. Basic Principles 97 B. Dynamic Behavior 102 C. Noise Characteristics 104 D. Giles Parameters 107 III. Requirements for Submarine Systems 109 A. Noise Figure 109 B. Hydrogen Sensitivity 111 C. Power Consumption 111 D. Polarization-Dependent Loss 111 E. Polarization Mode Dispersion 112 F. Polarization-Dependent Gain 112 G. Comparison with Terrestrial Requirements 113 IV. Related Technology 115 V. Single-Channel EDFAs 117 A. Gain Peak Wavelength Determination 117 B. Parameters That Influence GPW 119 C. Self-Filtering Effect 119 D. Design Rules 122 E. Gain Compression and Pump Wavelength 123 F. Glass Composition 124 G. Signal-to-Noise Ratio 124 VI. Multichannel WDM EDFAs 126 A. Gain Bandwidth 126 B. Glass Composition 127 C. Gain Equalization 129 D. Equalization Technology 131 VII. EDFA Impairments 132 A. Polarization Effects 133 B. Spectral Hole Burning 133 C. Modeling of Spectral Hole Burning 135

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D. Other Limitations 136 VIII. Operation with L-Band EDFAs 138 A. System Performance 138 B. Field Implementation Issues 140 C. C þ L-Band Systems 140 IX. Implementation of Raman Amplification 142 A. Principle of Raman Amplification 142 B. Practical Implementation as Preamplification EDFAs C. All-Raman Amplified Submarine Links 145 X. Further Amplification Perspectives 147 References 148

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5 Ultra-Long-Haul Submarine Transmission OLIVIER GAUTHERON AND OMAR AIT SAB

I. Introduction 158 II. Key Features of Long-Haul Transmission Systems 158 A. A Technical Challenge: High Capacity per Optical Fiber 158 B. Optical Signal-to-Noise Ratio 160 C. Reduction of the Propagation Impairment 163 D. Submarine Line Terminal Equipment Features 166 E. Repeater Supervisory and Fiber Fault Localization 169 F. Q Budget and Typical Repeater Spacing 173 III. Gain Equalization 177 A. Power Preemphasis 177 B. Fixed-Gain Equalizer 180 C. Tunable Gain Equalizer 184 D. Impact of Nonoptimal Gain Equalization 186 IV. Chromatic Dispersion and Nonlinear Effects 188 A. Nonlinear Kerr-Type Effects 188 B. Stimulated Raman Scattering 191 C. Transmission Experiments 193 V. Forward Error Correcting Codes 200 A. Performance Requirement in Submarine Systems 200 B. Introduction to Forward Error Correction 201 C. Channel Model and Fundamental Limits 202 D. Practical Forward Error Correction Schemes in Submarine Transmission Systems 204 E. Reed–Solomon Codes 205 F. Concatenated Codes 206 G. Turbo Product Codes 208 H. Examples of FEC Scheme Performances for Submarine Transmission Systems 209 VI. Technology Evolution 210 A. Modulation Format 210

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B. C þ L-Band Erbium-Doped Fiber Amplifier 212 C. Transmission Systems with Distributed Raman Amplifiers D. 40-Gbps Wavelength-Division Multiplexed Transmission Experiments 219 VII. Conclusion 223 References 224

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6 Unrepeatered Transmission ERIC BRANDON AND J.-P. BLONDEL

I. II. III. IV. V.

VI.

VII. VIII. IX.

Introduction 229 Recent Developments 230 Applications 235 System Configurations 236 Unrepeatered System Technologies 237 A. Line Fiber 238 B. Postamplification 239 C. Preamplification 240 D. Raman Amplification 241 E. Remote Amplification 246 Limitations Induced by Nonlinear Effects 249 A. Stimulated Brillouin Scattering 249 B. Kerr Effect 250 C. Stimulated Raman Scattering 253 Power Budget Calculation 257 Main Laboratory Achievements 257 Installed Unrepeatered Systems 261 A. Deployed Unrepeatered Systems 261 B. Safety Aspects 264 References 265

7 Polarization Effects in Long-Haul Undersea Systems C. R. MENYUK, B. S. MARKS, I. T. LIMA, JR., J. ZWECK, Y. SUN, G. M. CARTER, AND D. WANG

I. Introduction 270 II. Propagation of Polarized Light in an Optical Fiber Transmission System 273 A. Fiber Propagation 273 B. Polarization Mode Dispersion 277 C. Polarization-Dependent Loss and Gain 282 D. Comments on Notation and Nomenclature 286

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III. Reduced Stokes Parameter Model 288 A. Model Formulation 288 B. Theoretical Validation 291 C. Experimental Validation 299 D. Applications to Transoceanic Systems References 304

301

8 Nonlinear Transmission Techniques and Solitons S. WABNITZ

I. Introduction 307 II. Nonlinear Pulse Propagation 308 A. Periodic Loss Averaging 310 B. Soliton Perturbation Theory 311 C. Soliton–Noise Interactions 313 D. Soliton 2-R Regeneration 314 E. Soliton–Soliton Interactions 316 F. Polarization Multiplexing 316 G. Soliton 3-R Regeneration 318 III. Dispersion-Managed Solitons 319 A. Variational Representation 320 B. Dispersion-Managed Soliton–Noise Interactions C. Dispersion-Managed Soliton Example 321 D. Self-Phase Modulation 322 E. Dispersion-Managed Soliton 2-R Regeneration F. Cross-Phase Modulation 326 G. Doubly Periodic Maps 327 H. Nonlinear Chirped Return-to-Zero Pulse 329 I. Dispersion-Managed Soliton 3-R Regeneration J. Dispersion-Managed Soliton Distributed Raman IV. Conclusions 336 References 337

III

SUBMARINE EQUIPMENT 9 Submerged Plant NEVILLE J. HAZELL AND CHRISTOPHER E. LITTLE

I. Overview of Submerged Plant 344 II. Repeaters 346 A. Optical Topology 346 B. Drive and Control Electronics 350 C. Supervisory Functionality 350

321

324

330 Amplification

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D. Power Unit and Protection 353 III. Equalizers 354 A. Passive Equalizers 355 B. Active Tilt Equalizers 355 IV. Branching Units 357 A. Full Fiber-Drop Branching Units 358 B. Wavelength Add=Drop Branching Units 359 C. Power Module 360 V. Mechanical Engineering of Submarine Equipment 363 A. Internal Design Aspects 364 B. External Aspects of Design 365 VI. Power-Feed Equipment for Submarine Equipment 366 A. Network Powering 367 B. High-Voltage Generation 369 C. Other Functions 369 VII. Reliability 370 A. Quality Control and Qualification 371 B. Reliability of Submerged Plant 372 C. Reliability of Power-Feed Equipment 373 VIII. Future Trends in Submarine Equipment 374 References 375

10 Terminal Equipment KATSUO SUZUKI

I. Introduction 377 II. Transmission Equipment for Wavelength-Division-Multiplexed Systems 380 A. Submarine Line Terminal Equipment for 2.5-Gbps WDM Systems 380 B. Submarine Line Terminal Equipment for 10-Gbps WDM Systems 385 III. Supervisory and Network Management Systems 397 A. Outline of Network Management System 397 B. Details of Submarine Element and Network Management 399 C. Integration with Terrestrial Systems 402 D. Standard Interface between EM and NM Layers 403 E. Implementation of the CORBA Interface 404 IV. View on Future Developments 407 A. Increasing the Number of Multiplexed Wavelengths 408 B. Increasing the Line Bit Rate 409 C. Downsizing of Equipment 409 V. Conclusion 410 References 410

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11 Network Architectures for Submarine Systems HOWARD KIDORF

I. Introduction 413 II. Application of Undersea Cable Systems in Global Networking 414 A. Domestic Networks 414 B. Regional Networks 416 C. Interregional Networks 416 III. Branching Units 416 IV. Protection Mechanisms: Linear and Ring 420 A. Reducing the Amount of Protection Equipment 424 V. Protection Mechanisms: Optical Cross-Connects and Mesh Protection 427 VI. Non-SDH=SONET Undersea Networking 430 VII. Future of Submarine Networks 432 References 433

12 Submarine Fiber SCOTT R. BICKHAM AND MICHAEL B. CAIN

I. Introduction 435 II. Optical Waveguide Fabrication and Theory 438 A. Fabrication 438 B. Waveguide Theory 440 III. Fiber Attributes 441 A. Attenuation and Bending 441 B. Cutoff Wavelength 443 C. Mode Field and Effective Area 444 D. Dispersion 445 E. Dispersion Compensation and Equivalent Effective Area 448 IV. Summary and Characteristics of Next-Generation Fibers 451 References 452

13 Cable Technology JEAN FRANC ¸ OIS LIBERT AND GARY WATERWORTH

I. Introduction 454 II. Cable Requirements 454 A. General Requirements 455 B. Pressure and Temperature Range 455 C. Water and Gaseous Ingress 456 D. Manufacturing and Installation Requirements

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III. Cable Characteristics 457 A. Cable Types 457 B. Mechanical Characteristics 461 C. Electrical Characteristics 466 IV. Cable Design 469 A. Optical Fiber 469 B. Optical Package 475 C. Inner Strength Member 479 D. Cable Insulation 482 E. Water Blocking 484 F. Armor Protection 484 G. Hydrogen Protection 486 V. Cable Qualification 488 A. Fiber Microbend Sensitivity Tests 488 B. Fiber Macrobend Sensitivity Tests 490 C. Optical Performance after Cable Manufacture 490 D. Fiber Sensitivity to Hydrogen 491 E. Thermal Tests to Simulate Cable Laying 491 F. Thermal Tests to Simulate Cable Storage 491 G. Radial Permeation of Cable Structures 492 H. Dry Thermal Test for Accelerated Aging 492 I. Long Length Tensile Test 492 VI. Conclusion 492 References 493

14 Marine and Maintenance (From Inception to the Grave) JOHN HORNE

I. Introduction 498 II. Choice of a Cable Route 498 A. Feasibility and Desktop Studies 499 B. Key Areas of the Desktop Study 500 III. Marine Survey and the Available Tools 502 A. Burial Assessment Survey 503 B. Surveys to Determine Water Depth and Sea Bottom Profile IV. Route Engineering 507 A. System Route Engineering 507 B. Slack Planning 507 C. Marine Installation Program 511 D. The Suppliers’ Manufacturing Program 511 V. Tools Used for Marine Installation and Repair 512 A. Cable Ships 512 B. Ploughs 514 C. Remotely Operated Vehicles 515

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VI.

VII. VIII. IX.

D. Autonomous Underwater Vehicles 517 E. Cable Grapnels 517 F. Software Tools 518 Marine Installation Activities 518 A. Cable-Loading Activities 521 B. Shore-End Landings 522 C. Surface Laying of Cable 525 D. Ploughed Lay 525 E. Cable and Pipeline Crossings 526 F. Cable Splices 527 G. Laying a Branching Unit 529 H. Postlay Inspection and Burial 530 I. Power-Feeding Safety 531 J. Bow Working 532 System Maintenance Capabilities and Cable Repair Operations A. Typical Surface-Laid Cable Repair Operation 535 Maintenance Support Facilities 538 The Grave 539 References 540 Index 541 List of Titles in Optics and Photonics Series Limited Warranty and Disclaimer of Liability

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CONTRIBUTORS

Omar Ait Sab (Chapter 5) was born in Casablanca, Morocco, in 1971. He received the Eng. degree in electronics and computer engineering from the Ecole Nationale d’Ingeńieur de Brest in 1993 and the Ph.D. degree from the University of Bretagne Occidentale, Brest, France, in 1998. He joined Alcatel in 1998 as a research engineer. He is currently with the System Design Department of Alcatel Optics where he is in charge of the design of enhanced forward error correction codes for DWDM transmission systems. His professional interests include channel coding and decoding algorithms, iterative decoding, turbo codes, joint source-channel coding, and optical transmission. Dominique Bayart (Chapter 4) was born in 1967 and graduated as a physics engineer from INPG, Grenoble, and from Grenoble University (Diplome d’Etudes Approfondies) in 1990. He joined Alcatel Research and Innovation (Marcoussis, France) in 1991 in the Optoelectronic Unit. In 1993, he moved to the Optical Systems Unit where he has designed successive generations of WDM amplifiers. In 1994, he became study leader, and in 1998 group leader for optical amplification. He is now deputy manager for the Transmission Unit as well. He has contributed to several world records for capacity in both submarine and terrestrial experiments. He has presented numerous papers at

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major conferences (OFC, ECOC, OAA, and LEOS) and has authored or coauthored nearly 70 technical papers and filed 25 patents. From 1998 to 2001, he has been a member of the technical program committee of the OSA Topical Meeting on Optical Amplifiers and Their Applications. He recently coauthored with E. Desurvire the book Erbium-Doped Fiber Amplifiers, Device and System Developments, Volume 2, and in 2001 received the Alcatel Distinguished Technical Staff Award. Scott R. Bickham (Chapter 12) was born in Las Vegas, New Mexico, in 1966. He received a B.S. in physics from Purdue University in 1988 and a Ph.D. in condensed matter physics from Cornell University in 1995. His dissertation work and subsequent postdoctoral appointments at the Naval Research Laboratory and Los Alamos National Laboratory focused on modeling nonlinear optical phenomena in crystalline and amorphous materials. In 1999, Dr. Bickham joined the fiber development group at Corning, Inc., in Sullivan Park, New York, and currently leads a team that models the characteristics, production, and performance of optical fibers. Jean-Pierre Blondel (Chapter 6) was born in 1965 in France. He graduated in 1989 from ENSTB, a French university specializing in telecommunications and related technologies. His first position was at an Alcatel research center from 1990 to 1993, where he worked on erbium optical amplification and the applications for submarine, terrestrial, and CATV systems. In 1993, he moved to the Alcatel division devoted to optical system implementation. Between 1993 and 1995, he worked on the design of 10-Gbps terrestrial systems and on the implementation of a submarine contract in the Asia Pacific region. Between 1995 and 2000, he was in charge of the system design of submarine unrepeatered systems. Since 2000, he has also been in charge of the optical design of terrestrial transmission and routing systems. He has authored or coauthored more than 15 patents and more than 30 communications or publications. Eric Brandon (Chapter 6) was born in Germany in 1967. He graduated from a French engineering school, where he specialized in applied optics and electronics. He jointed Alcatel in 1993 and was responsible for the development of a submarine line terminal transmitter. He was also involved in several unrepeatered transmission experiments that set world records. Since November 1995, he has worked in the System Design Department within Alcatel Submarine Networks and since May 2000, he has been in charge of the unrepeatered system design group. He has authored or coauthored more than 20 technical papers, mainly dealing with world transmission records, and presented some of them at several international conferences, including the OFC and ECOC. He has also authored or coauthored about 14 patents, some of which are already being implemented in transmission products. Michael B. Cain (Chapter 12) joined Corning, Inc., in 1986 as a senior development engineer in the Telecommunication Product Development

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group at Sullivan Park, New York. Currently, he is the technology manager for Corning’s Optical Fiber Division. He holds 14 patents in optical fiber and associated technology areas. Dr. Cain holds a bachelor’s degree in chemical engineering from the University of Wyoming, and he also received his doctorate in chemical engineering from the University of Wyoming in 1986. Jose´ Chesnoy (Volume Editor and Chapter 1) is presently head of the System Design and Technology Department in the Optics Group of Alcatel. He graduated from Ecole Polytechnique in 1977. After receiving a Ph.D. in 1981 on femtosecond laser physics, he entered the Centre National de la Recherche Scientifique. He joined Alcatel’s research organization in 1989 as head of the research unit on optical systems and fibers at the Alcatel Corporate Research Center. Since 1995, he has been head of System Development in the Submarine Business Division, which was extended to include the Terrestrial Network Division in 1999. During the course of his technical career, Dr. Chesnoy has been granted more than 50 patents in the field of fiber optics. Present responsibilities include the system definition of terrestrial and submarine fiber optics systems, from the design of transport network (optical transmission and routing) for the core and metro applications to the assessment of new technologies for these systems. Dr. Chesnoy was vice chair of the SubOptic 2001 international convention and has been nominated to be chair of the program committee for SubOptic 2004 planned for Monaco. Ge´rard Fouchard (Chapter 2) has been an active participant at the senior official level in the submarine cable story for the past 40 years. Early on, he was an onboard testing officer; a promoter of Atlantic, Mediterranean, and South AsiaIndian cable maintenance agreements from 1964 to 1974; and managed the submarine cable complex of La Seyne sur Mer from 1974 to 1984. Then, while with France Cables and Radio, he was closely associated with the implementation phases of major submarine systems such as Atlantis 1 and 2, Sea-Me-We 1, 2, and 3, SAFE, and SAT 2 and 3 from 1984 until 1998. He currently offers his expertise in the construction of fiber optic networks to the oil industry and scientific projects. Philippe Gallion (Chapter 3) received the Doctorat de Troisie`me Cycle from the University of Rheims in 1975 and the Doctorat d’Etat from the University of Montpellier in 1986. He joined the Ecole Nationale Supe´rieure des Te´lećommunications (Te´lećom Paris) in 1978 where he is currently a professor. He also currently lectures at several French and foreign institutions including the University Pierre et Marie Curie, the Ecole Supe´rieure d’Optique in Orsay, and the Ecole Polytechnique in Palaiseau. Dr. Gallion has made pioneering contributions in the areas of laser noise, injection locking, semiconductor laser modulation chirp and tuning, and optical communications systems. His present research topics includes theory, conception, modeling, and characterization of functional devices and their applications in advanced optical digital communication systems and networks. He is author or coauthor of more than

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150 technical papers and communications and he has acted as supervisor for more than 40 Ph.D. thesis students. He is a member of the Optical Society of America and a senior member of the Institute of Electrical and Electronics Engineers. He is chair of the IEEE Laser and Electro Optics Society French chapter. Olivier Gautheron (Chapter 5) was born in 1964 in France and graduated from the Ecole Polytechnique (1986) and Ecole Nationale Supe´rieure des Te´lećommunications de Paris (1988). He joined Alcatel in 1988 as a research engineer to study optical transmission systems including optical amplification, wavelength-division multiplexing, and coherent detection. Since 1994, he has been involved in the design of long-haul optical submarine transmissions and in 1998, his team reported on the first laboratory demonstration of a 32 10 Gbps transmission over more than 6000 km. Olivier Gautheron is currently heading the System Design Department where the potential of new technologies such as enhanced forward error correction codes, dispersion-managed fiber, 40-Gbps transmission, and Raman and L-band amplification are evaluated. Neville J. Hazell (Chapter 9) was born in Surrey, England, in 1957. He earned a B.A. degree in natural sciences, primarily in applied physics, from Churchill College, Cambridge University, England, in 1978. Until 1983 he worked in the area of development of optical fiber telecommunications in the national grid, including the commissioning of the first deployments of 8- and 34-Mbps PDH systems. Since 1983, he has worked on the development of all generations of optical submarine systems, at different times leading teams working on cable, SLTE, reliability, components, PFE, and submerged equipment. He was on the technical subcommittee of SubOptic 2001. Currently he is deputy technical director of product development at Alcatel Submarine Networks Ltd., United Kingdom, with responsibilities across all products developed for submarine networks. He is a Fellow of the IEE. John Horne (Chapter 14) has been involved in the development, planning, and implementation of submarine communications systems since 1969. In the 1980s he was responsible for fiber optic development activities at British Telecom Research Laboratories, Martlesham Heath, which supported the introduction of BT’s first optical fiber submarine systems. He was also responsible for managing the major international transmission centers at the heart of BT’s digital transmission network. He left BT in 1996 and has since worked as a consultant. At SubOptic 2001, the premier convention for the industry, he was vice-chair of the Papers Committee responsible for organizing the session titled Cable Installation and Repair. Jean Jerpahagnon (Chapter 1) was born in 1936. He graduated from Ecole Polytechnique (Paris) with a Ph.D. in physics. Dr. Jerpahagnon is presently Chairman of the Board of the French Network for Research in Telecommu-

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nications, Chairman of the Board of Optics Valley (France), and a member of the Management Committee of the SubOptic conference. With a background in solid-state physics, quantum electronics, and nonlinear optics, he has been in charge of research and development programs on optical systems and components successively at Bell Laboratories, France Telecom, and Alcatel. As the technical director of the Transmission Department of Alcatel, he has been in charge of the definition and development of several transoceanic optical systems, TAT 9 and TAT12/13 in particular. Howard Kidorf (Chapter 11) is director of the Services Engineering Division at Tyco Telecommunications in Eatontown, New Jersey. After joining AT&T Bell Laboratories in 1984, he spent his career in the field of undersea optical communications. His first responsibilities were toward the design and manufacture of 280- and 560-Mbps regenerative undersea repeaters. Since then, he has been responsible for the design of Tyco Telecommunications’ optically amplified repeater and the development of large-scale test facilities to investigate high-capacity DWDM technologies. In his recent research activities, Mr. Kidorf has been investigating wideband optical amplifier technology, Raman amplifiers, and advanced error correction codes. Currently, Mr. Kidorf has the responsibility to develop services for the Tyco Global Network. He has a B.S.E.E degree from Rutgers University and an M.S.E.E degree from Rensselaer Polytechnic Institute in Troy, New York. Jean-François Libert (Chapter 13) received his engineering degree from Hautes Etudes Industrielles of Lille (France). He joined Alcatel in 1984 where he was involved in the development of optical submarine cable designs and new technologies for cable and joint manufacturing process and metrology. He then held the position of technical directorate manager and of cable competence center manager for the Optical Submarine Cable division. Currently, his principal work is on advanced materials and cables and on cable transmission for submarine application. Ivan T. Lima, Jr. (Chapter 7) was born in Juazeiro-BA, Brazil, in October 1971. He received the B.S. degree from the Federal University of Bahia, SalvadorBA, and the M.S. degree with thesis from the State University of Campinas, Campinas-SP, Brazil, both in electrical engineering. He worked at Banco do Brasil (Bank of Brazil) for nine years, where he was an information technology specialist. He is currently a research assistant and Ph.D. candidate in electrical engineering at the University of Maryland, Baltimore County. Christopher E. Little (Chapter 9) was born in Tauranga, New Zealand, in 1960. He earned B.Sc. (Hons. I) and Ph.D. degrees in laser physics from Macquarie University, Sydney, Australia, in 1984 and 1987, respectively. In 1988, he was a physics lecturer at Macquarie University, and in 1990–1999 was a lecturer and then a reader in physics at St. Andrews University, Scotland, leading teams working on high-power lasers, plasma physics, pulsed power, and develop-

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ment of the world’s most efficient high-power visible laser. He has published more than 90 papers on related topics in journals and conference proceedings, edited two books on laser physics, and written a third titled Metal Vapour Lasers—Physics, Engineering and Applications (1999). He has been on the organizing committees of many international conferences, and in 1995 organized the first international conference on metal vapor lasers, sponsored by NATO. Currently he is manager of product reliability at Alcatel Submarine Networks Ltd., United Kingdom, and works on submerged product development. Brian S. Marks (Chapter 7) was born September 29, 1973. He received B.S. degrees in mathematics and physics from North Carolina State University in 1995 and a Ph.D. in applied mathematics from Northwestern University in 2000. Currently, he is a research associate in the Photonics Research Group of the Computer Science and Electrical Engineering Department, University of Maryland, Baltimore County, as well as the Laboratory for Physical Sciences at University of Maryland, College Park. His research interests include fiber optic polarization effects, nonlinear wave propagation, and numerical solution of partial differential equations. He is a member of SIAM, OSA, and IEEE. Curtis R. Menyuk (Chapter 7) was born in 1954. He is currently a professor in the Computer Science and Electrical Engineering Department at the University of Maryland, Baltimore County (UMBC), and is chief scientist at PhotonEx Corporation. For the last 15 years, his primary research area has been theoretical and computational studies of fiber optic communications. The equations and algorithms that he and his research group at UMBC have developed to model optical fiber transmission systems are used widely in the telecommunications industry. He is a member of SIAM and the American Physical Society, and he is a fellow of the Optical Society of America and the IEEE. He is a former UMBC Presidential Research Professor. Yu Sun (Chapter 7) received the B.S. degree from the University of Electronic Science and Technology of China and the M.S. degree from the Institute of Semiconductors, Chinese Academy of Sciences. She joined the department of computer science and electrical engineering, University of Maryland, Baltimore County, in 1997 and has since been engaged in research on polarization effects in high-bit-rate recirculating loop systems. Yu Sun is a member of the Optical Society of America and the IEEE/LEOS. Katsuo Suzuki (Chapter 10) joined Fujitsu Limited, Kawasaki, Japan, in 1971 and graduated from Fujitsu Technical College, Kawasaki, Japan, in 1979. He has been engaged in the development of optical submarine line terminal equipment and its management system for 280-Mbps, 560-Mbps, 1.8-Gbps, and DWDM submarine communication systems. He has also been engaged in the system engineering for a number of submarine communication projects. He is currently a manager in the System Engineering Department of Fujitsu’s Submarine Telecommunications Division.

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Stefan Wabnitz (Chapter 8) received a laurea degree in electronics engineering from the University of Rome in 1982, a M.S. degree in electrical engineering from Caltech in 1983, and a Ph.D. in applied electromagnetism from the Italian Ministry of Education in 1988. From 1984 until 1996 he was a member of the research staff at the Optical Communications Department of the Ugo Bordoni Foundation in Rome, Italy, working on the theory and applications of nonlinear optical devices and fibers. In 1996 he received a physics professorship from the University of Bourgogne in Dijon, France, and joined their nonlinear fiber optics research team. In 1999 he took a leave of absence from the university to join the Alcatel Optical Communications Research Department in Marcoussis, where he worked on implementations of the optical soliton theory to all-optical communication systems. In March 2001 he moved to the photonics department of Xtera Communications in Allen, Texas, to carry out research and development of novel long-haul optical communication systems based on Raman amplification. Gary Waterworth (Chapter 13) was born in London in 1960. He was employed by STC Submarine Systems Limited at Greenwich, London, in 1979, working in the Marine, Equipment, Cable, and Jointing Departments, before moving to project management. In 1988 he started work on the first 1550-nm regenerative repeater and branching unit designs. He led the engineering team to introduce the first optically amplified repeaters into manufacture in 1993 for Northern Telecom before developing the first WDM repeaters and branching units for Alcatel Submarine Networks. He managed the engineering interface between Alcatel and co-contractors including Tyco, NEC, Fujitsu, Hitachi, and Pirelli before moving on to manage tenders for submarine cable in Calais, France, in 1998. Mr. Waterworth is now a senior manager in Alcatel’s Product Development Division in Greenwich. He obtained a First Class Honors Degree in metallurgy and materials in 1986 and is a chartered engineer and a member of the Institute of Mechanical Engineers. John Zweck (Chapter 7) has a Ph.D. in mathematics from Rice University (1993). He has performed research in differential geometry, human and computer vision, and optical communications. He is currently a member of the Optical Fiber Communications Laboratory in the Department of Computer Science and Electrical Engineering at the University of Maryland, Baltimore County.

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FOREWORD

Following a period of extraordinary growth and technological progress over the course of the last 10 years, the submarine networking industry appears to be ‘‘taking a break’’ before entering into what promises to be a new era of development. This provides a fortuitous opportunity to put into perspective the many milestones this industry has achieved since its rebirth with the laying of the first transoceanic optical system in 1988, primarily by focusing on the technological developments that have proven necessary to help people communicate and by attempting to portray the future of submarine networks. These are the main objectives and, I believe, the great achievements of this book. Offering a unique perspective and full coverage of technical and nontechnical aspects of the optical submarine technology world, this work has only been made possible thanks to the invaluable involvement of representatives from all of the industry leaders. I want to convey my deep appreciation to all the contributors who have spent considerable time and effort contributing their most comprehensive—and comprehensible—articles on these topics. This oeuvre is intended to generate interest among various audiences. To telecom carriers and service providers, it offers a complete overview of a submarine network project, from system design to network elements and architecture, highlighting the interactions among the different players. To stu-

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dents, who will follow in our footsteps in the years to come, it reveals the magic of submarine networks. To paraphrase the Beatles, I would write that we all live in a yellow submarine which takes us on a magical mystery tour. Indeed, each day in submarine networks is a day of discovery. In addition, this book is aimed at helping those looking toward the future to foresee new directions in submarine network development. In my opinion, submarine technological breakthroughs will go beyond increasing the number of wavelengths per fiber and the bit rate on each fiber. Tomorrow we will be moving toward intelligent submarine networking, allowing carriers to dynamically allocate their bandwidth thanks to distributed intelligence along submarine pipes. These superhighways will prevent Internet traffic jams by adding lanes when necessary on the busiest routes. Furthermore, it appears likely that global infrastructures, providing city-to-city interconnections, will become the privileged choice as the convergence between terrestrial and submarine optical technologies intensifies. The value of this volume is that it opens our minds to what the future can bring to submarine networks with a specific view on the convergence of submarine and terrestrial optical technologies. Optics is the only technology able to serve the development of advanced telecom applications around the world—including the Seven Seas. I sincerely hope you will enjoy this book as much as I have. Christian Reinaudo President, Alcatel’s Optics Group

PREFACE

During the 1990s, the international telecommunication network was completely renewed, owing to a large extent to networking via undersea fiber cables. The Information Superhighway is based on this submarine backbone. This unprecedented decade of progress was driven by successive technology breakthroughs in the areas of optical fibers, optical amplification, and wavelength-division multiplexing. More than 50 million digital phone channels can now be bridged through a single cable across the Atlantic or Pacific Ocean—what a difference when compared to the first transatlantic telegraph cable, which could transmit one single word per minute in 1858! The technology of undersea communication systems is reaching a plateau, as has happened several times already in its history. After the SubOptic 2001 international conference in Kyoto, the time was deemed right to prepare a reference book on the technical area of undersea fiber communication systems. So this book’s goal is to cover in depth all aspects of this domain, from fiber and cable design to optical amplified system technology, as well as provide a global view of the historical and operational aspects of the undersea telecommunication system. We expect that this book will be useful not only to experienced engineers, but also to newcomers to the field and to operators who want both a good

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understanding of and a global view of the field. The technical funding of submarine optical systems has also become the basis of all terrestrial fiber systems. This book will thus be useful to students in all fields of optical communication technologies. The different chapters were prepared by an international high-level group of authors from leading companies and universities. They are the owners of this successful achievement and I am grateful to them for their fruitful efforts. I hope that this book will soon become a technical reference and useful tool for readers that will permit them to gain a good understanding of the present and future evolutions of high-capacity fiber communication systems. Jose´ Chesnoy


PART

I

INTRODUCTION


1 INTRODUCTION TO SUBMARINE FIBER COMMUNICATION JOSE´ CHESNOY Alcatel Optics Group, Nozay Cedex, France

JEAN JERPAHAGNON Optics Valley, Palaiseau, France

I. INTRODUCTION II. CONFIGURATION OF A SUBMARINE COMMUNICATION SYSTEM III. THE ADVENT OF TERABIT OPTICAL TECHNOLOGY A. The Birth of Optical Technology B. The First Transoceanic Optical Systems C. Optical Amplification D. WDM Optical Systems IV. EVOLUTION OF SUBMARINE SYSTEMS IN THE 2000s V. OBJECTIVES AND OUTLINE OF THE BOOK References

I. INTRODUCTION The laying of the first transoceanic communication cables was a big event in the second half of the 19th century. It was seen as the conquest of the deep sea and as a tremendous spanning of the distances between continents and was considered to be on the same level of importance as the space adventure in the second half of the 20th century. After this heroic period, submarine cables evolved slowly in the background, and people have not generally realized that the past 10 years have seen a complete revolution of the communication backbone with the introduction of fiber optics in submarine cables: In fewer than 10 years, the capacity per cable increased by a factor exceeding 10,000, leading to the possible transmission of more than 100 million simultaneous phone calls across the ocean. No other Undersea Fiber Communication Systems Copyright 2002, Elsevier Science (USA). All rights reserved.

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technology can now compete with submarine cables, which have acquired a monopolistic position in the voice and data international communication backbone. Figure 1 illustrates how this optical generation has led to a dramatic leap in the capacity carried per cable compared with that which evolved through three successive technologies since the laying of the first cable across the Atlantic in 1858. The roots of optical communication systems are two major inventions: the laser (1960) and the optical fiber concept (1964–1966). These two inventions play about the same role for optics as the invention in 1949 of the bipolar transistor played for microelectronics. The birth date of optical communication systems is 1970 with the demonstration, within a few months, of the first continuous-wave operation, at room temperature, of a gallium arsenide (GaAs)-based laser on one hand, and of the possibility of obtaining very low loss (20 dB=km around 850 nm) silica optical fiber on the other hand. The ‘‘miracle’’ was that the so-called silica first transmission window matched the wavelength of the GaAs laser. The technology then evolved through several steps: single-mode fiber; second and then third windows (1300 and 1500 nm), where the attenuation of silica fibers is optimum (0.2 dB=km at 1500 nm); optical amplification by rare earth to replace electronic regeneration; and finally wavelength division multiplexing (WDM) to carry multiple wavelengths (presently more than 100), each carrying a different data stream on a single-mode fiber.

FIGURE 1 Evolution of cable capacity across the ages. The dramatic growth of cable capacity for optical cable is illustrated by three systems: the TAT8 optical regenerated system, the TAT12=13 optically amplified system, and the Apollo DWDM amplified system.

1. INTRODUCTION TO SUBMARINE FIBER COMMUNICATION

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II. CONFIGURATION OF A SUBMARINE COMMUNICATION SYSTEM The configuration of a submarine system appears to have changed little since the establishment of the industry, but in fact the WDM fiber technology that is used has led to a full, in-depth revolution. Figure 2 gives a general view of the main equipment involved. The cable is composed of an optical core protecting the optical fibers, surrounded by a copper conductor to power-feed the submerged equipment from the shore and an insulator to isolate the workings from the sea. The mechanical strength is achieved by steel wires, with important additional wire layers in shallow waters, where the cable can be subjected to external aggressions from anchors or fishing activity. The optical fiber itself is a key element, optimized to be fully adaptable to the latest transmission capacity. The repeaters are units that regenerate the optical signals, after attenuation by propagation through each span, at regular positions along the cable, around 50 km apart from each other. The repeaters currently contain optical amplifiers based on laser amplification through a doped fiber pumped optically by semiconductor laser pumps fed electrically by the cable. Optical equalizing equipment is also inserted regularly to control the optical spectral response of the system. Because of the leaps forward in optical amplification technology, the evolution has been toward more optical bandwidth and more amplifiers per repeater to support a larger number of fibers. The branching units are submerged equipment that permit connections between more than two points, that is, double landing to different locations

FIGURE 2

Configuration of a submarine system.

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on the coast or distribution of part of the traffic to a secondary landing point. Branching units are complex pieces of equipment not only at the optical level but also at the electrical level since they are key elements for powering reconfiguration. All submerged equipment is designed for extreme conditions of depth, up to 8000 m (that means 800 atmospheres of pressure) and corrosion resistance. Reliability qualification testing is performed to ensure a lifetime of 25 years with practically no ship repairs for internal faults. The cable usually lands on a beach and the fibers arrive in a cable station with:

Power-feed equipment that electrically feeds all the active submerged equipment, especially the repeaters. Terminal transmission equipment that emits the laser light modulated by the communication signal and receives from the receive fiber the communication signal arriving from the other continent. The transmitter operates by means of the modulation of a high-quality colored semiconductor laser whose output is combined (multiplexed) through the transmission fiber. The optical light is modulated on and off to constitute the bits of information. The receiver contains semiconductor detectors for each received wavelength after demultiplexing. The information bits are thus reconstructed and feed the terrestrial communication backbone. A network management system that allows the operator to monitor the systems through a computer by getting the status information and the alarms in case of failure. It is also a configuration tool for the system throughout its life.

In the cable station, the submarine system is connected to the terrestrial network, and the information flow is distributed to the different terrestrial communication nodes down to the end customer.

III. THE ADVENT OF TERABIT OPTICAL TECHNOLOGY A. The Birth of Optical Technology Right from the start of the laser era, it was obvious that this new invention would induce drastic changes in the telecommunications world. The first idea had been to use free-space propagation either in the visible (ruby and helium–neon) or in the middle infrared (carbon dioxide), but the limitations due to atmosphere perturbations (fog, rain, etc.) rapidly became clear and the applications of the free-space concept have been restricted to only a few niches (short-distance communications, for instance, interbuilding links or communications between satellites).


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The breakthrough came from a change in the material choice and the ability to produce optical silica fibers that guided the light by total internal reflection. Instead of using traditional glass techniques, chemical vapor deposition methods, which were already used for semiconductors, were introduced. This enabled Corning in 1970 to produce a fiber with an absorption loss as low as 20 dB=km around 850 nm [1]. Further improvements in the technique by 1972 resulted in losses of about 4 dB=km for the so-called ‘‘first window’’ (see Fig. 3). Semiconductor lasers are very attractive provided they can be operated in a continuous-wave mode at room temperature. Because silicon and germanium are inadequate (indirect bandgap materials do not allow laser action), the work has been concentrated on III–V compounds and particularly on GaAs because the work on it was more mature. The first demonstration of a laser action in GaAs was made in 1962: It was in a pulsed operation at liquid helium temperature (4 K), far away from the required conditions. The laser was a p–n junction with direct polarization, and because of the intrinsic properties of the bulk material (variation with temperature of the minority carrier’s diffusion length), there was no hope of significant improvement in the laser characteristics. To overcome this basic physical limitation, the idea has been to use gallium arsenide=gallium aluminum arsenide (GaAs=GaAlAs) heterostructures to spatially confine the minority carriers. This has been very successful and the first laser action continuous wave at room temperature was obtained at Bell Laboratories in 1970 [2]. The match between the lasing wavelength and the silica first window was pure coincidence. The basic conditions for testing optical fiber telecommunication systems were fulfilled. To simplify the fiber splicing and connecting of components (emitter to receiver), multimode fibers (core diameter of 50 or 62.5 mm, enabling multitransverse modes of operation) were chosen. Testbeds for about 10-km links

FIGURE 3 Optical windows in optical fiber systems.

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at 34 or 45 Mbps were realized in the second half of the 1970s, followed by the first mid-distance repeaterless industrial systems in the early 1980s.

B. The First Transoceanic Optical Systems Rapid progress was made in splicing and connecting techniques, showing that in contrast with what was felt at the start, the use of single-mode fibers (with a core diameter of a few micrometers) was the more promising challenge to face. In addition, further progress in fiber manufacturing (mainly through better material purification) led to evidence of the second window around 1300 nm, with an attenuation of about 0.4 dB=km (see Fig. 3). Moreover, the bulk silica chromatic dispersion vanishes close to 1300 nm; it was therefore possible to propagate high-bit-rate pulses with minimum pulse broadening. In view of these results, the submarine industry and operators dared to decide to build the TAT8 (transatlantic) system by pioneering the use of 1300-nm singlemode techniques at 280 Mbps [3]. This decision demanded the solution of a number of technical problems, from connectors to branching units. The most severe challenge was the repeater, with the need to make an optical=electrical conversion, then to electrically regenerate the signal, and finally to make an electric=optical conversion. Two key points needed to be addressed: 1. Electronic circuits at 280 Mbps with good reliability were needed. This was achieved without too much effort. 2. The emitters and receivers inside the repeater needed to be reliable and have a long lifetime. Note that to emit and receive at 1300 nm, the GaAlAs compounds were no longer adequate. One has to deal with the quaternary alloys of gallium indium arsenic phosphor (GaInAsP), which have the advantage of allowing the tailoring of the emission and reception wavelengths as a function of the alloy composition. An extensive research and development program was undertaken over several years by the system providers, leading to the successful installation and start of operation of TAT8 at the end of 1987, quickly followed by TPC3 (transpacific link) with the same technology. In the meantime, the minimum absorption of silica fibers was shown to be 0.2 dB=km [4] with a relatively small chromatic dispersion still at 1550 nm—the third window—a wavelength range compatible with the GaInAsP technology. As a consequence, the TAT9 and TPC5 systems were installed and operated in late 1989 at 560 Mbps per fiber. TAT9 had a ‘‘Y’’ configuration, with one end in the United States and two ends in Europe (Great Britain and France). The branching unit was an undersea ‘‘active’’ multiplexer, allowing for adjustable bitrate allocation between Great Britain and France, a unique feature that was not reproduced later.


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C. Optical Amplification When completing the development and industrialization of the 560-Mbps system, most players were thinking in a very naive way that the newly developed system would cope with the needs for some time and, consequently, it was not urgent to think about a new higher performance system. It soon became obvious that a 2.5Gbps system was needed, in agreement with the synchronous digital hierarchy (SDH) scheme, to meet the demand for increasing traffic. So the question was, should we go on with the traditional repeatered system concept or should we jump into the newly emphasized optical amplification approach? Traditional regeneration solutions had in their favor the ‘‘known technology’’ argument, with limited problems on availability of the 2.5-Gbps circuits with the required reliability. A system (CANTAT3) was developed along these lines and installed by STC, but it was only a ‘‘one-shot action.’’ The second possibility was to jump into the ambitious approach of optical amplification. For a number of years, many laboratories had been working on the ‘‘natural scheme’’ of the semiconductor amplifier. However, it turned out that some basic physical properties of these amplifiers were not compatible with the requirements of longdistance systems, especially when taking into account the possibility of WDM. By contrast, the already well-known erbium-doped fiber amplifier with a metastable (1-ms lifetime in the excited state) upper level was very promising and is now a key technology of modern optical communication [5]. The decision was made to go with the erbium fiber optical amplifier approach in view of the very promising prospects and to apply it to TAT12=13 as well as for TPC5. Besides the challenge to design a nonregenerated system and to define its characteristics including noise accumulation (as in the old analog systems), two technologies had to be designed: A high-quality dispersion-shifted fiber with low attenuation and low polarization effects was needed because the signal had to be transmitted end to end across the ocean. The second enabling technology was the semiconductor optical pumps for the erbium amplifier. The choice has been a GaInAsP quaternary alloy, for which the materials technology was in a more advanced and safer state. This new generation has opened a brand new approach for demonstrating the components’ reliability based on a ‘‘constructive quality approach,’’ which showed, over time and based on milestone reviews, that the objectives were more and more likely to be met. At the same time, the introduction of terrestrial SDH systems with improved operation administration and maintenance characteristics led to the need to make submarine and terrestrial systems compatible for an overall network efficiency. TAT12=13 and TPC5 were laid in 1995, finally carrying a 5-Gbps bit rate per fiber [6].

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D. WDM Optical Systems The race for more capacity gained speed in 1995 and the optical amplifiers permitted a new scheme based on WDM that is simply the transmission together of a collection of colored signals at different wavelengths on the same fiber [7]. Sea-Me-We 3, a huge system linking Europe to Mediterranean countries, to Asia, and to Japan and Australia, was based on this WDM technology at 8 2:5 Gbps per fiber. Sea-Me-We 3 in addition has implemented a new WDM branching unit based on wavelength add and drops. Since the introduction of WDM, the demand for new systems has expanded, with tens of systems now linking the continents, each new system having more capacity that the ‘‘old’’ system laid only a year before. The capacity per fiber increased in 3 years from 4 and 8 2:5 Gbps to 16 2:5 Gbps (Southern Cross). The channel capacity then moved from 2.5 to 10 Gbps, and the number of wavelengths increased again from 16 (Japan–U.S. cable network) to 40 (Flag Atlantic) to more than 100 in 2001. The terabit era is open, emphasized by the fact that cables moved from two fiber pairs (two bidirectional communications) to eight fiber pairs. This progress in WDM technology resulted simply from a smooth improvement of the amplifier and from other technologies becoming mature. In particular, semiconductor and passive optical components have been specifically designed, with GaAs lasers replacing completely the GaInAsP to pump optical amplifiers, and WDM lasers became better controlled, so channel density could be increased [dense WDM (DWDM)]. At the same time, the development of extremely powerful signal processing to correct errors in the terminal after transmission [forward error correction (FEC)] was a key enabling technology [8].

FIGURE 4

The demonstrated and installed capacity per fiber since 1990.


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Figure 4 illustrates the evolution of the capacity per fiber, which doubled every year in the laboratory, achieving 3.65 Tbps (365 10 Gbps) in 2001 [9]. In parallel, the system implementation is accelerating, achieving the same capacity with a delay decreasing from 4 years in 1990 to 2 years in 2001.

IV. EVOLUTION OF SUBMARINE SYSTEMS IN THE 2000s The evolution of the capacity per fiber seems to have paused, and the evolution of the offered product is diversifying:

The installed large cables are not all deployed with full capacity. Upgrades can be achieved by adding wavelengths and presents a smooth solution created by WDM deployment. Lower capacity regional networks that complete the intercontinental backbones are needed. They are based on the combination of repeatered and unrepeatered systems. Network functionality to interconnect new cables with already installed systems is a cost-effective solution permitted by the large number of systems already existing. Evolution of topologies toward meshed topologies is open to a bright future. City-to-city interconnection is a cost-effective way to avoid the stop at the shore to drop the traffic where it is needed. The search for even higher capacity is still open, with solutions offering a choice between expansion of the bandwidth by additional amplifier bands (the long wavelength, so-called L band) and the increase of bandwidth through Raman amplification. The increase of the channel bit rate to 40 Gbps is still an open problem [10], requiring solutions that will accommodate transoceanic distances. Who would risk forecasting the capacity per fiber 10 years from now, given that the more ambitious forecasts in the past were proved to be dramatically pessimistic?

V. OBJECTIVES AND OUTLINE OF THE BOOK This book is intended to give a detailed view of the evolution that led to the present optical submarine communication systems, the theoretical and practical background of the design rules of optical submarine systems, and the technology needed. Finally, related industrial developments are described, from the definition of equipment to the installation process. The content is organized as follows: This introduction is followed by a chapter from Ge´rard Fouchard, in which he gives a complete overview of the historical developments, from the first age to the systems installed in 2002.

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Part II details the background of the design of modern submarine optical systems and their enabling technologies. In Chapter 3, Philippe Gallion describes the theoretical background of optical communications from modulation to reception, with a complete view of signal quality from electrical to optical noise sources, especially for systems with optical amplifiers. Dominique Bayart discusses optical amplification in Chapter 4, giving a comprehensive overview of key fiber amplifier technology, both erbium and Raman, including both the basics of the technology and the elements needed to properly understand signal and noise generation through chains of amplifiers. Ultra-long-haul submarine transmission is covered by Olivier Gautheron and Omar Ait Sab in Chapter 5. They describe the theoretical and practical aspects of designing a WDM optically amplified line, including FEC techniques. In Chapter 6, Eric Brandon and Jean Pierre Blondel provide a complete overview of the specific area of unrepeatered transmission systems. Polarization effects in optical systems are discussed by Curtis Menyuk et al. in Chapter 7, which presents the theory of polarization effects in optical fiber systems and the system penalties from these important phenomena. In Chapter 8, Stefan Wabnitz describes nonlinear transmission techniques and solitons, giving an overview of nonlinear propagation in optical fiber systems and possible solutions to use these effects to enhance the potential of long-haul transmission systems. Part III details the implementation of submarine equipment, including all of the technologies involved in a submarine system. Submerged plants are discussed by Neville Hazell and Christopher Little in Chapter 9; terminal equipment and network management are covered by Katsuo Suzuki in Chapter 10; network architectures for submarine systems and the overall transport network of which submarine systems are a key part are detailed by Howard Kidorf in Chapter 11; submarine fiber is discussed by Scott Bickham and Michael Cain in Chapter 12; cable technology is covered by Jean François Libert and Gary Waterworth in Chapter 13; and related marine and maintenance activities are detailed by John Horne in Chapter 14. This book is intended primarily to give a full overview of the technologies involved in submarine optical transmission. Nevertheless, it is striking that optical transoceanic systems have played a leading role in testing and promoting new optical technologies. The design of terrestrial optical equipment is presently harvesting the fruits of the pioneering submarine optical design. This book will be quite helpful for understanding common designs of optical communication systems that involve powerful optical techniques. The editor is especially grateful to all of the contributors, who invested their time to produce high-quality chapters, most of which are original contributions. This top-level panel of contributors makes this collective book a unique synthesis that could not be found anywhere before and could not have been achieved without their active involvement.


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REFERENCES 1. F. P. Kapron, D. B. Keck, and R. D. Maurer. Appl. Phys. Lett. 17, 423 (1970). 2. I. Hayashi, M. B. Panish, P. W. Foy, and M. Sumski. Appl. Phys. Lett. 17, 109 (1970). 3. Special issue on undersea lightwave communication, J. Selected Areas in Communications SAC-2, 6 (1984). 4. T. Miya, Y. Terunuma, T. Hosaka, and T. Miyashita. Electron. Lett. 15, 106 (1979). 5. E. Desurvire. Erbium Doped Fibre Amplifiers, Vols. 1 & 2. Wiley, New York (1994, 2001). 6. G. Balland, R. M. Paski, and R. A. Baker. In Proceedings of SubOptic 1993, p. 78 (1993). 7. J. Chesnoy, O. Gautheron, L. Le Gourrierec, and V. Lemaire. Alcatel Telecomm. Rev. 3Q98, 184 (1998). 8. O. Ait Sab. In Proceedings of SubOptic 2001, Part 4.2.6, p. 496 (2001). 9. G. Vareille, B. Julien, F. Pitel, and J. F. Marcerou. 3.65 Tbit=s (365 11:6 Gbit=s) transmission over 6850 km using CþL band with 22.2 GHz channel spacing and NRZ format. In Proceedings of the ECOC 2001, Part D.M.1.7, p. 14 (2001). 10. J. X. Cai, M. Nissov, A. N. Pilipetskii, C. R. Davidson, R. M. Mu, M. A. Mills, L. Xu, D. Foursa, R. Menges, P. C. Corbett, D. Sutton, and N. Bergano. 1.2 Tb=s (32 40 Gb=s) transmission over 4500 km. In Proceedings of the ECOC 2001, Part D.M.1.2, p. 4 (2001).


2 HISTORICAL OVERVIEW OF SUBMARINE COMMUNICATION SYSTEMS GE´RARD FOUCHARD A&G Fouchard, Le Seyne sur Mer, France

I. INTRODUCTION II. THE ERA OF TELEGRAPHY OVER SUBMARINE CABLES A. The Early Age of the Electric Telegraph (1800–1850) B. The British Era of Submarine Cable (1850–1872) C. The Global Network (1872–1920) D. Cable and Radio Competition (1920–1960) E. Technical and Economical Aspects III. THE ERA OF TELEPHONE ON COAXIAL CABLES A. The Earliest Telephonic Submarine Cable Trials B. The First Generation of Coaxial Submarine Cable (1850–1961) C. The Second Generation of Coaxial Submarine Cable (1960–1970) D. Wideband Submarine Cables (1970–1988) E. Technical and Economical Aspects IV. THE ERA OF FIBER OPTIC SUBMARINE CABLES A. From Analog to Digital (1976–1988) B. Regenerated Fiber Optic Cables and the Consortium Era (1986–1995) C. Optical Amplification and WDM Technology (1995–2000) D. Cable Ships and Offshore Works V. CONCLUSION References

Undersea Fiber Communication Systems Copyright 2002, Elsevier Science (USA). All rights reserved.

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I. INTRODUCTION Communications are now a permanent part of human life. In offices, home, and cars, a wide variety of devices (telephone, fax, radio, e-mail, TV, mobile phones) provides telecommunications that simplify work, leisure, and domestic activities. Of course, all of these services did not appear overnight. They took more than 150 years to develop. Up to the mid-19th century, the means of communication were the monopoly of governments. All empires dispatched their written documents and governmental instructions using racers, horses, pigeons, coaches, ships, sometimes optical signals (smoke, flags, lights, etc.), or a combination of these. Commercial, financial, and finally private traffic appeared in the early 19th century. The optical networks built by the Chappe brothers through continental Europe (1793–1830) and the British Admiralty along the southern coast of England at the end of the 18th century were the ultimate form of optical network, used for long-distance transmission of governmental and intelligence messages. They were simply more sophisticated than versions previously used. Two inventions of the Industrial Revolution changed the world: electricity and steam power. The new transportation facilities were based on the force of steam. Steamships and railways reduced distances and helped organize a global world. The electric telegraph initially installed along railway lines for monitoring traffic also offered facilities for public telecommunications traffic. This instantaneous transmission of information, which had previously been limited to the ‘‘speed of a man on a horse,’’ crossed seas and oceans:

It took 30 years (1837–1866) and the invention of Morse code to send a message by transatlantic commercial telegraph using electricity. It took 80 years (1876–1956) and Bell’s invention of the telephone to speak through a transatlantic commercial system (TAT1) using frequency transmissions on a coaxial cable. Only 20 years elapsed between Kao and Hockham’s assumptions on fiberglass potentialities in 1966 and the first optical fiber transatlantic commercial submarine cable TAT8 in 1988. The coded light allowed the transmission of all telecommunications facilities (fax, voice, pictures, and video).

For 150 years, submarine cables had to cohabitate with wireless communications: radio (1920–1960) and satellite (1956). This was a source of progress and emulation, never a cause of obsolescence for both telecommunication techniques.

2. HISTORICAL OVERVIEW

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II. THE ERA OF TELEGRAPHY OVER SUBMARINE CABLES A. The Early Age of the Electric Telegraph (1800–1850) 1. Morse’s Invention Conquers the World Samuel Morse, an artist and traveler, imagined an electric telegraph on board the sloop Sully while traveling from Europe to the United States in 1832. Morse’s idea condensed all previous notions: Volta battery, electric line (one or two wires), a transmitter (two digits), and an electromagnet for reception, equipped with a recorder. The digital code was a revolution, making Morse the father of modern telecommunications. As with all good inventors, Morse was not seen as a prophet in his own country (the United States). Patented in 1837, his invention demonstrated the reliability of the electric telegraph between Baltimore, Maryland, and Washington, D.C. In May 1845, he transmitted the first message—‘‘What hath God wrought’’—to Congress. He then tried to promote his invention in Europe but had to wait almost 30 years to obtain worldwide recognition. Morse had two good ideas: the code and the recorder. His colleague, A. Vail, came up with the idea of fitting one leaf to the magnet to print the signal on a strip of paper. Consequently, the Morse telegraphic line was made using:

An electricity source (battery) and a transmitter able to cut the circuit according to a conventional code An electric line used by the current between the transmitter and the receiver An electromagnet fitted with an armature for ordering=monitoring a recorder to reproduce the signal

All European countries developed their domestic systems along railway lines: Great Britain (William Cooke and Charles Wheatstone in 1837), France (Breguet and Foy, on the Paris–Rouen line in 1844), Germany (Shilling, on the Frankfort–Berlin line in 1848), and Russia. Most national European networks were completed by 1870. Advanced networks were built in the United States and India. Two types of development followed:

Private networks offering services to the public were installed in the United Kingdom and the United States, with no fewer than 14 companies operating in Ohio in 1852. Following France’s example (November 29, 1850), other European countries created a monopoly for telegraph public services.

In the United Kingdom, all private networks were nationalized on April 1, 1868, to create a national network under the control of the General Post Office. Private users, merchants, banks, newspapers, and news agencies (Havas, Reuters, Continental, the Associated Press) used services offered by electric telegraph companies as well as governmental administrations. Traffic increased

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dramatically and national networks needed to be interconnected. Prices were harmonized and regulated. The first international agreement was signed between Germany and Austria in October 1849 and international coordination was recognized. The ITU (International Telegraph Union) was founded in Paris (1865) and the Morse code was universally adopted. 2. Terrestrial Long Haul Lines The United States and Russia immediately understood the great interest in the telegraph, as did the United Kingdom. At that time, it took more than 2 weeks to go from New York to San Francisco by horse and 40–50 days from Moscow to Vladivostok. The first railway line was built in 4 months in 1869 between Omaha and San Francisco. Three others were installed by 1881. In these vast territories, and in others like India, South America, Africa, and Australia, railways and telegraph helped civilization and unification. In 1857, Moscow was linked to Saint Petersburg, Odessa, and Varsovia; the creation of the trans-Siberian line was under way. (It was put into operation in 1871.) Almost immediately, Romanov came up with the idea of linking Europe to the United States by the Bering Strait. Russia came to an agreement with U.S. engineers to link Vancouver to Alaska. By 1866, 7000 km of the Trans-Siberian was built and most of the Alaska line was completed. The Indo European Telegraph Service, promoted by a UK company, opened the Turkish line in 1865, but operators speaking different languages provided poor service. Germany had recently been unified and was developing its telegraph network and beyond, one objective being to reach India via Turkey. Siemens, a private company, built an alternative line through Russia, Caucasia, and Persia. This line was put into service on January 19, 1870. In 1850, the distances to link London to the faraway lands of the British Empire were, for example, 15 days to Halifax, 100 days to Bombay (the Suez canal did not exist), and more than 120 days to Australia. For the British Empire, the terrestrial solution was an opportunity, but a submarine solution would have been preferable.

B. The British Era of Submarine Cable (1850–1872) 1. Unsuccessful Attempts (1850–1860) To connect the English telegraph to the European network, Wheatstone proposed a submarine cable in 1840. However, the French monopoly on the telegraph and the lack of electric telegraph lines and necessary insulation to protect the submarine cable were two critical issues. The gutta made from Malaysian hevea trees (Dr. William Montgomerie) was not discovered until 1843; S. W. Silver and Faraday invented the process of coating copper wires with gutta–percha in 1845. The Gutta Percha Company was created on February 4, 1845, and started production in London.


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Once the first trials were successful, Jacob and John Watkins Brett founded La Compagnie du Cable Sous-marin de la Manche in Paris and ordered the cable to cross the Channel. The first submarine cable was laid between Calais and Dover on August 28, 1850, but was immediately recovered by a fisherman believing to have recovered a ‘‘golden alga’’ in his net. The Brett Brothers founded a second company, the Submarine Telegraph Company, in London and successfully laid the first submarine cable between Gris Nez and Abbott Cliff in September 1851. By December 15, 1851, the first international telegraph line was working between Paris and London. This success was a great event, opening a ‘‘new boundary.’’ The British government then identified two main targets:

First, to connect England with Ireland, other British islands and the Channel Islands, and all European and Nordic countries. On the other side of the Atlantic, a project was under way to link Newfoundland to North America. Second, to link the United States to Newfoundland and Ireland (1858) and India to Europe (1860).

In France, connecting Corsica (1854) and Algeria (1858) became the main priority. Spain and Greece also wanted a cable from the mainland to the Balearic and major islands. Only the British built an industry offering submarine cables. In 1856, American entrepreneur Cyrus Field obtained a concession for 50 years from the British government of Atlantic Provinces to lay submarine cable in Newfoundland. He met John Brett, Charles Bright, and Whitehouse in London and founded the Atlantic Telegraph Co. on April 20, 1856. The company ordered 2500 miles of cable from RS Newall Ltd. and Glass Elliot Co.; the insulated conductor had been provided by the Gutta Percha Co. After loading, both the cable ships Niagara (Newall cable) and Agamemnon (Glass Elliot cable) started the lay from the middle of the Atlantic and completed the work on August 5, 1858, but Thomson’s up-to-date galvanometers were not installed until August 10. The inaugural message sent by Queen Victoria to President Buchanan took more than 30 hours to be transmitted: ‘‘England and America are united. Glory to God in the highest and on Earth, peace, good will toward men.’’ The transmission speed, initially supposed to reach 3 words per minute, did not exceed 1. On September 1, 1858, the cable failed permanently and the decision to abandon was made on October 20. For 20 days, 723 messages were transmitted using a pile of 480 elements (about 700 V), which was supposed to be the cause of the damage. However, despite this glorious failure, the attempt clearly demonstrated the feasibility of the enterprise. Two years later, the Red Sea and India Telegraph Co. formed by Lionel Gisborne laid a cable provided by RS Newall from Suez to Karachi in 1859– 1861. Two expeditions were required to complete the lay. The cable never worked from one end to the other. The company lost £800,000 and collapsed. During this period of time, other cables were laid in the Mediterranean and Black seas. When

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a cable failed in water deeper than 200 m, it could not be repaired and was abandoned. From 1850 to 1859, 20,000 km were laid; only 5500 km laid in shallow waters remain in operation in 1960. The British government was concerned about the huge loss of 50 million francs given to support the companies in charge of connecting India and America. The Board of Trade appointed a commission of eight members managed by Capt. Douglas Galton in December 1859. 2. The Blue Book of the Board of Trade Commission The work started on December 1, 1859, and lasted until April 1861. Four members appointed by the Private Trade Council (D. Galton, C. Wheatstone, W. Fairbank, and G. P. Bidder) and four members of the Atlantic Telegraph Co. (Edwin Clark, C. F. Varley, Latimer Clark, and George Saward) met for 22 sessions with 43 engineers, electricians, and marine officers. They investigated all attempts, successful or not, to assess the best way to build, lay, and maintain telegraphic submarine cables. They investigated all materials (copper, steel, iron, gutta, ropes, etc.), the work at sea (route survey, cable work, equipment used, laying and repair procedures), test equipment and methods, jointing material and procedures, and transmission equipment. They tried to understand the effect of temperature and pressure on materials and cable, the effect of tension on composite cable, corrosion, and the effect of the sea (tide, swell, and currents as well as sea life). The commission’s ‘‘Blue Book,’’ published in April 1961, recommended specifications for cable manufacturing, commissioning, jointing and testing, laying, and test procedures. Because no existing ship was clearly suitable for laying and repair operation, a typical cable ship was designed and for the coming days, the Great Eastern was identified as the only existing cable ship suitable for laying a transatlantic cable. The report was a model of scientific investigation used for the benefit of all future submarine cable business. Recommendations also covered the financial structure of operational companies as well as industrial merging. As a result, two companies were formed: Siemens Brothers in 1865 (Siemens & Halske) and the Telegraph Construction and Maintenance Co. (hereafter called Telcon) by merging Gutta Percha and Glass Elliott. Other companies gradually reduced their activity and collapsed, RS Newall in 1870 and Hooper in 1877. Except for the RS Newall factory located in Gateshead, all industry was located in London along the river Thames: Siemens & Halske in Greenwich and Charlton on the south side of the river and all the other factories on the north side, Hooper’s Telegraph Works Ltd. in Milwall, and the Indian Rubber, Gutta Percha, and Telegraph Works Co. in North Woolich. Telcon was founded on April 7, 1864, and John Pender was appointed first chairman. With W. Gooch, they started to work on a new project across the Atlantic and secured the Great Eastern on June 30, 1866. In 1868, Gooch took over chairmanship of Telcon and Pender became a promoter and founded operational companies to link England to the rest of the world.


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3. The British Network (1863–1872) Following the glorious failure of the year 1858, Cyrus Field was not successful in finding money in the United States but found great interest from the board of Telcon, who agreed to convert their participation into shares of Atlantic Telegraph Co. Therefore, the Great Eastern and the associated vessel Caroline left the Thames on July 23, 1865. They started the lay and made repairs twice but stopped work at the third fault, due to the lack of recovery rope to complete a repair at a depth of 3600 m. A new company, the Anglo–American Telegraph Co., was founded by merging Atlantic Telegraph and the New York, Newfoundland, and London companies. Telcon provided 2730 nautical miles (nm) of cable to lay a new cable 17 nm from the first one and repair it. Work was successfully completed in September 1866. It was a great success that had unexpected consequences: The terrestrial link under construction across Alaska was abandoned. American engineers reported that mineral richness was discovered during the work and convinced the government to purchase the territory from Russia. The agreement was signed on May 29, 1867, for $7.2 million. The transatlantic cable of 1869 was French (Brest–St. Pierre–Cape Cod), but the technology was the same as that used for the 1866 cable because the cable was made by Telcon and was laid by the Great Eastern. Shares of the company were taken up by the British. Then, the French company was sold to Anglo in 1873. In 1870, the Great Eastern laid the Bombay–Aden cable for the BritishIndian Telegraph Co. Eastward. John Pender’s companies (Eastern and Associates) had already installed the cables from Porthcurno (Cornwall) to Gibraltar, Malta, and Alexandria, from Suez to Aden and Bombay, from India to Singapore, and then from Singapore to China and to Australia (Darwin). Commercial service between London and Adelaide through the Australian domestic network began on October 21, 1872. In Scandinavia a Dane, C. F. Teitgen, seriously competed against British companies for two routes, from the United Kingdom to Norway and Russia. In 1870, he formed the Great Northern Telegraph Co. (GNTC) by grouping all Scandinavian interests. At that time, the Russian project to the United States across the Bering Strait was still in progress, and had been since 1865 when the Russian–Western Union agreement was signed. Following the success of the transatlantic cable, the Russians diverted the trans-Siberian line to Vladivostok, hoping to connect Russia and Japan. Teitgen secured the concession from Russia against the British and operated the network from Scandinavia to China and Japan. Submarine cables to Nagasaki, Shanghai, and Hong Kong were laid in 1870 and 1871 and commercial operation of the Great Northern, China, and Japan Extension Telegraph began on January 1, 1872. Then, three cables were laid from Denmark to Sweden, the United Kingdom, and France (1873) to divert the traffic from these countries to British lines.

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In 1872 in Copenhagen, GNTC built the first cable ship constructed primarily for repairing submarine cables: CS HC Oersted spent its time in either Far East or European waters up to the breaking up of the company in Copenhagen in 1922. In 1863, the French government built a factory in Toulon, which was transferred to La Seyne sur Mer in 1881, the year it purchased its first cable ship, Dix-Dećembre. The insulated core was imported from the United Kingdom and the cable manufactured for the coastal network. Germany also developed its industry. The first cable was built in 1854 by Felten & Guillaume, and the second was laid in 1856 across Constance Lake. The first Japanese-manufactured submarine cable was laid in 1874 by the steamship Densimu Maru between Honshu and Kyushu. Because Japan is made up of 3900 islands, the amount of domestic cable laid between 1874 and 1904 increased sharply: 144 cables over 2250 nm (1904). Initially, GNTC ships were used to lay the domestic cables, leading up to the construction of the CS Okinawa Maru in 1896. Seven ships were launched before 1940. In the United States, there were no industrial attempts at that time, and the aforementioned trials were peanuts in comparison with the efforts of the British Empire to produce all the necessary submarine cable to girdle the world. C. The Global Network (1872–1920) These first attempts to form a British monopoly did not prevent Pender’s companies from continuing to girdle the world. Brazil and the South American coast, South Africa, East and West Africa, and New Zealand were linked by duplicated lines to make the restoration of traffic easier. However, the time had come for the British Empire to share the work with other companies. In the United States, the Western Union Telegraph Co. (hereafter called WU), a pioneer in land telegraph, started to work on submarine cables in 1873 (Key West–Cuba) and leased the three transatlantic cables of both Direct United States Telegraph Co. and the American Telegraph and Cable Co. founded by Jay Gould in 1881. Supported by the most important North American domestic network, WU was the partner of European companies, mainly the Anglo–American Cable Co. inside the pool of transatlantic cables, and harmonized the prices with the British company. Two years later, in 1873, the Commercial Cable Company (CCC) was created in New York by John W. MacKay (a mine owner) and Gordon Bennett (a newspaper owner), two businessmen unhappy about paying the tariffs offered by existing telegraph companies and the poor services they offered, especially to newspapers. CCC started to lay three transatlantic cables in 1883, 1884, and 1894. French companies, penalized by the war of 1870 against Germany, came back to the North Atlantic to lay transatlantic cables in 1879 and 1902 and a cable to Africa (Brest–Dakar) in 1905. The French government installed a Mediterranean network in 1892 (Algiers) and 1893 (Bizerte) and a governmental factory in


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La Seyne sur Mer in 1881. Two private factories were also built in France by the Societe Industrielle des Telephones in Calais (1891) and by Grammont in SaintTropez (1892). The list of all telegraph cables laid in the Atlantic from 1858 to 1928 shows 25 cables. Only the first four cables were abandoned before 1900. When Brest–St. Pierre was the victim of an earthquake near Newfoundland in 1929, it was not repaired. Twenty-one cables remained in operation from the date of installation until 1962. From 1875 to 1960, operators alternated between periods of very hard competition and quiet cooperation. The U.S. government strongly defended competition favorable to the interests of the two American companies, Western Union and Commercial Cable groups. In 1912, the Anglo–American board decided to transfer the network to Western Union and the two groups worked smoothly with their associates: Western Union, Italcable, and German DAT on the one hand and CCC and CFCT (Compagnie Francaise des Cables sous-marins Telegraphiques) on the other. In the Pacific Region, two cables were laid in 1900–1903 and in 1926: 1. San Francisco–Honolulu–Midway–Guam and Japan and a Guam–Philippines–Shanghai branch. CCC installed this cable. 2. Vancouver–Fanning–Fiji–Australia, with a branch from Fiji to New Zealand. A cable agreement was signed on June 5, 1896. This cable was owned by the Pacific Cable Board—the governments of Canada and New South Wales, Australia. A second cable covering Vancouver–Fanning–Fiji–Australia–New Zealand was laid in 1926. Before installation of the Canada–Australia cable, Eastern objected to the laying of an expensive cable since Canada and Australia already had connections to the United Kingdom. The Pacific Cable Act was not approved until August 17, 1901. The cable was built by Telcon and was laid by CS Colonia, built with the intention of laying the longest section of 3458 nm between Vancouver and Fanning Island. The first message was sent on October 31, 1902, and the opening of the service caused emotion similar to that felt at the laying of the first transatlantic cable in 1858. The transmission speed of the cable was close to 200 words per minute, compared with the 10 words per minute of the 1866 transatlantic cable. From England to India, Eastern installed successively six whole cable systems, except in the Red Sea (where only five were installed). Each system represents more than 6500 nm. The last system (6.585 nm) was laid in 1921– 1922. Figure 1 shows a map of Eastern’s cable system in 1872 and 1922. Germany’s first state-owned cables were run between the United Kingdom and Germany in 1866 and 1871 to send the traffic on the Anglo–American Co. transatlantic cables. In 1882, the German Union Telegraph Co. laid a direct cable manufactured by Telcon to Valentia. Then, German entrepreneurs wanted to have their own company, the German Atlantic Telegraph Co., which ordered two

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FIGURE 1

Eastern’s cable system as of 1872 (top) and 1922 (bottom).


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transatlantic cables from Telcon in 1900. Later, to be independent from any foreign cable manufacturer, an important network was manufactured by Felten & Guillaume, including two other transatlantic cables laid in 1903–1904 as well as duplicated cables to West Africa between 1908 and 1911. German submarine cables were also laid in the Pacific region. D. Cable and Radio Competition (1920–1960) In 1895, following a year of experiments, Marconi patented radio communication and started long-range experiments. In 1897, a first signal crossed the Channel between Wimereux and England. Then, in 1901, two stations built at Pouldhu (Cornwall) and Signal Hill (Newfoundland), 2000 nm away, exchanged the first transatlantic radio communication. But in 1907, when Marconi opened the first radiotelegraph service from Ireland to Canada using low frequencies (long waves), he did not endanger the submarine cable companies. The competition started in the 1920s when decametric waves allowed the exchange of voices. The radiotelegraph offered facilities different from those used previously. The first transatlantic telephone was put into operation in January 1927. The telegraph companies improved their competitiveness:

In 1923, Commercial Cable Co. laid a new transatlantic line (Waterville– Azores–Canso) using a cable 500=204 (1100=450 lb). The 14-mm diameter was the largest ever made to improve the transmission speed by increasing inductance. Western Union and its European associates preferred to install Krarup cables. Western Union patented Permalloy, a nickel–iron alloy, for loading cable in 1921, and Telcon preferred to use Mumetal, a copper–nickel–iron alloy, on the transatlantic laid in 1924, which operated at 400 words per minute, the fastest ever achieved across the Atlantic. A new Pacific cable (Canada–Australia) was laid in 1926 by the new ship Dominia that allowed 200 words per minute.

All cables featured automatic transmitters, amplification at reception, regenerators, and mechanical signaling. So, in the long run, cables offered a competitive option to radio. As a result, most governments agreed that their radio and cable both provided significant services. General Ferrie, a French pioneer of radio communications during World War I, said, ‘‘If the submarine telegraph cable was discovered following the radio, then it would be considered as a great improvement.’’ Radio and cable companies certainly considered that possibility and merged or worked together. In England, Imperial and International Communications Ltd. was founded in 1929, renamed Cables & Wireless in 1934. The profits of cable routes (the Atlantic, Indian, and Pacific oceans and the Mediterranean Sea) were used to develop radio and inland networks between Europe and other continents.

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Radio became strategic during the Second World War, when communication needs increased sharply. Cables were objectives and enemies extensively destroyed the network. During WWII, all factories located in the United Kingdom, France, Germany, and Italy were destroyed. On March 21, 1941, CS Faraday 2 left London after loading all available cable from the Greenwich factory. She joined a convoy of five, increasing speed to make Milford before dark. Following a German aircraft attack, two bombs hit her, in the stokehold and oil fuel bunker, and the ship became a mass of flames. Eight men were killed, 25 survived, and the cable stock was lost as well as the ship. It was also common practice during WWII to recover cable from existing enemy, neutral, or even allied cable. In 1945, the German network was shared among the Allies. The submarine cable network was refurbished, necessitating huge investments and much cable ship activity. Telegraph cable remained in service despite the competition from radio. In the North Atlantic area, the first coaxial cable was laid across the Atlantic in 1956 between Oban (Scotland) and Clarenville (Newfoundland). When the second coaxial cable was laid across the Atlantic from Penmarc’h (France) to Clarenville (Newfoundland) and became operational in 1959, the telegraph line network was abandoned (1962). Each telephone channel offered the capacity of an existing telegraphic network.

E. Technical and Economical Aspects 1. Submarine Cable Business Overview (Industries and Operating Companies) The list of the cables forming the World Submarine Network was recorded by the ITU (International Telegraph Union). Nineteen editions, carefully established, were issued from 1877 to 1977. The peak of the network was recorded in 1928 in the 12th Edition, with more than 355,000 nm (about 650,000 km). Some cables were governmental (60,500 nm); others were private (284,000 nm). Cables owned by state agencies or administrations were used as shortcuts to connect islands near the coast or to build a colonial network. In 1922, the following was noted: 1. Norway had 1294 cables covering more than 4,019 km. The government of Norway laid its first cable in 1857. 2. British Islands (United Kingdom and Ireland): 276 cables, more than 20,810 km. 3. Sweden: 236 cables, more than 907 km. 4. Japan: 214 cables, more than 14,486 km. 5. Denmark: 181 cables, more than 976 km. 6. Italy: 97 cables, more than 5,832 km. 7. France: 96 cables, more than 30,810 km.


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As a result, all of these governmental organizations owned fleets of cable ships to maintain their networks. In 1922, the apportionment of private cables among group of interests was as follows: 1. 2. 3. 4. 5. 6.

Eastern Group (UK), with associates: 167,860 km Commercial Cable Company (USA): 53,916 km Western Union Telegraph (USA): 53,466 km Western Telegraph: 40,462 km French companies (CFCT and SUDAM): 33,433 km GNTC: 15,614 km.

From 1925 to 1930, the Italian company Italcable laid a network in the Atlantic from the Azores to South America (15,500 km), and Germany was once again in the position of having to rely on foreign connections, laying 24,000 km from 1921 to 1929, mostly manufactured in Germany. Very few companies were able to make submarine cables insulated with gutta–percha at this time. Six companies were still operating in 1940. Two British companies, Telcon (Greenwich) and Siemens Brothers (New Woolich), undertook the construction of the biggest part of the world network by obtaining electrical section from Indian Rubber and the Gutta Percha Co. The latter had a factory in Persan–Beaumont near Paris, which continued manufacturing until 1926. By 1950, Telcon had manufactured 385,000 nm of submarine cable. In France two companies had factories; SIT (later called Cables de Lyon, then Alcatel) had one in Bezons (manufacturing electrical sections) and one in Calais (inaugurated in 1890 for the protection of submarine cables), and Grammont had the Pont de Cheruy and Saint-Tropez factories, built in 1891, which stopped production in 1926. Of some importance as well was the factory of l’Administration des P&T in La Seyne sur Mer, which constructed and repaired the coastal cables. In Germany, the factory in Nordenham Seekabelwerke was built in 1901. Germany developed its own industry very quickly; Felten & Guillaume built the first cable in 1854, and the second was laid in 1856 across Constance Lake. German entrepreneurs wanted to have their own industry, cable ships, and operating companies. Felten & Guillaume manufactured 24,000 nm to build a network in the Atlantic to the United States (1900–1904) and West Africa (1908– 1911) and in the Pacific. This network was further shared with the United Kingdom and France. In 1926, following the First World War, Felten & Guillaume built a new network, which was lost again in 1945. From 1898 to 1914, more than 25,000 nm of German cable was made there to create a network that was dismantled in 1918. Manufacturing began again in 1920 to create a second German network shared among the Allies in 1945. In Italy, Pirelli installed one cable factory in La Spezia in 1886 using core made in their main plant in Milan. They first began manufacturing cables to

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connect the islands near the Italian peninsula. Pirelli built the cable ship Citta di Milano in the United Kingdom in 1886 to install the cables ordered by the Italian administration. In Japan, a factory in Yokohama opened in 1874, manufacturing primarily coastal cables. We should note that no submarine cable factory existed in the United States, even though both Western Union and Commercial Cable Co. were thriving and were responsible for transatlantic and transpacific traffic. The Europeans, who were competing for the transatlantic lines, concentrated their efforts on building colonial networks, which were not terribly profitable. 2. Transmission Improvements The transmission speed is given by the formula V ¼ kF/RC, where R is the cable resistance (in O), C, the cable capacitance (in farads), F, the frequency of the signal, and k, a constant dependent on the insulation (gutta-percha, paper, polyethylene, etc.). Then, the transmission speed is limited by the huge capacitance and the resistance of the submarine cable. In telegraphy, the transmission speed is given in words per minute or in center hole (CH) counts, that is, the number of holes (letters and spaces) on the paper per minute. The transatlantic cables laid from 1858 to 1928 showed an improvement of the transmission speed from 1 to 170 words per minute. Research on transmission laws, new designs of cable and equipment, and clear procedures and training contributed to these results. On the first submarine cables (United Kingdom–France and domestic cables), the Morse equipment transmitter sent one polarity only, with a discharge of the cable between each elementary signal. The difficulties arose with the longhaul systems: Their capacity was in the range of 0.3 mF, their resistance in the range of 2–9 O=nm, and their voltage did not exceed 60 V. How can you send a message quickly when RC ¼ 6 sec for the longest transatlantic cables? The solution was to implement these changes: 1. The systems were operated on charge=discharge current and not direct current. 2. Following the charge on one polarity, a discharge was made by applying the opposite polarity. The ‘‘recorder code’’ is derived from Morse code, where þ and have the same time but are separated by a ground between each signal (a code with three moments). 3. A capacitance of 100 mF was inserted between the transmitter and cable and between the receiver and cable to avoid telluric currents. 4. The receiver was a galvanometer (ultrasensible mobile frame). In the early years (1850–1860), manual transmission was facilitated by the double key and a mirror at the reception. The transmission speed was directly related to the operator’s ability to read the signal; only two to five words per minute were transmitted on the first transatlantic cables.


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From 1860 to 1910, improvements were introduced: 1. The siphon recorder, proposed by William Thomson in 1867, provided records of weak signals on a narrow strip of paper. These immediately became standard procedure on long oceanic cables. 2. Duplex transmission was used from 1873 onward. Muirhead developed the method to build an ‘‘artificial line.’’ Both stations could send a message simultaneously. Therefore, the transmission speed was doubled. 3. In 1880, the Morse keyboard perforator, forerunner of the teleprinter, was invented. Therefore, the transmission speed was given by the ‘‘center hole’’ of the punched tape. 4. The last significant improvement was developed by Heurtley in 1908. A moving coil similar to that of the siphon recorder is attached to two wires. The wires were heated by the electric current flowing through them and cooled by two small blowers, one of which was farther away. Since resistance depends on temperature, the resistance of the first wire decreased and that of the other increased. This upset the balance of the electrical circuit of which the two wires were a part and produced an amplified signal large enough to operate an electromechanical relay and generate a new pulse. Consequently, the same transatlantic cable provided 10 words per minute (1867), then 20 (1873), 50 (1880), and 120 (1920). The output of the cable is optimized when the diameters p offfiffiffi the copper conductor (d) and the gutta insulation (D) are as follows: D=d ¼ e ¼ 1:65. In addition, the improvement of the transmission objective had to be compatible with the economic conditions of the manufacturing of cables and the speculation on the prices of raw material (copper and gutta). 3. Cable Ships and Offshore Works The cable ship was born with the idea of the submarine telegraph cable. In the 1850s, steam was just beginning to be used for sea navigation and offered the possibility to manage a laying operation following a scheduled route. The Great Eastern, one of the earliest launched, began as a transoceanic packet steamer and could transport all the necessary coal from London to Australia without any stops. For that reason, she was recommended by the Galton Commission to lay the first transoceanic cables from Europe to the United States and India. Later, cable ships were designed from the outset specifically for cable laying and repair. The first cable ship ever designed for repair work was the Danish CS Oersted, built in 1870 by GNTC to maintain the Far East cables, 20 years after the first Franco–British ship laid submarine cable. Then, the two British manufacturers Telcon and Siemens Brothers, launched their CS Hooper and Faraday 1 for laying purposes in 1871 and 1872, respectively. The French CFCT built CS Pouyer-Quertier, which was similar to the Faraday 1, in 1879. Although these

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vessels (mainly those laying cable) needed to be modernized and refitted from time to time, they seldom required extensive conversions. Cable ship owners included cable operators, governments, and cable manufacturers. Cable Ships and Submarine Cables [1] lists more than 300 used over a period of 120 years, covering the telegraphic submarine cable era. This includes a wide range of vessels from converted barges used to lay a few miles of coastal cable to purpose-built cable ships that saw 30 or more years of service on all oceans. The worldwide cable ship fleet was estimated to be about 50 vessels throughout the period. III. THE ERA OF TELEPHONE ON COAXIAL CABLES A. The Earliest Telephonic Submarine Cable Trials Graham Bell patented the telephone in 1876 and development has continued since. To cross the seas and to connect all islands located close to a mainland, a coaxial structure was used: The copper conductor was insulated with gutta protected with a second conductor. This outer conductor protected gutta from teredos, a type of mollusk. The first telephonic cable (one conductor) was laid in 1891 between France and the United Kingdom. At that time, the best structure of the cables had two or four conductors to provide three telephone and one telegraph circuit. The loading (Pupin or Krarup) was also the technical solution to reduce the loss. Two cables were laid between Gris Nez and Abbots Cliff in 1910 (Pupin) and 1912 (Krarup). The 1939 issue of the ITU log book shows that this coastal network was developed mainly in Norway, Japan, the United Kingdom, and France. Following World War I, cables were insulated with paper rubber and cabled per four conductors (fourth). Between the United Kingdom and France, three cables were laid in 1930 (7 fourth), 1933 (19 fourth), and 1939 (7 fourth plus 16 pairs). This last cable was still being used in 1960 and each conductor pair offered 12 high-frequency circuits. Lee de Forest invented the thermo-ionic valve in 1906. Then, amplification of the signal made possible the development of long-distance transmission of a voice signal. Some routes were equipped before World War II: Key West–Havana (1922 and 1931) and Italy–Sardinia (1932). The British Post Office had developed a submarine cable specification for a transmission of 80–100 nm to cross Bath Strait between Australia and Tasmania in 1935. The cable was isolated with gutta–percha and provided either six telephone channels or one radio circuit. The French Post Office developed an amplifier to operate one channel between Toulon and Ajaccio in 1934, the aim being to link Algeria to France. In 1927, when Lindbergh crossed the Atlantic Ocean in the Spirit of Saint Louis, the British Post Office opened the first transatlantic telephone service by radio, and in 1929 the ‘‘French way’’ was opened. At that time, submarine cable technology was not able to transmit voice across the Atlantic.


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The key invention, polyethylene, was discovered by ICI in 1933, and the first coaxial cable insulated with polyethylene was manufactured in the United Kingdom just before the war. Cables were laid between the United Kingdom and France, the Netherlands, and Ireland. Two other cables were installed, between Pirou (France) and Jersey. The path was laid for the future, and laboratories worked on the following basis: 1. Long-lived and reliable thermo-ionic tubes 2. Mechanical housing of amplifiers able to withstand the high pressure of depths 3. Direct current power-feeding 4. Cable able to keep its transmission capabilities after loading and laying operations 5. Monitoring and fault location from both terminals

B. The First Generation of Coaxial Submarine Cable (1950–1961) In the United Kingdom, the first repeater was bidirectional in a rigid housing. The trial took place during the war, in June 1943, between Anglesey and the Isle of Man. A similar repeater was laid in 1946 between Borkum and Lowestoft in Germany, followed by the laying of two cables in the North Sea (Norway, Denmark). The first deep sea trial was held in 1951. Part of TAT1, between Newfoundland and New Brunswick, was laid in 1956. In the United States, Bell Labs started to work on the target of crossing the Atlantic. The proposal was to lay two unidirectional cables fitted with flexible repeaters to make the laying operation easier from a drum that was 1.80 m in diameter. The first link (24 channels) was laid in 1951 between Key West, Florida, and Havana, Cuba. The system was improved to offer 36 channels over 6000 km. Then, San Francisco–Hawaii and TAT1 were laid in 1956 and 1958, respectively. In France, the first targets were Corsica and North Africa. The program was established in 1939. Two developments were carried out during the war: vacuum tubes by CSF and flexible repeaters by the French Post Office. Toulon–Ajaccio was installed in 1946 using a rigid repeater, but the repeater deployed between Cannes and Nice in 1950 was flexible. When Marseilles–Algiers was installed in October 1957, it was the first bidirectional cable in deep sea offering 60 channels. In 1956, Felten & Guillaume and Norddeutsche Kabelwerke (Germany) deployed one 60-channel system between Denmark and Germany. In 1961, two 120 channel systems were laid between Denmark and Poland and Denmark and England. In 1962, the German industry built ICECAN between Denmark, Scotland, and Iceland (79 repeaters over 1800 nm).

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Pirelli (Italy) was associated with the construction of submarine cable in the Mediterranean Sea using repeaters that were manufactured either in England or in France. From 1957 to 1961, two British companies, Submarine Cable Ltd. (SCL) and Standard Telephone and Cable (STC), linked the North Sea and the Mediterranean Sea; the German and French suppliers provided only a few cables. AT&T, a new entrant as a manufacturer, led the way with long-haul systems installed from California to Hawaii and across the Atlantic (TAT1 and TAT2). However, AT&T did not manufacture cable and had no cable ships. The TAT1 cable was made in the United Kingdom and the CS Monarch installed the cable. The TAT2 cable was shared among the British, French, and German manufacturers and installed by the CS Ocean Layer. This ship burned, fortunately at the end of the operation. TAT2 was revolutionary for several reasons: 1. The TAT2 Construction and Maintenance Agreement is the first example of an agreement between a consortium of users. 2. AT&T purchased whole circuits and reserved the right to sell irrevocable rights of use (IRU) either to ‘‘record carriers’’ or to European operators other than France or Germany. 3. Manufacture of the TAT2 cable was shared between F&G (Germany) and Cables de Lyon (France) under Bell Labs specification and inspection. 4. TAT2 was the first cable operating 3-kHz circuits and equipment to convert 3- to 4-kHz channels, manufactured by CIT (France) and located in both terminal stations.

C. The Second Generation of Coaxial Submarine Cable (1960–1970) A new generation of submarine cable was developed from 1957 to 1962. A new type of cable (lightweight) and a rigid repeater were designed to increase the capacity to satisfy the demand. The idea to include steel wire armor inside the center conductor resulted in a bigger coaxial cable that was lightweight as well. Three specifications were developed, with associated sea trials, in the United States, France, and the United Kingdom. The repeater was rigid, as already developed by the British Post Office for STC and SCL and by F&G. French and American manufacturers adopted the design, which presented the only possible way to increase the number of circuits. The bandwidth of the system increased from 500 kHz (60 channels) to 1 MHz (96–138 channels), and even 3 MHz (SAT1). SAT1, which was installed by STC from Portugal to South Africa in 1969, had the largest capacity system using vacuum tubes (3 MHz, 270=360 channels). During the period from 1961 to 1969, the system capacities were generally 60=80, 96=128, or 120=160 channels (4 kHz=3 kHz), and two networks were built.


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The first network was deployed by the British industry: STC and SCL. In July 1858, the Commonwealth Conference agreed to recommend the provision of a ‘‘round-the-world’’ telephone system for an estimated cost of £88 million. CANTAT1 was activated in 1961, followed by the transpacific COMPAC (Canada, Hawaii, Suva, New Zealand, and Australia) in 1963. Then, the program was updated and SEACOM was installed between Australia, Guam, Hong Kong, and Singapore from 1965 to 1967. United Kingdom–Portugal and SAT1 (1969) offered the connection to South Africa. Cables & Wireless ordered Pacific lines. Then, they sold IRUs to other operators (AT&T, Hawaii Telecom, KDD, OTC). The cable ships Monarch and Mercury shared the marine installations. In addition, STC and SCL installed a network for Italian and Spanish operators in the Mediterranean Sea and to the Canary Islands (PENCAN1, 1965). The second network was built by AT&T. Equipment was manufactured by Western Electric in their factories in Clark (repeaters) and Baltimore (cable). The network was a star throughout the United States. TAT3 was manufactured in 1963, TAT4 in 1965, and TPC1 (Hawaii, Guam, Philippines), Hawaii 1, and Hawaii 2 from 1962 to 1964. Because of the Cold War, AT&T built buried terminal stations protected from nuclear risk (Tuckerton, New Jersey; St. Hilaire, France; and Widemouth, Cornwall). The contribution of other suppliers was less important. F&G worked mainly for American military agencies (cables around Vietnam). Curiously, they stopped their contribution in 1970 when the Japanese industry started to manufacture cable for the transpacific TPC1. French industry built a significant network in the Mediterranean Sea from France to Corsica, Tunisia, Morocco, Israel, and Lebanon from 1965 to 1970. From 1958 to 1965, six transatlantic cable systems (TAT1 through TAT4, CANTAT, and SCOTICE–ICECAN), two transpacific systems (COMPAC–SEACOM, HAW–TPC1), and SAT1 were the largest projects ever installed. The projected cable across the Indian Ocean initially planned by the British industry to ‘‘girdle the world’’ was finally abandoned because of the low traffic stream across that ocean and the future installation of satellite facilities. Note that the permanent telephone line between the White House and the Kremlin, instituted during the Cold War by U.S. President Kennedy and USSR Premier Khrushchev and known as ‘‘the red telephone,’’ was routed on the GNTC network (ICECAN– SCOTICE). The national operators owned domestic networks and maintained bilateral relations with other national operators. ITU was the appropriate forum to elaborate technical specifications and tariffs (the ITU Recommendations). Cooperation was the key word of international relations, instead of the competition of the telegraphic era, facilitated by the continuous development of demand (10– 15% per year). The marine services of the major operators founded the Cable Damage Committee in 1958 [now the International Cable Protection Committee (ICPC)]. The main goal of this entity is to promote the safeguarding of undersea cables

34

GE´RARD FOUCHARD

from human and natural hazards, as well as the funding of projects and programs that are beneficial to the protection of submarine cable systems. Specific actions were promoted based on the International Convention of 1884 for the protection of submarine cables from the fishing industry. ICPC developed methods of jointing and testing aboard cable ships during repair operations. In the 1970s, ICPC members took part in discussions related to the definition of the new Law of the Seas (1982 Montego Bay Convention).

D. Wideband Submarine Cables (1970–1988) During the final period of the coaxial era, the transistor allowed an increase of the bandwidth and reliability. Another key item was the beginning of production by the Japanese industry: OCC (cables), NEC, and Fujitsu (repeaters and equipment) installed their first coaxial analog submarine systems between domestic islands for KDD and NTT in 1970 and 1971. At that time, the German industry ceased production of submarine cable systems and Submarine Cable Ltd. merged with STC. AT&T continued to lead the technology and install networks around the United States. TAT5 (720 channels) and TAT6 (4000 channels) were laid in 1970 and 1975, respectively. STC (United Kingdom) and Alcatel (France) offered a range of products to comply with the demand. STC led the market by offering each system ahead of their competitors:

5 MHz: 480-circuit system, Norway–Denmark, 1967 14 MHz: 1840-circuit system, Spain–Canary Island, 1971 40 MHz: 3600-circuit system, Rome–Palermo, 1977

Alcatel–Submarcom offered a similar range of systems (5, 12, and 25 MHz). As demand grew dramatically, from 1970 the network doubled, even tripled, with the new generation of submarine cable systems operating from 5 to 40 MHz: TAT5 through TAT7, CANTAT2, and ATLANTIS 2 in the Atlantic region, ANZCAN, TPC2, and TPC3 in the Pacific region, and Sea-Me-We. The first cable between European countries and the Far East was laid between Marseilles (France) and Singapore in June 1986. From Singapore, connections to Japan, Korea, and Australia were made available by other submarine cables; AT&T did not participate in the construction but purchased circuits to avoid two satellite steps between the United States and the Middle East (Saudi Arabia and Egypt). At the end of the period, STC announced the installation of 193,000 km and 8800 repeaters and Alcatel 75,000 km and 1200 repeaters. AT&T’s production was lower than that of STC, even considering the construction of the military cables not listed in available databases.


35

E. Technical and Economical Aspects 1. Submarine Cables and Telecommunication Satellites On April 6, 1965, Early Bird, the first telecommunication satellite, opened the era by offering 240 telephone circuits or one TV channel across the Atlantic Ocean. The public could not believe that the era of the submarine cable had closed. An international operating company, Intelsat, promoted the satellite industry; all operators owned Intelsat shares and benefited from the satellites’ business. Satellites provided telephone circuits and TV channels and worldwide coverage, even for countries without a seashore. These circuits were leased to Intelsat shareholders and were fully associated with the space program, ‘‘the new frontier’’ proposed by President Kennedy. Satellites provided most of the transpacific circuits and were the only connections for Indian and Middle East countries. The construction of the telephone network was managed to satisfy the demand of the operators and was carefully managed by the U.S. Federal Communications Commission (FCC). The American company Comsat managed the telecommunication space program under U.S. government control because only the U.S. industry had access to technology. U.S. industry manufactured and launched satellites for Intelsat up to 1980. The European rocket Ariane was used for only part of the Intelsat 5 program (beyond 1980). From the birth of the Intelsat organization in 1965, satellites and submarine cables were able to offer the same range of services for the carriers of telecommunications. Table I shows the development of cable and satellite programs from 1965 to 1990. Across the Atlantic, prices per circuit were equivalent and the telephone traffic was balanced between the routes. Submarine cable offered a better telephone quality and shorter transmission delays at a better price for distances shorter than a transatlantic crossing, such as across the English Channel and the Irish, North, Caribbean, China, and Mediterranean seas. The submarine cables did not provide video or television transmission. 2. Network Maintenance and Cable Protection The wording of construction and maintenance agreements (CMAs) was the forum to elaborate the configuration of new projects and explore future technology. The TAT and TPC systems were the first cables of a new generation and provided the opportunity to standardize the new generation of equipment. To maintain existing systems in operation, regional agreements were built to minimize maintenance costs. Major operators (AT&T, BPO, C&W, French PTT) were at the same time ship owners and service providers inside a geographic construction and maintenance agreement. From 1965 to 1985, such CMAs were elaborated in the North Sea, the Atlantic Ocean, the Mediterranean Sea, the South Pacific (Fiji), the Yokohama zone, the North Pacific, the Hawaii zone, Southeast Asia, and the Indian Ocean. CMAs were based on the following basis: ship

36

GE´RARD FOUCHARD

TABLE I Capacity of Intercontinental Satellites and Submarine Cables from 1965 to 1990 Notes

Dates

Satellite programs

Transcontinental submarine cablesa

1965

Intelsat 1 Early Bird Lifetime: 3 years

Atlantic: 6 cables (500 ccts) Pacific: Japan–US: 0 cable Australia–US: 0 cable Indian: 0 cable

1966–1967

Intelsat 2 4 satellites 1500 circuits or 4 TV channels Lifetime: 3 years

Atlantic: 6 cables (500 ccts) Pacific: Japan–US: 1 cable (128 ccts) Australia–US: 1 cable (80 ccts) Indian: 0 cable

1968–1970

Intelsat 2 4 satellites 240 circuits or 1 TV channel Lifetime: 5 years

Atlantic: 7 cables (1200 ccts) Pacific: Japan–US: 2 cables (128 ccts) Australia–US: 1 cable (80 ccts) Indian: 0 cable

1971–1975

Intelsat 4 7 satellites 4000 cctsþ2 TV channels Lifetime: 7 years

Atlantic: 7 cables (3000 ccts) Pacific: Japan–US: 2 cables (970 ccts) Australia–US: 1 cable (80 ccts) Indian: 0 cable

1975–1978

Intelsat 4A 6 satellites 6000 cctsþ2 TV channels Lifetime: 7 years

Atlantic: 4 cables (8400 ccts) Pacific: Japan–US: 2 cables (970 ccts) Australia–US: 2 cables (1920) Indian: 0 cable

1980–1985

Intelsat 5 & 5A 15 satellites 12,000 cctsþ2 TV channels Lifetime: 7 years

Atlantic: 5 cables (12,400 ccts) Pacific: Japan–US: 2 cables (970 ccts) Australia–US: 2 cables (1920 ccts) Indian: 1 cable (1000=2500)

Sea-Me-We 1 girdled the world in June 1986

1989–1992

Intelsat 6 5 satellites 24,000 cctsþ3 TV channels Lifetime: 13 years

Atlantic: 4 cables (80,000 ccts) Pacific: Japan–US: 2 cables (17,000 ccts) Australia–US: 2 cables (1920 ccts) Indian: 2 cables (10,000 ccts)

Digital satellites and fiber optic cables

The worldwide network imagined by Clarke is completed in 1969 by Intelsat

a The lifetimes of the submarine cable systems were not included because they are generally not in service beyond 10–15 years.

coverage paid as insurance (standing charges) and additional costs of the ship, such as fuel and personnel (running costs), paid per operation. Therefore, maintenance could be budgeted on a yearly basis in the range of 1.5–3% of the historical cost of the system. These organizations promoted repair procedures and standard handling, testing, and jointing equipment.


37

Repair operations were generally caused by fishing activities and anchoring (70%). Other causes are technical (15%), geological (10%), and unknown (5%). During the decade from 1960 to 1970, the rate of faults caused by the intensive development of fishing activities increase dramatically. A great number of faults were recorded in the vicinity of Newfoundland and two ships were permanently based in Saint John’s to carry out about 30 to 40 repairs per year on TAT1, TAT2, ICECAN, and CANTAT. Another region experienced new fishing problems when early in 1970, a series of cable breaks began to occur off Green Hill in water about 40 m deep, subsequently defined as being caused by local quahoggers. The quahog is a thick-shelled American clam, which was just beginning to be harvested. Since 1967, submarine cables have been buried as a means to eliminate cable breaks caused by fishing activities on the continental shelves and, in some areas of the world, to a reported depth of 1500 m. The first commercial use ever of a ‘‘sea plough’’ was made using AT&T Sea Plough 3, which retrofitted TAT3 and TAT4 off New Jersey over the length of the continental shelf. Sea Plough 3 was first operated by CS John Cabot in 1967 and has been operated by CS Vercors since 1975. TAT3 and TAT4 were refurbished in 1967, and in 1969 TAT5 was the first cable buried on the continental shelves of both Spain and United States. After that, burial was implemented wherever possible, reducing the faults from increased fishing activity. Thus triggered a rapid evolution in cable jetting with manned submarines, culminating in the remotely operated vehicle (ROV) in 1976, when the SCARAB program was developed by the service providers of the Atlantic Cable and Maintenance Agreement (AT&T, BT, FPTT, C&W, and Teleglobe). 3. Cable Ships and Offshore Works The development of submarine cable networks generated a need for a new generation of more powerful cable ships with a storage area for rigid repeaters. The main cable-laying ships were Long Lines (AT&T), Cable Venture, Neptune, and Mercury (C&W), and Marcel Bayard and Vercors (French PTT), and they installed most of the network of coaxial cables. From 1960, the basic newly built cable ship had diesel–electric engines to provide more power and flexibility than the steam engines of the cable ships of the telegraphic era. Transversal propellers helped to drive the ship. Navigation aids were significantly improved with the development of electronic positioning (Decca, Transit, Omega) offering continuous positioning and improving the navigation during the laying. Traditional astronomical positioning remained a requirement of only the oldest captains, as complementary navigation aid. Since the mid-1970s, new techniques have been implemented to improve the laying and repair operations: 1. Multibeam bathymetric equipment to determine the profile along the cable route during the survey

38

GE´RARD FOUCHARD

2. Satellite positioning to improve the navigation route and the location of the cable 3. Software aid to carefully follow the proposed cable route during the laying 4. Linear engines appropriate to repeater deployment 5. Sea ploughs for burial work during the main lay 6. ROVs to achieve the burial requirement immediately following laying and repair operations From 1970 to 1990, the work at sea dramatically improved, sometimes inspired by new techniques developed by the oil industry and oceanographic research. The target was to find solutions to improve the safety of existing cables and to reduce the fault rate ratio as well as the duration of repairs.

IV. THE ERA OF FIBER OPTIC SUBMARINE CABLES A. From Analog to Digital (1976–1988) The stagnation of coaxial cable technology arose with TAT6 in 1976, and the latest developments of new systems were done by STC (NG 45 MHz) and KDD (STM 140 MHz). In all developed countries, switching digital technology was generalized, as well as digital transmission systems on copper and coaxial wires. The first fiber optics were installed in terrestrial networks from 1982, and interfaces between analog submarine coaxial systems and digital terrestrial cables or microwaves (TMUX) were needed and developed, but they reduced the capacity and did not provide a long-term solution. Fiberglass appeared to be the most appropriate solution for a new step in submarine telecommunications, and the first challenge, once again, was to cross the Atlantic Ocean. The roots of optical fiber were found in 1966 in England when two British scientists of Standard Telecommunications Laboratories (STL, a research division of ITT=STC) reported that ‘‘A fiber glass material constructed in a cladded structure represents a practical optical wave guide. . . To be compared with existing coaxial cable, this form of waveguide has a larger information capacity and possible advantages in basic material cost’’ [2]. A decade later, in 1977, a 4km stretch between Hitchin and Stevenage, north of London, was installed by STL. The system operated at 140 Mbps at a wavelength of 850 nm transmitted over a graded-index multimode fiber. We were close to the reliable solution for a submarine cable system since gallium arsenide-based optoelectronic components were reaching a mature development level. Four major research centers, Standard Telecommunications Labs (United Kingdom), Bell Labs (United States), CNET (France), and KDD R&D Laboratories, decided to use the bright new single-mode fiber operating in the second window at 1300 nm (instead of multimode fibers at 850 nm, as used in most


39

terrestrial systems) to take advantage of the lack of dispersion and lower loss (0.4 dB=km). Consequently, a new development had to be refined, including design of laser diodes, photodiodes based on indium phosphide semiconductor optoelectronics, and associated integrated circuits to implement the needed digital regeneration in the submerged repeater. Other aspects needed to be redesigned: cable and repeater mechanical power-feeding equipment and protection from nuclear and electromagnetic pulse (IEMN). In the United Kingdom, the partnership between operators (BT and C&W), universities, and STC was well developed. In the United States, AT&T integrated research (Bell Labs), manufacturing, and network operations. The new technology was thought to provide an opportunity to differentiate satellite and cable technologies. In Japan, many companies had developments on the subject: NEC, Fujitsu, Hitachi, and Mitsubishi. Each operator had a different target: NTT needed high capacities for the domestic interisland network, and KDD needed long-haul systems with associated repeaters for international connections. In France, France Telecom and Alcatel divided the submarine cable development program to realize their first commercial link between Marseille and Ajaccio (Corsica) in less than 24 months. When the transatlantic TAT8 was planned (280 Mbps per fiber pair operated at 1300 nm), two goals were specified: the possibility of branching units to derive fibers and the integration of portions (segments) built by different suppliers. Then, AT&T, Alcatel, and STC built the three proposed portions to the United States, France, and the United Kingdom, respectively. Simultaneously, AT&T and KDD developed the transpacific TPC3. The structure of the cable and the reliability of the components (lasers, integrated circuits, and receivers) were the key items. Consequently, lasers and receivers were duplicated in the first systems. The first trials on fiber optic submarine cables carried out by the ‘‘Big Four’’ from 1980 to 1988 (TAT8) are detailed in Table II. B. Regenerated Fiber Optic Cables and the Consortium Era (1986–1995) A significant fiber optic network was installed from 1988 to 1995. Submarine fiber optic cables were laid from England to Belgium, Ireland, France, the Netherlands, Germany, and Denmark. France, Italy, and Spain installed domestic cables to Corsica, Sardinia, Sicily, Balearic, and the Canary Islands. Japan developed its domestic network. New suppliers took the benefit of the new technology to propose to the market repeaterless systems [Pirelli (Italy), Siemens (Germany), STK (Norway) and Ericsson (Sweden)]. TAT8 was commissioned in October 1988, offering a capacity of 7680 channels operating at 64 kbps, and managed to derive fiber pairs through a branching unit. Consequently, each terminal station located in the United States,

40

TABLE II

First Trials on Fiber Optic Submarine Cables, Carried Out by the ‘‘Big Four’’ from 1980 to 1988 (TAT8) STC BTI 1980

Country

United Japan Japan Kingdom Loch Fyne Izu Peninsula Sagami Bay Loop Inatori Kawazu 10 10.2 1.5

Location Landing points Cable length (km) Cable designc Water depth (m) Number of regenerators Number of pairs Wavelength (mm) Transmission rate (Mbps) a b

c

NFJ NTT 1980

4MM 2SM SM Shallow 200

NFJ NTT 1981

CGE CNET 1985

United States

France

1500

6 MM Deep

4 SM 2500

6 SM 70

1

2þ2

4þ2

8

3

— 1.3 280

2 1.3 280

— 1.3 280

2 1.3 280

3

NFJ KDD 1982

NFJ NTT 1982

Japan

Japan

Japan

6 SM 1300

4 SM 1000

12 SM 5000

2 SM þ 4 MM 1000 Deep

2

2

2

0

— 1.3 300

2 1.3 400

6 1.3 274–420

3 1.3 34

AT&T 1982

Alcatel CNET 1982

AT&T Telefon 1985

NFJ KDD 1981

United France States Sagami Sagami Sagami 500 nm Mediterranean Bay Bay Bay Bermuda Sea Ninomia Ninomia Yahatano Ship Loop Cagnes-JuanLoop Loop les-Pins 4.5 50 45 18.2 20

1

0

6 fibers 6 SM 700 500 1000 1500 1 1

3 1.3 140

— 1.3 6.4–32–100

3 1.3 400

3 1.3 280

STC BTL 1983

CNET CGE 1984

United France Kingdom Atlantic Mediterranean Sea Ship loop Port Grimaud, Antibes 80

STC BTI-RTB 1987

United Kingdom Canary Mediterranean North Sea Islands Sea (UK-B5) L. Cantera– Marseille– Broadstar Las Cailletilas Ajaccio Oostende 104 400 112

280

Suppliers: NFJ, NEC + Fujitsu; Alcatel, Cables de Lyon & CIT; STC (Standard Telephones & Cables Ltd.). Promoters: BTL, British Telecom Laboratories; CNET, Centre National d’Etudes des Telecommunications; Telefon., Telefonica de Espana; BTI, British Telecom International; RTB, Regie des Telecommuncations Belges. Type of fiber: MM, multimode; SM, single mode.

GE´RARD FOUCHARD

Suppliera Promoterb Date


41

France, and the United Kingdom was connected with the other two via a fiber pair. TPC3, using the same technology and facilities, was built in 1989 by AT&T and KDD. TAT8 and TPC3 demonstrated the feasibility of joining segments manufactured by different suppliers and of including branching units for derivations at a capacity of 140 Mbps. Then, AT&T laid a system from Florida to Venezuela (Trans Caribbean System), STC between Hong Kong and Taiwan, and NEC a Malaysia domestic. Alcatel built EMOS (Italy–Greece–Turkey–Israel) with Pirelli and TASMAN (Australia–New Zealand) in 1990. TASMAN was an opportunity for Alcatel to set up a cable factory in Australia in 1992. STC lost the Mediterranean and Australian markets. During the development of TAT8 fibers, the research community discovered that a second window operating at 1550 nm could be used. The advantage is a 0.18 dB=km fiber loss instead of 0.4 dB=km loss, which reduced the number of repeaters and the cost of the systems. The capacity of 560 Mbps per fiber pair was offered for the new TAT9 and TPC4, and five transatlantic submarines cables were installed from 1991 to 1995. Transpacific TPC4 (1992) was interconnected at Guam with PACRIM West and at Hawaii with PACRIM East, giving a wet connection to Australia and New Zealand. Sea-Me-We 2 completed the loop around the world in 1994. Then, CANTAT3 (2.5-Gbps capacity per fiber pair) was the latest long-haul regenerated cable technology designed by STC. Another revolution started in 1994. On January 1, the U.S. Federal Communications Commission decided that competition was not offered in the telecommunication business and broke up AT&T’s monopoly. The effect was not immediate; AT&T gave birth to ‘‘Baby Bells’’ operating the local networks and kept the long-distance operation and the management of the submarine cable technology. On the other side of the Atlantic, the conservative government of Maggie Thatcher introduced new competition rules for the benefit of Cable & Wireless and others and privatized British Telecom. The next steps came with the liberalization of telecommunications in the European Economic Community (EEC) and the deregulation of the telecommunications trade and services by the World Trade Organization (WTO). Now, the competition was not only opened between suppliers but also between operators. However, the consortium model continued to manage the major submarine cable systems despite the new rules. Three private cables were laid during the period: PTAT1 (private transatlantic, 1989), Transpacific (NPC, 1991), and Flag, initiated immediately following TAT12 (1995). The Flag idea was developed to compete against Sea-Me-We 2. A new way was shown, but private investments faced a difficult time during this period. New countries started to take advantage of the fiber technology: India, the Middle East, China (connected to Japan), Russia (connected to Denmark in 1992

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GE´RARD FOUCHARD

and to Japan and Korea in 1995), Argentina, and Uruguay (linked to Brazil and Europe in 1994). The 565-Mbps capacity offered either 15,360 or 23,040 telephone channels on a fiber pair. The fiber optic submarine cable system is summarized in Table III.

TABLE III Transatlantic Fiber Optic Submarine Cables (1988–2001)

Length (nm)

Year

Name

Landing West

Landing East

Contractors

1988

TAT8

United States

France–United Kingdom

6705

1990

PTAT1

Ireland–United Kingdom

1991

TAT9

United States– BER United States

Simplex=AT&T–STC– CDL=CIT STC

France–United Kingdom– Spain

Simplex=AT&T–STC– CDL=CIT

8000

1992

TAT10

United States

Germany–Netherlands

7500

1993

TAT11

United States

France–United Kingdom

1994 1995

CANTAT3 Columbus 2

Canada United States– Mexico

Ireland–United Kingdom Spain–Portugal–Italy

Simplex=AT&T–STC– CDL=CIT Simplex=AT&T–STC– CDL=CIT STC Simplex=AT&T–Pirelli– Alcatel

1996– 1997 1998

TAT12=13

United Kingdom–France

OCC, Pirelli

13,000

AC1

United States (2) United States

Germany

Simplex

8000

1999

Gemini

United States

United Kingdom

1999

Columbus 3

United States

Spain

AT&T SSI, Alcatel

6260, 5865 10,000

2000

Flag Atlantic 1

United Kingdom–France

Alcatel

12,570

2001

TAT14

United States (2) United States (2)

KDD–SCS (Pirelli)

15,000

2001

Yellow 2 (AC2)

United States

Denmark–Germany– Netherlands–France– United Kingdom United Kingdom

Tyco

6500

2001 2001 2002

Hibernia Tyco Atlantic Apollo

United States United States United States (2)

Ireland–Spain United Kingdom France–United Kingdom

Tyco Tyco Alcatel

8000 7500 13,000

a b

7341

6500 6500 11,000

Read capacity as follows: M, Mbps; G, Gbps. Read cable capacity as follows: 2 4 80 10 G ¼ 2 cable 4 fiber pairs 80 lambda (colors) 10 Gbps.

43


C. Optical Amplification and WDM Technology (1995–2000) Based on work developed in the United States, Japan, and Europe, the industry began to consider optically amplified systems to either achieve longer repeater spacing or increase the capacity offered. The great advantage is to compensate the fiber loss, without any need for optical=electrical conversion of the signal, by analog amplification of a digital signal. However, any new technology had to prove its feasibility and reliability.

Cable ships

Owners

Initial capacitya,b

Full capacitya,b

Capacity E4=STM1

Long Lines, Alert, Thevenin Cable Venture, Mercury, E Sharp Long Lines, John Cabot, Vercors Long Lines

Consortium

2280 M

2280 M

4

CW=Mercury– Sprint Consortium

4420 M

4420 M

12

2560 M

2560 M

8

Consortium Consortium Teleglobe–BT AT&T–TMX, Telefonica– Marconi Consortium

3560 M 3560 M 32:5 G 2560 M

3560 M 3560 M 32:5 G 2560 M

12 12 60 12

225 G 210 G 2482:5 G 280 G 2262:5 G 30 G 222:5 G 10 G 246010 G 2400 241610 G 2640 G

2235 G 230 G 24162:5 G 2160 G 2262:5 G 30 G 282:5 G 40 G 246010 G 22400 G 241610 G 2640 G

360

4210 G 80 G 4210 G 160 G 221410 G 2280 G 121610 G

44810 G 1920 G 243210 G 2560 G 246410 G 22560 G 248010 G

8000

Dock Express, Skandi Hav Innovat.–Nexus, Fresnel, Vercors Global Sentinel

Global Crossing (MFS) Worldcom, Cable & Wireless Consortium

Fresnel

Flag

Innovat.–Nexus,

BT–CW–WDC– FT–DTAG– AT&T–SP Level 3, Global Crossing 360 Networks

Fresnel, Vercors

Vercors

Tycom Cable & Wireless

1000 190 250 15,000 4000

12,000 16,000 20,500

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GE´RARD FOUCHARD

In 1990, two directions were explored to produce optical amplifiers, the semiconductor laser amplifier (cousin of the laser used as a transmitter) and the erbium-doped fiber amplifier. Surprisingly, the second, more imaginative way was easier to operate and rapidly provided better performance. The new era started with TAT12=13 and TPC5, which were laid during the years 1994 and 1995. They offered a capacity of 5 Gbps per fiber on a single wavelength, which is twice the higher demonstrated regenerated system. Soon, forward error correction (FEC) was proposed and implemented by Alcatel to improve system performances and decrease costs. It could not be implemented on the TAT12=13 system but was on all further 5-Gbps amplified systems. During the completion of these new amplified systems, the research laboratories showed that technology could be improved by multiplexing several wavelengths on the 1550-nm bandwidth (wavelength-division multiplexing, WDM). Interestingly, the full adoption of the SDH (synchronous digital hierarchy) led to a decrease of the channel capacity from 5 to 2.5 Gbps (STM16) when WDM was first deployed. Sea-Me-We 3 was the first system developed on the above basis. The system, at a total cost of US$1.35 billion, provided digital connectivity to 33 countries, in 39 terminal stations from northern Europe (Germany, Belgium, United Kingdom, France) to Singapore and from Singapore to Japan, Korea, and Australia. The consortium of 93 investors managed 40,000 km of cables and repeaters for a total specified with 8l (wavelengths); the delivery of traffic to land stations was done by wavelength add and drop. All suppliers participated in the project: AT&T (before merging with Tyco), Alcatel, Pirelli, KDD, and Fujitsu built the whole system in July 1999. At the birth of the new millennium, new projects were awarded to consortia: China–United States (the longest optical transmission with 12,000 km from coast to coast), Southern Cross (Australia–New Zealand–United States–Hawaii–Japan), SAFEþSAT3 (around Africa), and Atlantis 2 (from Europe to Brazil). All of these systems were implemented between 2000 and 2002. WDM technology offered new opportunities to upgrade systems by adding wavelengths. This was done for TAT12=13 in 1999, upgrading each fiber by 3 wavelengths. The second opportunity was the increase of capacity per wavelength from 2.5 to 10 Gbps (STM64) and the increase in the number of wavelengths. Japan–United States was the first 10-Gbps WDM system with 16 wavelengths, and soon TAT14 with the same capacity per fiber. Apollo’s total capacity is 80 wavelength times 10 Gbps per fiber pair. The new operators born with the deregulation in the United States found enough financing to deploy five new transatlantic systems, most of them in a ring (AC1 and Yellow by Global Crossing, Gemini by Worldcom, Apollo by 360 Networks, Tyco Atlantic by Tyco) from 1998 to 2001, offering a capacity of about 10,000 Gbps across the pond. A worldwide network was deployed and the capacity offered increase sharply. It is 4,640 Gbps in both Americas, 14,320 Gbps in the Pacific, and 19,220 Gbps in Pan-Asian regions. Other


45

pharaonic projects were planned: Oxygen (370,000 km, 270 landing points) and Africa One (around Africa), but they are still in the planning stage. To cope with the market demand, factories have increased their capacity of production to reach more than 150,000 km=year. Industry follows the demand of capacity offered to new customers, mainly to Internet users. In less than 10 years, the total length of fiber optic cables around the world has reached about 650,000 km, more than the telegraphic network installed in the past 100 years.

D. Cable Ships and Offshore Works The huge development of the network was followed by a transformation of the cable ship fleets. During the telephone era, the ‘‘historical’’ operators had monopolies in their countries. They owned cable ship fleets to offer installation services to the suppliers and maintenance facilities to other operators through cable and maintenance agreements. That time is over. On October 1, 1987, BT Marine became a subsidiary of British Telecom and in 1995 merged with Cables & Wireless Marine. In 1996, AT&T sold its fleet and industry to Tyco. In 1999, Temasa, the subsidiary of Telefonica, was sold to Tyco, and CW-Marine became Global Marine when purchased by Global Crossing. Alcatel in 1999 purchased Danish Telecom Marine, as well as CTC. France Telecom Marine was founded on January 1, 2000, following the legal status already adopted by Electra (Italy), E Marine (UAE), ACPL (ASEAN countries), and cable ship companies in Japan, Korea, South Africa, and Brazil. All maintain domestic and international networks.

FIGURE 2 Evolution of transmission capacity over the Atlantic Ocean from 1860 to 2001.

46

GE´RARD FOUCHARD

The cable-laying ships are generally owned by the suppliers (Tyco and Alcatel). The number of ships available on the market increased sharply between 1995 and 2001 from 60 to 140 units according Cable Lay and Maintenance Vessels [3]. Stiff competition is expected in the coming years. The basic rule of a submarine cable installation is to carefully follow the route identified during the survey. On the continental shelves, cable is buried in depths up to 1000 m and sometimes 2000 m. According to fishing activities, the burial depth is in the range of 1–3 m. When the ploughing system has not reached the target depth, an ROV using jetting tools is deployed. Near the landing point, wheel or rock trenches are generally used to protect the cable against anchoring. When a cable crosses a pipeline, specific protection is used (mattresses, rock dumping, coat protections). Near Singapore, the safety of the cable landings requires a specific deep burial (up to 10 m) from the shore to 30 km offshore. Cable installation has become more professional, sophisticated, and costly. Cable repair operation procedures have been modified following the new installation rules. ROV, jointing, and testing facilities are available to offer appropriate maintenance services to cable owners. The owners have a choice between existing cable maintenance agreements or services provided by the suppliers.

V. CONCLUSION Between 1860 and 2001, the submarine cable network was able to provide a full range of services, including telegraph, telephone, fax, data, video, and now multimedia over the Internet. The capacity offered to telecommunications users during that time, based on the crossing of Atlantic, which was the beginning of any new technology, is shown in Fig. 2. The parallel expansion of the international network based on cable and satellites from 1960 to 1990 was complementary and was carefully managed by the U.S. authorities. The launching of telecommunications satellites, providing TV and telephone services, was more appreciated by the public than the abyssal conquest of the sea by the submarine cables. Nowadays, with fiber optics, a submarine cable can transport 100 times bigger traffic per fiber than a satellite channel. Submarine cables are thus now constituting the backbone of the voice, data, and Internet international network. The global fiber optic network is shown in Fig. 3. Liberalization of telecommunications, new operators, and high-level financial investments have dramatically increased the network extension. Private investors, like domestic operators, private companies, oil industry and scientific programs develop their submarine cable systems worldwide. Internet and TV services are fully dependent on the submarine cable network.


FIGURE 3

The global fiber optic network.

47

48

GE´RARD FOUCHARD

REFERENCES 1. K. R. Haigh. Cable Ships and Submarine Cables. Adlard Coles Ltd., London (1968). 2. Proc. IEE 113(7), (July 1966). 3. OPL. Cable Lay and Maintenance Vessels. Houston (2001).

BIBLIOGRAPHY 4. H. Barty-King. Girdle Round the Earth: Cable and Wireless. Heinemann, Boston (1979). 5. C. Bright. The Story of the Atlantic Cable. Georges Newnes Ltd., London (1903). From Elektron to E-Commerce-150 Years of Laying Submarine Cables. Alcatel, France (2000). 6. Les Grande´s Dećouvertes: Les Te´lećommunications. UIT, Geneva (1991). 7. C. N. N. Nair. The Story of Indian Overseas Communications. VSNL (1988). 8. C. E. Roden and A. G. Richardson. Submarine Cable Mechanics and Procedures. Bell Laboratories, New Jersey (1974). 9. S. Shimura. International Submarine Cable Systems. KDD Tokyo (1985). 10. The Law of the Sea. United Nations, Geneva (1983). 11. D. Vierus. Kabelleger aus aller Welt. Transpress (1989). 12. H. D. Wilkinson. Submarine Cable Laying and Repairing (1896). 13. World’s Submarine Telephone Cable Systems. U.S. Department of Commerce, Washington, DC (1980, 1984, 1990). 14. S. Zweig. Les tre`s riches heures de l’humanite´. Belfond (1989).

PART

II

SUBMARINE SYSTEM DESIGN


3 BASICS OF DIGITAL OPTICAL COMMUNICATIONS PHILIPPE GALLION Ecole Nationale Supe´rieure des Te´lećommunications, Paris, France

I. OPTICAL CHANNEL AND THE MULTIPLEXED DATA A. Optical Bandwidth B. Optical Channel Capacity C. Binary Optical Channel and the Symbol Probabilities II. MODULATION FORMATS AND MODULATION BANDWIDTH A. Parameters to Be Modulated B. Spectrum of Digitally Modulated Signals C. Modulation Formats D. Modulation Implementation III. SIGNAL AND NOISES AT THE RECEIVER A. Photodetector Sensitivity and Optical-to-Electrical Signal Conversion B. Noise Generation and Demonstration Mechanisms at the Receiver C. Noise Addition in Optical Amplification D. Optical Signal-to-Noise Ratio IV. RECEIVER PERFORMANCE EVALUATIONS A. Electrical Signal-to-Noise Ratio Definition B. Bit Error Ratio and Receiver Sensitivity Definitions C. Shot-Noise-Limited Ideal Detection D. Amplifier Less Thermal-Noise-Limited Detection E. Detection of Preamplified Optical Signals Acknowledgments References


51

52

PHILIPPE GALLION

The early optical fiber communications system deployed in the late 1970s exhibited very poor performance. The major reasons for this were the fiber loss in the 0.8-mm wavelength window used, the multimode guiding characteristics, and the natural wide spectral width of the optical source. The latter was several degrees larger than the modulation-induced bandwidth because the early semiconductor lasers operated in multimode and unstable frequency regimes. The optical modulation behaved like an on–off keying of a wideband optical noise source, reducing the digital communication technique to a minor aspect of system development. Now, the great technological progress made with fiber and with the devices for using fiber allows us to take greater advantage of digital communication techniques in order to improve system performance. Current system development is a very exciting field that combines advanced information and digital communication theory concepts with the most recent device-oriented developments and advances in physics on the dynamics, noise, and nonlinear propagation characteristics of optical signals. Three illustrative examples of multidisciplinary key issues today are the high spectral efficiency modulation techniques, which can economize the optical bandwidth (increasingly a rare resource), the understanding and modeling of amplifier quantum noisegenerating system penalties, and the forward error correction (FEC) techniques, to improve overall system performance. Another interesting feature of the field is the need to address theoretical and engineering aspects at the same time, thanks to its fundamental nature and to the rapidly growing applications foreseen for this domain. The main objective of this chapter is to present a comprehensive approach to the basic concepts of digital optical communications. A number of very good textbooks [1–11] have been written for the field and they already contain the fundamentals about digital optical communications. Standard discussions and illustrations are often to be found in many of them and attribution of certain material to any single source is often a difficult task. The aim of this chapter is to focus on issues of current interest, such as the understanding and modeling of optical noise and the basics of how to go about improving spectral efficiency and exploitation of the potential of the optical channel. The first section is related to the basic concepts of information and digital communication theory in the optical domain. Although a detailed explanation of information theory development is beyond the scope of this chapter, a heuristic presentation of its bases and of the optical channel capacity is nevertheless proposed. The binary information sequence and the asymmetric binary optical channel are introduced. Section II is devoted to the properties and the performances of the various modulation formats of optical signals. The different modulation parameters for the optical field are presented first. The general discussion of spectral occupancy of baseband and optically modulated signals is applied to the nonreturn to zero and return to zero modulation formats whose bandwidth and properties are shown. A short presentation on the drawbacks of actual optical modulation

3. BASICS OF DIGITAL OPTICAL COMMUNICATIONS

53

implementations and their system impairments completes this section. Section III provides a system-oriented approach to noise generation and noise demonstration at the receiver level. The various noise sources are discussed and their individual contributions to the photocurrent fluctuation variance are expressed. The influence of additive optical amplitude noise on the receiver is also discussed, in terms of photocurrent variances. Optical amplification, preamplification, and the diverse number of amplifier types are key issues for current system developers. The general expression of the minimum amplitude additive noise of any optical amplifier is derived. The given approach is valid for any type of amplifier and generalizes the specific derivation of amplified spontaneous emission, usually used for laser amplifiers. Direct consideration of the amplification noise as an optical random amplitude process greatly simplifies the analysis, avoiding the randomization of the average spontaneous emission rate generally used for laser amplifiers. Section IV considers receiver performance by dealing with the various noise contributions to the output electrical signal-to-noise ratio. Performance is discussed in terms of the bit error ratio (BER) and receiver sensitivity is expressed in photons=bit. The performances of the ideal shot-noise-limited receiver, of the thermal-noise-limited photodetector, and of the optically preamplified photodetector are discussed and compared. I. OPTICAL CHANNEL AND THE MULTIPLEXED DATA A. Optical Bandwidth Optical fiber communication systems use carrier frequencies in the near-infrared region of the electromagnetic spectrum. The typical value of the optical carrier frequency n is 193 THz for a wavelength in the 1550-nm range. Depending on the high value of the carrier frequency, a large modulation bandwidth is likely when there is a simple optical transposition of the narrowband communication techniques, used in the radio-frequency range, in which the modulation bandwidth is equal to only a few percentage points of the relative modulated carrier frequency. The expected modulation bandwidth gain (as compared to the radiofrequency range) is in the ratio of the carrier frequencies. Using a radio-frequency carrier reference of 2 GHz, the expected bandwidth gain is 10,000. Beside the high value of the carrier frequency, another key feature of the optical communication field is the wide low-loss window of silica optical fibers, which allows an overall guided optical bandwidth of the order of 10 THz. B. Optical Channel Capacity 1. Information and Entropy The channel capacity C is defined in information theory [12–14] as the largest rate at which information can be transmitted with the smallest possible

54

PHILIPPE GALLION

error probability. An appropriate definition of the information I(x) will consider that an event X ¼ x of a stochastic process X, having a high probability pðxÞ, conveys less information than an event occurring with less probability. The definition of information I ðxÞ should also have an additional law for the joint occurrences of independent events for which the probabilities are multiplied. The information is therefore measured by log pðxÞ. The base of the logarithm, usually selected as either e in the field of physics or 2 in the field of digital communications, determines the unit. In the latter case, units are ‘‘bits’’ and the information I ðxÞ is expressed as I ðxÞ ¼ log2 pðxÞ. The ensemble average value of I ðxÞ, over all the possible occurrences of the stochastic process X, is called the differential entropy: ð þ1 pðxÞ log2 pðxÞ dx ð1Þ HðX Þ ¼ 1

This definition should be considered a natural generalization of the discrete variable result (no attention is paid here to its physical meaning or possibly troublesome mathematical features). The signal with the largest entropy is the most interesting one to be transmitted. It is easy to show that a zero-mean Gaussian probability distribution with variance s2x , given by 1 x2 pðxÞ ¼ pffiffiffiffiffiffi exp 2 ð2Þ 2sx sx 2p

maximizes the input entropy for a given input signal power [12–15] and therefore yields the maximum average information input into a communication channel: 1 Hmax ðX Þ ¼ log2 2ps2x e 2

ð3Þ

2. Communication Challenge In a communication channel, the realization of an output event Y ¼ y provides information about an original input one X ¼ x [12–14]. The output observation increases the input probability from pðxÞ to the joint probability pðx=yÞ. The mutual information is defined as the logarithm of the ratio of these two probabilities: I ðx; yÞ ¼ log2

pðx=yÞ pðxÞ

ð4Þ

The average conditional information, also called the conditional entropy HðX ; Y Þ, can be expressed as: ð þ1 HðX =Y Þ ¼ pðx=yÞ log2 pðx=yÞ dx ð5Þ 1


55

The average value of the mutual information I ðX ; Y Þ is the difference between the input entropy and the mutual entropy: I ðX ; Y Þ ¼ HðX Þ HðX =Y Þ

ð6Þ

which expresses the improvement of input knowledge, and therefore the entropy reduction provided by the output observation information. It is easy to show that the mutual information is symmetrical, meaning that I ðX ; Y Þ ¼ I ðY ; X Þ. The communication challenge is to obtain the best possible value for such mutual information. The maximum theoretical value of the mutual information is the channel capacity. 3. Waveform Communication Channel Capacity The highest achievable capacity of the continuous optical channel [16, 17] can be obtained by considering that the input and output signals are the optical field waveforms EðtÞ within a limited bandwidth Bo . Let us suppose that the output signal y ¼ Eo ðtÞ is obtained by addition of an independent noise process N ðtÞ to the input signal x ¼ Ei ðtÞ. Assuming that both the input signal and the additive noise have a zero-mean Gaussian probability distribution, with variances s2x and s2N , respectively, the output signal is also a Gaussian random process, whose variance is s2y ¼ s2x þ s2N . It is obvious that HðY =X Þ ¼ HðN Þ and the average mutual information is expressed as: 1 1 I ðX =Y Þ ¼ HðY Þ HðN Þ ¼ log2 ð2ps2y eÞ log2 ð2ps2N eÞ 2 2

ð7Þ

The information theory proves that these Gaussian conditions maximize mutual entropy. Then Eq. (7) gives the channel capacity, expressed in bits per second, as: 1 s2 C ¼ log2 1 þ 2x ð8Þ 2 sN Assuming a limited optical bandwidth Bo , the involved signals can be sampled at discrete times with a sampling frequency 2Bo. The average powers are PS or N ¼ 2Bo s2S or N . The channel is used at a rate 2Bo and the capacity can finally be expressed in the form initially derived by Shannon [12]: PS C ¼ Bo log2 1 þ ð9Þ PN Bandwidth is not the only key issue in increasing channel capacity, since the noise power is in general a function of bandwidth. 4. Waveform Optical Channel Capacity The optical channel capacity cannot be increased indefinitely, despite the wide optical bandwidth available in the optical range. As shown in Section III, the minimal single-sided optical noise power spectral density is SN ¼ hn=2, where h ¼ 6:63:1034 J s is Planck’s constant and the minimum average optical noise

56

PHILIPPE GALLION

power PN ¼ ðhn=2ÞBo is proportional to the bandwidth. Therefore, the optical channel capacity, treated in terms of optical field, is: 2PS ð10Þ C ¼ Bo log2 1 þ hnBo Thus, the capacity of the optical channel is limited by signal-to-noise considerations, including amplifier noise, fiber dispersion, and fiber nonlinearity impairments. The theoretical value of the channel capacity, obtained by continuous signal assumption, must be considered an ultimate limit. We should note that information theory provides no information on any practical means of achieving this limit. The theoretical spectral efficiency is defined as the ratio of the channel capacity to the optical bandwidth. The photon energy hn is of the order of 1019 J, for a wavelength in the 1500-nm range. By assuming, for instance, that the average optical power is 50 dBm, the spectral efficiency can be significantly larger than 1 bps=Hz, depending on the optical bandwidth. The best reported values for today’s optical communication systems are far less than this. The reasons for this poor performance lie in the use of the optical power as the information carrier, instead of the optical field itself, in the low efficiency of the optical digital modulation format, in the degradation induced by the information process, and so on. The high bandwidth limit of the optical channel capacity, given by Eq. (10), is: C¼

2PS 2P log2 e ¼ 1:44 S hn hn

ð11Þ

Assuming again, for instance, an average optical power of 50 dBm and a photon energy hn in the 1019 J range, the channel capacity is the 10þ11 bps range. C. Binary Optical Channel and the Symbol Probabilities The binary sequence to be transmitted is usually available in the form of an electrical signal taking one of two random discrete values. The simplest representation consists of an electrical current or voltage, which is either ‘‘on’’ or ‘‘off.’’ These two possibilities represent the symbols of the digital message In and are called ‘‘bit 1’’ and ‘‘bit 0,’’ respectively. The finite time duration of each bit is called the bit period T, and Rb ¼ 1=T is the bit rate. By using a discrete case version of Eq. (1), the information entropy of a binary message is: HðX Þ ¼ pð1Þ log2 pð1Þ pð0Þ log2 pð0Þ

ð12Þ

in which pð1Þ and pð0Þ ¼ 1 pð1Þ are the probabilities of transmitting ‘‘1’’ and ‘‘0,’’ respectively. It is easy to confirm that the information entropy is maximum, meaning a binary message is more informative, when the symbols ‘‘1’’ and ‘‘0’’ have the same probability of occurring. Therefore, receiver performances are discussed in Section IV based on the assumption that pð1Þ ¼ pð0Þ ¼ 1=2.


57

FIGURE 1 Model for the binary optical channel.

Figure 1 represents the modeling of the binary optical channel. Pð0=1Þ is the probability of deciding that 0 is received when 1 is transmitted, and Pð1=0Þ is the probability of deciding 1 when 0 is transmitted. As discussed in Section IV, the use of the optical power as the information carrier leads to a nonadditive noise and therefore to different noise distributions when the symbols 0 or 1 are transmitted. The optical channel is usually only made symmetrical by an appropriate tuning of the decision level, so the above assumption may be not optimal from an overall system point of view. However, we consider, in this chapter, only very low error probabilities. For high error probability systems, improvements may result from the use of more advanced information representation.

II. MODULATION FORMATS AND MODULATION BANDWIDTH A. Parameters to Be Modulated Deliberate variations of one parameter of the electrical field of the light have to be introduced to represent the information signal to be transmitted. This operation, making the light the carrier of the information, is called optical modulation. We restrict our discussion here to digital modulation. The choice of the varying parameter and the way to accomplish this change are key issues in recovering the carried information from the receiver. Let us first consider a single propagation mode and an unmodulated optical carrier of single frequency n0. Omitting the spatial dependence, the associated optical field can be written in the form: EðtÞ ¼ Re½A exp j2pn0 t ¼ Re½jAj exp jð2pn0 t þ jÞ

ð13Þ

where Re denotes the real part, A is the complex amplitude, and j is the optical phase. Each of these field parameters may be eligible for the modulation. The modulation of polarization is also possible for free-space optical communications [1], but is difficult to implement in standard optical fiber communications, which

58

PHILIPPE GALLION

do not preserve it through propagation. Phase modulation such as phase shift keying (PSK) or frequency modulation such as frequency shift keying (FSK) or more sophisticated modulation such MAQ or M-ary give excellent performances in the radio-frequency range and may be implemented in optics. However, the standard optical receivers are only sensitive to the optical intensity I ðtÞ ¼ AðtÞA*ðtÞ and disregard the information carried by the optical phase and the frequency. The modulation formats involving optical phase or optical frequency require coherent detection techniques [9, 10, 18]. Furthermore, frequency and phase are difficult to control and to preserve through nonlinear propagation. Moreover, additional sensitivity to phase noise may degrade receiver performance. For these reasons, the bipolar modulations using antipodal signals with symmetric positive and negative values of the complex amplitude are not, for instance, presently used in optical communications. According to these considerations, the simplest modulation technique consists of digital changes in the modulus of amplitude (or the intensity), restricted to two positive levels, to accommodate the nonlinear nature of the optical channel. The simplest amplitude shift keying (ASK) technique, obtained when one of the two levels equals to 0, is called on–off keying (OOK). OOK modulation is easily implemented by direct modulation of a semiconductor laser or by electroabsorption or electro-optic modulation of a continuous-wave (CW) optical signal. A more advanced technique is to conserve (symbol ‘‘1’’) or to suppress (symbol ‘‘0’’) pulses, with optimized time and frequency properties, in a periodic optical pulse stream [3–11].

B. Spectrum of Digitally Modulated Signals 1. Optical Power Spectrum of Modulated Signals Let us assume that the modulated optical signal has a frequency content concentrated in a narrow band of frequency around the optical carrier frequency n0 . For an optical carrier frequency of the order of 200 THz, this assumption is justified for a modulation at a bit rate up to 100 Tbps. Such signals are referred as quasi-monochromatic signals in the optical engineering field and as bandpass signals in communication engineering. The real value of the modulated optical signal is usually represented by EðtÞ ¼ Re½AðtÞ exp j2pn0 t

ð14Þ

where AðtÞ is the complex envelope, also called the equivalent low-pass signal. Because EðtÞ is a stochastic process with an infinite energy, its Fourier transform does not exist. Assuming that EðtÞ is a stationary process and according to the Wiener–Kintchine theorem, the distribution of the optical power SE ð f Þ as a function of the frequency f, called the power spectrum density, can be obtained as


59

the Fourier transform of the autocorrelation function of the optical field [13, 14, 19]: ð þ1 RE ðtÞ expðj2pf tÞ dt ð15Þ SE ð f Þ ¼ 1

The autocorrelation function of the optical field is defined as the ensemble average RE ðtÞ ¼ hE*ðtÞEðt þ tÞi. Because EðtÞ is real, RE ðtÞ is an even function and we have SE ð f Þ ¼ SE ðf Þ meaning that the two-sided optical spectrum is symmetrical. RE ðtÞ can be expressed as a function of the autocorrelation function of the complex envelope RA ðtÞ ¼ hA*ðtÞAðt þ tÞi by 1 RE ðtÞ ¼ Re½RA ðtÞ exp j2pn0 t 2

ð16Þ

Using the Wiener–Kintchine theorem, the two-sided optical power spectrum is expressed as a function of the baseband power spectrum: 1 SE ðnÞ ¼ ½SA ðn n0 Þ þ SA ðn n0 Þ 4

ð17Þ

The factor of 1=4 in Eq. (17) shows that the complex envelope power is twice that of the real field and that the two-sided optical spectrum doubles the contribution to power. The baseband power spectrum is obtained by the Fourier transform of the autocorrelation function of the complex envelope: ð þ1 RA ðtÞ expðj2pf tÞ dt ð18Þ SA ð f Þ ¼ 1

The autocorrelation function of the complex envelope is in general not symmetrical. The spectrum of the modulated optical field is a simple transposition of the spectrum of the complex envelope, so the bandwidth discussion can be limited to the baseband spectrum. For this reason the optical bandwidth is twice the baseband spectrum bandwidth. 2. Baseband Power Spectrum of Modulated Signals Let us consider the complex envelope, that is, the equivalent low-pass optical signal AðtÞ, as the product, in the consecutive time slots of duration T, of the transmitted symbols In by the pulse function aðt nT Þ: AðtÞ ¼

n¼þ1 P n¼1

In aðt nT Þ

ð19Þ

The transmitted symbols of the digital message are In , T is the bit duration, and RB ¼ 1=T is the bit rate. The term aðtÞ represents the finite energy signal pulse, with time duration equal to, or smaller than, T. The latter assumption is specific to the optical field when power modulation is used, since the generation of simultaneous orthogonal signals is not possible in this case. Because the

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PHILIPPE GALLION

transmitted information sequence is a random process, AðtÞ defined by Eq. (19) is an infinite energy stochastic process and its Fourier transform does not exist. When AðtÞ is assumed to be stationary, its power spectrum is easily calculated by considering AðtÞ as the linear filtering of the information sequence through a filter with an impulse response I ðtÞ: I ðtÞ ¼

n¼þ1 P n¼1

In dðt nT Þ

ð20Þ

where d denotes the Dirac function. According to the basics of signal processing, the output power spectrum SA ðf Þ of this filter can be expressed as follows: SA ð f Þ ¼ j~að f Þj2 SI ð f Þ

ð21Þ

in which SI ðf Þ is the power spectrum of the data sequence and j~að f Þj2 is the energy spectrum of the pulse, equal to the square modulus of its Fourier transform, defined as: ð þ1 a~ ð f Þ ¼ aðtÞ expðj2pftÞ dt ð22Þ 1

According to the Wiener–Kintchine theorem, the power spectrum of the data sequence SI ð f Þ is obtained by the Fourier transform of its autocorrelation function, RI ðtÞ, defined as the ensemble average: RI ðtÞ ¼ hI ðtÞI ðt þ tÞi ¼

þ1 P

þ1 P

n¼1 m¼1

hIn Im idðt nT Þdðt þ t mT Þ

ð23Þ

in which hIn Im i is the discrete time autocorrelation function of the symbols. Assuming a stationary data sequence and introducing the variable p ¼ m n; RI ðtÞ is rewritten as RI ðtÞ ¼

þ1 P

p¼1

hIn Inþp idðt pT Þ ¼

P 1 þ1 r ð pT Þdðt pT Þ T p¼1 I

ð24Þ

in which rI ð pT Þ ¼ T hI ðtÞI ðt þ pT Þi is the continuous time correlation function of the symbols. Denoting mI and s2I as the mean value and the variance of the information symbols, respectively, and assuming independent symbols, their correlation function is: 2 sI þ m2I for p ¼ 0 ð25Þ rI ð pT Þ ¼ m2I for p 6¼ 0 Equation (24) can then be rewritten as RI ðtÞ ¼

P s2I m2 þ1 dðtÞ þ I dðt pT Þ T T p¼1

ð26Þ


61

The Fourier transform of Eq. (26) gives the power spectrum of the data sequence SI ð f Þ: P s2 m2 þ1 n ð27Þ SI ð f Þ ¼ I þ 2I d f T T n¼1 T

By reporting Eq. (27) in Eq. (21), the baseband power spectrum is finally expressed as [9, 14]: P

n

2 s2 m2 þ1 n ð28Þ SA ð f Þ ¼ I j~að f Þj2 þ 2I

d f

a~ T T T n¼1 T

This spectrum consists of the sum of a continuous component, directly related to the pulse spectrum, and a discrete frequency component. The latter usually vanishes in radio-frequency communications, in which the use of a zero-mean data sequence, using antipodal signals, is possible. This must be considered for the ASK data sequence for which In ¼ 0 or 1 and therefore m2I ¼ s2I ¼ 1=4. Assuming a Fourier transform limited time-bandwidth product for a pulse with duration T, the main contribution to the discrete spectrum is at zero frequency. For pulses shorter than T or for chirped pulses, the discrete terms of higher order must be considered. C. Modulation Formats 1. NRZ Modulated Signal Nonreturn-to-zero (NRZ) modulation consists of turning on the light during the total bit duration when the symbol to be transmitted is ‘‘1,’’ and to suppress it completely when the symbol to be transmitted is ‘‘0.’’ Figure 2a shows this simplest and easily modeled pulse shape format. The pulse profile is in the following form: 1 for 0 < t < T ð29Þ aðtÞ ¼ 0 elsewhere with the square Fourier transform: j~að f Þj2 ¼

T sin pTf pTf

2

ð30Þ

The general expression for the baseband modulation spectrum is obtained by using Eq. (30) in Eq. (28), which can be simplified to 2 T sin pTf 1 ð31Þ þ dð f Þ SA ð f Þ ¼ 4 pTf 4 Figure 3 presents the normalized power spectrum for the NRZ modulation format. When an actual spectrum is observed, the relative height of the discrete part of the spectrum depends on the setting of the spectrum analyzer. For this

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PHILIPPE GALLION

FIGURE 2 Coding of the binary sequence ‘‘0101101’’ by using (a) NRZ, (b) rectangular shaped RZ, and (c) Gaussian pulse RZ modulation formats.

reason the continuous part and the discrete part of the spectrum are represented separately. As a result of an average transmission over half of the time, the normalized optical power is ð þ1 1 ð32Þ SA ð f Þ df ¼ PNRZ ¼ 2 1 The two terms of Eq. (31) have equal contributions in the total power. In addition, half of the remaining power is wasted in the noninformative discrete component of the spectrum, which corresponds to the DC value of the modulated power. However this value, obtained for NRZ coding, is the maximum value that can be achieved by ASK modulation. The low spectral spread of NRZ coding makes it less sensitive to chromatic dispersion, but the time profile of the pulses makes it very vulnerable to consecutive pulse overlap and intersymbol interference, leading to system impairment. A long sequence of identical symbols leads to a transmitted signal without any information on the digital period and phase, making synchronization at the receiver difficult. Furthermore, the mean value of the binary sequence changes as a function of the transmitted data, producing the so-called baseline


63

FIGURE 3 (a) Continuous and (b) discrete parts of the normalized power spectrum for NRZ (e ¼ 1) and RZ (e ¼ 0:5) modulation formats with the same value of the pulse energy.

wander, making the electronic process at the receiver more difficult. As discussed in Section II.D.1, the very sharp leading and trailing edges of the pulse may be associated with high-frequency chirping, depending on the type of modulator used.

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2. RZ Modulated Signal For return-to-zero (RZ) coding, the pulse of light has duration eT significantly narrower than the bit duration T. The rectangular RZ pulse profile is of this form: 1 for 0 < t < eT ð33Þ aðtÞ 0 elsewhere The parameter e < 1 is called the duty cycle of the modulation. Figures 2b and 2c show the coding of the binary sequence rectangular shaped RZ ðe ¼ 0:5Þ and Gaussian pulse RZ modulation formats. The baseband modulation spectrum of the square shaped RZ modulation can be stated as follows: SA ð f Þ ¼

2 P sin pen 2 T e2 sin peTf 1 þ1 n þ d f peTf 4 n¼1 pen T 4

ð34Þ

Figure 3 presents the normalized power spectrum for the NRZ ðe ¼ 1Þ and RZ ðe ¼ 0:5Þ modulation formats with the same value for the pulse energy. For the reason mentioned earlier, the continuous part and the discrete part of the spectrum are represented separately. Compared to the NRZ case, the RZ spectrum spread is enlarged by the reciprocal of the time shortening factor e, leading to a higher bandwidth and therefore to a noise penalty at the receiver. Discrete components disappear when me is equal to an integer. The total normalized optical power of the continuous part of the RZ spectrum is reduced by a factor e compared to the NRZ coding using the same peak power. For a given value of the averaged modulated optical power, the RZ modulation allows a pulse peak power enlarged by a factor 1=e compared to the NRZ case. The larger spectral spread of RZ coding makes it less tolerant to chromatic dispersion, but the smaller time location of the pulses makes them more robust to consecutive pulse overlap. Thanks to the low time occupancy when pulse duration is very short (compared to the bit duration T), RZ coding can be used for optical time-division multiplexing (OTDM) implementations. RZ coding is also more resistant to optical fiber nonlinearity impairments. More sophisticated shapes for the pulse may be chosen for various purposes. A Gaussian pulse is very convenient for modeling and is also the result of a multifiltering effect. It is characterized by time and frequency profiles: t2 aðtÞ ¼ exp 2 ð35Þ and j~að f Þj2 ¼ 2pt2 exp½ð2pntÞ2 2t The soliton pulse may remain unchanged through dispersive nonlinear propagation. It is characterized by time and frequency profiles: t aðtÞ ¼ sech and j~að f Þj2 ¼ sech2 p2 f t ð36Þ t


65

D. Modulation Implementation 1. Frequency Chirping Optical modulation may be implemented by the direct modulation of semiconductor lasers [20] or, more usually, by external modulation of a CW optical signal, using electroabsorption or electro-optic effects [9–11]. In any implementation arrangement, modulation is obtained through the modification of the propagation conditions of the optical electrical field, along the z coordinate in the form: EðtÞ ¼ A exp j2pn0 ðt nz=cÞ

ð37Þ

in which c is the speed of the light in vacuum and n is the refractive index. Optical modulation is produced by the deliberate change of the real part Dn0 of the optical index, through electro-optic effect, or of the imaginary part Dn through laser gain or absorption control. The general expression for the refractive index nðtÞ of the driven modulating device is in the form: nðtÞ ¼ n0 þ Dn0 ðtÞ jDn00 ðtÞ

ð38Þ

As a consequence of the Kramers–Kronig relations, these changes are never completely independent. They are linked by the so-called phase-amplitude coupling factor [20, 21] a ¼ Dn0 =Dn00 , leading to simultaneous phase and amplitude modulations. By substituting Eq. (38) into Eq. (37) the chirp equation is obtained: djðtÞ a d ln I ðtÞ ¼ dt 2 dt

ð39Þ

in which I ðtÞ ¼ AðtÞA*ðtÞ is the optical intensity and j the optical phase defined by A ¼ jAj exp jj. The general solution of Eq. (39) for complex amplitude of the optical field is: AðtÞ ¼ jAðtÞjð1þjaÞ=2

ð40Þ

A general expression of the spectrum of AðtÞ as a function of the spectrum of jAðtÞj cannot be obtained. However, two usual solutions are the linear chirped Gaussian pulse [21]: ð1 þ jaÞt 2 aðtÞ ¼ exp ð41Þ 2t2 with the corresponding spectrum: "

ð2pntÞ2 j~að f Þj ¼ j~að0Þj exp 1 þ a2 2

2

#

ð42Þ

66

PHILIPPE GALLION

FIGURE 4 Normalized power spectrum of a Gaussian pulse for different values of the chirp parameter a.

and the chirped soliton pulse: h t ið1þjaÞ=2 aðtÞ ¼ sech z

ð43Þ

with the corresponding spectrum [22]: p p j~að f Þj2 ¼ j~að0Þj2 sech ð2pf t þ aÞsech ð2pf t aÞ 2 2

ð44Þ

The main effect of the frequency chirping is to broaden the modulation spectrum, leading to a dispersion penalty. However, under given conditions the chirp may first compensate the dispersion effect [10]. Figure 4 shows the spectrum of a Gaussian pulse for different values of the chirp parameter a. 2. Extinction Ratio and Relative Intensity Noise Depending on the laser or the modulator biasing conditions, a remaining optical power may exist when a ‘‘0’’ is transmitted. Additional noise and additional decision difficulty at the receiver are the results of a non-zero-mean optical signal, when the zero is transmitted. This modulation imperfection is characterized by the extinction ratio, defined as the ratio r ¼ P0 =P1 of the powers during ‘‘0’’ symbol and ‘‘1’’ symbol transmission, respectively. The noise affecting the optical source itself produces another system impairment. It is characterized by the relative intensity noise (RIN) term, defined as the ratio of the actual laser noise to the minimum shot noise level, discussed in Section III.B. It also leads to additional noise at the receiver.


67

III. SIGNAL AND NOISES AT THE RECEIVER The role of a digital communication optical receiver is to convert the incoming optical signal into an electrical signal and to make a decision for each received symbol. An optical signal at frequency n consists of a flow of photons carrying the individual energy hn, where h ¼ 6:63:1034 J s is the Planck constant. At the receiver, a photodetector first converts the incoming photons into a flow of electrons. Afterwards an electrical amplifier is used to increase the weak output signals up to the appropriate levels to drive the decision circuit. The decision circuit makes a firm decision about the symbol more likely to have been transmitted during a given time slot. Moreover, an optical amplifier can be used to enlarge the optical signal level before the photodetector. In this case, the optical noise added by the amplifier has to be considered.

A. Photodetector Sensitivity and Optical-to-Electrical Signal Conversion Because it uses the corpuscular aspect of the received light, a photodetector does not directly consider the optical field itself to be the signal. A photodetector considers only the instantaneous optical power averaged over an integration time t, determined by its electronic bandwidth [23–29]. Let us consider the reception of an averaged optical power P during the observation time t. The received optical energy is P t and the average received photon number, of individual energy hn, is n ¼

P t hn

ð45Þ

For a photodetector device with a quantum efficiency Z, the average number of electrons produced during the time t is n e ¼ Zn ¼ Z

P t hn

ð46Þ

Because each electron carries an elementary electrical charge e, the average value of the photocurrent is i ¼ Electrical charge ¼ e n e ¼ Ze P ¼ RP Time duration t hn

ð47Þ

in which R ¼ Ze=hn is the photodetector responsivity, usually expressed in A=W. In the 1550-nm wavelength range (optical C-band), that is, for a photon energy hn close to 0.77 eV, the typical values for InGaAs photodetector responsivity R are in the 0.9–1.2 A=W range.

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PHILIPPE GALLION

B. Noise Generation and Demonstration Mechanisms at the Receiver 1. Shot Noise or Quantum Noise Let us consider a corpuscular description of light, in which the optical signal, of frequency n, incoming to the photodetector device, is pictured as a constant rate flow of photons of individual energy hn. Because of the lack of correlation between the photons, their arrival times, at the receiver, are not correlated. As a result, the time delay between two consecutive photons is not rigorously constant and the photon arrival is a random Poisson process. In these conditions, even in the case of a constant rate r ¼ P=hn of photon arrivals, the exact number n of photons received during any observation time t is not exactly equal to rt. The latter value only corresponds to the averaged photon number n around which n is fluctuating according to the well-known Poisson statistic law [24–29]. This law states that the probability of receiving n photons when a mean number n is expected is pðnÞ ¼

ðnÞn expðnÞ n!

ð48Þ

The mean squared fluctuations of ðDnÞ2 ¼ n2 n 2 of n ¼ n þ Dn around its expected value simply equal the expected value n : ðDnÞ2 ¼ n

ð49Þ

Using an approach more closely associated with physics, Poisson fluctuations may be also considered as the first term of the fluctuation expression of Bose– Einstein statistics: ðDnÞ2 ¼ n þ n 2

ð50Þ

Whereas the first term corresponds to the corpuscular nature of light, the last one is a demonstration of its wave nature. Assuming that the detector has a high efficiency Z, one electron is produced for almost each incoming photon. The number of missing electrons is not sufficient to corrupt photon arrival statistics, and the photoelectron statistics produced merely replicate it. Accordingly, the number of produced photoelectrons also obeys the Poisson distribution with average value n e ¼ Zn and the mean squared fluctuations are as follows: ðDne Þ2 ¼ n e

ð51Þ

Using Eqs. (45) and (47), the corresponding mean square photocurrent fluctuations are e 2 e 2 e ð52Þ ðDiÞ2 ¼ ðDne Þ2 ¼ ne ¼ i t t t


69

Assuming an ideal integrator with an impulse response equal to 1 between time 0 and t, the electrical transfer function is 2 t sin ptf ð53Þ jHð f Þj2 ¼ ptf As shown in Figure 5, it is convenient to define the equivalent noise bandwidth Be ¼ 1=2t as the flat bandwidth providing the same amount of noise. Then, the photocurrent fluctuations are expressed by the Schottky relation: s2 ¼ ðDiÞ2 ¼ 2eRP Be ¼ 2eiBe

ð54Þ

This noise, which is a counterpart to the corpuscular nature of light, is called the shot noise or the quantum noise. The proportionality of the noise power to the observation bandwidth expresses the idea that, for a long observation time t (i.e., for a small value for the bandwidth), the effect of photon number fluctuations is smoothed. On the other hand, for a small observation time t (i.e., high value for the bandwidth), the number of photons involved in each observation time is small and very sensitive to fluctuations. This is a standard white noise characteristic and it is useful to write the variance of the photocurrent fluctuations as follows: ð þBe 2 2 Sð f Þdf with Sð f Þ ¼ ei ð55Þ s ¼ ðDiÞ ¼ Be

in which Sð f Þ is the two-sided spectral power density of shot noise expressed in A2 =Hz. However, we must point out that the shot noise is not an additive noise, as is expressed by the proportionality of the noise power to the value of the average photocurrent. It originates from the received optical signal itself and disappears when no optical signal has been received. As long as a large number of

FIGURE 5 The equivalent bandwidth of an ideal integrator with an impulse response equal to 1 between time 0 and t.

70

PHILIPPE GALLION

photoelectrons are produced during the observation time and despite the Poisson nature of the shot noise, considering the shot noise to be a continuous Gaussian noise with the same variance is usually a good approximation. The validity of this approximation is discussed in greater detail in Section IV.C. 2. Signal against Optical Noise Beating Because of the quadratic response of the photodetector, the optical receiver is sensitive only to the optical power. Under these conditions, the simultaneous reception of two optical fields may generate a cross-term product with frequencies within the observation bandwidth Be . When one of the optical fields is a noise, this random cross-term product is referred to as the so-called ‘‘beat noise’’ or ‘‘signal against optical noise beating’’ [30–33]. Let us consider the simultaneous reception of a deterministic optical field with a complex amplitude A exp jj and of an additive optical band-limited stationary Gaussian noise N ðtÞ with a flat spectrum in a passband bandwidth equal to Bo . It is assumed that both the deterministic field and the optical noise refer to the same polarization and can thus be represented with scalar notation. Figure 6 shows the standard phasor representation of a small random field in addition to a deterministic field. By using the standard decomposition of the amplitude noise N in an in-phase NI ðtÞ and a quadrature NQ ðtÞ component [14, 23, 25, 34–36], the resulting instantaneous power is the squared sum of the deterministic field and of the in-phase component of the noise. An appropriate normalization in which the optical power equals the squared field is assumed. Under the small noise approximation, this power can be written as: P ðA þ NI Þ2 A2 þ 2ANI

ð56Þ

Assuming an equal sharing of the total noise power PN between the two noise components, the resulting optical power fluctuates around its average value A2 with mean squared fluctuations: ðDPÞ2 4 A2 N I2 ¼ 4P P I ¼ 2P P N

ð57Þ

FIGURE 6 Phasor representation of the addition of a random small signal to a deterministic field.


71

in which P ¼ A2 ; P I ¼ P N =2, and P N are the deterministic signal power, the average power of the in-phase noise component, and the total noise power, respectively. Observing that only the optical noise spectral components within the spectral range Be on each side of the optical carrier frequency produce beating within the electrical bandwidth, the optical noise bandwidth contribution is determined by Bo ¼ 2Be and the noise power can be expressed as follows: PN SN Bo 2SN Be

ð58Þ

in which SN is the single-sided optical noise power spectral density in the singlepolarization mode. Denoting the detector responsivity as R, the variance of the corresponding photocurrent fluctuations is s2SIGNOISE 4R2 P SN Be

ð59Þ

3. Optical Noise against Optical Noise Beating When no deterministic field is present on the photodetector, the fluctuations of power are the result of squaring the noise alone. While only the in-phase noise component is considered in the signal against noise beating, both its in-phase and quadrature components are to be considered here. This term is usually referred as ‘‘noise against noise beating’’ [30–33]. The optical noise bandwidth Bo is the bandwidth of the optical noise process itself or is determined by an optical filter. As in any Gaussian process, the mean square of the power fluctuations is equal to the square of the mean power: ðDPÞ2 ¼ P N2 ¼ P I2 þ P Q2 ¼ ðSN Bo Þ2

ð60Þ

By using an approach associated more closely with physics, Gaussian fluctuations may be also considered as the second term of the Bose´–Einstein statistics fluctuation relation: ðDnÞ2 ¼ n þ n 2

ð61Þ

which corresponds to the wave nature of light, whereas the first one expresses its corpuscular nature. For a flat optical noise spectrum within a bandwidth Bo , the correlation function of the power is expressed as RPN ðtÞ ¼

R2N ð0Þ

þ

2R2N ðtÞ

¼ PN

2

sin pBo t þ Bo pBo t

2

SN2

ð62Þ

in which RN ðtÞ is the correlation function of the noise process itself. Then the power spectrum of the power fluctuations can be easily calculated by using the

72

PHILIPPE GALLION

Fourier transform. Disregarding the first term, which corresponds to the squared mean power, the second one gives the power spectrum of the power fluctuations: 2 SN ðBo jf jÞ for jf j < Bo ð63Þ SDP ð f Þ ¼ 0 for jf j > Bo This relation can be found directly by using a heuristic approach: The spectral spread of power is twice that of the noise since squaring ‘‘doubles’’ the frequency, a linear frequency decay is mandatory, and the integration of the spectrum has to produce the mean square of the power fluctuations [26]. The photodetector with responsivity R converts these fluctuations into current fluctuations with a lowpass filtering over the electrical bandwidth Be , leading to the photocurrent variance: ð þBe B s2NOISENOISE ¼ R2 SDP ð f Þdf ¼ 2mR2 SN2 Bo e Be ð64Þ 2 Be in which m ¼ 1 or 2 is the number of polarization modes producing this same noise contribution. In the usual case of a nonpolarized optical noise, the two polarization components produce the same noise against noise beating while only one of them produces the beating against a polarized signal. The value of m must be set to 2 in the later expression because PN refers to a single polarization. 4. Interpretation of Shot Noise as a Beat Noise Quantum noise is not a consequence of using the corpuscular description of light but a counterpart of the fundamental optical field fluctuation itself [37–42]. A quantum description of the optical field is beyond the scope of this section. However, the fundamental field fluctuations now play a key role in engineering noise description. They can be simply introduced by using a quasi-classical scheme to allow the use of traditional methods to describe the optical noisy field [36, 42]. Using the proportional relationship between the number of photons and the received optical power n ¼ P t=hn ¼ P =ð2Be hnÞ, the Poisson fluctuation relation can be interpreted as instantaneous power fluctuations with the following variance: ðDPÞ2 ¼ 2hnBe P

ð65Þ

Compared with the power fluctuations resulting from the beat noise given by Eq. (57), the power fluctuations associated with the shot noise are the consequence of the beating of the received signal with an additive noise N of in-phase components NI of power: PN ¼ hnBe

ð66Þ

Observing that optical noise spectral components within a spectral range Be below and above the optical carrier frequency produce beating within the electrical bandwidth, the optical noise bandwidth is Bo ¼ 2Be and the corre-


73

sponding single-sided optical power spectral density of noise in the singlepolarization mode is SN ¼ hn=2

ð67Þ

This additive noise that accompanies any optical field is usually referred in quantum electrodynamics to the zero-point field fluctuations or the vacuum fluctuations [37, 39]. It is an elusive noise since the zero-point field fluctuations cannot be detected alone. The addition of the zero-point field fluctuations to a classical deterministic field defines a so-called ‘‘coherent state of the light.’’ This noise is only observable through its cross-term product with another signal and is not directly observable. By using Bo ¼ 1=t; hn=2 can be interpreted as the minimum detectable value of the energy for an observation time t. This value is also the minimum value E0 ¼ hn=2 of the quantified energy En ¼ ðn þ 1=2Þhn of a harmonic oscillator, which is always present, but not available for exchange. For n ¼ 193 THz corresponding to a wavelength of 1550 nm, the zero-point field spectral density SN is 0.65 1019 W=Hz. 5. Thermal Noise As is well known in the electrical engineering field, the random thermal motion of electrons in a resistor yields to a fluctuating current iT , even in the absence of any applied voltage. Such a situation occurs in the equivalent load resistor RL of the photodetector. Although the average value of this current is equal to zero, its mean squared value is not, and must be added as a contribution to the photocurrent variance. This noise contribution is referred to as thermal noise or Johnson noise and is independent on the optical noise and on the received signal. It is usually modeled as a zero-mean stationary Gaussian stochastic process with the white two-sided power spectral density equal to [15, 16]: ST ð f Þ ¼

2kTE in A2 =Hz RL

ð68Þ

in which k ¼ 1:38 1023 J=K is the Boltzmann constant and TE is the equivalent noise temperature. Any actual optical receiver includes electronic amplifiers and circuits, which also contain thermal noise sources. It is convenient to take into account their contribution by a multiplying factor called the noise figure of the electrical amplifier or by considering an equivalent temperature higher than the effective one. The variance of the photocurrent is obtained by integration of its spectral density over the equivalent noise bandwidth of the electrical circuit: ð þBe 4kTE B ð69Þ ST ð f Þdf ¼ s2T ¼ ðDiT Þ2 ¼ RL e Be In current receivers, the attempt to reduce the thermal noise power contribution by increasing the load resistor RL is limited by bandwidth and impedance matching considerations. Assuming, for instance, an equivalent temperature TE ¼ 400 K, a

74

PHILIPPE GALLION

pffiffiffiffiffiffi pffiffiffiffiffi load resistor RL ¼ 50 O, the thermal noise current is sT = Be ¼ 21pA= Hz. For a bit rate RB ¼ 10 Gbps and using the minimum electrical bandwidth Be ¼ RB =2, the receiver thermal noise is found to be sT ¼ 1:4 mA. This value is roughly equivalent to the photocurrent produced by an optical power of 1.4 mW and is to be multiplied by 2 for 40 Gbps requiring a bandwidth four time larger. 6. Dark-Current Noise In the absence of any received light, a photodetector produces a small value of DC current in the picoampere range, referred as the dark current iDC . Its origin is the leaky current produced by the electrons flowing through the device due to thermal excitation processes. The lack of correlation between the released electrons causes the current to undergo fluctuations, also modeled as a shot noise process with a variance: s2DC ¼ 2eiDC Be

ð70Þ

C. Noise Addition in Optical Amplification A two-quadrature component description of noise is mandatory to our understanding of noise generation in optical amplifiers. Once again, so as to avoid a quantum description of noise, we will use a heuristic derivation in which the quantum nature of the light is simply introduced by a conjugation relation between the two noise components in the form of the well-known Heisenberg uncertainty product. 1. Noise Addition Necessity The photodetection of optically amplified signals is necessarily associated with an additive noise. This necessity is easily understood by returning to the model of the noise addition N ðtÞ in a deterministic optical field. As shown in Figure 6, while the in-phase component NI ðtÞ induces amplitude change and therefore power fluctuations, the quadrature component NQ ðtÞ induces phase fluctuations, which can be approximated by: Dj NQ =A

ð71Þ

According to the well-known energy equal-repartition principle, the total noise power is assumed to be equally shared between the two noise components. The mean squared phase fluctuations is thus expressed as follows: ðDjÞ2 P Q =P ¼ P N =2P

ð72Þ

in which P Q ¼ P N =2 is the average power of the quadrature noise component. Using Eq. (57) for the power fluctuations and Eq. (72) for the phase fluctuations,


75

the rms power and phase fluctuations product, independent of the signal power, is obtained: qffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffi ð73Þ ðDjÞ2 ðDPÞ2 ¼ djdP ¼ 2ðP I P Q Þ1=2 ¼ P N

The minimum value of the noise power is reached in the particular case of zeropoint field fluctuations as given by Eq. (66). Then, the product of the power and phase fluctuation is djdP ¼ hnBe

ð74Þ

Introducing the photon number n ¼ Pt=hn received during any observation time t and the time-bandwidth relation Be ¼ 1=2t this relation is the minimum value of the Heisenberg uncertainty product: djdn ¼

1 2

ð75Þ

Using dj ¼ 2pndt and the energy defined as E ¼ Pt this phase-number relation is converted into the most popular energy-arrival time relation: dEdt ¼ h=4p

ð76Þ

Let us consider an ideal noiseless phase-insensitive linear amplifier, which only amplifies, with a gain G, both the incoming signal and its fluctuations. The output number fluctuations are related to the input one by the relation dnOUT ¼ GdnIN , while the phase fluctuations are kept unchanged djOUT ¼ djIN . Output phase and photon number measurements fulfilling Eq. (75) are possible in principle. However, such measurements would imply that, at the same time, the input signal measurements fulfill: ðdj dnÞINPUT ¼

1 1 < 2G 2

ð77Þ

in contradiction to the Heisenberg minimum uncertainties product. The noiseless amplifier, therefore, cannot exist. Any amplifier must add additional output uncertainties that are introduced by an extra noise with an origin intrinsic to the amplifier itself [43]. 2. Minimum Added Noise Assuming an uncorrelated noise variance addition for each of the two quadratures, the minimum square uncertainty product that can fulfill the Heisenberg relation is 2 dj2OUT dPOUT ¼ ðdj2D þ dj2A Þ ðdPD2 þ dPA2 Þ ¼ G2 P N2

ð78Þ

in which djA and dPA are the amplifier contributions to uncertainty and djD and dPD the detector ones. Denoting P A ¼ P IA þ P QA and P N ¼ P ID þ P QD the corresponding noise powers shared between in-phase and quadrature components

76

PHILIPPE GALLION

for the amplifier noise and the detector noise, respectively, and using Eqs. (57) and (72), we can write Eq. (78) in the following form: ðP ID þ P IA ÞðP QD þ P QA Þ ¼ G2 P ID P QD

ð79Þ

Introducing the constants a and b, less than the unit, to express the inphase=quadrature noise power sharing in the following forms: P ID ¼ aP N ; P QD ¼ ð1 aÞP N

and

P IA ¼ bP A ; P QA ¼ ð1 bÞP A

ð80Þ

we can easily show that the minimum value of the added power is obtained for a ¼ b, reducing Eq. (79) to: ðP N þ P A Þ2 ¼ G2 P N2

ð81Þ

Using at last Eq. (66) for the minimum value of the detector noise power, we obtain the minimum extra noise power required at the output, to avoid violating the Heisenberg minimum uncertainties [43]: hn P A ¼ ðG 1Þ Bo 2

ð82Þ

This result is obtained for a phase-insensitive linear amplifier with a gain G and an optical bandwidth Bo ; equal to twice the observation bandwidth Be . By using Be ¼ 1=2t the product P A t ¼ ðG 1Þhn=2 can be interpreted as the minimum added noise energy at the output of an amplifier in the signal-polarization mode. For large values of gain G, it corresponds to an additional noise energy of half a photon during each observation time, at the input of an equivalent noiseless amplifier. This minimum value is independent of the nature of the optical amplifier used. It must be added to the amplification of the unavoidable input zero-point field fluctuations producing the input shot noise. The overall output optical noise power spectral density, in the signal-polarization mode, is therefore: SN ¼ ðG 1Þ

hn hn þG 2 2

ð83Þ

For large values of gain G it corresponds to a total noise energy of one photon during each observation time, at the input of an equivalent noiseless amplifier. The minimum equivalent total input noise, in a single-polarization mode, at the input of an ideal noiseless amplifier is thus twice the minimum value associated with the zero-point field fluctuations given by Eq. (67): SN ¼ hn

ð84Þ

For this reason, the noise figure F of an optical amplifier, expressing the added noise by the mean of a multiplying factor to the amplified input noise, has a minimum value equal to 2, in the high-gain limit.


77

3. Amplifier Excess of Noise Of course, actual optical amplifiers operate above this fundamental limit and add a larger amount of noise. The main reasons for this are the coupling loss and the fact that the net gain G is usually the result of the subtraction of local total gain and loss coefficients while their noise contributions add. This can be expressed by multiplying the added noise contribution by a factor K greater than 1 leading to the actual noise power density in the signal-polarization mode [36]: SN ¼ KðG 1Þ

hn hn þG 2 2

ð85Þ

An alternative approach is to assume a noise-free input signal and make reference to the unavoidable output shot noise, resulting in the output zero-point fluctuations. Equation (85) is then rewritten in the following form: SN ¼ FðG 1Þ

hn hn þ 2 2

with F ¼ K þ 1

ð86Þ

The first term in Eq. (86) appears as the total output noise supplementing the unavoidable minimum output zero-point fluctuations expressed by the second one. It is not the added noise supplementing the amplified input zero-point fluctuations that is included in it. F is the optical noise figure of the amplifier [44, 45]. It has to be pointed out that the minimum value of F obtained for an ideal amplifier is 2, while the minimum value of K is 1. It is a result of not considering the elusive zero-point fluctuations as an input noise producing a part of the output noise but as a property of the amplifier itself since they are present at the input even when no signals are detectable in this case. This factor 2 limit is not directly related to polarization, bandwidth, or to double cross-term considerations, as sometimes believed, but the result of Heisenberg conjugation between the two noise quadratures. 4. Laser Amplifier Example A typical example of optical laser amplifier output noise is amplified spontaneous emission (ASE) [46–50]. For a single polarization the average amplified spontaneous emission power in a single-sided optical bandwidth Bo is P ASE ¼ nSP ðG 1ÞhnBo

ð87Þ

where nSP is the population inversion factor, sometimes also called the spontaneous emission factor which is usually in the 1.5 to 2 range. An additional noise contribution due to coupling losses may be taken into account by a multiplicative factor. This mean power value is not the noise itself, as has sometimes been

78

PHILIPPE GALLION

considered to be the case, but the rms of the power fluctuations of a Gaussian process with the single-sided optical spectral density: SASE ¼ 2nSP ðG 1Þ

hn 2

ð88Þ

The overall optical noise spectral density, given by Eq. (86), can be recovered by adding the zero-point spectral density SN ¼ hn=2 to Eq. (88). The noise figure in this case is F ¼ 2nSP , with a lower limit of 2 for the fully inverted situation. In this case, the factor of 2 is explained by considering the input zero-point fluctuations to be one of the sources of the spontaneous emission in the amplifier, while the other half is produced by momentum fluctuations of the electrons at optical frequencies associated with the gain process itself. The ASE is therefore not the noise added to the amplified input fluctuations, but the noise added to the zero-point output fluctuations. As stated in Section III.B, to take into account the two orthogonal polarization states, a factor of 2 must eventually be used to multiply this value. This additive optical signal on the receiver generates its own shot noise contribution, a noise beating with the useful signal and also a noise resulting from its own power fluctuations, interpreted as noise against noise beating.

D. Optical Signal-to-Noise Ratio The evolution of optical signal and noise in an amplified transmission chain is usually characterized by the optical signal-to-noise ratio (OSNR) SNRo . The optical signal-to-noise ratio, at the output of an optical amplifier, is defined as follows: SNRo ¼

Average optical signal power GP ¼ Average optical noise power mSN Bo

ð89Þ

in which G is the optical gain, P the average input signal power, SN the singlesided output noise power density for a single polarization, m ¼ 1 or 2 is the number of polarization modes contributing to noise, and Bo is the optical bandwidth. By using Eq. (86) for the power density output noise, the OSNR at the output of an optical amplifier in the high-gain limit is expressed as SNRo ¼

P mFðhn=2ÞBo

ð90Þ

We usually consider the two polarization modes (m ¼ 2) of the noise and a reference optical bandwidth equal to 0.1 nm corresponding to Bo ¼ 12:5 GHz at a wavelength of 1550 nm. In this particular situation, the OSNR is expressed in decibels as SNRodB ¼ P dBm FdB þ 57:9

ð91Þ


79

IV. RECEIVER PERFORMANCE EVALUATION To derive the intrinsic receiver performances dealing with the various noise contributions, we will assume that the received signals are free of intersymbol interference, time jitter, and other system impairments.

A. Electrical Signal-to-Noise Ratio Definition As stated in Section III.B, the common approximation is to treat all output photocurrent noise contributions, including the shot noise contributions, as Gaussian random variables. The sum of Gaussian independent random variables is also a Gaussian random variable whose variance is equal to the sum of the individual variances. We have to consider all possible noise contributions, whose relative importance depends on operation parameters. The performances of a digital communication receiver, before the decisions, are usually characterized by the electrical signal-to-noise ratio (ESNR) SNRe defined as follows [2–11]: SNRe ¼

Average signal power ¼ Average noise power

i2 P 2 s

ð92Þ

NOISE CONTRIBUTIONS

The value of the load resistor RL, in the electrical power expressions, disappears through simplification. However, the meaning of the signal-to-noise ratio in optical communication differs significantly from that in the radio-frequency range, in which we are mainly concerned with additive Gaussian white noise (AGWN). The optical communications systems are usually treated in terms of power rather than in terms of optical field and the noise is not additive, since some noise contributions depend on the received signal. The signal is also itself a random process since it is always associated with the zero-point field fluctuations.

B. Bit Error Ratio and Receiver Sensitivity Definitions We assume that the average received power is equal to P 1 when the symbol 1 is transmitted and to P 0 when the symbol 0 is transmitted. Because some noise contributions depend on the received optical power, the photocurrent fluctuations are also functions of the transmitted symbol. The output photocurrent i fluctuates from one bit to another, around an average value i1 with the variance s1 when the symbol 1 is transmitted and i0 with the variance s0 when the symbol 0 is transmitted. At the decision time tD determined by the clock recovery circuit, the decision circuit compares the observed current value i with a threshold value iD . When i is found to be above the threshold value iD the firm decision that a 1 is transmitted can be made. When i is found to be below the threshold value iD the firm decision

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PHILIPPE GALLION

that a 0 is transmitted can be made. Figure 7 shows the probability distributions of the photocurrent for the two transmitted symbols. When, due to the signal and receiver noises, i is found to be above the threshold value iD , whereas the symbol 0 has been transmitted, an error occurs. In the same way, when i is found to be below the threshold value iD , whereas the symbol 1 has been transmitted, an error also occurs. Both of these two error sources degrade the performance of communication systems. The performance of a digital communication system is expressed in terms of bit error probability, also called the bit error ratio (BER), which is defined as the ratio of the number of wrong decisions to the number of transmitted bits: BER ¼ pð1ÞPð0=1Þ þ pð0ÞPð1=0Þ

ð93Þ

in which p(1) and p(0) are the probabilities of transmitting 1 and 0, respectively, and Pð0=1Þ is the probability of deciding that a 0 is received when a 1 is transmitted, and Pð1=0Þ is the probability of deciding 1 when 0 is transmitted. The two products express the two joint probabilities to make a wrong decision. The

FIGURE 7 Probability distributions of the photocurrent for the two transmitted symbols and selection of the decision threshold.


81

BER is also frequently referred as the bit error rate. However, this denomination is somewhat misleading since it is not the number of errors per unit of time that is considered, but the error probability. As mentioned in Section III.C, a binary message is more informative when the symbols 1 and 0 have the same probability to occur so that pð1Þ ¼ pð0Þ ¼ 1=2. The BER is thus given by: 1 BER ¼ ðPð0=1Þ þ Pð1=0ÞÞ 2

ð94Þ

Both the average and the variance of the photocurrent are different for bit 1 and bit 0. Using a Gaussian model, the probabilities Pð0=1Þ and Pð1=0Þ are written as follows [51, 52]: $ % ð iD i1 iD 1 ði i1 Þ2 1 pffiffiffi Pð0=1Þ ¼ pffiffiffiffiffiffi exp ð95Þ di ¼ erfc 2 2s21 s1 2 s1 2p 1 $ % ð1 1 ði i0 Þ2 1 iD i0 p ffiffi ffi erfc exp ð96Þ di ¼ Pð1=0Þ ¼ pffiffiffiffiffiffi 2 2s20 s0 2 s0 2p iD in which erfcðxÞ ¼ 1 erf ðxÞ is the complementary error function defined as ð 1 1 erf ðxÞ ¼ pffiffiffi exp½u2 du ð97Þ p x

Carrying over Eqs. (96) and (97) in Eq. (94) gives the BER: i1 iD 1 iD i0 pffiffiffi þ erfc pffiffiffi BER ¼ erfc 4 s0 2 s1 2

ð98Þ

The decision threshold iD is optimized to minimize the BER. The probability Pð0=1Þ and Pð1=0Þ are proportional to the two shaded areas on Figure 7. The optimum value is obtained when the two error probability contributions are identical. This is obtained when the two shaded areas in Figure 7 are equal. Because the two symbol transmission probabilities are assumed to be identical, this can be simply understood by observing that any departure from this optimal value leads to an increase of one of them being larger than the reduction for the other. The optimal threshold value equaling the two contributions to Eq. (98) is iD ¼

s0i1 þ s1i0 s0 þ s 1

ð99Þ

Tuning of the decision circuit at the level given by Eq. (99) yields the BER value of [51, 52]: i i0 1 Q BER ¼ erfc pffiffiffi with Q ¼ 1 ð100Þ 2 s1 þ s0 2

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PHILIPPE GALLION

For a very low value of BER, the usual approximation of Eq. (100) consists of keeping the first term of the series expansion of the erfcðxÞ function: BER

expðQ2 =2Þ pffiffiffiffiffiffi Q 2p

ð101Þ

Figure 8 shows the BER as a function of Q and the validity range of this approximation. The BER improves while Q is increasing and becomes lower than 1012 for Q larger than 7. The approximation is only valid for values of Q larger

FIGURE 8 (a) BER as a function of Q and (b) low BER approximation.


83

than 3 leading to a BER of less than 103 . The approximation is reaching its limit of validity for systems using high-performance FEC techniques in which the BER before correction is too low to justify it fully. Receiver sensitivity is often defined as the average optical power at which Q ¼ 6 leading to a BER equal to 109 . The most general expression of BER and of the sensibility requires much formalism. However, the relative importance of the various noise contributions changes dramatically depending on practical considerations. In the following sections, we discuss the more interesting configurations. The eye diagram usually pictures the quality of actual reception conditions. This results from the superposition of the different time slots, equal to the bit duration T, obtained by time slicing the received signal. The eye opening expresses the clear separation of the two symbol current probability distributions and therefore the ability to obtain a low probability of wrong decisions. Figure 9 displays a typical eye diagram situation and the corresponding optical and electrical received signals. The bit rate is 10 Gbps and the optical signal-tonoise ratio equals 28 dB. C. Shot-Noise-Limited Ideal Detection 1. Signal-to-Noise Ratio According to Eq. (47), the electrical signal current i, obtained by direct conversion of the optical power P is i ¼ RP . In the shot-noise-limited conditions, the non-signal-dependent noise terms are assumed to be negligible when compared to the shot noise contribution of the signal itself. Keeping only this dominant noise source contribution, the photocurrent variance is s2 ¼ 2eiBe according to Eq. (54), and the shot-noise-limited electrical signal-to-noise ratio is as follows: SNRe ¼

i2 i ZP ¼ ¼ 2eiBe 2eBe 2hnBe

ð102Þ

For a quantum efficiency Z close to unity, optical shot noise is equivalent to a single-sided spectral density 2hn which is four times the optical one since the electrical noise is a double cross term and since the electrical bandwidth is two times smaller than the optical one. The physical meaning of this expression can be clarified if we consider that the equivalent electrical bandwidth is related to the observation time t by Be ¼ 1=2t. The minimum value of the detectable energy obtained for SNRe ¼ 1 just equals the single photon energy hn. 2. Bit Error Rate and Receiver Sensitivity Assuming an optical power equal to P 1 during the 1 symbol transmission and a perfect extinction ratio, the average photocurrents for the 1 and 0 transmitted

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PHILIPPE GALLION

FIGURE 9 (a) Optical and (b) electrical signals and (c) corresponding eye diagram. The bit rate is 10 Gbps, the optical signal-to-noise ratio equals 28 dB in a 12.5-GHz Gaussian filter.


85

symbols are respectively i1 ¼ RP 1 and i0 ¼ 0, and the respective associated variances are s21 ¼ 2eiBe and s20 ¼ 0. Using the electrical bandwidth to the bit duration relation Be ¼ 1=2T ¼ RB =2, the general expression for the Q-factor given by Eq. (100) is simplified as follows: sffiffiffiffiffiffiffiffi RP 1 RP 1 Q ¼ pffiffiffiffiffiffiffiffiffiffiffi ¼ ð103Þ eRB 2eiBe

After the substitution of the photodetector responsivity expression given by Eq. (47), R ¼ Ze=hn, has been made, the optical power P 1 required during the 1 symbol is obtained: Q2 hn RB P 1 ¼ Z

ð104Þ

The average optical power P ¼ P 1 =2, required for Q ¼ 6, leading to a BER equal to 109 , is, for instance, as low as 46:3 dBm for a 10-Gbps receiver with a quantum efficiency Z close to the unit. The average photon number during bit 1 transmission is n 1 ¼ P 1 T =hn, and the average photon number during bit 0 transmission is n 0 ¼ 0. The average photon number per bit n ¼ ðn1 þ n0 Þ=2 ¼ n1 =2 required to obtain a given Q-factor is n ¼

Q2 2Z

ð105Þ

This is the minimum energy per bit required, by using the photon energy as the unit. Assuming also a quantum efficiency Z close to unity, the average photon number per bit required for Q ¼ 6, leading to a BER equal to 109 , is n ¼ 18 photons=bit

ð106Þ

However, because no noise is present when the symbol 0 is transmitted, the decision threshold is set close to 0 and the probability Pð1=0Þ is equal to zero. The bit error ratio is in this case only half of that given by Eq. (100): 1 Q BER ¼ erfc pffiffiffi ð107Þ 4 2

The value of Q leading to a BER equal to 109 is in this case 5.9, reducing n to 17 photons=bit. This value is too small to fulfill completely the conditions for approximating the Poissonian shot noise by a Gaussian noise. Because the probability Pð1=0Þ is equal to zero, a more accurate value is obtained by setting the decision threshold close to 0 and by using Poisson statistics for Pð0=1Þ directly. The BER is in this case 1 BER ¼ expðn1 Þ 2

ð108Þ

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PHILIPPE GALLION

The average photon number per bit required for a BER equal to 109 is: n ¼

n1 ¼ 10 photons=bit 2

ð109Þ

The poor approximation of the tail of a Poissonian function by a continuous Gaussian one explains the discrepancy between the two results. The shot-noise-limited situation can unfortunately be obtained only for a high signal level with an associated shot noise overcoming the thermal noise or under low-temperature operation. Furthermore, this detection is particular in this case since no errors are considered for the transmitted 0.

D. Amplifier Less Thermal-Noise-Limited Detection 1. Signal-to-Noise Ratio When no optical preamplifier is used, the noise sources are the shot associated with the received signal and the dark current as well as the thermal noise, with the respective photocurrent variances given by Eqs. (54), (69), and (70): s2 ¼ 2eiBe s2DC ¼ 2eiDC Be

and

4kTE B RL e

ð110Þ

with i ¼ RP

ð111Þ

s2T ¼

This leads to the general expression of the ESNR: i2 SNRe ¼ 2kTE Be 2 eði þ iDC Þ þ RL

In actual standard detection situations, the thermal noise is largely dominant and Eq. (111) for the ESNR is simplified to the following: SNRe ¼

RL R2 P 2 4kTE Be

ð112Þ

This is the situation for most PIN photodiode receivers whose noise is dominated by thermal noise and is independent of the average signal current. 2. Bit Error Rate and Receiver Sensitivity Because the noise is identical during the transmission of the two symbols, the communication channel is in this case completely symmetrical and the decision threshold is set at the midpoint: iD ¼

i1 þ i0 2

ð113Þ


87

Assuming a perfect extinction ratio, the average photocurrents for the 1 and 0 transmitted symbols are, respectively, i1 ¼ RP 1 and i0 ¼ 0. The respective associated variances s2T ¼ ð4kTE =RL ÞBe , and the Q-factor is Q¼

RP 1 2sT

ð114Þ

in which an optical power equal to P 1 during the 1 symbol transmission and a perfect extinction ratio are assumed. Again using the electrical bandwidth to the bit duration relation Be ¼ 1=2T ¼ RB =2, the optical power P 1 required to obtain a given Q value is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2Q Q 8kTE s ¼ R P 1 ¼ R T R RL B

ð115Þ

Because P 1 is proportional to the square root of the bandwidth, we are not able to express the receiver sensitivity in terms of a general expression of the average number of photons per bit. In typical practical situations, this number is within the range of a few thousands of photons per bit, expressing a very strong impairment caused by the thermal noise. If we consider, for instance, a RB ¼ 10-Gbps receiver with R ¼ 1 A=W, according to the example of Section III.B.5, sT ¼ 1:4mA and the average photon number per bit required for Q ¼ 6 is n ¼ 6500 photons=bit

ð116Þ

The corresponding average optical power P ¼ P 1 =2 is 21 dBm. The use of an avalanche photodiode [9, 10] with a built-in gain resulting from multiplication by collisions of the photoelectrons could improve this situation by decreasing the average optical power required down to 28 dBm. The performances are in this case limited by the spread of the built-in gain as a result of the stochastic nature of the collision process, something that increases the shot noise level. This performances remains far below the results of the detection of optically preamplified signal and we do not discuss it furthermore.

E. Detection of Preamplified Optical Signals 1. Signal-to-Noise Ratio The electrical signal i is obtained in this case by conversion of the preamplified optical power GP through an optical amplifier with net gain coefficient G and noise figure F. Its mean value is then i ¼ RGP . The major noise sources are, in this case, the noise against noise, the noise against signal beatings, and the thermal noise [30–33, 53] given by Eqs. (59), (64), and (69). By

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PHILIPPE GALLION

taking into account these three major contributions to the photocurrent variances, the ESNR is written as follows: ðGP Þ2 SNRe ¼ Be 2kTE B þ 2GP SN þ 2 2 mSN Bo 2 R RL e

ð117Þ

Disregarding the vacuum fluctuations, leading to the negligible amplified signal shot noise, in Eq. (86), the optical power spectral density of the additive noise at the amplifier output can be simplified to SN ¼ FðG 1Þ

hn 2

ð118Þ

In the high-net-gain approximation defined by SN FGhn=2, the thermal noise term becomes negligible and the ESNR is simplified to 2P 2 SNRe ¼ Be þ 4P FhnBe mFhn Bo 2

ð119Þ

Assuming an optical bandwidth Bo ¼ 2Be and an optical signal power level significantly larger than the optical noise power, the major noise contribution is the noise against signal beating. In fact, the noise against noise beating term is only important when the transmitted symbol is 0 and when the extinction ratio is excellent, reducing the signal-to-noise discussion to academic interest. Under this strong assumption, the ESNR is simply approximated by SNRe

P ¼ SNRo FhnBo

ð120Þ

where SNRo is the OSNR at the optical amplifier output given by Eq. (90) when the two noise polarization modes are considered. This output OSNR is F times smaller than the input one. 2. Bit Error Rate and Receiver Sensitivity Assuming a perfect extinction ratio i1 ¼ RGP 1 ; i0 ¼ 0, Eq. (100) for the Qfactor definition yields: 2 RGP1 RGP1 2 2 ð121Þ sSIGNOISE ¼ ðs2NOISENOISE þ s2T Þ1=2 Q Q After substitution of the noise variance expressions given by Eqs. (59), (64), and (69), assuming electrical bandwidth Be ¼ RB =2 and solving Eq. (121), the average optical power P ¼ P 1 =2, required to obtain a given Q-value is sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " # QS R m 2Bo 1 ST N B P ¼ Qþ þ ð122Þ 2 RB 2 G 2RB R2 SN2


89

Disregarding the vacuum fluctuations and using the power spectral density at the amplifier output given by Eq. (118), the average photon number per bit n ¼ n1 =2 ¼ P =ðhnRB Þ required to obtain a given Q-factor is: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi # " F G1 m 2Bo 1 2ST n ¼ ð123Þ Q Qþ þ 2 G 2 RB 2 RB R2 F 2 ðG 1Þ2 ðhnÞ2 As expressed by Eqs. (122) and (123), an increase in the optical gain G leads to a fast reduction of the thermal noise contribution. Figure 10 shows the number of photons per bit required to obtain Q ¼ 6 for different values of the amplifier noise figure F, as a function of the optical gain and the shot noise limitation. The pffiffiffiffiffiffi pffiffiffiffiffi thermal noise current is assumed to be sT = Be ¼ 21 pA= Hz, the bit rate RB ¼ 10 Gbps, the sensitivity R ¼ 1 A=W, the polarization mode noise contribution is m ¼ 2, and the electrical bandwidth Be ¼ RB =2. For gain larger than 30 dB, the amplification process overcomes the thermal noise. In this case, the average optical power P ¼ P 1 =2 required to obtain a given Q-value is simplified to sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi " ffi# P ¼ F QhnRB Q þ m 2Bo 1 ð124Þ 2 2 RB 2 Figure 11 presents the fundamental BER limitation of as a function of signal optical power for an optically amplified 10-Gbps receiver, for different values of the spectral efficiency RB =Bo, and for m ¼ 2; F ¼ 2, and R ¼ 1 A=W. The corresponding shot noise sensitivity limitation is also indicated.

FIGURE 10 Number of photons per bit required to obtain Q ¼ 6, for different values of the amplifier noise figure F, as a function of p the ffiffiffiffiffiffioptical gain and the corresponding shot noise limitation. pffiffiffiffiffi The thermal noise is sT = Be ¼ 21 pA= Hz; RB ¼ 10 Gbps; Be ¼ RB =2; m ¼ 2, and R ¼ 1 A=W.

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PHILIPPE GALLION

FIGURE 11 Fundamental BER limitation as a function of signal optical power of an optically preamplified 10-Gbps receiver, for different values of the spectral efficiency RB =Bo, and the corresponding shot noise sensitivity limitation. The parameters are m ¼ 2; F ¼ 2, and R ¼ 1 A=W.

The average photon number per bit n required to obtain a given Q-factor is [10, 53] as follows: sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffi! F m 2Bo 1 ð125Þ n ¼ Q Q þ 2 2 RB 2 Assuming a noise factor of F ¼ 2 and a number of polarization mode noise contributions of m ¼ 2, the average photon number per bit required for Q ¼ 6 leading to a BER equal to 109 is n ¼ 43:3 photons=bit:

ð126Þ

While the ‘‘noise against noise beating’’ contributes 7.3 photons=bit the ‘‘signal against noise beating’’ has a contribution of 36, which is twice that of the shotnoise-limited detection, according the minimum noise figure of 2 for the optical amplifier. The comparison of this value with other model results shows that the used Gaussian noise approximation provides a fair estimation of the optically amplified receiver sensitivity [53]. Figure 12 shows the number of photons per bit required as a function of the spectral efficiency RB =B0 for m ¼ 2 and for different values of the BER. An optical noise filter improves the spectral efficiency and receiver sensitivity. Polarization control of the signal allows the noise against noise contribution reduction and leads to an improvement of the sensibility equivalent to the halving an optical noise bandwidth B0 > 2Be . Assuming that under the limit assumptions discussed in Section IV.E.1, the noise against noise beating term is negligible, Eq. (124) is simply expressed as


91

FIGURE 12 Number of photons per bit required by an optically preamplified receiver as a function of the spectral efficiency RB =Bo, for m ¼ 2 and for different values of the expected BER.

P ¼ Q2 ðF=2ÞhnRB . Using Eq. (120) we have in this case the following very simple rule of thumb: Q2 SNRe

P 1 ¼ SNR0 2FhnBe

ð127Þ

These different results have been obtained under the assumption of an electrical bandwidth related to the bit rate by Be ¼ RB =2. According to Section II and to Figure 5, this is the minimum value required for an NRZ modulation format. For a given value of the averaged modulated optical power, an RZ modulation format with a duty cycle of e ¼ 0:5 allows a pulse peak power enlarged by a factor 2 as compared to the NRZ format. As shown in Figure 3, the required electrical bandwidth is in this case twice the NRZ one, leading to an identical theoretical Qfactor as expressed by Eq. (127). However, in practice, by narrowing the electrical filter of a RZ receiver, a sensitivity improvement around of 1.5 dB is usually reported.

ACKNOWLEDGMENTS The author would like to thank Didier Erasme, Alan Hornstein, Yves Jaoue¨n, Jorge Rodrigez, and Robert Vallet for comments and suggestions for improving the manuscript. It would have been impossible to write this chapter without the fruitful interaction with ENST students I had for many years during my lectures on optical communications and quantum electronics. While I alone remain

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responsible for the bugs in this chapter, I am grateful to Virginie Dallot, Lydia Lourdiane, and Mariam Kimiaei Asadi who carefully read the manuscript.

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4 OPTICAL AMPLIFICATION DOMINIQUE BAYART Alcatel Research and Innovation, Marcoussis, France

I. INTRODUCTION II. EDFA AMPLIFICATION PRINCIPLES A. Basic Principles B. Dynamic Behavior C. Noise Characteristics D. Giles Parameters III. REQUIREMENTS FOR SUBMARINE SYSTEMS A. Noise Figure B. Hydrogen Sensitivity C. Power Consumption D. Polarization-Dependent Loss E. Polarization Mode Dispersion F. Polarization-Dependent Gain G. Comparison with Terrestrial Requirements IV. RELATED TECHNOLOGY V. SINGLE-CHANNEL EDFAs A. Gain Peak Wavelength Determination B. Parameters That Influence GPW C. Self-Filtering Effect D. Design Rules E. Gain Compression and Pump Wavelength F. Glass Composition G. Signal-to-Noise Ratio VI. MULTICHANNEL WDM EDFAs A. Gain Bandwidth B. Glass Composition C. Gain Equalization D. Equalization Technology VII. EDFAs Impairments A. Polarization Effects B. Spectral Hole Burning Undersea Fiber Communication Systems Copyright 2002, Elsevier Science (USA). All rights reserved.

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C. Modeling of Spectral Hole Burning D. Other Limitations VIII. OPERATION WITH L-BAND EDFAs A. System Performance B. Field Implementation Issues C. C þ L-Band Systems IX. IMPLEMENTATION OF RAMAN AMPLIFICATION A. Principle of Raman Amplification B. Practical Implementation as Preamplification EDFAs C. All-Raman Amplified Submarine Links X. FURTHER AMPLIFICATION PERSPECTIVES References

I. INTRODUCTION The first generation of optical systems used electrical repeaters that detected and retransmitted the optical channel in order to bridge long distance [1]. In terms of optical transmission, the link was composed of successive small transmissions that were several tens of kilometers long. The major constraint was then due to the submerged electrical regenerators in terms of cost, capacity, and flexibility. Indeed, if electrical regenerators can process signals with relatively high speeds of modulation, their related cost increases dramatically with the bit rate. In addition, the bit rate they can handle is determined for the whole lifetime of the system, and the modulation format and signal protocol as well. Therefore, the use of optical amplification in order to avoid such expensive electrical regenerators was first promoted in laboratories, although this type of use was pushing strong constraints on the optical signal that would then have to cross thousand-kilometer-long distances. Optical amplification also presented the potential of using several wavelength-division multiplexing (WDM) channels. Raman amplification was investigated first [2]. This nonlinear process was demonstrated in the early 1970s at the same time as studies to improve silica glass in order to implement low-loss silica link fibers [3]. Raman amplification requires long interaction distances in order to provide gain. It appeared then to be the natural candidate for regularly compensating for the loss of optical fibers. In the late 1980s, when electrical repeaters seemed to have reached the maximum they could offer, waiting for the advent of coherent transmission, the demonstration of erbium-doped fiber amplifiers (EDFAs) changed our way of thinking [4]. Repeaters were not required any longer and the pump power that was required to provide significant gain in Raman amplification was reduced by a factor of 10 (at a minimum)! This was due to the very high gain efficiency of EDFAs and to the related level of loss in the link fiber impacting on the efficiency of Raman amplification. EDFAs then clearly appeared to be the key technology that could help optical networks grow and enable the next telecommunication revolution. An intrinsic background loss coefficient of several decibels per kilometer convinced researchers that distributed

4. OPTICAL AMPLIFICATION

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amplification could not be implemented with erbium-doped link fibers although they theoretically provide better noise performance. Compensating attenuation of the link fiber by discrete amplification (periodically spaced at a specific distance) has therefore been the winning scheme for signal power management. Because optical amplification is a key enabling technology of the development of modern submarine optical transmission systems, this chapter is dedicated to the understanding and the design of amplification means. We do not address all fundamental aspects of amplification, but merely discuss some important keys to understanding the design of past, present, and future submarine links from the amplification point of view. Considerations are inferred for cases of manythousand-kilometer-long links, in order to bridge, for instance, transoceanic (6000 km) or transpacific distances (9000 km). After having described the amplification principles and the general characteristics of EDFAs, the requirements imposed by their use in such submarine systems are discussed. Related technology and systems features are reviewed first for the case of single-channel operation, and then for the case of multichannel operation, focusing on the impact of the output signal-to-noise ratio (SNR). The limitations and constraints linked to the use of EDFAs are described. For the next generation, the pro and cons of using Raman amplification in addition to (or without) EDFAs, or the usefulness of implementing a new amplification bandwidth, such as the L-band, are discussed as well.

II. EDFA AMPLIFICATION PRINCIPLES In this section, basic principles and characteristics of erbium-doped fiber amplification are quickly reviewed in order to recall for the reader some important aspects that are needed to understand the design of submarine amplifiers. Clearly, a detail description is beyond the scope of this chapter; the reader should refer to other books offering extensive description of all effects, for instance, Ref. [4]. A. Basic Principles The first aspect concerns stimulated laser emission processes. An optical medium such as silica glass may convert some energy coming from a first light (pump) to a second light (signal) through a stimulated emission process. This energy process happens with the triple interaction of pump light (higher energy) or signal light (lower energy), and of glass (the amplifying medium that accumulates the energy of the pump but also absorbs the energy gap between these two lights, generally as optical phonons corresponding to the vibrational molecular states of the glass). The basis of the amplification comes from the population inversion between an upper level populated by the pump and a lower level, the energy gap between both being close to the signal energy. To improve the efficiency of the

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optical amplification process, it is useful to provide the material with some energy storage capability. This is the case when atoms or ions are excited from their fundamental ground-state levels to other metastable energy levels of higher energy. Depending on the lifetime of such excited-state energy levels, the efficiency of amplification may be strongly enhanced. Glass doped with trivalent rare earths such as erbium ions are good candidates for laser action in the glass matrix (Figure 1). The pump light is then absorbed in a first step by the erbium ions if its center wavelength matches the energy of one relevant excited-state levels of erbium. During a second step (lasting less than 1 ms), the erbium ions decay from this first excited-state level (or sublevel) to a metastable excited state, having a significant lifetime (10 ms in the case of erbium). During a third step, other incoming input photons will be duplicated through stimulated emission, resulting in some erbium ions returning to the fundamental ground-state level (see [4] for an in-depth analysis of the principles of amplification). When this effect occurs in an optical fiber, pump and signal beams are focused in the vicinity of the core of the fiber. By locating dopants inside this core, it is possible to maximize the level of interaction of incoming beams with dopants. In addition, cross sections (corresponding to the likelihood of interaction between one incoming photon with one erbium ion) are high compared to other rare earths (such as Pr3þ or Tm3þ ). Erbium ions exhibit different spectroscopic properties depending on the material where they are incorporated. A first important property concerns the nonradiative decay from one excited-state energy level to another energy level. The energy is then dissipated through optical phonons within the material, as vibrational energy. Several phonons may be created during the decay from one level to another in order to bridge the energy gap. Therefore, the lower the phonon energy, the more numerous the required phonons (and the less likelihood it is this happens). Phonon energy is determined by the glass composition. In the case of silica glass, its value makes the 4I11=2 energy level have an effective nonradiative lifetime of 1 ms. Phonons (thermal origin) then also aid the energy transfer process between the different Stark sublevels that correspond to the electrical field seen in the glass by the erbium

FIGURE 1

Simplified energy diagram for erbium ions illustrating the Boltzmann population distribution of the Stark sublevels.


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ions. Each energy level is indeed split into several sublevels. The resulting population of such sublevels is defined by a Boltzmann distribution law (which depends on temperature as a parameter), the sublevels of lowest energy being the most populated. Each energy level is therefore homogeneously broadened due to the contribution of these sublevels. In addition, due to inhomogeneity in the electrical field within the glass material, the different ions do not have the same exact values for the energy of their Stark sublevels. This induces an inhomogeneous broadening of this homogeneous line, resulting in a broader overall line shape for the emission and absorption spectra of the erbium ions. As seen later, these slight differences in the erbium energy levels may also result in a different saturation process occurring on the ions. This is the signature of the glass material. (In a crystal where electrical field is strictly uniform for all ions, this inhomogeneous broadening would not be observed, and the overall gain spectrum would narrow.) Excited ions may therefore amplify signals through stimulated emission. As seen in Fig. 1, this quasi-two-level amplification scheme may also include absorption of signal by erbium ions that are still in the fundamental state. Depending on the wavelength of the input light, the absorption or emission characteristics will be different. Ions that are in the fundamental state will instead absorb wavelengths from the Stark sublevels of lowest energy, which is the most populated in the related Boltzmann thermal law. The corresponding energy gap with the 4I13=2 metastable energy level will be thus higher. Conversely, ions that are in the 4I13=2 metastable level will correspond to lower energy gaps when deexciting through stimulated or spontaneous emission. Again, this is due to the Boltzmann law of population of Stark sublevels in the excited states. For instance, the likelihood of having an emission at shorter wavelengths is lower because fewer excited ions are in the Stark sublevels of highest energy. In the same way, absorption at longer wavelengths is less likely to occur because fewer ions from the fundamental state level can be excited to the Stark sublevels of highest energy. As seen in Figure 2, the technique named optical pumping that consists of absorbing pump light in order to excite erbium ions may be efficiently performed in the short-wavelength band of the absorption spectrum of the 4I15=2 to 4I13=2 energy transition, near l ¼ 1480 nm (pumping may also be performed at

FIGURE 2 Schematic of the pumping scheme for erbium-doped fiber amplifiers.

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l ¼ 0:98 mm in the 4I11=2 level). Emission and amplification are then obtained mainly between l ¼ 1525 nm and l ¼ 1565 nm when a high population inversion is reached. The amplification scheme therefore behaves like in a three-level laser system near l ¼ 1530 nm (significant potential absorption) and in a quasi-fourlevel scheme at longer wavelengths near (and above) l ¼ 1560 nm (nearly pure emission). Rate equations describe the effects of absorption, stimulated emission, and spontaneous emission on the populations of the ground and metastable states. For such a two-level system with k optical beams we have: P Pk ik sek dn2 P Pk ik sak n ðr; F; zÞ ¼ n1 ðr; F; zÞ n2 ðr; F; zÞ 2 t dt hnk hnk k k and nt ðr; F; zÞ ¼ n1 ðr; F; zÞ þ n2 ðr; F; zÞ are the local total erbium ion density composed of both ions densities for the excited-state and ground-state levels and where: Pk ¼ beam total power at position z in the fiber amplifier ik ¼ normalized optical intensity nk ¼ frequency of the optical beam r ¼ position in the radius direction of the fiber F ¼ angle position in the fiber sa and se ¼ erbium absorption and emission cross sections. This equation shows that the population inversion at z length is determined by the balance between the pumping rate and saturation induced at signal wavelengths. A remaining equation describes the propagation of the beams through the fiber: dPk ¼ sek dz

ð 2p ð 1 o

o

sak

ik ðr; fÞn2 ðr; f; zÞr dr dfðPk ðzÞ þ 2hnk DnkÞ

ð 2p ð 1 o

o

ik ðr; fÞn1 ðr; f; zÞr dr dfðPk ðzÞÞ

where Dnk is the frequency bandwidth of the kth optical beam, n2 is the population at z length, determined by the previous equation, and ‘‘’’ stands for ‘‘þ’’ in the case of forward pumping and ‘‘’’ in the case of backward pumping. Depending on the population inversion rate (count of excited ions over nonexcited ions), the signal will be amplified or absorbed (on its wavelength) along the doped fiber length with a gain level defined by the average populations ni of erbium ions in an excited-state level or in the ground-state level considered over the whole doped fiber length, giving: GðlÞ ¼ exp½GðlÞ ðse ðlÞ n2 sa ðlÞ n1 Þ L


101

where GðlÞ is the overlap of the mode field with the erbium-doped core. This overlap can be expressed as the ratio between the mode field area and the core area. Increasing the cutoff wavelength will enhance this overlap coefficient at a given wavelength. The dependency of this figure with wavelength is weak over the signal bandwidth. For low signal power (less than 30 dBm), the count of excited ions is not modified by the amplification of the signal. Then, very high gain efficiencies can be reached (several decibels per milliwatt of pump power). When the signal input power is increased, the count of excited ions may significantly decrease, leading to a lower gain seen by the signal (gain saturation [5]). For the highest signal powers, the output power can then be determined by the intrinsic background loss of the doped fiber (caused by scattering and unwanted ionic absorption) and by the pump power. One then defines the power conversion efficiency (PCE) of the amplifier as PCE ¼

Pout Pin Pp

where Pout and Pin are output and input signal powers launched in the doped fiber and Pp is the launched pump power. Although theoretically 98% (this figure corresponds to the ratio of the signal and pump photon energies), the highest possible percentages are around 80% to 90% with 1.48-mm pumping due to some parasitic up-conversion processes and around 55% to 60% with 0.98-mm pumping (against theoretical photon energy ratio of 63%). In the signal saturation regime, the gain decreases at a value defined as the difference between the signal output power allowed by the pump power and the signal input power. This variation in decibels of the gain as a function of signal input power is called gain compression (Fig. 3). Gain compression (DG) corresponds to the amount of decibels of gain that will be added when reducing

FIGURE 3 Diagram showing the signal output power (dBm) of an EDFA as a function of the signal input power (dBm) for two different pump powers showing the resulting gain compression (dB).

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the signal input power from its nominal saturating value down to the small signal regime (30 dBm): DGdB ¼ GdB ðPin ¼ 30 dBmÞ GdB ðPin ¼ Ps Þ where Ps is the nominal amplifier total input power. This gain compression is therefore a parameter that describes the level of saturation of the amplifier. To increase the amplification efficiency, it may be useful to play on the guiding parameters of the doped fiber in order to increase the overlap of the light beams with the doping area. To obtain highest gain efficiency, one can use a doped fiber with a low core diameter with doping only in the center of this core. Then, one pump photon will have a higher likelihood of meeting one erbium ion. For saturation signal input powers, along with quite large pump powers, the very high rate of photons crossing the fiber section makes it possible for almost all ions to see both pump and signal beams. Then, the advantage of having optical or doping confinement is not as clear. The relatively high emission and absorption cross sections of erbium ions indeed makes almost all of the ions located in the fiber core part of the amplification process (providing gain or loss), at the levels of powers used in practical amplifiers. For high output powers, optical confinement may even create the opposite effect. Indeed, to reduce fiber length (and potential loss), one can increase the count of ions potentially involved in amplification, that is, those in the core section of the fiber. Therefore, it may then be more relevant to increase (not to reduce!) the fiber core diameter. Actually, the intrinsic background loss coefficient of doped fibers (between 5 and 10 dB=km measured at l ¼ 1200 nm) does not affect amplifier performance, due to the short lengths of doped fibers that are used (a few tens of meters long). In addition, we can increase the erbium concentration in order to reduce the fiber length (taking care to avoid cooperative pair-induced effects [6–10]). In summary, a cutoff wavelength that enables single-mode operation at the pump wavelength, is chosen (around l ¼ 800 nm for 0.98-mm pumping and around l ¼ 1200 nm for 1.48-mm pumping, enabling splice monitoring at l ¼ 1300 nm). An index difference between 15 103 and 20 103 is then used (corresponding numerical apertures between 0.2 and 0.25). This creates core mode-field diameters that range between 6 and 8 mm, compared to 10 mm for conventional single-mode fibers. This choice of parameter also ensures a large manufacturing capability with high yields. For the same reasons, uniform doping of the fiber core is generally used.

B. Dynamic Behavior An important characteristic of EDFA concerns its behavior with time-dependent signals. As just described, the gain of an EDFA decreases when the power of an incoming input signal increases (gain saturation). Therefore, in the case of a modulated signal supporting numerical coding (with marks and spaces), the gain may be higher for ‘‘space’’ pulses than for ‘‘mark’’ pulses. Characteristic times


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governing the evolution of gain that is induced by a time-varying saturating signal are given by: tgain ¼

t Pp P þ s 1þ Psatlp Psatls

where t is the spontaneous lifetime of the excited state of erbium ions, and where Psat is given by: Psat;l ¼

pw2 ðlÞ se ðlÞ þ sa ðlÞ

where w is the mode-field radius of the light beam, and Psat represents the ‘‘sensitivity’’ of the amplifier to incoming signal or pump photon beams. This means that gain will follow signal variations for signal time periods lower than this characteristic time. Figure 4 shows the evolution with time of the output signal having a low-frequency modulation rate. When the frequency is increased above a few kilohertz (corresponding time periods below 1 ms), the gain stabilizes at a mean value corresponding to the mean signal input power. The output signal power does not suffer from any distortions. Indeed, for high bit rates, lowfrequency data streams contained in the numerical protocols used in telecom systems are above this frequency limit. The time behavior of an EDFA is dependent on the levels of pump and signal power (and wavelength). For highly pumped EDFAs, the amplifier recovers its gain level faster when the signal power is decreased. In the same way, the impact of a variation of the signal will be higher for highly saturating input powers. Thus, short wavelengths located near l ¼ 1:53 mm will induce a faster amplifier time response than will wavelengths located near l ¼ 1:56 mm (and above). This is due to higher cross-section values at such wavelengths (and lower saturation powers; see [4]). The spontaneous lifetime of the metastable 4I13=2 excited level is therefore not the sole reason for

FIGURE 4 Diagram showing the cross-gain modulation induced on a low-power probe signal by a saturating channel (binary modulated with time period of a few milliseconds) through the propagation in the amplifier.

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the corresponding frequency values. Indeed, this lifetime is only responsible for the decay time of the fluorescence power when the pump is turned off (and no saturating input signal is present). The time that is needed by the amplifier to recover its gain level when the signal is suppressed is determined by the pump power level and by the time required to bring the ions from the excited state to the metastable state related to the amplification process. For decaying from the 4I11=2 level in the case of 0.98-mm pumping, the effective lifetime of the 4I11=2 level is 1 ms, or for 1.48-mm pumping, from the upper Stark sublevels to the medium Stark sublevels of 4I13=2 experiments have shown recovery times of a few hundred microseconds [11]. The reason is not the thermalization time of the Boltzman distribution of the Stark sublevels, which is much faster (femtosecond range). This time behavior has been advantageously used in the case of submarine systems for on-site amplifier monitoring through the control of the pump’s driving current. Indeed, a modulation of the pump power induces a modulation of the gain level of the EDFA. Therefore, gain variations will be induced only if the time period of the pump modulation is lower than the gain characteristic time. A modulation will then be induced on the amplifier output signal power. To monitor this modulation at the link output, it is important for the time period of this modulation to be faster than the characteristic time given for signal saturation (see before). Indeed, a modulation rate that is too high would not be seen by the signals propagating through the amplifiers since the excited-state decay time acts as a low-pass frequency filtering. The best value for the frequency to apply to the pump current is therefore a compromise between induced gain variation and signal propagation. Such a compromise is function of input pump and signal average output powers. It is worth pointing out that the evolution of submarine systems such that they can operate with more numerous channel counts and, thus, higher pump and signal powers has modified the choice of the pump modulation frequency. As seen in Fig. 5, higher powers means lower characteristic times and thus a need to increase the modulation rate of the pump. The amplitude of the resulting modulation can then be used in order to monitor the gain of one particular amplifier in the chain. This technique has proven to be effective in an actual link and is still used in currently installed submarine systems.

C. Noise Characteristics In transoceanic transmissions, accumulation of noise along the amplifier chain is one important issue to address regarding the transmission of signals. The origin of noise is linked with the population of the metastable 4I13=2, which enables amplification of the signals through stimulated emission. Ions excited to the 4I13=2 energy level may indeed also relax to the fundamental ground-state level through radiative decay. Then, one photon is created, whose wavelength, phase, and polarization are randomly defined in their respective ranges of values. Noise photons that are coupled into the waveguide will propagate and be amplified at


105

FIGURE 5 Schematic illustrating the compromise (function of pump and signal powers) for the choice of the modulation frequency to apply to the pump light of one given amplifier in the link in order to transmit, through the signal power, some monitoring information to the link output. Upper curve: Decrease of the amplitude of the induced modulation of the gain of an amplifier when increasing the frequency of the modulation of the pump. Lower curve: Increase of the amplitude of the modulation transmitted by the signals after propagation in the link as a function of the frequency of this modulation.

their turn. This amplified spontaneous emission (ASE) noise power will accumulate along the link transmission. In an amplified chain with periodic link fiber attenuation and amplification of the signal, the output power of the amplifier levels off at a level corresponding to the saturated output power of the amplifier (mainly determined by the pump power level). This power is composed of noise and signal power. Indeed, at each amplifier a new noise contribution is added, making the amplifier gain slightly lower than the fiber span loss. The total amplifier output power (signal and noise) is indeed regulated to be the same for all amplifiers in the chain. For one amplifier taken alone, the quantity of noise that is added to the input signal for a given gain level is related to the amplifier noise figure. ASE power can be written as: PASE ¼ 2

neq GEDFA h n Bf C1

ð1Þ

where neq is the equivalent noise parameter, C1 is the amplifier input loss, GEDFA is the net gain of the amplifier (including input and output loss), h n is the energy of the noise photon at the related frequency, and Bf the optical filter bandwidth where this noise power is calculated. As defined in [4], neq G ¼ nsp ðG 1Þ where nsp is the noise parameter and not accounting for input or output loss and G is the gain of the doped fiber length alone. In submarine links, the amplifier gain lies between 10 and 15 dB. One should therefore pay attention to the exact formulation used for the ASE calculation. Using neq is more ‘‘physic sensitive’’

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and can be used with good accuracy to determine the net gain value of the amplifier (GEDFA ) in Eq. (1) instead of coming back to the doped fiber gain (which is the amplifier plus input and output loss). It can be shown that 2 neq =C1 stands for the amplifier noise figure. Indeed, a more precise formulation is NF ¼

1 þ 2nsp ðG 1Þ G

for a doped fiber gain G (no input and output loss considered). In this equation, the 2 stands for signal-to-noise beat product and it is assumed that the noise has a Gaussian distribution. For gain levels higher than 10 dB, the noise figure can therefore be written NF ¼ 2nsp

G1 2 neq G

ð2Þ

In Eq. (1), the 2 stands for the two polarization states. Suppressing noise on the opposite polarization state to the signal will not improve the signal quality because this would not remove the 2 from Eq. (2), which corresponds then to the beat on a photodiode of the optical signal with noise having the same polarization state [12]. In calculations, Eq. (1) should be expressed as follows for numerical applications: neq c2 PASE ðdBmÞ ¼ 10 log10 2 G h Dl þ 30 C1 l3 where Dl stands for the wavelength range where noise is calculated or measured (i.e., the width of the optical filter, usually the resolution of the optical spectrum analyzer). The value of neq determines the level of noise generated by the amplifier for a given gain value. Full inversion gives quantum limited noise performance (neq ¼ 1), and in the case of no input loss a noise figure of 3 dB. For a practical amplifier, one should add the amplifier input loss (around 1 dB due to the input coupler and pump-to-signal multiplexer). Values of neq of about 1 and 0.5 dB should be considered for 1.48-mm pumping and 0.98- mm, respectively, leading to noise figures ranging between 4.0 and 5.0 dB. Values of neq are higher at shorter wavelengths compared to longer wavelengths (the variations with wavelength increases when neq is higher). Values of neq also increase with amplifier saturation either due to the signal power [13] or due to ASE power in the case of high gain levels ( > 15 dB). The level of gain of submarine amplifiers makes unnecessary the implementation of isolators located at midstage to avoid self-saturation [14]. The value of neq is actually related to signal absorption rather than to emission cross section, which may be surprising because noise comes from spontaneous emissions. As an illustration, operation with full inversion gives rise to the highest decay rate of spontaneous emission, but also to the best noise figure. The value of neq is determined by the propagation of both noise and signal beams along the amplifying medium. Incoming noise or signal photons may be amplified (stimulated emission) or absorbed, like pump photons. In that


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case, the excited ion may induce in a second step stimulated emission and then amplify a noise or a signal photon. It may also create one spontaneous photon noise. One signal photon has thus been transformed into a noise photon. In contrast, if the incoming photon is a noise photon, it may be then recovered in the case of a spontaneous emission process that may follow its absorption (if the excited ion decays through a stimulated emission process, the signal-to-noise ratio is not changed). The neq values correspond therefore to the noise penalty due to the absorption of signal photons. For instance, at shorter wavelengths, absorption cross sections are the highest, leading to highest noise figures. When population inversion is decreased, more signal photons will be absorbed, leading to an increase of the noise figure. Conversely, in full inversion, no signal photon is absorbed and this results in the best noise figures. To improve the noise performance of an amplifier (and thus of a chain), it is therefore crucial to avoid signal absorption, especially in the first part of the amplifier and to lower the negative impacts of lossy devices by placing them after an amplifying section. It is worth pointing out that the intrinsic background loss coefficient of the doped fiber has a very low impact on the amplifier noise figure because of its low value (a few decibels per kilometer) compared to the length used in an amplifier (and this loss is distributed along the amplifying medium).

D. Giles Parameters To design an optical amplifier for submarine applications, it is important to perfectly characterize the doped fiber that is used. In an amplifier chain, the large count of EDFAs means that even small variations can accumulate along the propagation path and gives rise to important changes at the link output. To characterize the doped fiber, one should define the optical confinement of the signal and pump beams (lc, Dn, a) and also the doping concentration, and emission and absorption cross-section spectra. If the optogeometric parameters of the fiber are relatively easy to obtain, accurate measurements of the other parameters are not possible. To define guidelines in the optimization of the doped fiber itself, one should use a general model taking into account the spatial dependence of the optical beams using Bessel function formalism [15]. This enables us to define the impact of the cutoff wavelength or numerical aperture on, for instance, the amplifier efficiency and noise figure (this impact is weak as explained above). To design an amplifier from an existing doped fiber, it is useful however to make calculations from parameters measured on the doped fiber itself. Giles parameters [15] provide this possibility. The strong advantage they bring is that this model uses parameters directly available through measurements made on the fiber itself, without needing to know about any other parameters. Such parameters are: aðlÞ ¼ GðlÞ nt sa ðlÞ

absorption coefficient

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(gain per meter of length coefficient obtained when n2 ¼ 0, i.e., no pump, no signal) g*ðlÞ ¼ GðlÞ nt se ðlÞ

stimulated emission coefficient

(gain per meter of length coefficient obtained at full inversion, n1 ¼ 0) the background loss coefficient, and a saturating parameter x, defined as: z ¼ Psat;l ðal þ g*Þ=h nl l In these equations, GðlÞ stands for the signal to core doping overlap and Nt for the doping concentration and GðlÞ has a slight dependence with wavelength. The aðlÞ spectrum can be measured with an attenuation measurement with a white high source on a small piece of fiber. The gl* spectrum is measured owing to the fluorescence spectrum of a few-centimeter-long doped fiber, and calibrated in level through a gain measurement at full inversion for a short fiber length [16]. The saturating parameter x can also be measured directly. Its measurement is less accurate than that of other parameters but the impact of this parameter on the results is lower and related only to the simulated power performance, not to the amplifier gain spectral shape. Background loss is measured at a wavelength around 1250 nm, where the influence of erbium has vanished. It is very useful for such modeling to be performed directly from such parameters without needing to know the doping concentration or the absolute cross-section peak values of the fiber. The hypotheses of this model are the assumption of similar overlaps of optical beams with excited and unexcited ions (which is true for practical amplifiers) in addition to a homogeneously broadened behavior (no spectral hole burning, like in most other modeling approaches). The resulting equations for the population of erbium ions in the excited state become (steady-state):

and

P Pk ðzÞak hnk z n2 k ¼ P Pk ðzÞ ðak þ g*Þ nt k 1þ hnk z k dPk n n ¼ ðak þ gk*Þ 2 Pk ðzÞ gk* 2 2hnk Dnk ðak þ lk ÞPk ðzÞ dz nt nt

where Dnk is the frequency bandwidth of the kth optical beam, n2 is the population at z length, determined by previous equation, and ‘‘’’ stands for ‘‘þ’’ in the case of forward pumping and ‘‘’’ in the case of backward pumping. The measurement of such parameters therefore enables us to characterize perfectly the doped fibers that are manufactured, in comparison with one previous reference fiber for instance. To simulate the spectral transfer function of the doped fiber, we must avoid any spectral distortions in the absorption and emission spectra. The accuracy provided by optical spectrum analyzer (0.1 dB), however, is not compliant with the need to simulate chains with hundreds of amplifiers


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(0.01 dB required [17]). To further improve the accuracy of the parameters, we can measure the g* coefficient at different wavelengths (by measuring the gain of a fully inverted doped fiber length). This may help to correct error variations that can be observed in the measured fluorescence spectrum. If further corrections should be still required, then a circulating loop should be set up in order to accumulate the gain spectrum of the amplifier through numerous rounds, and to deduce the required g* l spectrum in order to fit with the output spectrum of the loop.

III. REQUIREMENTS FOR SUBMARINE SYSTEMS Submarine links potentially require an ultra-long-haul amplifier chain (up to 10,000 km long) with high repair costs, and one single end power supply for the whole system. The choice of the amplifier characteristics and device technology should therefore consider such features [18]. First, to ensure high signal-to-noise ratio at the link output, it is crucial to keep the signal power at a high level along its propagation along the link. This means we must implement short lengths of link fibers between two successive amplifiers in order to have a reduced span loss and thus limit the signal attenuation before meeting amplification. This means the loss between two successive amplifiers will be in the range of 10 to 15 dB, depending on the total link length and on the amplifier signal output power allowed by nonlinear effects in the link fiber. Indeed, Kerr effects (self-phase and cross-phase modulation) and four-wave mixing result in a maximum per-channel power of around 0 dBm, meaning the EDFA total signal output power ranges between þ12 and þ15 dBm as a function of the channel count [19] (for 16 to 32 channels for instance).

A. Noise Figure To bridge transoceanic distances while keeping the SNR high, it is crucial to limit the noise contribution added by the successive amplifiers. The impact of this added noise on the output SNR can be calculated as follows: n DP P 1 1 ASEi ¼ þ SNRn SNR0 i¼1 Pouti

obtained from

1 1 ¼ þ SNRn SNR0

ðL

dPASE ðzÞ z¼0 Psignal ðzÞ

This equation can also be expressed in a more physical manner: Just consider how signal and noise powers propagate along the chain experiencing gain and loss at each span along with summation of the noise contributions at the different amplifier sites.

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We then have: SNRkout ¼

out Psignal

Noiseout

in Psignal GkN LossNk

¼

Po GkN LossNk þ PASE GkN 1 LosskN 1 þ þ PASE

where Po is the noise at the link input (which is the first amplifier), and k stands for the signal wavelength of the signal. Assuming the gain is different than the loss, this equation can then be simplified to: SNRout ¼

¼

in Psignal

Po þ

1 GkN LossNk PASE GkN LossNk 1 Gk Lossk in Psignal

Po þ

NF hnk Dnk 1 GkN LossNk GkN 1 LossNk 1 Gk Lossk

If, however, we assume gain equals loss, we get: SNRkout ¼

in Psignal

Po þ N PASE

¼

in Psignal

Po þ N NF hnk Dnk

To get values in decibels, merely use 10 logðxÞ of the previous equation, paying attention to the fact that a conversion figure of 30 should be applied in order to express the signal input power in dBm units. As seen before, each amplifier noise contribution (expressed in dBm) is a linear function of the amplifier noise figure. An increase of 1 dB of the EDFA noise figure reduces by 1 dB the SNR at the output of the link (by increasing the noise floor by 1 dB). This noise floor is caused by the addition of the noise of each amplifier. To compensate for a noise figure that is 1 dB higher, we need to reduce the amplifier count by 1 dB, that is, by 21%, in order to keep the same noise floor. Using EDFAs with a noise figure of 6 dB instead of 5 dB may therefore mean reducing the maximum link distance from 10,000 km to 7950 km (thus not reaching China coasts from the United States, for instance!). A higher noise figure can also be compensated for by reducing the span loss, thus resulting in a higher count of amplifiers for a given distance (i.e., thus inducing a higher cost for the link). It is therefore crucial to keep the amplifier noise figure very low in order to fully exploit the system capability in terms of distances that can be reached and to optimize the cost of the link. Other important characteristics concern the system lifetime, which should exceed 25 years with less than three repairs during that time. All devices incorporated in the amplifier should therefore comply with such lifetime requirement. This has been a major limiting factor for the implementation of 0.98-mm pumps in submarine amplifiers for a long time (as discussed later).


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B. Hydrogen Sensitivity An important potential degradation process could be the degradation of the doped fiber due to hydrogen [20–22] generated within the hermetic repeater block during the system lifetime. This hydrogen passes through the erbium-doped fiber coating into the silica glass. This induces creation of OH molecules, with its related absorption peak near l ¼ 1:43 mm and its absorption band tail up to wavelengths including l ¼ 1:55 mm. The characteristics of the EDFAs may therefore be seriously damaged due to this aging process [23]. Experiments have been conducted to analyze and predict the evolution rules of this effect [24– 28]. It has been shown that erbium-doped fibers have same sensitivity to hydrogen as conventional link fibers [29]. They do not require any specific coating to cope with this hydrogen diffusion, compared to other types of fiber. The higher Al, Ge concentration or the erbium ions have no specific added effect (the addition of La co-doping may be used to reduce the hydrogen sensitivity [30]). The loss penalty induced by hydrogen has been assessed to be as low as 0.04 dB for 20 m of EDF exposed to 0.001 atm (10 times more than the typical value for hydrogen pressure in the repeater!) after a 25-year lifetime at 40 C [26], showing it is in fact not an actual issue for submerged doped fibers.

C. Power Consumption A last important requirement of the submarine amplified link is that power consumption should be kept as low as possible because the driving voltage of the whole link is limited to a given value by the technology of the cable (see related discussions). This voltage corresponds to the summation of all bias voltages of each dissipating device located along the link. The same current travels through all of these devices, which are connected from an electrical point of view in a serial configuration. Power consumption (driving voltage in particular) is therefore an important parameter that should be accounted for in components that may be incorporated in the amplifier such as pumping devices or active control devices.

D. Polarization-Dependent Loss Polarized signal channels (DFB lasers) are used and needed at the transmitter side of the link because signal modulators are efficient only with polarized optical channels. Therefore, like any type of optical link, the different parts of a submarine link should cope with the different polarization states of the signal channels (that may nearly randomly change along propagation). In submarine applications, the effects due to each component may be accumulated up to several hundred times and thus possibly induce strong impairments in the link performance [31] (although such effects are very small when considered for a single

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device). A particularity of the polarization state of an optical signal is that it may evolve with time depending on constraints in the cable or other unpredictable effects. Therefore, to avoid such hundred-times effects, it is crucial to strictly avoid any polarization sensitivity in the devices incorporated in the amplifier. This concerns polarization-dependent loss (PDL) of passive components and polarization-dependent gain in the erbium-doped fiber amplifiers. A severe choice of the technologies compliant with a submerged application in terms of reliability and polarization sensitivity (less than 0.1 dB of PDL required, and with some adaptations in some cases) has now made possible the incorporation of isolators, pump-to-signal multiplexers, fusion couplers, or equalizing gain filters (made with fiber Bragg gratings) in link amplifiers. Continuous attention should be paid, however, to such requirements for all new candidate devices.

E. Polarization Mode Dispersion The doped fiber medium itself may also be affected by such possible impairments. A first possible effect concerns the polarization mode dispersion (PMD) that may be induced by the doped fiber [63, 127]. This PMD (corresponding to different group velocity on signal polarization state) may be caused by the nonperfectly circular shape of the doped fiber section. Countermeasures have therefore been taken in the manufacturing process of the doped fiber. One straightforward technique consists of rotating the preform during the drawing process of the fiber, thus averaging all possible imperfections in the shape of the fiber section and thus avoiding any PMD in the doped fiber as well as in all the other components.

F. Polarization-Dependent Gain Another important effect that may be encountered by the propagating channels is a possible change of gain generated inside the doped fiber upon the signal polarization state. This effect is called polarization dependent gain (PDG; also more accurately called polarization hole burning). It is not linked with an intrinsic polarization dependency of the gain provided by the amplifier. Indeed, the stimulated emission process is independent of the polarization of the incoming photon, and the guiding properties of the waveguide ensure a polarization insensitivity of the transmission characteristics of the optical beams. The PDG effect is due to an anisotropy of the erbium ions that are oriented randomly in the glass matrix with regard to the local electrical field, thus modifying their likelihood of interaction with incoming photons. Thus, when the amplifier is driven into saturation, erbium ions corresponding to the signal polarization state will see an excess gain saturation compared to ions corresponding to the orthogonal polarization state [33, 34] giving rise to different gain on polarization [35–39].


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The impact on the system is that ASE polarized orthogonally to the signal experiences more gain than does ASE having the same polarization as the signal. The accumulated enhancement of orthogonal ASE will decrease the amplifier output power available for the signal and impact on the output SNR [33, 34]. As an illustration, in the case of a saturation inducing a gain compression of 6 dB (typical values for submarine amplifiers), a gain difference of around 120 103 dB can be observed. For 100 amplifiers, the accumulated difference is as high as 12 dB! In case of a polarized incoming pump light, ions corresponding to this polarization state are more likely to be excited by the pump beam. The same ions will then also be more sensitive to incoming signals having the same polarization as the pump light. When the excited ion count decreases due to saturation caused by the signal photons having polarization states orthogonal to the pump polarization state, PDG due to the pump will add to PDG due to the signal. If the signal polarization is the same as the pump polarization, then the two effects may compensate each other. In the case of deployed systems with numerous amplifiers, accumulated PDG induced by the pump polarization is nulled, because the signal polarization is different at each amplifier and not correlated with the polarization of the different pumps. A solution consists of changing the polarization of the signal rapidly with time at the transmitter side. Indeed, if the signal polarization state is changed orthogonally fast enough, the effect of PHB will be averaged. Measurements carried out to determine the transfer time of this transient effect have shown similar time values (around 100 ms) compared with transient times corresponding to saturation time response [40]. By changing the polarization state of the signal at a rate much faster (i.e., f > 10 kHz), the impact of PDG is suppressed [41–44]. With the use of numerous channels in last generation’s systems, the polarizations of the different channels’ signals are independent. This means it is no longer necessary to have this polarization modulation because the average incoming polarization is actually carried out on the different channels themselves (that compose the propagating WDM multiplex). PDG is therefore not an issue for submarine systems, as far as, again, attention has been paid to make this effect not have an impact. G. Comparison with Terrestrial Requirements Compared with requirements for EDFAs for terrestrial applications [4], major important differences make the two types of amplifiers definitely two different products. First, the reliability of land-based equipment is somewhat relaxed, corresponding to a 15-year required lifetime, whereas, as mentioned earlier, submarine systems are designed for 25 years and a minimum of repairs (which have to be done by a ship), which implies a requirement for relability and redundancy of all critical components. However, terrestrial equipment should enable operation over a wide temperature range (5 to þ70 C; or 40 to þ85 C in storage conditions). This wide temperature range makes necessary the need to

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implement cooling means for the highest temperatures and compensation means for temperature-sensitive devices. In submarine amplifiers, heat is dissipated from the outer side of the repeater container into the sea. Such a container is designed to make the heat go through the box from the pump device to the outer side, ensuring moderate temperatures at all points. The temperature of the deep sea is indeed around þ5 C. Specific care is taken for repeaters located near coasts or in shallow water in order to guarantee no pump failures due to high temperatures. This constant temperature of the devices and the doped fiber incorporated in the amplifier make possible the ability to perfectly tailor the gain spectrum of the submerged EDFAs, owing to very accurate equalizing filters and to the concatenation of hundreds of amplifiers. This would not be possible for land-based amplifiers whose gain cannot be guaranteed below 1 dB for a 30-nm bandwidth partly due to such temperature changes (while a few tenths of a decibel of gain excursion is reached for submarine amplifiers). Another important difference is the fact that the infrastructure itself of terrestrial systems determines the actual characteristics of the amplifier that should cope with important variations of the span loss between two amplifier sites. In addition, for economical reasons, the same type of amplifier must be used along this nonuniform link. In submarine systems, the link is manufactured at the same time as the amplifiers and much attention is paid to guaranteeing constant attenuation loss between amplifier values, while the amplifier has been designed to perfectly adapt to the link characteristics. A last point concerns the high gain (22–28 dB) of the amplifiers incorporated in land-based systems and allowed by the margins given on the SNR due to the reduced total link length. Gain equalizers therefore compensate for much larger gain excursion values than in submarine amplifiers and should therefore be located at an amplifier’s midstage so as not to have their equalizing loss impact the amplifier output power. In contrast, such filters can be placed after the single section of doped fiber that composes the amplifier in case of submarine applications. In addition, the dispersion compensating fiber is part of the submarine transmission link (such as standard single-mode fiber used to compensate for dispersion of a nonzero dispersion-shifted fiber, for instance, or reverse dispersion fiber used to compensate dispersion of the SMF). Land-based amplifiers should, however, incorporate DCF at the amplifier’s midway. This affects their noise figure, which is around 5.5 dB at T ¼ 25 C (but may reach higher values of around 6 or 7 dB for specific higher signal input power or ways of operation). The design and the implementation of submerged amplifiers are therefore strongly different compared to land-based systems. As a conclusion, one could say that the amplifier is considered to be somewhat part of the link in case of a submarine system (the design and manufacturing of both are completely interdependent then), whereas it is considered to be just one device (among others) in the case of land-based systems. The high count of accumulated amplifiers makes the requirements for their realization and implementation in submarine links very stringent.


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IV. RELATED TECHNOLOGY It is important also to minimize the optical components incorporated in a submarine amplifier in order to keep the complexity low and the reliability high and to reduce the impact of the nonideal characteristics of passive components that may accumulate along the link. Therefore, single-stage amplifier are used consisting of one piece of doped fiber, one pump-to-signal multiplexer (this means one pump access), a fusion monitoring coupler, and an output isolator. Indeed, the reduced gain level (ffi 12 dB) at which the amplifiers are operated makes it unnecessary to use an output isolator to avoid oscillations inside the amplifier. Forward pumping is performed owing to the low insertion loss of the pump multiplexers. Indeed, the slight impact of this loss on the amplifier noise figure (around 0.4 dB) is compensated by the better noise parameter offered by forward pumping. In addition, in the case of pump failure resulting in reduced pump power, forward pumping ensures the pump will be present at the doped fiber input and thus retain a moderate noise figure; this noise figure would increase dramatically in the case of backward pumping if pump power were to be reduced (particularly for 0.98-mm pumping where the higher absorption of the pump at l ¼ 0:98 mm ensures that almost all of the pump is absorbed after a few meters long of doped fiber). The first generation of amplifiers, however, used 1.48-mm contrapumping due to the more mature technology provided by these types of pumps, which were InP technology based. This type of pumping was the first type carried out based on the laser diode pumping of an EDFA [45]. Optical power conversion efficiencies are somewhat reduced with 1.48-mm pumping due to some unabsorbed residual pump power in the case of submarine amplifiers, leading to optical PCE around 40%. One happy consequence has been the finding that this unused output pump power gives rise to some tenths of Raman gain to the signals when propagating after in the link! To cope with aging of the pump diode, the driving current (voltage in case of submarine systems) is increased with time in order to ensure the required pump power level. The laser diode has a spectral multimode Fabry-Perot spectrum around 15 nm width, centered near l ¼ 1470 nm. The 1.48-mm pumping does not allow the amplification medium to reach full inversion. Indeed, when the population inversion is increased, the high count of excited ions produces stimulated emission at the pump wavelength and thus compensates for the lower likelihood they have to interact in that way with 1.48-mm photons. This amplification process of photon pumps balances the absorption process of those photons, leading to some transparency at such wavelengths. The highest inversion rate that can be reached with 1.48-mm pumping therefore corresponds to the transparency at the pump wavelength. This highest inversion increases for shorter wavelengths where emission cross sections decrease quite a bit compared to absorption cross sections. This maximum inversion will determine the lowest noise parameter achievable with this pump wavelength. Due to this process of amplification of

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some pump photons, it is very difficult to fully absorb 1.48-mm pump power, making the related PCE somewhat reduced compared to the highest achievable values. It is worth pointing out that noise and power performance for pumping with a broad pump spectrum are similar to those with a single- frequency pump source (corresponding to the RMS center value of the pump spectrum). The lowest noise parameters for 1.48-mm pumping are around 0.5 dB at l ¼ 1560 nm and 1 dB at l ¼ 1:53 mm. This leads to overall noise figures of around 4.5 dB depending on the signal wavelength. The 0.98-mm pumping allows full inversion of the erbium population to be reached [46]. Its pump technology needed more development time than 1.48-mm technology before it could be used in submarine systems with reliable conditions in recent generations of systems [47, 48]. If the related power conversion efficiency is smaller (maximum theoretical efficiency of 63%), a high absorption rate of the pump light is seen because stimulated emission does not happen at this wavelength owing to the low (1-ms) effective lifetime of the 4I11=2. This means the actual optical PCE for practical submarine EDFAs lies between 40% and 50% with 0.98-mm pumping. In addition, the better electrical efficiency of the pump diode compensates for this lower PCE. With this type of pumping, improvements of 0.5 dB have been performed on the amplifier noise figure with co-pumping that is mandatory. It is worth pointing out that pump multiplexers for 1.48-mm pumping are bulk multiplexers, whereas for 0.98-mm pumping they are fusion-coupler multiplexers (which were bulk multiplexers also in the early 1990s). The advantage of fusion-coupler multiplexers has been a more simple manufacturing process and reduced insertion loss for the first generation of amplifiers using 0.98-mm pumping [49]. However, progress made in the technology of passive components has made the insertion loss of the two types of multiplexers somewhat similar. To further increase the EDFA output power in order to enable more numerous channels for next-generation systems, polarization beam multiplexers may be used in order to couple two different 0.98-mm pumps in the same fiber [128]. If needed, wavelength-division multiplexing of pumps can be used as well. Such multiplexing techniques enable us to keep the architecture of amplifier simple with a single pump access. In addition, this multiplexing technique provides some redundancy, because pump power is ensured at the pump path located at the amplifier input if one pump were to fail. This kind of redundancy is also used between the two fiber pairs corresponding to upstream and downstream signal transmission. In that case, as illustrated in Fig. 6, the two pump powers that feed two amplifiers at a link fiber pair are coupled together within a 50=50 fusion coupler, with each output fiber connected to a different amplifier. This pump arrangement ensures some pump power for the amplifiers of the two links in case one pump were to fail. Characteristics of devices incorporated in the amplifier should therefore ensure no polarization dependency, high reliability, and reduced power consumption. Such features will still govern the implementation of possible new devices in the amplifiers such as a spectral slope compensator


FIGURE 6

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Setup for amplification means of a fiber pair with pump redundancy.

[50] or active spectral gain equalizer. Voltage-controlled devices will be more suited to submarine systems in order to provide active control in the link. V. SINGLE-CHANNEL EDFAs When concatenating several EDFAs (five or more) along a link, the evolution of the total (signal þ noise) output power of the amplifiers is a function that levels off rapidly along the link. Indeed, when representing the gain of an EDFA as a function of the signal output power, one clearly sees this curve dropping rapidly, limited by the highest saturated output power of the EDFA. This saturated output power is mainly determined by the available pump power, in the case of practical submarine amplifier that incorporates a sufficient doped fiber length to guarantee absorption of most of the pump power. The signal output power of such an EDFA is therefore weakly dependent on the signal input power in the highly saturated input power regime. As a consequence, the output power of EDFAs placed in a link cannot increase to higher values than the maximum values determined by their saturated output power. This is quite logical because the total power propagating in a link cannot grow indefinitely. If, after several amplifiers (we will see later what happens for the first amplifiers in the chain), their total output power is clearly determined, their total input power and corresponding gain are then also fully determined. The difference between output and input powers of the EDFA is then equal to the span loss of the link (i.e., the attenuation value of the link fiber located between two successive EDFAs). A. Gain Peak Wavelength Determination In single-channel operation, the maximum gain value upon wavelength of the amplifier is equal to the link span loss. Indeed, a link composed of numerous

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amplifiers with a constant span loss is, to some extent, similar to a deployed laser cavity where the gain of the amplifying medium matches, after a short transient period, the cavity loss. The amplification rate of the doped fiber, that is, the gain per meter of doped fiber that is produced, is therefore fully determined for a given span loss and doped fiber length. If the output power of an EDFA operated with an input saturating signal is weakly dependent of the channel wavelength as far as single-channel operation is concerned, this is not fully the case for submarine single-channel systems. Indeed, a large amount of broadband ASE propagates along with the signal channel. Their respective power levels are in competition concerning power conversion in the amplifier. The amplifier thus behaves in a quasi-WDM amplification regime, with wavelength dependence of the output power as a function of the average population inversion in the doped fiber. However, at the same time, a major part of the propagating power is contained in the sole signal channel thus significantly relaxing the wavelength dependency of its output power. We will see that this provides the system with some tolerances for the span loss determination. As described in detail later, the coefficient of gain per meter of length (which depends on the signal wavelength) increases with the rate of population inversion in the doped fiber. As seen in Fig. 7, the spectral shape of this gain coefficient changes with the inversion rate favoring shorter wavelengths (near l ¼ 1:53 mm) for higher inversion rates. Lower inversion rates favor longer wavelengths (near l ¼ 1:56 mm or more, of lowest energy). EDFAs may exhibit gain peak either near l ¼ 1:53 mm (narrow range of only 1 or 2 nm in width) or near l ¼ 1:56 mm, which gives a broader range of gain peak wavelength (GPW) of a few nanometers in width. These ranges are determined by the cross-section spectra of the erbium glass, and they may change slightly depending on the glass host composition as described later. For a link incorporating amplifiers with a given doped fiber length, the span loss between amplifiers determines the average (upon fiber

FIGURE 7 Normalized calculated gain spectra for erbium ions in silica glass host as a function of signal wavelength (nm) for different average population inversion ratio in the amplifier.


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length) population inversion. In other words, the population inversion rate adapts so that the corresponding gain level matches the link span loss [51, 52], thus determining the gain peak wavelength of the amplifier [53]. This GPW is only a function of the doped fiber length (for a given glass composition) and of the loss compensated for (link span loss þ input and output amplifier loss). B. Parameters That Influence GPW Increasing pump power may have the effect of increasing the related amplifier output power, and thus the corresponding amplifier signal input power, but the maximum gain will not change and will still be given by the link span loss. Therefore, the GPW of the amplifier will not be changed. If one replaces the 1.48mm pump modules of all (or same) amplifiers in link with 0.98-mm pump modules ensuring similar amplifier output powers, the GPW would not be changed as well (we assume the same loss for the pump multiplexer). Indeed, with the signal channel being located at amplifier GPW, the maximum gain of the amplifier is still determined by the link span loss (same value), thus fully determining the average population inversion along the doped fiber length. The 0.98-mm pumping may change the required pump power and amplifier noise figure compared to 1.48-mm pumping, but the same amplifier gain spectrum will be exhibited by the amplifiers operated in the link. The spectral transfer function of the passive components (like pump multiplexers) may slightly shift the GPW exhibited by the doped fiber of the amplifier and therefore creates some difference between both (no more than a few tenths of a nanometer). During a system’s lifetime, an increase in link fiber loss and component loss will slightly decrease the GPW. However, because the amplifier’s operation is driven mainly by the power of the single signal channel, the output power will not be modified significantly, thus preserving system margins. This determination of the GPW of the amplifiers by the link span loss is based on the fact that the output power of the EDFAs (which is determined by the pump power) cannot grow indefinitely. Clearly, if one were to use an amplifier with randomly chosen total output powers, then each amplifier would exhibit a different maximum gain level, and thus a different GPW. In this unrealistic case, no steady state would be found in the link. For better control of the levels of powers propagating in the link, the total output power of the link is therefore regulated to a constant value during the system lifetime through the adjustment of the pump power. C. Self-Filtering Effect An important issue for the first transoceanic links that were designed was whether or not there was a need for optical filtering with a passive device in order to ensure enough power for the signal channel and suppress ASE. Using a filter at each amplifier means that the amplifier (including the filter) will provide gain only in the filter window. Then, the signal wavelength should be placed in the

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center of the filter transmission function. The center wavelength of this filter should be selected at a wavelength that the doped fiber can efficiently amplify. However, EDFAs exhibit a flat signal output power on wavelength when deeply saturated by a single input channel. (There is no competition with another channel or with broadband ASE due to the filter, making all the amplifier power available for the channel). But the use of such selective filters does not guarantee the system will work. Indeed, if we consider that each amplifier including filter has a gain function f ðlÞ and that the transfer function of the span loss is flat upon wavelength, the accumulated gain and loss at the link output is f N ðlÞ=LossN where N is the amplifier count. Figure 8 shows the effect of concatenation of numerous amplifier gain shapes along propagation in a link. The same behavior would be observed for concatenated filter transfer functions. The width of the accumulated filter is therefore very narrow even on the basis of an ideal case where all filters perfectly exhibit a same center wavelength (the tolerance on this value is very low, less than 0.1 nm for a transoceanic link). Filter-based solutions, therefore, did not seem very practical to implement (without talking about the PDL value of the filter). However, if one carefully locates the signal channel exactly on the top of this gain spectrum, its power will propagate through the amplified chain while keeping a high level without a filtering device [54]. Noise contributions at other wavelengths will not propagate (a stop-band filter may be implemented in order to supress ASE located near the 1.53-mm bump). Alternatively, if one locates the signal outside the gain peak region, then it will disappear during the propagation seeing higher loss than gain. In that case only noise contributions located near the GPW will be transmitted. In the first amplifiers of the link, a steady state has not yet been reached, making the amplifier gain spectrum somewhat different than in the nominal case in the link where ASE power is significant. An experiment may consist of launching no signal input power in the link. In that case, the first amplifiers will exhibit a high gain level corresponding to the small signal input power regime, that is, to a high population inversion rate, with

FIGURE 8 Calculated effect on the available signal bandwidth of the concatenation of numerous in-line filters as a function of amplifier count (respectively 1, 10, 50, 100, 150, and 200). Mismatch between the center wavelengths of the different filters (not accounted here) would make the curves appear even narrower.


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gain peak located near l ¼ 1:53 mm. ASE power from this amplifier will propagate in the link (accumulating with contributions of other additional amplifiers) and thus saturate the amplifiers that follow. Let us look now at the output spectrum of the link. The amplified noise power will act then in the same way as the signal power. The amplifiers will be saturated and their population inversion will adapt so that their maximum gain level will match the loss seen between two doped fibers. The noise contribution of each amplifier sees the accumulated gain function of the remaining part of the link. The addition of such contributions gives at the link output a Lorentzian spectrum having a peak wavelength located at the amplifier GPW. Its spectral dependency as a function of amplifier count N can be expressed as: tot PASE ðlÞ ¼

1 ½GðlÞ LossðlÞN 0 PASE ðlÞ 1 GðlÞ LossðlÞ

0 is the noise coming from one single amplifier, gain and loss being where PASE almost equal at the gain peak wavelength. The noise spectrum at the output of the link therefore exhibits a line located at the amplifier GPW and is shown in Fig. 9 for the case of three different average population inversion rates of the amplifiers. This technique, which consists of measuring the noise output spectrum without a propagating signal, enables us to determine accurately the self-filtering wavelength of the link [54, 55]. The signal channel should then be located at this wavelength. Depending on the gain per unit of length of doped fiber (i.e., on the average population inversion), GPW is exhibited near l ¼ 1:53 mm or near l ¼ 1:56 mm. Figure 10 shows the corresponding accumulated normalized gain function for the same average inversion rates as in Fig. 9. The noise figure is around 1 dB higher near l ¼ 1:53 mm than near l ¼ 1:56 mm, and the related gain bump is much narrower. Therefore, amplifiers

FIGURE 9 Calculated ASE output spectra after propagation in the link (no signal, loss flat with wavelength) as a function of the wavelength (nm) for three different average population inversion ratios (count of excited ions over count in total ions) in the amplifiers (0.65, 0.6, and 0.55 corresponding to doped fiber lengths of 14.43, 20.06, and 26.48 m, respectively, and a span loss of 12.22 dB). Amplifier count is 200.

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FIGURE 10

Calculated accumulated gain spectra (normalized) after propagation in the link (loss flat with wavelength) as a function of the signal wavelength (nm) for three different average population inversion ratios in the amplifiers (0.65, 0.6, and 0.55 corresponding to doped fiber lengths of 14.43, 20.06, and 26.48 m, respectively, and a span loss of 12.22 dB). Amplifier count is 200.

have been designed to offer self-filtering near l ¼ 1:56 mm. Attention has been paid to locating the GPW of the EDFAs at wavelengths high enough that they will provide tolerance on the length of doped fiber incorporated in the amplifier and not risk making the related GPW jump from the 1.56-mm region to the 1.53-mm region [56]. Therefore, a GPW located near l ¼ 1558 nm was selected for the first-generation systems although the range of possible wavelengths was several nanometers wide. It is therefore possible to transmit a single channel through the amplifier chain with high output SNR (and it is even better than the solution using filters due to its broader gain profile!). The amplifier therefore offers a selffiltering capability owing to the concatenation of successive almost identical gain spectra compensating the link span loss at their gain peak wavelength [57]. D. Design Rules One should then address the issue of design rules for such types of EDFAs for the case of single-channel transmission. Indeed, we know that the doped fiber length determines the GPW of the amplifier when it will be incorporated in the link. However, other important parameters are also functions of the fiber length, like the amplifier noise figure and gain compression. Gain compression (which is the increase of the gain, expressed in decibels, that one observes when suppressing the saturating input power) is very useful to the practical implementation of such amplified links. For an increase of one span loss (due to an increase in cable loss at a specific location for instance) or of a decrease of one EDFA output power (one pump fails for instance), the signal input power of the next EDFA may be decreased by several decibels. In that case, the gain of this amplifier will increase, due to reduced saturating input power. If the amplifier has a gain compression of 5 dB, its gain may increase by 4 dB for a 10-dB decrease in its input power. This means that its output power will decrease by 6 dB. The next amplifier will also recover part of the missing signal input power (3 dB for instance), and the third


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amplifier too. Therefore, this 10-dB loss in signal power will be recovered with only the three next amplifiers and the impact on the OSNR at the link output will be limited (a self-healing effect). Actually, the pump power of the amplifiers is controlled in order to regulate the amplifier total output power at a constant level. Therefore, the count of amplifiers required to recover this lost power will be one or two at a maximum. However, if not enough gain compression is provided, the gain will not increase enough. The pump power enhancement will not meet the required EDFA output power target before reaching its maximum current limit value. In such a case, the extra added pump power is not fully absorbed by the doped fiber and is lost as residual output power. In addition, when the input signal is lower, pump absorption is lower because the population inversion increases, making less numerous ions in the ground-state level. Such ions may potentially absorb pump photons. To enable the absorption of this extra added pump power and provide a higher gain compression to compensate for the decrease of signal input power, a higher fiber length may be used. This is useful, however, only if a lower gain coefficient per unit of length (i.e., a lower corresponding population inversion) is performed for a given span loss value. But this will also increase the self-filtering wavelength toward a higher wavelength, along with an increase of the amplifier noise figure due to the lower population inversion. Increasing the doped fiber length to increase gain compression is then obtained in that case at the expense of a noise penalty. This can be avoided by the use of an optimum glass composition as discussed later. E. Gain Compression and Pump Wavelength It is worth pointing out that 0.98-mm pumping provides greater gain compression compared to 1.48-mm pumping. Indeed, if almost all pump power is absorbed in the high signal input power (saturating) regime at both pump wavelengths, much more 0.98-mm light is absorbed compared to 1.48-mm light in the small signal input power regime. This is due to the empty excited 4I11=2 level, which prevents any stimulated emission at l ¼ 0:98 mm, which is not the case for 1.48-mm pumping. Therefore, the almost fully absorbed 0.98-mm light in the small signal regime provides high gain. This gain will be helpful in the case where some extra gain is required to compensate for extra loss or pumping failure. Related gain compressions range between 6 and 10 dB with 0.98-mm pumping, whereas values range between 4 and 7 dB with 1.48-mm pumping [128]. It is noteworthy that greater gain compressions are obtained for wavelengths located in the 1.53-mm region compared to the 1.56-mm region (due to the high 1.53-mm gain peak observed in the small signal regime). This (single) advantage for having self-filtering near l ¼ 1:53 mm was not significant enough to change the choice of the signal wavelength for the system. In fact, values of gain compressions obtained for wavelengths located near l ¼ 1:56 mm are high enough to provide the self-healing effect described earlier.

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F. Glass Composition The location of the GPW of an EDFA operated at a given population inversion rate may be slightly modified by the glass host composition [58, 59]. Slight modifications of the Stark sublevel energies modify the cross-section spectra. Aluminum is known to increase the Stark splitting of the energy levels, thus increasing the width of the ground-state and excited-state bands. High aluminum co-doping (several weight percent) enables GPW at wavelengths as low as l ¼ 1529 nm at full inversion, and shift the GPW of the 1.56-mm bumps toward higher wavelength for the reduced population inversions at which submarine amplifiers are operated (around 60% inverted ions). The use of fibers with a high aluminum concentration enables us to keep the same GPW compared to an amplifier with a longer doped fiber length having the same erbium concentration and a lower aluminum concentration (0.3 wt% [60]). For the same GPW and similar gain compression, the amplifier noise figure can then be improved by several tenths of a decibel. In addition, the use of highaluminum fibers allows the lowest possible cooperative effects between erbium ions (two erbium ions in the 4I13=2 state level, which interact and leave the metastable energy level) that occur in the case of increased erbium concentration. With high-aluminum-concentration fibers, erbium concentration providing an unpumped 1.53-mm peak absorption of around 4 dB=m was enabled without significant gain or noise penalty caused by cooperative effects. The manufacture of such doped fibers with high-aluminum codoping requires perfect control of the different process in order to make fibers with reproducible characteristics and a purely circular core section. Such techniques are now well controlled, allowing the use of high-aluminum-concentration doped fibers in submarine systems. With such an amplifier and doped fiber design, a single signal channel can be propagated through the link with gain compression or GPW as required by the system, along with high SNR at the output of the link.

G. Signal-to-Noise Ratio The output power of the EDFA is spectrally located mainly near its GPW. This power thus sees a gain equal to the loss. Along the propagation, each amplifier adds its own noise contribution [61]. The EDFA output power is therefore composed of the amplified input light (incoming signal and noise) and of some added noise. We have Pout ¼ Loss Pin

ð3aÞ

Pout ¼ G Pin þ ASE

ð3bÞ

and


125

where Pout and Pin are the amplifier total input and output powers, Loss is the link span loss, ASE is the amplified spontaneous emission located under the signal channel, and G is the gain seen by the signal channel. The gain G experienced by the signal channel is thus slightly lower than the loss, corresponding to the accumulated noise power at the signal wavelength. This noise power (function of the amplifier noise figure at this wavelength) will determine the SNR that will be measured for the signal channel at the link output. The difference induced by noise on the gain value can be calculated as follows. We have indeed ASE ¼ G NF Bf h n

ð4Þ

where NF is the amplifier noise figure at the signal wavelength, Bf the width of the noise spectrum, and h n the energy of the photon at the signal wavelength. From Eqs. (3a), (3b), and (4), we have G¼

Loss Loss ¼ Loss a 1þ NF h n Bf Pout

ð5Þ

with NF ¼ 5 dB, l ¼ 1558 nm, Bf ¼ 20 nm, and Pin ¼ Pout =Loss ¼ 3 dBm, we get a1 ¼ 0:99892, which does not seem to have an impact at first look at the signal output power. However, when considering numerous amplifiers (200 for instance), this gives, when a is expressed in decibels, an accumulated penalty of 0:941 dB on the output signal power. This reduces by this same figure the SNR at the link output, but this remains quite low compared to the penalty due to the addition of noise (several tens of decibels, as shown in next equation). Assume the noise contribution at the signal wavelength of each amplifier propagates with loss compensation, resulting at the end of the link in as many noise contributions as there are amplifiers. The output SNR is therefore: h c2 out dBm SNRdB ¼ Pin 10N log a NFdB 10 log N 10 log Dl þ 30 ð6Þ l3 where N is the amplifier count, and Dl the width of the filter where the SNR is expressed. The figure 30 on the right side of Eq. (6) corresponds to the conversion of signal input power from a unit scaled in watts to one scaled in milliwatts. Noise at the link input is neglected. As mentioned earlier, the term 10N log a is very weak compared to the other ones (it is of course even lower in the case of large WDM channel count having large SNR). Equation (6) particularly shows that an increase of 3 dB of the noise figure reduces by a figure of 2 the maximum link distance at given SNR. Equation (6) also shows that decreasing the span loss by 3 dB for a fixed EDFA output power enables us to double the link distance with similar SNR. For an attenuation of the cable of 0.22 dB=km, this would mean reducing the span distance between amplifiers from 45 km (10 dB) to 31.5 km (7 dB). The first transoceanic link, also accounting for margins, experienced a span loss of 10 dB and signal output power of þ3 dBm for the 6000-km-long distance. This gives an output SNR of

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24.8 dB expressed in 0.1 nm in the case of Eq. (6), which clearly provided quite healthy margins for a 5-Gbps bit rate. Clearly, part of such margins have been used to guarantee the system lifetime. Such margins, along with the use of a forward-error corrector code, allowed the later addition of two other channels (therefore dividing by a figure of three the available output power for each channel). This reduces the output SNR by 4.8 dB, still giving a 20-dB output SNR in 0.1 nm, which is compliant with required margins (actually, a little less since loss is not perfectly compensated for the three channels due to the gain profile). Transmission over the transoceanic distance with four WDM channels was also reported [62] without filtering owing to the large bandwidth of the erbium gain peak region. To further increase the capacity, work has then been clearly devoted to the ways to increase the available bandwidth in order to add new additional channels, as described next. VI. MULTICHANNEL WDM EDFAs Wavelength-division multiplexing of optical channels at fixed bit rate is a straightforward technique that allows us to keep the same SNR for all those channels compared to single-channel operation. The total signal output power of the EDFAs is then shared by the different channels [32, 64]. Operating the link with 8 WDM channels instead of only one would thus require an increase in the EDFA output power by 9 dB to keep the same SNR for a given link configuration (span loss, distance). This may then cause detrimental cross nonlinear effects and require heavy pumping means to ensure such an output power level. The generation of submarine links that was deployed after the first pioneer 5-Gbps-based systems [65] used a 2.5-Gbps line rate. This reduced bit rate provided a nearly 3-dB margin on the SNR while making signal pulses far more robust against nonlinearities and PMD, for instance. In addition, such a bit rate meets the telecom standards for bit rate and the capacity is then shared over several independent optical channels [66]. Progress made on pumping technology, and later, use of 0.98-mm pumps allowed the EDFA output power to be increased and thus the line bit rate increased from 2.5 to 10 Gbps in current systems. A. Gain Bandwidth As seen earlier, the natural gain profile offered by EDFAs leads to an extremely narrow overall transmission transfer function when concatenated over more than 100 times. An optical channel that sees a gain level lower than the link span loss will see its signal power decreasing along propagation path in the amplifier chain, and thus its SNR too. To enable the addition of new channels, a first step has consisted of investigating the means to broaden this gain profile in order to relax the requirements related to passive filtering means. At the start, the goal was to reduce the EDFA gain excursion in the spectral region located near l ¼ 1555 nm,


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in the range of around l ¼ 1545 to 1560 nm. If avoiding the use of passive equalizing means seemed out of reach [67, 68], the use of specific glass compositions could provide some help. It is important to take advantage as much as possible of the available glass composition by choosing an appropriate population inversion rate. As seen from Fig. 7, the average degree of inversion of the doped fiber can be adjusted in order to give a flatter gain profile on the desired wavelength range, thus minimizing the related gain excursion. We have GdB ðlÞ ¼ GðlÞ ½se ðlÞ N2 sa ðlÞ N1 nt L

ð7Þ

where GdB ðlÞ is the gain profile expressed in decibels, GðlÞ is the overlap of the optical field with the doped core region, sa and se are the absorption and stimulated emission cross sections, respectively, N1 and N2 are the partial population density rate (N1 þ N2 ¼ 1), nt is the erbium concentration, and L is the doped fiber length. The value of GðlÞ does not vary significantly on the signal wavelength range for the conventional step-index doped fiber. Its overall level at such wavelengths is determined by the cutoff wavelength of the fiber. We have therefore the gain excursion between two wavelengths located in a 30-nm spectral range accurately approximated by: DGdB ¼ G nt ½Dse N2 Dsa N1 L

ð8Þ

leading to the figure of merit (normalized gain excursion [69]) DGdB Dse N2 Dsa N1 ¼ GdB se N2 sa N1

ð9Þ

where GdB may be, for instance, the gain level taken at the gain peak wavelength or at a specified wavelength located in the considered wavelength range. There is an optimal degree of inversion that gives N1 and N2 values that minimize the ratio expressed in Eq. (9) for any wavelength chosen in the desired wavelength range. The highest value of this ratio corresponds thus to the gain excursion between the gain peak value (over the wavelength range) and the gain dip (or if no gain dip is exhibited, between the extreme wavelengths of the range). Equation (9) shows that a given glass composition (and therefore a given emission and absorption cross-section spectra) will always provide the same figure of merit for the amplifier gain flatness over a given wavelength range [69]. For a given gain peak level of a given wavelength range, the corresponding lowest normalized gain excursion that is achievable with a given fiber will always be the same, whatever the amplifier doped fiber length, pumping wavelength, or total output power. B. Glass Composition For instance, a fiber highly doped with aluminum [70] will always provide a lowest gain excursion of 14% of the gain peak level between l ¼ 1528 nm and l ¼ 1562 nm. For a gain level of 14 dB for the doped fiber, the lowest related gain

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excursion will be 2 dB with a degree of inversion equalizing gain levels at the two extreme wavelengths. With a low-aluminum-concentration (0.3%) erbium-doped fibers, the related figure of merit for the same wavelength bounds is 23%. As seen in Fig. 11, a high-aluminum concentration leads to a flat gain in the 1.55-mm range with a small bump near l ¼ 1555 nm. The use of specific alternative glass compositions has been proposed. The most promising one was that of co-doping with phosphorus [71]. In that case, a gain bump may be exhibited near l ¼ 1:54 mm that may fill the gain dip of AlGe-doped fibers at this wavelength. In that case, spectral gain contributions of both P and Al should be required. The use of two successive doped fibers of different compositions in a hybrid configuration was proposed, leading to a broadened gain spectrum [72]. Clearly, using a serial combination of two fiber lengths of the same glass host composition (each one with a given related degree of inversion) will lead to the spectral characteristics of a single piece of fiber (length equal to the sums of both lengths) exhibiting a mean average degree of inversion function of each fiber length and inversion. Indeed, Eq. (9) gives for a given signal wavelength in the case of two fibers, 1 and 2: 1 2 DGdB ¼ DGdB þ DGdB N 1 L þ N22 L2 N 1 L þ N12 L2 ¼ G nt Dse 2 1 Dsa 1 1 ðL1 þ L2 Þ L1 þ L2 L1 þ L2

ð10Þ

where Ds stands for the variation of the related cross section over the specified wavelength range. With two fibers having different glass host compositions (i.e., different cross-section spectra), Eq. (10) gives two independent terms for DGdB, that cannot compensate each other at all wavelengths at the same time. Degrees of inversion may be found in each fiber in order to minimize the overall gain

FIGURE 11 Calculated EDFA gain spectra with gain excursion over the 1530- to 1560-nm range, minimized (gain peaks balanced) as function of signal wavelength (nm) for three different glass host compositions including low (0.3%) and high (7%) aluminum concentration and aluminum (3%)– phosphorus (3%) composition.


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excursion in the desired wavelength range. It is noteworthy that as many doped fibers having different glass compositions as optical channels should be required in order to allow to produce a same gain level for all these channels. It has been proposed that both Al and P be incorporated in the same doped fiber in order to produce the same spectrum as that of the hybrid configuration [73]. This has been demonstrated with a fiber where the locations of the P co-dopants and of the Alcodopants were different. In that case, the cross-section spectra of the Er3þ ions are modified separately upon their spatial location. This type of fiber, however, is difficult to manufacture with high reproducibility. Indeed, when P and Al dopants are in the same location, they give rise to Al2PO4 aggregate formations, thus suppressing the related spectral modifying effects on the Er3þ ions spectra. C. Gain Equalization Progress made on the equalizing filter technology allowed the increase of the usable amplification bandwidth while using highly Al-doped erbium doped fibers [74], thus not requiring more sophisticated hybrid architectures or a modified glass host composition. Actually Al fibers offer the lowest gain excursion [75], in particular over the 1545- to 1562-nm range, as well as over the 1528- to 1568-nm range. Such fibers, therefore, were well adapted for the first generation of transoceanic WDM systems and for later generations that exploit the whole erbium gain bandwidth. In addition, Al also allows increased erbium concentrations while keeping low-level pair-induced effects linked to the formation of clusters (not present due to improved erbium solubility in silica glass). As calculated above, the required gain filtering contrast was below 1 dB over 20nm range for amplifiers operated with Al fibers. This gain equalization consisted of flattening the small bump located near l ¼ 1555 nm [76–81], when the degree of inversion was optimized to almost equalize both 1.53- and 1.56-mm bumps. This 1.53-mm gain peak can be filtered out easily. Operation over a broadened spectral range also guarantees stability of the gain spectrum when facing slight variations in the average degree of inversion. Equation (8) can be indeed differentiated as dDGdB ¼ G nt L ðDse þ Dsa Þ dN2

ð11Þ

Equation (11) gives the spectral variations of the gain as a function of a variation of the average inversion rate. It is worth pointing out that the transfer function of any equalizing filter is not present in Eq. (11) because its spectral contribution is fixed and does not change with variations in population inversion in the amplifier. Operating the amplifier with a reduced gain excursion (gain bumps balanced for instance) will not provide a better gain stability compared to a distorted (a slope for instance) gain profile that has been flattened by passive equalization means. The terms expressed in Eq. (11) will grow at wavelengths corresponding to the highest cross-section values, i.e., near l ¼ 1:53 mm, thus corresponding also to the lowest values of saturating powers (Psat ðlÞ [4]). Therefore, it will be less

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critical to manufacture amplifiers with gain equalization near l ¼ 1:55 mm compared to gain equalization including the 1.53-mm gain bump [82] due to the increased sensitivity to the required average degree of inversion at such wavelengths, and thus to the doped fiber length or erbium concentration. However, if some gain filtering capabilities may be provided to the amplifiers for a WDM operation, the issue of the required accuracy in gain equalization should also be addressed first. For that purpose, one can calculate the SNR at the output of the chain while considering added noise contributions and signal powers seeing a gain level equal to the span loss of the link (with a given gain excursion of DG=2 expressed in decibels, the total gain excursion between highest gain and lowest gain in the wavelength range being DG). Gain is supposed to be equal to the span loss in average over the wavelength range . The output SNR is (and also equal to the medium gain value), expressed as G given by: SNRN ¼

where:

Ps Ps ¼ 2 3 ð12Þ 1 P 1 1 1 Bo þ ASE 1 þ þ þ N 1 P 6 mN 7 m m mG Bo þ ASE 4 1 5 mG 1 m

SNRN is the SNR at the link output after N amplifiers and fiber spans is the average gain of the amplifier over the signal wavelength spectrum (G is G equal to the link span loss) is the gain seen by a given channel (m < 1 for the less favored channels) mG Bo is the noise power of the input signal channel in the considered bandwidth PASE is the amplified spontaneous emission at the signal wavelength Ps is the channel signal power at the first amplifier input. For amplifiers that are not flat, the gain excursion (DG, expressed in decibels) is the most limiting factor determining the SNR at the link output, as seen here: SNRmin N ¼ because

Ps 10DGN =20 1 Bo þ NF h n Bf 10DG=20 1

G DG ¼ 10 log ¼ 10 log m 2 mG

ð13Þ

Bf with m corresponding then to its worst value and PASE ffi NF h n m G (with G 1). Therefore, after a 130-amplifier chain (corresponding to a 6500-km length with a 50-km span between two amplifiers) with 9:5-dBm per-channel signal input power for the EDFA (corresponding to an output power of þ14:5 dBm with


131

16 channels and 12-dB gain to compensate for 50 km of cable link) and exhibiting a noise figure of 4.5 dB, the SNR at the chain output would be 16.64 dB (expressed in 0.1 nm) with ideally flattened amplifiers [after Eq. (6)]. With a filtering error as low as 0.01 dB, the penalty on this SNR would be only 0.33 dB [after Eq. (13)]. However, if the error increases to 0.1 or 0.15 dB, then the penalty rises to 3.62 and 5.69 dB, respectively. This result is somewhat pessimistic because pre-emphasis can compensate partly for this penalty, but it shows nevertheless the need for a tight filtering in order to flatten EDFAs used in WDM long-haul submarine applications. EDFAs flattened to 0.1 to 0.2 dB are possible, but their characterization is not easy due to the limits in accuracy (0.1 dB) of the available measurement equipment (specific techniques may be used then, based on loop experiments for instance). The required accuracy for the filters, however, can be obtained from specific technologies of equalizing filters, although they also tend to reach just to their limits. D. Equalization Technology In-fiber Bragg grating (IFBG) filters [83, 84] have shown to be the most effective technique for providing a gain equalization function owing to the short-period grating technology [85]. Such types of filters are free from bending loss sensitivity, temperature sensitivity (although less critical for submarine applications), and polarization-dependent loss, as opposed to long-period grating filters [86]. In addition, this technique is well suited and reproducible for equalizing filters requiring low contrast. Slanted Bragg gratings [87] have been implemented then that reflect the unwanted power into the fiber cladding. (The former use of straight Bragg grating equalizers required the use of a specific isolator in order to block the reflected light). Each grating may compensate for a given gain bump. Several (one to three) gratings are necessary to fully equalize the conventional band of EDFAs (1530–1560 nm). Specific techniques are successfully used in order to compensate gain bump shapes that are not fully symmetrical, which is the case for EDFAs when a high accuracy is required. Measurement techniques used to characterize the transfer function of such filters are limited, however, to around 0.1 dB, corresponding to optical spectrum analyzer accuracy and while light source stability. Therefore such filters are carried out with tolerances that compare with the ideal required gain equalizing function. Thin-film filters and long-period gratings (LPGs) can also be used with success. Additional filters are built that compensate for the accumulated error function in the equalizing filters and for the variation due to dispersion in loss value of devices incorporated in the amplifiers. Such filters are located every 10 or 20 amplifiers before the acumulated excursion between signal powers become detrimental to their SNR. In addition, specific filters may also be manufactured after the assembly of the link cable, just before loading in the cabling vessel, in order to compensate for the added extra spectral distortions induced by the assembly and mounting with cable. With such high care paid to the design and

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manufacturing of the link, it is possible to realize a high SNR and system margin for all channels within a short time. Figure 12 shows the improvement brought by slanted IFBG filters on the output spectrum in the case of a transoceanic link compared to the spectrum obtained without equalization. Gain filtering therefore ensures a flattened amplifier gain spectrum with moderate penalty on the required pump power due to low insertion loss and contrast. Because they are placed at the amplifier output, no induced noise penalty results from the use of filters. The next generation of submarine systems will be implemented with a bandwidth of more than 30 nm [129] and potentially 40 nm and more [88, 89] owing to such filter technology and an increased pump power in order to compensate for much higher filter contrast (3 dB and more against around 1 dB for first generations). This perfect compensation allied with a highly reproducible process for manufacturing the doped fiber are key elements that have made possible use of a broadened bandwidth and thus the addition of numerous channels. Such outstanding performance, however, is also allowed by the control of all limiting effects that may prevent the system from working or from being manufactured with the required characteristics as described now.

VII. EDFAs IMPAIRMENTS Clearly, increases in system total throughput capacity are somewhat limited by many different system issues, such as cross nonlinearities, spectral slopes of devices, and dispersion compensation, that should be addressed before thinking about further increasing the channel line rate or the channel count. Providing a bandwidth that is twice as broad does not result in instantaneous doubling of the

FIGURE 12 Experimental signal output spectra and worst SNR measured in 1-nm bandwidths from a transoceanic link (80 amplifiers) without equalizing filters and with slanted in-fiber Bragg grating equalizers.


133

channel count without having conducted the prior work of adapting the other system parameters. When we discuss EDFA limitations, we must concern ourselves with the characteristics intrinsically related to the amplification process or EDFA manufacturing process that prevent us from obtaining SNR values higher than they already are or that prevent us from further increasing the span loss between amplifiers or link length. Such limiting characteristics are either related to single-channel management or to multiwavelength effects. A. Polarization Effects First, single-channel effects such as PMD or PDL have been carefully managed since long-haul amplified submarine systems were first implemented. Devices incorporated in the EDFAs such as isolators or gain equalizing filters have been designed to exhibit PMD and PDL values that are significantly low so as to ensure a low accumulated effect on the optical channel for the case of the longest link distance (9000 km). Suppressing such polarization effects has also required more sophisticated designs for the IFBG filters in order to address this issue. However, this has not impacted the error of the filter much compared to the required loss profile. Another effect related to polarization but intrinsic to the doped fiber medium, which has been described previously, concerns polarizationdependent gain (PDG) (also called polarization hole burning). As discussed earlier, this effect related to signal-induced saturation is no longer a limitation because scrambling means for the polarization of the signal have been implemented. With a high channel count, the polarization effect induced by the saturation carried by the different channels (having different polarization states) adds some average to the overall effect and relaxes the need for such signal polarization scrambling. B. Spectral Hole Burning Also due to signal-induced saturation in the doped fiber medium, spectral hole burning (SHB) [90, 91] is a major limitation of amplified WDM systems with a high channel count. The main reason lies in the fact that we cannot compensate for this effect. In addition, accurate predictions are most difficult to carry out. SHB (described previously) acts as a selective oversaturation of specific erbium ion classes due to a precise matching of signal wavelengths with their corresponding Stark energy sublevels. Gain contributions of a given ion class to the overall amplifier gain spectrum will be dependent on the specific values of energy of the related Stark sublevel (determined by inhomogeneities in the local electric field in the glass in contrast to a crystal) and of their population density (i.e., of the related induced saturation). Clearly, the overall gain spectrum of the amplifier may be distorted due to this SHB effect. The most well-known induced distortion is the hole that is induced in the gain spectrum in the spectral vicinity of a saturated channel. In that case, spectral

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gain contributions produced by the Stark sublevels that perfectly match the signal wavelength will be lower for such specific ions. The simultaneous effect of SHB (that decreases one Stark sublevel overall population density) and of thermal distribution (that will thermally adjust the population of all Stark sublevels) works to reduce the impact of the saturation of the given Stark sublevel by broadening this oversaturation to neighboring Stark sublevels. This gives rise to a hole in the gain profile around the saturating channel wavelength whose width is determined by temperature. Increasing the temperature will increase this homogeneous broadening (and thus the hole width at the expense of its depth), whereas lower temperatures will reduce and make deeper this hole in the gain profile. Because it is not possible to operate the amplifier at a lower temperature where the effect of homogeneous broadening vanishes, a system designer should account for the holes induced by each signal channel in the amplifier gain profile at room temperature [92–94]. With a signal wavelength multiplex composed of equal-power channels, the slight related holes in the amplifier gain profiles gives a flat average gain profile since the wavelength spacing between channels ( < 1 nm) is much lower than the hole width (around 10 nm at T ¼ 5 C). Only a slight increase of the gain on the edges of the gain profile (where no channel is present) is observed. In that case, SHB does not distort the overall gain profile because the sum of the different contributions has a flat transfer function. Problems may be encountered when some channel powers increase compared to other channels [95]. Indeed, as seen previously, the spectrum of a wavelength multiplex suffers from spectral distortions during its propagation in a long-haul submarine link (due to the summation of all spectral distortions), resulting in a significant excursion between channel powers at the link output. SHB could be seen (wrongly) at first glance to be a regulating effect because the most favored channels will see a slightly lower gain due to the SHB they induce. This will indeed slightly reduce the power excursion between channels (the correcting effect, however, being much lower than the effect creating this SHB). The detrimental effect actually comes from the distortions induced in the amplifier gain spectrum due to thermal broadening. Other channels, located a few nanometers aside from the most favored ones, will also see an induced reduced gain level, while such channels may not be gain favored like the channels that create the SHB effect. This will result in a decrease in the SNR of such neighboring channels [96, 97]. Therefore, unperfected loss compensation for all channels, which comes with system aging, actually results in additional spectral distortion in the channel multiplex for which a passive gain equalizer cannot be designed that will compensate for this problem. SHB is also a limiting effect in the implementation of pre-emphasis of the less favored channels. This technique consists of increasing the power of the worst channels at the transmitter side at the expense of the best channels, leading to the same SNR for all channels at the link output. This can be performed while keeping constant the EDFA output powers and decreasing the transmitted power of the best channels. However, the highest predistortion that can be performed at


135

the link input in order to compensate for a given excursion in output SNR is limited by SHB.

C. Modeling of Spectral Hole Burning Modeling helps to define system margins, taking into account the added SHBinduced SNR degradation depending on different case studies for increases in loss compensation imperfections. This enables us to quantify such SHB effects that are linked to other aging processes. However, a general model accounting for specific emissions and cross sections related to each Stark sublevel [4] is quite complicated: first, because the numerical convergence of the degrees of inversion related to each Stark sublevel may make the model unable to reach the result; and second, because the spectroscopic data needed to feed such types of model are still not fully determined with enough accuracy. Significant variations remain between published results concerning the energy range of each Stark sublevel and even concerning their count [98]! The vitreous nature of the material hosting the erbium ions means that the glass structure itself is not well determined and subject to changes depending on the manufacturing process used. Qualitative modeling may therefore be performed to help us understand the SHB process and related parameters [95], but such modeling is not appropriate for calculating the actual impact in terms of SNR that will be seen at a link output as a function of a given imperfection in the compensation of span loss. A macroscopic approach for the phenomena may therefore also satisfactorily complement the use of analytical modeling for the gain [97]. Such a macroscopic approach is based on measurements of the hole depth induced by SHB at room temperature as a function of signal wavelength, channel spacing, and count. Such measurements can be accurately performed with a technique based on gain profile measurement with a saturating white input noise [99]. The profile of the hole induced in the gain spectrum by a given channel is determined by homogeneous broadening and thus temperature. Its depth (at given temperature) is a function of saturation (thus being expressed by the level of gain compression). This hole transfer function can be approximated as: 2

DGðlÞ ¼ bðlsat Þ CGðlsat Þ eðllsat =DlÞ

ð14Þ

where Dl is around 12 nm at T ¼ 25 C, and b is a scale coefficient because gain compression (CG) does not seem to be the single driving parameter. As seen in Fig. 13, Eq. (14) gives a fair fitting of the measured differential gain profile. When several channels each induce a hole in the amplifier gain spectrum, such a hole will be dependent on the gain compression at the channel wavelength but also on the competition with the hole burning induced by the other channel. Indeed, at fixed gain compression, the hole depth will not be the same depending on whether or not a neighboring channel is present. Experiments show that the gain distortion induced by each channel is modified by the distortions induced by

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FIGURE 13 Measured and calculated gain hole due to spectral hole burning (SHB) observed in the spectral gain profile of an EDFA in the case of a saturating signal located at l ¼ 1544:4 nm.

other channels. The overall gain distortion in the amplifier gain spectrum is expressed as the summation of the effects produced by the N channels, leading to Eq. (15): DGðlÞ ¼

i¼N P i¼1

½bðli Þ CGðli Þ

P j6¼i

aðlj Þ CGðlj Þeðlli =DlÞ

2

ð15Þ

At first approximation, the a and b coefficients may be considered to be wavelength independent. Without the subtracting terms, the calculated gain distortion assumes that the hole depth induced by a given channel is almost independent of neighboring saturating channels [100]. However, it is more accurate to account for this effect as is done in Eq. (15). The determination of the a and b coefficients for given doped fiber type, however, remains the major difficulty with the implementation of Eq. (15).

D. Other Limitations Other well-known parameters such as noise figure or power consumption are also limiting parameters in system performance. Clearly, it is not possible to significantly further decrease the EDFA noise figure (already improved as a result of 0.98-mm pumping) but, of course, values 1 dB lower would enable larger span loss! If the total output power can be enhanced by using several multiplexed pump modules, the choice of increasing this figure is driven by the acceptable level of nonlinearities in the system and by the electrical power available for the amplifiers. The total output power of the EDFAs cannot, therefore, be considered a limiting factor. The technology determining the total electrical power that can


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be handled by the cable is instead the point from which some improvements may be realized. A last significant limitation comes naturally from dispersion between values characterizing the different devices and doped fiber incorporated in the amplifier. Indeed, insertion loss of passive components evolves between tolerances that can be offered by the corresponding technology. Loss of the splices with the doped fiber and between conventional fibers is also subject to uncertainties during manufacturing steps. This may give rise to variations in the total loss of incorporated devices of several tenths of a decibel. In addition, any uniformity in the erbium concentration along the doped fiber length will cause gain changes at the point where the fiber length will be taken from the spool. By maintaining strict control of the manufacturing process, and by accurately characterizing the doped fiber, erbium quantities incorporated in an EDFA can be precisely determined and adjusted (through doped fiber length modification) so that the observed difference in insertion loss of passive devices does not impact the resulting average degree of inversion in the doped fiber at fixed input and output powers. It is also crucial to ensure perfectly reproducible Al concentrations in order to ensure that this nominal degree of inversion always provides the same gain spectrum matching the transfer function targeted for the equalizing filters. With a high level of technology and skilled manpower, such requirements are satisfactorily fulfilled. Fortunately, the relatively low gain of the EDFAs used in submarine links (around 12 dB) means that short doped fiber lengths can be implemented. The related amplifier output power is also quite moderate (around 12–15 dBm for a 23-nm bandwidth), thus reducing, along with the use of short fiber lengths, the impact of nonlinearities that may occur within the amplifier (four-wave mixing, cross-phase modulation) or even of PMD (although not a nonlinearity), which could be encountered in EDFAs used in terrestrial applications [4] in the case where design rules have not accounted for such effects. In conclusion, system capacity is not strongly limited by technologies implemented for the amplification means even if some extreme cares in design and manufacturing should be observed. Nonlinearities and impairments occurring along the propagation in the link cable are clearly more limiting parameters even if very high spectral efficiency and capacity have been shown recently over long distances with the C-band only [129]. However, the potential limitations described above may make more stringent the broadening of the amplification bandwidth used (up to 40 nm), thus making such effects have a higher impact. For instance, keeping a perfect match between the gain spectrum with the filter spectrum including an erbium cross-section peak wavelength (1.53 mm), or using a gain-filtering filter that exhibits a contrast of several decibels instead of tenths of decibels, results in quite different operating conditions than when operating in the case of a 14-nm bandwidth located near l ¼ 1550 nm! However, technology for submarine equipment has been demonstrating for years that next-generation products made possible what has seemed

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impossible to do at the time the previous generation was released! Innovation may ensure that the same rules apply for future generations.

VIII. OPERATION WITH L-BAND EDFAs As seen from Fig. 7, the gain profile of erbium-doped fiber amplifiers shifts toward longer wavelengths when the average degree of inversion in the doped fiber is reduced to values closed to 40% inverted ions. In that case, the amplifier becomes absorbent in the conventional band (1530 nm; 1560 nm) while gain may be provided at longer wavelengths (1560 nm; 1610 nm) [101, 102] limited by the signal excited state to 4I9=2 level). It is worth pointing out that EDFAs operated in this long-wavelength band (L-band) involve specific Stark sublevels and related cross-section spectra compared to C-band EDFAs. Indeed, such a long wavelength will correspond to the lowest energy gaps between the 4I15=2 and 4I13=2 energy levels. This concerns upper Stark sublevels of the ground-state level and lower Stark sublevels of the excited metastable state. The Boltzmann distribution ruling the populating of such Stark sublevels is known to populate Stark sublevels of the lowest energy (i.e., lower Stark sublevels), therefore making more likely stimulated emission in the L-band than ground-state absorption. The amplifier therefore operates in a quasi-four-level system, with macroscopic absorption cross sections at the signal wavelength much lower than the corresponding stimulated emission cross sections (and also much lower than in the C-band, leading to much longer fiber lengths). Because there is almost no absorption of the signal photons by erbium ions, the EDFA exhibits a low noise figure although the (average) degree of inversion is low. A. System Performance A 0.98-mm forward pumping gives the best noise figure owing to the high degree of inversion that is made possible at the amplifier input. This is, however, at the expense of a high gain peak near l ¼ 1:53 mm in the first meter of the doped fiber. This leads to significant power lost in ASE emitted in the C-band and to selfsaturation by this noise, thus degrading the noise parameter of the amplifier. Specific techniques must therefore be implemented in order to guarantee quantum limit noise figures but at the expense of an increased complexity. Actually, submarine amplifiers are operated under significant saturation induced by the signal power. Higher noise figures are then observed leading to values a half decibel higher than in the case of similar C-band EDFAs. The 0.98-mm pumping is less efficient for signals in the L-band than in the C-band (only 25% power conversion efficiency compared to 40% at least for practical C-band 0.98-mm EDFAs). A shift of the pumping wavelength down to l ¼ 965 nm may improve the efficiency but leads also to somewhat higher noise figures. It is efficient to use a backward 1.48-mm additional pump in order to reach the desired output power.


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For a channel loading taking advantage of the full 30-nm bandwidth of L-band EDFAs, this corresponds to total output power of around 15 dBm. The high related efficiency ( 60%) means that a low 1.48-mm power is required (only several tens of milliwatts). Equalization of the related gain profile is less critical and more simple to carry out at a given (large, i.e., ffi 30-nm) bandwidth because an average degree of inversion may be found that offers an almost perfectly flat gain profile in the short-wavelength half part of the L- band with a broad bump in the second part of the gain spectrum (Fig. 14). The related gain equalization may be then provided by a single Bragg filter with a lower related contrast at the same bandwidth (2–3 dB compared to 3–4 dB in the C-band). Doped fibers used for L-band application exhibit a nearly four times higher erbium concentration in order to reduce fiber length and its possibly related loss or nonlinear effects. High aluminum co-doping is then used in order to allow for such a high erbium concentration without suffering from a noise penalty. Unlike in C-band applications, high Al concentrations (several wt%) or the use of other co-dopants in addition to Al in silica fibers [103] does not lead to further bandwidth broadening compared to moderate Al concentrations (a few tenths wt%). Other co-dopants that also increase the erbium concentration in order to decrease doped fiber length (and possible nonlinear effects) can be used as well, such as Yb with 1.48-mm pumping [104], or La [105], or Bi [106]. Such L-band EDFAs have been intensively implemented in conjunction with C-band EDFAs in various system experiments in the case of terrestrial WDM systems [4]. Concerning long-haul submarine applications with L-band EDFAs, a self-filtering effect was demon-

FIGURE 14 Measured gain spectra of an EDFA operated in the L-band as a function of the signal wavelength (nm). Doped fiber length has been optimized to provide a gain of 10 dB when adding an equalizing filter at the amplifier output while minimizing the contrast of the transfer function of the required filter.

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strated in a first step with a wide bandwidth [107], then followed by system experiments [108–111]. A 7300-km-long link with amplification of 10 Gbps channels located in both C- and L-bands has been performed, resulting in record total throughput of 3 Tbps. Therefore, although showing significantly higher spectral hole burning in the L-band than in the C-band [112] (three times higher and broader [113]), the implementation of EDFAs in long-haul L-band submarine laboratory experiments has been successful. B. Field Implementation Issues The choice to implement or not this additional band either in parallel with the C-band or standing alone alternatively to the C-band is clearly driven by other considerations involving economical aspects and cable management issues. Using L-band EDFAs instead of C-band EDFAs may be a possibility leading to relaxed gain equalizing filter requirements in the case of large ( 30 nm) amplification bandwidths. Indeed, the lower required contrast at fixed bandwidth compared to C-band EDFAs will reduce the related loss when implemented at the amplifier output. However, the resulting lower required pump power is obtained at the expense of around 0.5-dB higher noise figure. Obtaining the same SNR at the link output would require an increase in the total signal output power of the amplifier, making this solution less attractive. A balance between the corresponding increase in nonlinear effects (somewhat limited due to a slightly higher effective area at longer wavelengths) and the improvement in power consumption will determine which is the most relevant approach. However, minimizing nonlinear effects in the system has always been preferred. C. C þ L-Band Systems Another way of implementing this L-band may be as a complement to the C-band in order to provide twice the amplification bandwidth. Using the two types of repeaters (C and L) in parallel with input and output splitband multiplexers to separate channels does not appear to be clearly advantageous. Indeed, insertion loss of such multiplexers at input and output (two times 0.5 dB) will reduce by around 1 dB the system margin (span loss increased by 1 dB at fixed amplifier spacing), and thus reduce it for the C-band channels as well. This lost decibel could be recovered by a new design for the system, leading to extra costs related to the C-band channels. Under such conditions, using two link fibers, each one operated in the C-band, may provide a better power budget and reduced cost compared to using both types of amplifiers in parallel. Finally, the design of the amplifiers should also be adapted in order to reduce the penalty due to splitband multiplexers and the number of total incorporated devices in both parallel EDFAs. Indeed, specific architectures of repeaters can then be defined specifically for such C þ L applications in order to make them cost effective, as described next.


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L-band channels may be amplified first in a C-band EDFA stage before reaching the splitband multiplexer and then being amplified in an additional doped fiber length whose degree of inversion is optimized for L-band operation. However, short fiber lengths used for C-band EDFAs provide very low gain levels in the L-band, thus lying below 5 dB (and even lower, down to 2 dB) for the longest L-band wavelengths. It is therefore crucial to minimize the loss seen by the L-band channels between the two successive amplification steps. In particular, the multiplexer used to couple a backward 1.48-mm pump in the first amplification stage may be located after splitband separation (in the path dedicated to Cband channels). This enables us to reduce interstage losses seen by L-band channels and allows for a low noise figure, although we have very low gain in the first stage for such channels. With this configuration, C-band channels (and with a proper design, L-band channels) are not attenuated by the splitband multiplexer before reaching their amplifying path, while extra output power may be provided to account for the output multiplexer. Such design used in C þ L band amplifiers means that there is no impact on the overall link span loss due to splitband multiplexers (which are then hidden within their architecture). In addition, a single 0.98-mm pump used in the common amplification stage then replaces two different pumps in the case of pure parallel band EDFAs. Therefore, amplifiers specifically designed for operation over both C þ L-bands may be clearly attractive in the case of long-haul submarine links in order to increase the system capacity, improve noise performance, and reduce power consumption and cost compared to C- and L-bands in parallel. This approach has been studied in the case of terrestrial applications (seamless C þ L-band EDFAs) but has not yet been popular in commercial systems because capacity upgrades in terrestrial systems (and thus upgrades in amplification bandwidth) are implemented only when capacity increase needs for it. This is not the same for submarine links where submerged equipment should incorporate all the components that enable it to cope with the ultimate expected capacity for the link at the start of the system’s life. This allows some cost savings compared to systems built to comply with successive capacity upgrades. In conclusion, developing a new type of EDFA with the related technology for terminal equipment will result in significant costs if the system is to be usable in submarine systems. Such costs have already been paid to provide with broadened C-band EDFAs operating over large bandwidths ( > 30 nm), even if manufacturing tolerances are pushed to their limits. It seems, therefore, from the amplification point of view that a further increase in the total capacity [88] and the limitation of number of link fibers per cable will be more motivating for the implementation of a new L-band window in addition to the C-band (with the possible architecture adaptations for C þ L operation described above) rather than an L-band stand-alone transmission window. New dispersion maps (SMF fiber compensated by RDF fiber) speak in favor of such an evolution. The answer may also come again from further developments and innovations coming from research.

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IX. IMPLEMENTATION OF RAMAN AMPLIFICATION Raman amplification [2] has been recently reanalyzed in order to compensate for one limitation due not to EDFAs, but to their lumped (or discrete) way of implementation at which they are operated. Distributed Raman amplification was first looked at as possibly enabling us to spread over the full span link fiber the nonlinearities added to the signal along its propagation, therefore allowing for their local perfect compensation, which would be useful in the case of solitonbased transmissions [4]. However, link fiber attenuation and pump technology at that time made such solutions impractical. Implementations of erbium-doped fiber amplification were also originally considered with distributed amplification for submarine transmissions with a doped link fiber, but were not practical due to increased fiber loss [114]. Progress on pump technology driven by the advent of EDFAs in almost all optical telecom applications may benefit now as distributed Raman amplification becomes possible. Clearly, the ability to distribute gain and thus to regularly compensate for the loss of the attenuation fiber looks like a very powerful technique to improve SNR at the link output [115, 116]. Indeed, in Eq. (13), the amplifier signal input power is then increased by the extra distributed gain offered by Raman amplification. Taken into account the noise brought about by Raman amplification, this technique may provide several decibel improvement in the SNR at the link output. There remains then the need to take a close look at its actual implementation in the case of massive WDM systems, where total nonlinearities seen by the signal channels should be kept the same and where each effect occurs more than 100 times along the link propagation for long-haul submarine transmissions. A. Principle of Raman Amplification Raman amplification is based on a stimulated Raman scattering process involving pump and signal photons on one hand, and the optical phonons of the glass material, on the other hand. This is a nonlinear effect and is, therefore, polarization dependent and requiring high power densities. This inelastic process converts one pump photon into a signal or noise photon of different wavelength owing to the optical phonons of the material (corresponding to the vibrational states of the Si-O glass molecular structure) that may absorb the related energy difference. This energy given to the glass corresponds to the energies of such phonons, giving a broad spectrum of possible Raman interaction as a function of the energy shift of the scattered light [2]. This spectrum exhibits a peak for a 13.2-THz frequency shift in the case of Si-Ge glass with a top width of around 10 nm. It represents the likelihood of interaction of pump power with the fiber glass. Figure 15 shows this Raman gain coefficient (CR ¼ g=Aeff ) as a function of the frequency shift in the case of NZDSF, SMF, and RDF fibers where g is the Raman material coefficient (spontaneous emission or stimulated emission spec-


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FIGURE 15 Raman gain coefficient Cr (W1 km1 ) measured with a 1486-nm pump wavelength in the case of a reverse dispersion fiber (RDF), a standard single-mode fiber (SMF), and a negative nonzero dispersion fiber (NZDSF) as a function of the frequency shift (THz) of the signal channel with the pump channel.

trum for the Stokes process) and Aeff is the effective area of the fiber and represents the overlap between the pump beam, signal beam, and Ge profile of the fiber. Aeff is relatively close to the section of the fiber core and increases with signal and pump wavelength, reducing the efficiency of this nonlinear effect. Therefore, differences seen between the three curves are mainly due to variation of their core diameter (to be precise, of their effective area) and of the Ge concentration. However, when such curves are peak normalized, a similar spectrum is exhibited, except for a small peak at f ¼ 15 THz due to silica. This shows that Ge does not strongly distort the normalized gain profile. This gain spectrum is only dilated when pump power is changed, resulting in a scale effect on the overall gain spectrum [117]. A double gain peak level therefore gives a doubled gain excursion over a given wavelength range. Implementation of Raman amplification in a practical system is therefore quite simple as far as its spectral gain contribution is concerned. The normalized gain profile is indeed the same for any gain levels in a given fiber, and exhibits very slight differences from two fibers having different index profiles, core diameters, or Ge concentrations. In addition, there is no energy storage in any supposed-to-be energy levels. Phonon energy vanishes rapidly in the glass, making the probability that a signal photon will be reabsorbed into a pump photon (anti-Stokes process) very low. Depending on the characteristics of the fiber in terms of the CR coefficient or of fiber attenuation (particularly at the pump wavelength), required pump power to reach a given peak gain may be strongly

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different. Amplification of signal photons may therefore be provided by stimulated Raman scattering, with a gain level function of the wavelength difference with the pump light. This amplification process is far less efficient when compared to that of EDFAs. In addition, to obtain significant gain, the pump power used in distributed Raman amplification is much higher than signal power. Therefore, the pump energy transferred in the process of stimulated emission remains low compared to the involved pump power level in the case of practical distributed Raman amplification. This means that this Raman gain is weakly dependent on the total signal power or on the channel count. This is an advantage in terms of practical implementation, but also requires perfect control of the pump power. Backward pumping is therefore usually used to average the effects of pump instabilities and its RIN noise. The extra gain seen by a signal channel due to distributed Raman amplification (provided by a pump channel) can be expressed as shown here: dB GON=OFF ¼

10 g 1 eap L r Pp ln 10 Aeff ap

ð15Þ

where G (dB) is the gain at the signal wavelength Pp (mW) is the pump power Aeff is the Raman effective area of the fiber L is the fiber length and (1 eap L Þ=ap can be approximated by 1=ap if the interaction length is much higher than the effective length defined as Leff ¼ 1=ap (where ap is the attenuation at the pump wavelength). This is the case for distributed Raman amplification. This extra gain is also called the on–off gain because it accounts only for gain due to stimulated emission and not for signal attenuation in the link fiber. It therefore corresponds to the increase in signal output power when pump light is turned on. Link fiber attenuation of the pump light therefore strongly impacts this on–off gain. For example, a pump power of 300 mW gives a maximum on–off gain of 16 dB with a link attenuation of 0.2 dB=km and of 13 dB with a link attenuation of 0.25 dB=km at the pump wavelength in the case of a NZDSF link fiber (Aeff ¼ 67 mm2). It is worth pointing out that Raman gain (expressed in decibels) that is produced is a linear function of the pump power. This is because no gain saturation is induced by signal power in distributed preamplification, making the amplification process operate like that of a small-signal input power regime. This is quite different compared to EDFAs, which are operated in saturation for having large output power. Their output power is then a linear function of the pump power, making their gain, expressed in decibels, a logarithm function of the pump power. Impact on gain of variations in pump power will therefore be much higher in the case of Raman preamplification compared to EDFAs. Specific care should


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therefore be taken in order to accurately ensure the required pump power through the system lifetime. B. Practical Implementation as Preamplification EDFAs In this case, pump power is launched in the link fiber in a direction that is backward to the signal, owing to a pump multiplexer located just below the EDFAs [118]. The Raman gain that is provided increases the signal power at the input of the next EDFA. If one could neglect the spontaneous Raman noise, this distributed on–off gain would be equivalent to a decrease of the link span loss between two EDFAs and could result in an improvement of the SNR at the link output of the same value. However, spontaneous Raman emission is not negligible although it is locally emitted at the quantum limit. This nearly reduces by half the SNR improvement due to the Raman gain. In addition, EDFAs will see their total signal input power growing by several decibels but at the expense of an increase of their noise figure. Their signal output power should also be reduced in order to keep the same number of total nonlinear effects seen by the channel over a given span of the link. Indeed, signal powers will be higher at the end of each span due to Raman amplification thus adding nonlinearities to the system. This need to decrease the signal power results then, in its turn, in a decrease in the output SNR of the link. Finally, when making the check of win and loss, the advantage of Raman preamplification before EDFAs is not clear in the case of long-haul submarine links. The low potential benefit would be at the expense of extra power consumption and the cost of at least one additional pump (with a related polarization beam multiplexer to ensure polarization independence). Also, additional pump units should be used for reaching a broad aggregate amplification bandwidth [119, 120]. In that case, the pump lights located at shorter wavelengths may also experience extra attenuation due to Raman amplification of the pumps of higher wavelength. A stronger power should be therefore provisioned for such pump. Therefore, to implement Raman amplification without any gain provided by EDFAs, pure distributed all-Raman amplification has been reconsidered [121]. C. All-Raman Amplified Submarine Links If issues related to gain stability can be addressed relatively simply owing to strict control of the pump power level, this all-Raman implementation gives rise to other ones [122]. In submarine links, the gain required to compensate for one span loss is about 10–12 dB, which changes considerably the required total Raman pump power compared with a few decibels extra gain provided as preamplification. If the power efficiency is clearly lower than for EDFAs, the use of several WDM pumps enables us to broaden the usable amplification bandwidth without requiring gain equalizing filters with high contrast at each span.

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The gain bandwidth may therefore be increased toward shorter or longer (at choice) wavelengths just by implementing enough pump channels [119, 120] (four pumps are enough to provide a nearly flat bandwidth of 26 nm [123], and eight are used to give a 65-nm bandwidth [130]), not necessarily linked with the location of the erbium gain spectrum. Figure 16 shows the related output spectrum in the case of a 40-Gbps-based 2400-km-long submarine link with all-Raman amplification. In that case, the use of distributed Raman amplification also affects the choice of the dispersion map and therefore the type of link fiber that is used (with somewhat different Raman gain coefficients). If problems linked with EDFA spectral hole burning vanish (there is no spectral hole burning in the case of single-pumped Raman amplifiers), other issues to be addressed appear such as double Rayleigh scattering [124, 125], pump interactions, or accumulated (unwanted) nonlinear effects. Indeed, the higher level of Raman gain in the link fiber may increase the impact of signal photons that are reflected two successive times by a Rayleigh effect (becoming then incoherent noise photons because the distance seen by the reflected light is higher than the coherence length for DFB lasers) and whose power (which is proportional to the gain squared) may cause some incoherence interference [126]. As seen later, for such significant gain values distributed over long fiber lengths, this effect may be strongly detrimental. Another issue concerns interactions between pumps, whose total power required to compensate for a 12-dB loss is quite high (several hundred milliwatts are required). Pump channels of shorter wavelength will be absorbed more rapidly in the link due to a slightly higher link attenuation, and also because they will be depleted at the benefit of pump channels of longer wavelengths (and thus will provide a less distributed gain). The gain for the related signal channels will therefore be lowered, thus reducing

FIGURE 16

Signal output spectrum of an all-Raman loop experiment after a 2400-km long transmission with a 40-Gbps signal line rate. Resolution bandwidth was 0.1 nm. Signal bandwidth is 25.6 nm. Link fiber span was composed of TeralightTM and Reverse TeralightTM fibers.


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their related SNR. Increasing the low-wavelength pump power may help to avoid this lower gain, but care must be taken that this added pump power is not totally transferred to the other pump wavelengths. This effect of Raman pump interaction can therefore be compensated only to some extent, not completely, and therefore may raise crucial issues for practical wideband ( 40-nm) Raman amplification bandwidths. Using a shorter wavelength for forward pumping while using a longer wavelength for backward pumping may help to address this issue [130] at the expense of possible other issues linked with the RIN of the pumps or with some instabilities. Further implementations will determine if such limitations may be overcome. Foreseen advantages procured by an all-Raman amplification approach (no gain distortion or increased noise with signal saturation, high aggregate bandwidths without requiring tight filtering, etc.) should be assessed with regard to the noise penalty paid to double Rayleigh scattering and extra cost and power consumption due to the related lower gain efficiency. In addition, the improvement in noise performance of distributed-gain links compared to lumped-gain links is actually relatively modest as far as operating at fixed accumulated nonlinearities is concerned. Clearly, the possible noise improvement of SNR may be useful to transmit 40 Gbps channels with the required SNR at the link output and the same target distances and similar link spacing between pumps as compared to current systems. However, all impairments seen by 40-Gbps channels during their propagation should be addressed then.

X. FURTHER AMPLIFICATION PERSPECTIVES Erbium-doped fiber amplifiers have revolutionized undersea transmission systems owing to their outstanding characteristics and adaptation possibilities, which could further increase the total throughput capacity from first-generation singlechannel systems toward ultrawide dual-band systems that allow amplification of hundreds of channels. All of the possibilities concerning the ultimate utilization of their potential bandwidth are still quite far from having been fully exploited in the case of systems currently under deployment (or development) or even in the case of future research work still to be performed on seamless ultrawideband EDFAs designed for long-haul submarine applications. In parallel, explosions in new active devices offered by recent technology implementations will provide new degrees of freedom in the way submarine systems are operated. Until now, all devices (passive or active, like pumps) incorporated in a submarine link have been designed to exhibit fixed characteristics with variations with time being as low as possible. The availability of variable attenuators, dynamic slope compensators [50], and dynamically adjustable gain equalizers [130] soon will help to relax the requirements put on all passive devices and give new margins to the system. By placing such components at some locations along the link (each 10 or 20 amplifiers), it will be possible to

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ensure perfect control of the channel power along the whole propagation, therefore providing a high-output SNR during the entire system lifetime. Reliability, power consumption and insertion loss will determine the best technology for such devices but several candidates are already in the running. These adjustable devices will be useful for addressing SHB issues, the impact of mismatch of the equalizing passive filters with doped fiber gain spectrum as a result of manufacturing-induced variations, and so on, in order to enable the implementation of ultrawideband submarine links (with or without Raman pumping). Implementation of 2R or 3R regenerators that might replace optical amplifiers is not mature, making such an evolution impractical for the near future. The first reason is the still higher costs that result due to the complexity of the realized function and thus of the device. A second reason is that, in contrast to fiber amplifiers, the devices proposed so far are not broadband, making them impractical for optical systems handling hundreds of channels. Future work may lead to new types of devices addressing such issues and may give rise to another optical ‘‘revolution.’’ But that is another story, and during this time period, erbium optical fiber amplification is doing the work!

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5 ULTRA-LONG-HAUL SUBMARINE TRANSMISSION OLIVIER GAUTHERON AND OMAR AIT SAB Alcatel, Submarine Networks Division, 91 625 La Ville du Bois, France

I. INTRODUCTION II. KEY FEATURES OF LONG-HAUL TRANSMISSION SYSTEMS A. A Technical Challenge: High Capacity per Optical Fiber B. Optical Signal-to-Noise Ratio C. Reduction of the Propagation Impairment D. Submarine Line Terminal Equipment Features E. Repeater Supervisory and Fiber Fault Localization F. Q Budget and Typical Repeater Spacing III. GAIN EQUALIZATION A. Power Preemphasis B. Fixed-Gain Equalizer C. Tunable Gain Equalizer D. Impact of Nonoptimal Gain Equalization IV. CHROMATIC DISPERSION AND NONLINEAR EFFECTS A. Nonlinear Kerr-Type Effects B. Stimulated Raman Scattering C. Transmission Experiments V. FORWARD ERROR CORRECTING CODES A. Performance Requirement in Submarine Systems B. Introduction to Forward Error Correction C. Channel Model and Fundamental Limits D. Practical Forward Error Correction Schemes in Submarine Transmission Systems E. Reed–Solomon Codes F. Concatenated Codes G. Turbo Product Codes H. Examples of FEC Scheme Performances for Submarine Transmission Systems VI. TECHNOLOGY EVOLUTION A. Modulation Format B. C þ L-Band Erbium-Doped Fiber Amplifier Undersea Fiber Communication Systems Copyright 2002, Elsevier Science (USA). All rights reserved.

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C. Transmission Systems with Distributed Raman Amplifiers D. 40-Gbps Wavelength-Division Multiplexed Transmission Experiments VII. CONCLUSION References

I. INTRODUCTION The first generation of long-haul submarine optical wavelength-division multiplexing (WDM) transmission systems proposed a capacity per fiber of 8 2.5 Gbps over 5000 km (Sea-Me-We 3, for example) or 16 2.5 Gbps over 8000 km (Southern Cross). The growth of the market led recently to the laying of a new generation of WDM transmission systems based on 10-Gbps modulation per wavelength and a large number of wavelengths [1]: 42 10 Gbps over 6300 km (FLAG Atlantic), 68 10 Gbps and 105 10 Gbps over 2200 km (Med Nautilus and i2iCN, respectively). These 10-Gbps WDM transmission systems rely on qualified technologies such as C-band erbium-doped fiber amplification (EDFA) and nonzero-dispersion-shifted fiber. Looking ahead, system suppliers are also considering transmission capacities above 1 Tbps per fiber at the research level; this would require new technologies such as C þ Lband EDFA, broadband distributed Raman amplifiers, dispersion managed fiber, highly efficient forward error correction code, and 40-Gbps modulation including optical regeneration. The purpose of this chapter is to present the main design rules applied in long-haul transmission systems; current techniques as well as the potential of new technologies under study are discussed.

II. KEY FEATURES OF LONG-HAUL TRANSMISSION SYSTEMS A. A Technical Challenge: High Capacity per Optical Fiber The design of long-haul submarine transmission systems (Fig. 1) is aimed at providing the customer with data channels at low cost, thus leading the system suppliers to provide huge capacity per fiber. Note that in an amplified transmission system, the cable can include only up to eight fiber pairs [2, 3], which is much less than a terrestrial cable, because of mechanical constraints concerning the repeater and the cable as well as electrical issues raised by the requirement of high power feeding [4]. Therefore, with a transmission capacity of 1 Tbps per fiber, the maximum total capacity of a longhaul submarine cable is 8 Tbps. To understand why the market has pushed the development of transmission systems capable of transmitting huge capacity per fiber, it is interesting to run a simple cost evaluation for three different configurations of a 5-Tbps, 6000-km-long transmission system:

5. ULTRA-LONG-HAUL SUBMARINE TRANSMISSION

FIGURE 1

159

Schematic of a long-haul submarine optical transmission system.

Configuration 1: 1 cable of 4 fiber pairs, 84 10 Gbps per fiber Configuration 2: 1 cable of 8 fiber pairs, 42 10 Gbps per fiber Configuration 3: 2 cables, each cable composed of 4 fiber pairs with 42 10 Gbps per fiber

The relative cost of the terminal, the repeaters, the cable and the marine installation is depicted in Fig. 2. Figure 2 demonstrates that the cheapest configuration is the one offering the highest capacity per fiber (configuration 1). In any case, note that the terminal represents the largest part of the cost. This means that increasing the capacity above 8 Tbps per cable would raise the critical issue of the terminal cost reduction, which is a new concept in submarine transmission systems [5]; actually, in previous submarine system generations, most of the cost was represented by the marine installation and the wet plant equipment. The design of a long-haul transmission system relies on the management of the following fundamental system features:

FIGURE 2 Relative cost of the different equipment of a submarine system in three different configurations.

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Repeater spacing, noise, and output power Fiber chromatic dispersion and nonlinear effects Terminal parameters: modulation format and forward error correction code efficiency

B. Optical Signal-to-Noise Ratio The first objective of the line design is to obtain a high optical signal-to-noise ratio (SNR) per wavelength while avoiding strong pulse distortion. In addition, because a submarine transmission system is designed for a 25-year lifetime, SNR degradation due to cable repairs and component aging must be taken into account. 1. SNR-Based Q-Factor: Definition The transmission quality is given by the bit error rate (BER), which is itself translated into the so-called Q-factor through the following formula: ð 1 Q 2 x y2 BER ¼ erfc pffiffiffi with erfcðxÞ ¼ 1 pffiffiffi e dy ð1Þ 2 p 0 2 Without pulse distortion, the Q-factor is deduced from the optical SNR using the following formula [6]: ðe 1Þ sffiffiffiffiffiffiffiffi 2SNR Bopt 1 SNR-based Q ¼ rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi erþffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi SNR SNR Be 1þ4 þ 1 þ 4e 1þe 1þe

ð2Þ

This result is obtained through the definition of the Q-factor: Q¼

SP1 SP0 s1 s0

ð3Þ

where S is the receiver responsivity (S 1 A=W), P1 ðP0 Þ is the mark (space) optical level, e is the extinction ratio (e ¼ P1 =P0 ), Bopt is the receiver optical filter bandwidth, Be is the electrical receiver bandwidth, s1 ðs0 Þ is the mark (space) electrical noise amplitude, and SNR is the optical signal-to-noise ratio measured in the optical bandwidth Bopt : 2 Bopt Be ÞS 2 s21 ¼ ð2P1 NASE Be þ NASE

s20

¼ ð2P0 NASE Be þ P1 þ P0 2 SNR ¼ NASE Bopt

2 NASE Bopt Be ÞS 2

ð4Þ

ð5Þ

ð6Þ


161

2 where ð2PNASE Be ÞS 2 is the signal–ASE beat noise, ðNASE Bopt Be ÞS 2 is the ASE– ASE beat noise, and NASE is the amplified spontaneous emission (ASE) spectral density. The optical SNR is given by the formula: k N hnB P 1 f opt ¼ SNR j¼1 Pin;j

ð7Þ

where Pin;j is the mean repeater #j input power per wavelength, Nf the optical amplifier noise figure, and k the number of cascaded optical amplifiers. A good analytical approximation is obtained when all span losses and repeater output powers are equal and when the accumulated ASE power is negligible compared to the signal power: SNR ¼

Pin kNf hnBopt

ð8Þ

Note, however, that the SNR also depends on the gain flatness of the optical link: If the spectral response of the amplifier chain is not flat, power preemphasis has to be applied at the transmit terminal in order to equalize the SNR over the wavelength multiplex at the link output. However, the higher the required preemphasis, the lower the equalized SNR at the link output. As a result, the optical amplifier gain flatness has to be managed carefully in order to reduce the required preemphasis; for that reason, different types of optical filters are inserted in the link. 2. SNR Degradation Due to Cable Repairs and Component Aging The SNR is different during start-of-life (SOL) and end-of-life (EOL) conditions due to aging of repeater and fiber components and cable repairs. The calculation of this SNR reduction over 25 years is based on the following assumptions:

Five percent of the repeaters exhibit a pump failure. The typical output power drop of a pump-failed repeater is equal to 3 dB. The fiber attenuation increase is þ0:005 dB=km over 25 years. The extra loss due to cable repairs is the following: 3 dB for a cable repair in deep water (depth > 1000 m), one repair required every 1000 km; and 0.5 dB for a cable repair in shallow water (depth < 1000 m), one repair required every 20 km. The cable repairs and the pump-failed repeaters are supposed to occur in separate repeater sections.

From Eq. (7) and the last point mentioned above, we realize that SNR degradation does not depend on the localization of the cable repairs and the pump-failed repeaters. SNR degradation instead depends on the system length, as demonstrated through the following calculations carried out for a short and a long link length:

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Short system: The link length is 2000 km, including 1000 km of shallow water. The repeater count is 30 and the span length is 70 km. Long system: The link length is 6000 km, including 1000 km of shallow water. The repeater count is 120 and the span length is 50 km.

In SOL conditions, the fiber attenuation is 0.2 dB=km and the repeater output power is the same for all repeaters in both systems (its value has no impact on the result and is normalized to 1 mW). The SNR degradation is deduced from Eq. (7): k P SNRSOL P in 1 ¼ SNREOL j¼1 Pin;j k

ð9Þ

2000-km Link:

SOL: 30 amplifiers with 14-dBm input power EOL: 14 amplifiers with ð14 þ 1:75 þ 0:35Þ-dBm input power (cable repair in shallow water þ fiber aging) 14 amplifiers with ð14 þ 0:35Þ-dBm input power (fiber aging) 1 amplifier with ð14 þ 3 þ 0:35Þ-dBm input power (one pumpfailed repeater þ fiber aging) 1 amplifier with ð14 þ 3 þ 0:35Þ-dBm input power (one cable repair in deep water þ fiber aging) As a result, k P SNRSOL P 101:4 14 14 2 in ¼ 1:4 ¼ ¼ þ þ SNREOL j¼1 kPin;j 30 101:61 101:435 101:735 and the SNR degradation due to cable repair and aging is therefore 10 logð1:4Þ ¼ 1:5 dB. 6000-km Link: SOL: 120 amplifiers with 10-dBm input power EOL: 20 amplifiers with ð10 þ 1:25 þ 0:25Þ-dBm input power (cable repair in shallow water þ fiber aging) 89 amplifiers with ð10 þ 0:25Þ-dBm input power (fiber aging) 6 amplifiers with ð10 þ 3 þ 0:25Þ-dBm input power (pump-failed repeater þ fiber aging) 5 amplifiers with ð10 þ 3 þ 0:25Þ-dBm input power (cable repair in deep water þ fiber aging) As a result, k P SNRSOL P 101 20 89 11 in ¼ ¼ þ þ ¼ 1:21 120 101:15 101:025 101:325 SNREOL j¼1 kPin;j


163

and the SNR degradation due to cable repair and aging is therefore 10 logð1:21Þ ¼ 0:85 dB. Therefore, it appears that the SNR degradation is higher for short systems than for long systems: for short systems ( 2000 km) featuring a 70-km span length and 1000-km shallow water, the SNR degradation due to cable repair and fiber aging is 1.5 dB, whereas for long systems ( 5000 km) featuring a 50-km span length and 1000-km shallow water, SNR degradation is only 0.8 dB. C. Reduction of the Propagation Impairment The signal transmission quality in long-haul submarine systems is mainly degraded by:

The pulse distortion due to the interplay between nonlinear effects and the fiber chromatic dispersion [7] The optical level fluctuations and pulse distortion due to polarization effects occurring in the line fiber and the optical amplifiers

1. Transmission Impairment Due to Nonlinear Effects This is the impairment due to the interplay between the fiber chromatic dispersion and the nonlinear effects. This is evaluated from transmission experiments carried out in laboratories as the difference between the measured Q-factor and the theoretical SNR-based Q-factor calculated from Eq. (2). The propagation impairment for long-haul transmission systems ranges typically from 2 to 3 dB (Fig. 3).

FIGURE 3 Example of propagation impairment observed on a 16 10-Gbps transmission over

9000 km.

164


The main nonlinear effects affecting long-haul submarine transmissions are stimulated Raman scattering (SRS) and Kerr-type effects. SRS induces a power crosstalk between the transmitted wavelengths; actually, the upper wavelengths are amplified by the lower wavelengths. This crosstalk has a static component that can be eliminated by a gain flattening filter placed in each amplifier, and a dynamic component that is reduced when increasing the number of wavelengths or the fiber chromatic dispersion [8]. The Kerr effect consists of the variations in the fiber refractive index with the optical intensity. This in turn induces a phase modulation of the transmitted wavelength through self-phase modulation (SPM) or cross-phase modulation (CPM) and also generates new optical carriers through the four-wave mixing (FWM) process [9]. For the CPM and the FWM, the amplitude of the nonlinear effect depends on the chromatic dispersion of the fiber. In particular, the CPM and the FWM effects increase when the chromatic dispersion and the wavelength spacing are reduced. Moreover, the SPM or the CPM induces a pulse distortion only when combined with a nonzero fiber chromatic dispersion. Therefore, careful management of the fiber chromatic dispersion is required to reduce the impact of nonlinear effects on transmission quality. Two types of chromatic dispersion mapping are considered today: current transmission systems include a non-zero-dispersion-shifted fiber (NZDSF), although in research laboratories, transmission experiments are carried out with a dispersion managed fiber (DMF). The DMF consists of the combination in each span of a nondispersion-shifted fiber (NDSF) and a reverse dispersion fiber (RDF). The advantage of the DMF compared to the NZDSF is the nonvariation of the chromatic dispersion over the wavelength range. Note also that an appropriate modulation format applied at the transmit side can be efficient for reducing the pulse distortion along the link; this is the case for the chirp return-to-zero (CRZ) format used today with the NZDSF map. 2. Time-Varying System Performance The signal transmission quality is not stable over a long period of time due to the polarization effects occurring along the propagation path. The time-varying system performance (TVSP) is deduced from testbed experiments where the fluctuations of the Q-factor are measured over a long period of time. From this measurement, a Gaussian distribution is fitted to the measurements in order to deduce the standard deviation (s) and the average (mean Q) of the Q-factor distribution. Figure 4 shows the Q-factor recorded during 24 hr in an 80 10-Gbps, 6700km transmission; the standard deviation of the Q fluctuation is equal to 0.16 dB. The probability of observing a Q-factor lower than mean Q 4s (respectively, mean Q 5s) is 3:2 105 (respectively, 2:9 107 ). As discussed in a later section, the severely errored second ratio (SESR) of a 5000-km transmission should be less than 2:4 105 . To provide sufficient margin compared to the SESR requirement, the Q-factor considered in the Q budget table is mean


165

FIGURE 4 Q-factor measurement over 24 hr in an 80 10-Gbps, 6700-km transmission; the standard deviation of the Q fluctuation is equal to 0.15 dB.

Q 5s. The TVSP impairment is therefore defined as equal to 5s. Its typical value observed through experimental investigation is below or close to 1.2 dB. In the experiment mentioned in Fig. 4, the TVSP impairment deduced from a 24-hr measurement is equal to 0.8 dB. The following polarization effects are the main sources of Q-factor fluctuations:

PDL (polarization-dependent loss): This corresponds to the dependence of the insertion loss of passive components to the signal state of polarization (SOP). PHB (polarization hole burning): This corresponds to the dependence of the optical amplifier gain to the signal SOP [10]. PDG (polarization-dependent gain): This corresponds to the dependence of the EDFA gain to the pump SOP. The PDG can be considered for EDFA as equivalent to the PDL for passive components and the impact on the transmission quality is the same as the PDL. PMD (polarization mode dispersion): This corresponds to the dependence of the fiber refractive index on the signal SOP [11].

The PHB is an effect that is significant in single-wavelength transmission since the degree of polarization (DOP) of a laser source is close to 100% unless a

166


polarization scrambler is used. In WDM transmission systems including a large number of wavelengths, however, the DOP of the optical stream is close to 0% due to the random distribution of the different wavelength SOP. This effect becomes therefore negligible in a WDM transmission system. The PDL (including its equivalent for EDFA, the PDG) has a nonnegligible impact on system performance in WDM systems. It induces a random SNR fluctuation characterized by its mean value and its standard deviation. Calculations show that the mean penalty is much lower than the standard deviation penalty [12]: For a link composed of 100 optical amplifiers, each amplifier featuring a 0.15-dB PDL þ 0.05-dB PDG, the mean PDL=PDG-induced penalty is 0.15 dB whereas the standard deviation of this penalty is 0.37 dB, resulting in a TVSP impairment of 1.8 dB (5 times the standard deviation) pffiffiffiffiffiffiin ffi the Q budget table. (In this calculation, the fiber PMD is equal to 0:35 ps= p km ffiffiffi .) Note also that the mean PDL as well as its standard deviation varies as k where k is the number of optical amplifiers. Concerning the PMD the phenomenon is different: The PMD arises from the nonuniform distribution of the fiber refractive index, thus resulting, to a first order, in a polarization-dependent group velocity. At any time, two orthogonal SOPs corresponding, respectively, to the ‘‘fastest’’ and the ‘‘slowest’’ SOP of the link can be defined and are called the principal SOPs (PSOPs): these two PSOPs as well as their differential group delay (DGD) vary randomly during the life of the system. The PMD is, at the first order, equal to the average value of the DGD. Calculations as well as experimental investigations have demonstrated that the PMD varies as the square root of the fiber length. The impact of this first-order PMD does not depend on the number of transmitted wavelengths since it impacts each wavelength independently. Unless the SOP of the optical pulse is equal to one of the two PSOPs of the link, the PMD results in a pulse distortion. The impact of the PMD on the system performance can be summarized as follows [13]: The transmission performance degradation is deduced from the random variation of the DGD (which follows a Maxwellian distribution) as well as the random variation of the signal SOP. The probability of observing a penalty greater than p (in decibels) is equal to eZp where Z ¼ 16T 2 =AphDti2 with A ¼ 25 for a Gaussian-like pulse shape, T is the bit duration, and hDti is the PMD. Therefore, if hDti=T is lower than 0.1, the probability of observing a penalty higher than 1 dB is less than 3 107 , which is compliant with the SESR requirement (see the section on forward error correction code). For a system pffiffiffiffiffiffiffi length of 6000 km, this results in a required maximum PMD of 0:12 ps= km. This requirement is met today by most of the manufactured cables in long-haul WDM 10-Gbps transmission systems. D. Submarine Line Terminal Equipment Features The submarine line terminal equipment (SLTE) includes several functions that are aimed at improving the transmission quality. These key features can be separated


167

in two groups: on one side are the functions that behave as an analog signal processor and on the other side is digital signal processing represented by forward error correction coding. 1. Analog Signal Processing One function of the terminal is to combine the individual wavelengths into the line fiber at the transmit side and to extract each wavelength at the receive side before optical detection. This function is achieved through passive components called optical multiplexers and demultiplexers. In addition, the terminal should include optical fiber spools dedicated to chromatic dispersion precompensation (transmit side) and postcompensation (receive side). The compensating fiber and the optical multiplexer=demultiplexer exhibit significant insertion loss that has to be compensated for by optical amplifiers. The combination of the passive component and the optical amplifiers in the SLTE has to be carefully designed in order to avoid significant SNR degradation through the terminal optical paths. Indeed, due to the increasing number of wavelengths, the optical noise generated by the SLTE can become nonnegligible compared to the ASE noise generated by the optical repeaters. Note also that the appropriate amount of chromatic dispersion compensation placed in the transmit and receive terminals has to be precisely adjusted: a 6700km transmission experiment over NZDSF has been carried out to evaluate the Qfactor degradation due to chromatic dispersion postcompensation mismatch (Fig. 5). From Fig. 5 it follows that for the terminal chromatic dispersion management, an accuracy better than 100 ps=nm is required to keep the Q-factor degradation below 0.5 dB.

FIGURE 5 Q-factor degradation due to nonoptimal chromatic dispersion postcompensation for a 32 10-Gbps transmission over 6700 km of NZDSF.

168


Another key function of the SLTE consists of launching the wavelength comb into the line fiber with the appropriate optical power per wavelength. This process is called power preemphasis and is optimal when all data channels feature the same transmission quality at the link output. The SLTE is also responsible for launching the wavelengths with the appropriate modulation format. The current format usually installed in 10-Gbps WDM submarine systems is called chirp return-to-zero (CRZ) [14] since it consists in one stage of RZ amplitude modulation followed by a stage of bitsynchronous phase modulation. Actually, when combined with nonzero chromatic dispersion and nonlinear effects, the phase modulation is converted into amplitude modulation acting as pulse shaping. The amplitude of the phase modulation increases with the accumulated chromatic dispersion experienced by each transmitted wavelength at the link output; therefore, the amplitude of the phase modulation is not the same for all wavelengths and is adjusted to obtain the best transmission performance for each channel [15]. Furthermore, the insertion of bit-synchronous polarization modulation per wavelength can be implemented in the transmit terminal in order to mitigate polarization effects [14]. All optical pulses experience similar pulse distortion along the propagation path (which is not the case with a low-speed scrambler) and the pulse power can be recovered with appropriate electrical filtering after detection. Practically, high-speed polarization modulation is obtained with an external LiNbO3 phase modulator [16] and suffers from inherent spurious phase modulation. Therefore, the design of an actual 10-Gbps WDM system is aimed at reducing the polarization effects occurring in the transmission rather than inserting a high-speed polarization scrambler for each wavelength in the terminal. 2. Digital Signal Processing In addition to the analog signal processing described above, the terminal includes digital signal processing through the FEC (forward error correction). The FEC is a highly effective way to provide additional system margin also called net coding gain defined as follows: Net coding gain ðdBÞ ¼ Q-factor after error correction ðdBÞ

Qb factor before error correction ðdBÞ

In the above formula, Qb is the normalized Q-factor per information bit defined as: total bit-rate ð10Þ Qb ¼ Q measured before correction þ 10 log data bit-rate The target bit error ratio (BER) after error correction in submarine systems is usually equal to 1013 and the required Q-factor before correction is called the Q limit.


169

The standard FEC already used in currently installed 2.5- and 10-Gbps WDM links employs a single Reed–Solomon (RS) code featuring a net coding gain of 5.8 dB: a BER of 104 before correction (Qb ¼ 11:5 dB) leads to a BER of 1013 after correction (17.3-dB Q-factor). The emergence of 10-Gbps WDM links, however, requires more powerful codes formed for example by the concatenation of two Reed–Solomon codes resulting in a net coding gain close to 8 dB. A step further is to increase the number of decoding stages (so-called ‘‘iterations’’) without changing the encoder stage at the transmit side. Finally, new types of FEC are currently being researched such as block turbo codes based on a soft decision that samples the received pulse on several levels: the code handles no longer binary but multilevel information, enabling a coding gain of 10 dB.

E. Repeater Supervisory and Fiber Fault Localization 1. Repeater Supervisory The goal of this function is to track the evolution of each repeater pump current during the life of the system in order to assess the aging process and thus enable the forecasting of a repeater pump failure. The repeater pumping scheme is such that half of the pumps can fail while still ensuring the required system performance. This repeater supervisory function also monitors the repeater input power as well as the repeater output power. The principle of this repeater supervisory is the following: An interrogation message is sent from the terminal to one repeater through low-frequency ( 150-kHz) modulation of the transmit multiplex. The modulation index should be as low as possible in order to avoid any degradation of the data transmission quality. Note also that this modulation frequency has to be higher than the frequency cutoff of the EDFA ( 10–50 kHz) in order to avoid modulation index fading through the amplifier chain. The response of the repeater is sent back to the SLTE through a modulation of the amplifier gain (obtained through pump power modulation). The frequency of the pump power modulation has to be carefully chosen; if this frequency is much lower than the EDFA frequency cutoff, the modulation will be attenuated by the amplifier chain and will drop to an undetectable level. On the other hand, if the frequency is too high, there is no transfer of the pump modulation to the EDFA gain. Typically, the optimum frequency range is 10–50 kHz, depending on the EDFA configuration. The modulation index of both the interrogation and the answer is typically 4%, which ensures sufficient excursion for the supervisory signal detection as well as very low degradation of the data transmission quality. Actually, if the supervisory modulation index is m, expressed in percentage (the maximum index value being 200%), then the Q-factor degradation in decibels is equal to 10 logð1 þ m=2Þ. A 0.2-dB penalty corresponds to a 10% modulation index.

170


2. Fiber Fault Localization The repeater supervisory function is efficient for monitoring the span loss since both the repeater input power and output power are recorded. This, however, gives no information on the exact location of a fiber default if any. Therefore, another technique has to be applied in order to exactly monitor the attenuation profile of each span of the link. This technique is based on coherent optical timedomain reflectometry (COTDR). The principle of OTDR consists of launching an optical pulse of duration T into the fiber and measuring the return optical power versus time (Fig. 6). When the optical fiber under test does not suffer from any constraints, the optical fiber can be considered as a chain of sections of length d ¼ vT =2 that acts as a distributed optical mirror with a reflection coefficient g. Therefore, when launching an optical pulse in the fiber at t ¼ 0, the power received at t ¼ 2x=v is proportional to ge2ax and represents the power reflected by the section at a distance x. Here a is the fiber loss per meter ( 5 105 m1 ), v is the light speed in the fiber ( 2 108 m=s), and g¼

b ð1 eavT Þ 2a

where b is the local fiber Rayleigh backscatter coefficient (b 107 m1 ). If T ¼ 10 ms, g ¼ 40 dB. The resolution of the OTDR is vT =2, hence, 1 km for a 10-ms probe signal.

FIGURE 6

OTDR principle.


171

Note that the attenuation of the received backscatter signal is twice the loss of the optical fiber (measured in decibels). Thus, measuring the backscatter power with a log scale (using dBm unit for example) gives a linear response versus time or versus length since the correspondence is t ¼ 2x=v. OTDR performance is characterized by the SWDR (single way dynamic range), which is the maximum one-way attenuation (expressed in decibels) that the backscatter signal can experience to keep a level above the OTDR noise floor. In an amplified transmission system, because of the optical isolator placed in each optical amplifier, the backscatter signal of the transmit fiber has to be transmitted to the terminal station by the return fiber. The optical coupling between the transmit and return fiber is achieved in each amplifier pair of the repeater by means of fiber couplers [17–19]. Note that there are two ways to implement this cross coupling: either by physically coupling the outputs of the transmit and return repeater or by physically coupling the output of the transmit repeater to the input of the return repeater [20] (Fig. 7). However, with this technique, the ASE of the return amplifiers and the backscatter signal of the transmit fiber copropagates on the return fiber, thus leading to very poor SNR for the OTDR signal. To solve this issue, heterodyne detection of the OTDR signal is used. The principle of this technique is to mix the optical received signal with a local optical oscillator in order to provide an electrical signal at an intermediate frequency. This electrical signal then passes through a very narrow electrical filter to reduce the noise power. With the heterodyne detector, the dominant noise is the local oscillator– ASE beat noise (2POL NASE Be ) and the electrical signal power is given by the local oscillator–signal beat (POL Ps ). Therefore, the electrical SNR detected with a heterodyne receiver is equal to Ps =2NASE Be where Ps is the backscatter signal level, NASE the optical ASE spectral density, and Be ¼ 2=T . For a 0-dB electrical SNR, the minimum required signal Ps (in dBm) is equal to Ps ¼ 3 þ PASE , with

FIGURE 7 COTDR configuration with two types of cross coupling: output to input or output to output.

172


PASE ¼ NASE Be . One way to increase the SNR is to carry out N times COTDR measurements: The signal amplitude is proportional to N and the noise amplitude is proportional to N 1=2 (since the noise power is proportional to N ), thus multiplying the SNR by N 1=2. Since the duration of one measurement is equal to twice the propagation time along the link, N ¼ 210 measurements can be carried out in 10 s for a 5000-km link. As a result, the SWDR (in decibels) of the COTDR is: SWDR ¼ ðPs 3 PASE þ 5 log N Þ=2

ð11Þ

On the other hand, Ps ¼ Pout þ B þ C, where Pout is the COTDR probe power at the repeater output (in dBm), B ¼ 10 log g, and C is the output–output transmitreturn fiber cross-coupling transmission (25 dB typically). Therefore, we obtain: SWDR ¼ ðPout þ B þ C 3 þ 5 log N PASE Þ=2

ð12Þ

ðall figures; except N ; in dBÞ

It appears from the above formula that the lower the ASE level of the return fiber, the higher the COTDR SWDR. In order to minimize the ASE level on the return fiber, it is necessary to load this return fiber with an optical signal whose wavelength is different from the COTDR wavelenth. It is also clear that the SWDR increases with Pout ; therefore, the highest SWDR is obtained when the COTDR probe power is maximum, which means when all data wavelengths of the transmit fiber are removed (the out-of-service condition). When in service, use of the COTDR is possible but at the cost of lower SWDR. To evaluate the typical SWDR of a COTDR, a calculation is carried out for a 32 10-Gbps transmission over 6000 km composed of k ¼ 120 repeaters featuring a þ10-dBm output power, a 5-dB noise figure (Nf ) and 10 dB of gain. In that case, we obtain for T ¼ 10 ms: PASE ¼ khnNf G2=T ¼ 9:7 108 W or 70 dBm

With Pout ¼ 10 dBm, N ¼ 1024, C ¼ 25 dB, and B ¼ 40 dB, we obtain: SWDR ¼ ð10 40 25 3 þ 15 þ 70Þ=2 ¼ 13:5 dB which corresponds to 67.5 km ‘‘visible’’ length for a fiber attenuation of 0.2 dB=km. The received backscatter signal versus time (or length) shows a sawtooth trace: The depth and the length of each tooth is equal to the span loss and the span length, respectively. Figure 8 represents a COTDR trace measured over a chain of four amplifier pairs: The span loss is 9 dB, the COTDR SWDR is equal to 22 dB, and a 10-dB loss included in the middle of the span 3. The solid line is the measured trace and the dashed line represents the nominal trace in span 3 when there is no attenuation. The laser connected to the return fiber is the loading optical source that enables us to reduce the ASE level generated by the return


FIGURE 8

173

Setup and COTDR trace of a four-amplifier pair chain.

amplifiers. Since no cross-coupling is used just at the output of the COTDR, it is not possible to detect the signal backscattered by the first span as clearly shown in Fig. 8. To detect a fiber fault in a shore end, a standard OTDR is usually employed. Clearly, the dynamic range of the COTDR depends on the transmit amplifier output-to-return amplifier output cross-coupling coefficient C, which value is typically 25 dB. The higher the cross-coupling transmission, the higher is the COTDR dynamic range. On the other side, this value should be kept below 25 dB to avoid transmission degradation induced by coherent Rayleigh noise [21]. This effect results from the interactions between the backscattered data wavelengths of the transmit fiber and the data wavelengths propagating on the return fiber. The two wavelength sets are superimposed if the wavelengths are exactly the same in both directions, which is usually the case in a transmission system. F. Q Budget and Typical Repeater Spacing 1. Q Budget Table Each DLS (digital line section or ‘‘point-to-point’’ transmission) of a submarine system is characterized by the Q budget table that aims at listing the different effects affecting the transmission quality. The reason for using the Q-

174


factor to quantify the transmission quality is the following: If the transmission quality is limited by the signal–ASE beat noise, the Q-factor deduced from Eq. (2) with an infinite extinction ratio is: Q2 ¼

P

ð13Þ

SNASE Be

In that case, Q2 is equal to the optical SNR measured in an optical bandwidth equal to the receiver electrical bandwidth Be . This simple relationship between the SNR and the Q-factor explains why the Q-factor is usually expressed in decibels and why it is used to quantify the different system impairment: QdB ¼ 20 log Q 10 logðSNRÞ. The typical Q budget table of a DLS is shown in Table I. The table consists of two columns: The first one is dedicated to the SOL conditions and the second one to the EOL conditions. Note that the impairments are the same in both cases and that the main difference is the SNR-based Q which is reduced in EOL conditions due to the cable repairs and component aging. To take into account the aging of the terminal, the SLTE Q is also slightly reduced in EOL conditions. The system margin is given by the difference between the segment Q and the Q limit required before error correction. The meaning of the different lines is summarized below: Line 1—SNR-based Q-factor. The SNR-based Q-factor is given by Eqs. (2) and (7). Line 2.1—propagation impairment. This corresponds to the impairment due to the interplay between the fiber chromatic dispersion and the nonlinear effects. Line 2.2—nonoptimal preemphasis impairment. The launch power of each wavelength into the link has to be adjusted in order to ensure the same transmission quality for all wavelengths at the link output. This process is called

TABLE I

1 2.1 2.2 2.3 2.4 2.5 3 4 5 6 7

Typical Q-Budget Table for a Submarine Transmission DLS

SNR-based Q-factor (dB) Propagation impairment Nonoptimal preemphasis impairment Supervisory impairment Manufacturing and environment impairment Time-varying system performance Line Q value SLTE Q value Segment Q value Minimum required Q before correction Segment margin

Start-of-life (dB)

End-of-life (dB)

17.5 2.0 0.4 0.2 1 1.2 12.7 24.1 12.4 8.7 3.7

14.7 2.0 0.4 0.2 1 1.2 9.9 22.9 9.7 8.7 1.0


175

power preemphasis and is nonoptimal when one (or several) channels exhibit degraded performance compared to other channels; 0.4 dB is allowed in the power budget table for this nonperfect transmission quality equalization. Line 2.3—supervisory impairment. This impairment is due to the overmodulation required for the repeater supervisory. If the modulation index is less than 10%, the supervisory impairment is kept below 0.2 dB. Line 2.4—manufacturing and environment impairment. This line covers the performance difference between the specified and manufactured equipment, including the performance degradation induced by environmental effects such as temperature, shocks, and so on. Line 2.5—time-varying system performance. This corresponds to the Qfactor fluctuations, mainly due to polarization effects. Line 3—line Q value. Line 3 ¼ line 1 7 line 2.1 7 line 2.2 7 line 2.3 7 line 2.4 7 line 2.5. Line 4—SLTE Q value. Due to the noninfinite SNR and nonperfect electronics of the SLTE, the Q-factor obtained when the transmit terminal is directly connected to the receive terminal is not infinite and is called the SLTE Q. Line 5—segment Q value. Since both the line Q and the SLTE Q contribute to the overall system performance, the segment Q-factor is deduced from line 3 and line 4 through the formula: 1 Q2Segment

¼

1 Q2Line

þ

1 Q2SLTE

ð14Þ

Using Eq. (13), Eq. (14) can be understood as Segment noise ¼ Line noise þ SLTE noise Line 6—Q limit before correction. This corresponds to the minimum Qfactor required before error correction to achieve the required transmission quality after correction. This value depends on the type FEC used. Line 7—system margin. Line 7 ¼ line 5 7 line 6. The EOL system margin is usually equal to 1 dB.

2. Typical Repeater Spacing The design of a long-haul submarine transmission system aims at proposing the minimum repeater count for a given transmission length. The calculation of the repeater spacing is carried out through the following process:

Step 1: Calculate the required SOL segment Q: SOL segment Q ¼ Q limit þ Requested EOL margin þ Allowance for cable repair and aging

Step 2: Estimate the maximum repeater output power per wavelength and the associated propagation impairment. In long-haul transmission systems, the launch power is limited by the pulse distortion due to nonlinear effects and

176


chromatic dispersion: The repeater optical output power leading to the highest Q-factor is deduced from laboratory transmission experiments. The pulse distortion depends on the system length, the number of wavelengths, the wavelength spacing, the fiber type (effective area, chromatic dispersion), and the modulation format. In short-haul systems, the launch power is mainly limited by the available pump power in the repeater. Step 3: Calculate the required SNR in SOL conditions. First, the SNRbased Q-factor is deduced from the formula: SNR-based Q ¼ SOL segment Q þ Propagation impairment þ TVSP þ Nonoptimal preemphasis þ Supervisory induced impairment þ Manufacturing impairment

Then the SNR is calculated from the SNR-based Q through Eq. (2). A corrective factor is applied, if needed, to take into account the SNR degradation due to the nonuniform spectral response of the amplifier chain. Finally, the repeater count k is obtained through Eq. (8). The typical repeater spacing as well as the repeater count required for a 68 10-Gbps transmission versus the link length is depicted in Fig. 9. In Fig. 9, the repeater output power is þ14 dBm for short span lengths and þ13 dBm for long span lengths since the pump power is usually not sufficient to achieve simultaneously high gain and high output power. The EDFA noise figure is 4.5 dB. In addition, this calculation includes a 0.5-dB SNR degradation due to the nonuniform EDFA gain shape. The impact of the gain equalization process on the SNR is discussed in the following section.

FIGURE 9 Typical repeater spacing for a 68 10-Gbps transmission system.


177

III. GAIN EQUALIZATION The nonuniform spectral response of the optical amplifier chain can lead to prohibitive SNR degradation for long-haul transmission systems. Therefore, two techniques are implemented in order to compensate for this effect:

At first, each wavelength of the multiplex is launched into the line fiber with an appropriate optical level aiming at equalizing the SNR (more generally the BER) of all wavelengths at the link output. This is the power preemphasis process. To keep the level of the preemphasis to a reasonable value, gain flattening filters have to be inserted in the link. There are actually three types of gain flattening filters: (1) a gain flattening filter in each optical amplifier, (2) a fixed-gain equalizer placed about every 10 amplifiers in order to compensate for the residual nonuniform spectral response of the amplifier chain, and (3) a tunable tilt equalizer placed about every 10 amplifiers that compensates for the gain distortion due to the component aging and the cable repairs.

A. Power Preemphasis The first issue to be considered in the design of WDM transmission systems is the nonuniform spectral response of the optical amplifier gain. This leads to SNR distortion over the wavelength comb at the link output unless power preemphasis is applied at the transmit side. In addition, the higher the amplifier gain distortion, the higher the required preemphasis and the lower the equalized SNR. The goal of this section is to assess the required preemphasis as well as the associated SNR degradation versus the amplifier gain excursion over the wavelength comb. Hereafter, we consider the transmission of three wavelengths l1 , l2 , and l3, pffiffiffi that experience a relative gain per amplifier of 1, g, and g, respectively. In this model, all optical amplifiers are identical and the total accumulated ASE noise provided by the amplifier chain is supposed to be negligible compared to the signal power. The amplifier output power is constant as well as the amplifier input power, which is normalized to 1 W. In the case of a chain of N perfectly flat gain amplifiers, the SNR for a three-wavelength transmission is equal to SNR0 with: SNR0 ¼

1 3NNf hnBopt

ð15Þ

At the output of amplifier k we have: P2;k

P1;k þ P2;k þ P3;k ¼ 1 pffiffiffik ¼ P1;k g X2 and P3;k ¼ P1;k gk X3 P P X2 ¼ 2;0 and X3 ¼ 3;0 P1;0 P1;0

ð16Þ

178


where Pi;k is the optical power of wavelength i at the input of amplifier k þ 1. The power preemphasis of l1 , l2 , and l3 is, respectively, X1 ¼ 1, X2 , and X3 . From Eq. (16) we can deduce: pffiffiffi 1 P1;k ¼ g1;k P1;0 with g1;k ¼ ð1 þ X2 gk þ X3 gk ÞP1;0 pffiffiffi ! X3 g k 1 1 P2;k ¼ g2;k P2;0 with g2;k ¼ 1 þ pffiffiffik þ P2;0 ð17Þ X2 X2 g ! X2 1 1 with g3;k ¼ 1 þ pffiffiffik þ P3;k ¼ g3;k P3;0 P X3 g k 3;0 X3 g

where gi;k is the gain experienced by wavelength i after propagation through the first k amplifiers. At the input of amplifier k þ 1, the ASE noise provided by amplifier k at wavelength i is equal to hnNf Gi;k Bopt ðwith Gi;k ¼ gi;k =gi;k1 Þ and is noted KGi;k with K ¼ Nf hnBopt ¼

1 3N SNR0

Since the noise provided by optical amplifier k passes through amplifiers k þ 1 to N , it experiences a gain equal to gi;N =gi;k . Therefore, at the end of the link, the noise at wavelength i provided by amplifier k is equal to K gi;N =gi;k1 . Noise (i), the noise at wavelength i at the output of the link, is the sum of the noises provided by all amplifiers: 1 1 1 þ þ gi;k þ þ gi;N NoiseðiÞ ¼ Kgi;N ð1 þ gi;1 1 Þ

ð18Þ

which gives the following result for the 3 wavelengths:

with

SNRðl1 Þ1 ¼ KðN þ AX2 þ BX3 Þ pffiffiffi SNRðl2 Þ1 ¼ KðN þ A g 1N X21 þ AX3 X21 Þ pffiffiffi SNRðl3 Þ1 ¼ KðN þ Bg 1N X31 þ A g 1N X2 X31 Þ pffiffiffiffiffiffi 1 gN A¼ pffiffiffi 1 g

and

B¼

ð19Þ

1 gN 1g

The equalization of the three SNRs leads to the following result: SNR0 ; SNR ¼ 3 pffiffiffiffi X 1 gN ð1 þ GÞ 1þ 3 2N 1 g pffiffiffiffiffiffiffiffiffiffi 1N X3 ¼ g

pffiffiffi !2 8 1þ g pffiffiffiffiffiffi with G ¼ 1 þ X3 1 þ g N

ð20Þ ð21Þ


FIGURE 10

179

Optical power and SNR evolution along the link with optimal power preemphasis.

Figure 10 depicts the optical power and the SNR of each wavelength along the link when the preemphasis is applied to equalize the SNR at the link output. The system preemphasis is given by the power excursion over the multiplex at the transmit terminal output and is usually expressed in decibels. In the above calculation, the preemphasis is j10 logðX3 Þj. Note from Eq. (21) that the required preemphasis (in decibels) is equal to half the link gain excursion (in decibels) for N 1. Another deduction from Eq. (21) is that the higher the required preemphasis, the lower the equalized SNR. The same preemphasis and equalized SNR calculation has also been carried out with two wavelengths. In the case of the two-wavelength transmission, we obtain: SNR ¼ 2

SNR0 1 1 gN 1 þ X2 N 1g

ð22Þ

with the preemphasis X2 ¼ and SNR0 ¼

pffiffiffiffiffiffiffiffiffiffi g1N

ð23Þ

1 2GNf hnBopt

is the SNR obtained in the case of perfectly flat gain amplifiers with twowavelength transmission. Note that the preemphasis is the same with three- or two-wavelength transmission [see Eqs. (21) and (23)], whereas the SNR degradation is higher for the two-wavelength transmission configuration. This result is confirmed by numerical calculations carried out with 100 wavelengths. Figure 11 represents the SNR degradation versus the preemphasis for N ¼ 100 amplifiers. Regardless pffiffiffiffiffiffiffiffiffiffiof the number of wavelengths, the required preemphasis is equal to j10 logð g 1N Þj (where g is the amplifier gain excursion over the spectral range) but the equalized

180


FIGURE 11 SNR degradation compared to ideal flat gain amplifier chain versus the required preemphasis for N ¼ 100 amplifiers in the case of 2-, 3-, and 100-wavelength transmission.

SNR degradation compared to optimum flat gain depends on the wavelength count. It appears in Fig. 11 that SNR degradation is reduced when increasing the number of wavelengths but does not change significantly for more than three wavelengths. In general, a WDM system is designed to ensure that the SNR degradation induced by the nonuniform spectral response of the amplifier gain is kept below 0.5 dB, which means that a maximum 7-dB preemphasis should be targeted, thus requiring a total accumulated gain excursion over the transmit multiplex lower than 14 dB.

B. Fixed-Gain Equalizer 1. Need for Fixed-Gain Equalizers in Very Long-Haul WDM Transmissions Practically, the gain flatness of individual EDFAs over very broad bandwidth is typically 0.3 dB. Figure 12 depicts the spectral response of one EDFA gain with and without a gain flattening filter. Without a gain flattening filter, the gain excursion is 3 dB over the 32-nm wavelength range (1533–1565 nm), whereas this excursion drops to 0.25 dB when the appropriate gain flattening filter is inserted in the EDFA. Although the gain excursion is drastically reduced with the insertion of gain flattening filters, this is not sufficient to ensure good transmission quality. Actually, when cascading 169 EDFAs with 0.25-dB gain distortion, the accumulated gain excursion is expected to be 42 dB. Due to spectral hole burning, the measurement carried out in the laboratory shows a gain excursion of only 30 dB (Fig. 13) at the output of a 6700-km link including 169 EDFAs (13 orbits in a recirculating loop setup composed of 13 EDFAs).


FIGURE 12

181

Spectral response of an EDFA gain without and with a gain flattening filter.

FIGURE 13

Optical spectrum at the output of a 6700-km link composed of 169 EDFAs featuring a 0.25-dB gain distortion over the 32-nm wavelength range.

In this measurement, the launched optical spectrum is composed of 32 wavelengths (with 1-nm wavelength spacing) and all wavelengths are launched with the same optical level at the line input. To reduce the accumulated gain distortion, it is necessary to insert periodically along the link extra gain flattening filters called fixed-gain equalizers (FGEQs) to compensate for the residual amplifier gain distortion [22]. For that purpose, a FGEQ has been inserted in the circulating loop, thus leading to a periodical gain equalization every 513 km (length of the loop). Figure 14 depicts the FGEQ spectral response inserted in the loop.

182


FIGURE 14

Optical spectrum at the 6700-km link output including a FGEQ every 513 km.

Figure 15 shows the optical spectrum at the 6700-km link output with a flat launched optical spectrum. The total gain excursion is reduced to 5 dB due to the gain equalization achieved by the 13 cascaded FGEQs. 2. Optimum Spectral Response of the FGEQs The purpose of this section is to evaluate the optimum spectral response of the FGEQ as well as the required number of equalizers versus the amplifier residual gain distortion. Here, N is the total repeater count. The following calculation is carried out in the simple case of a two-wavelength transmission

FIGURE 15

Spectral response of the FGEQ inserted in the 513-km recirculating loop.


183

with FGEQs placed periodically along the link. The number of FGEQs is M 1 and m ¼ N =M is the number of amplifiers between two consecutive FGEQs. The relative gain of l1 and l2 per amplifier is 1 and g, respectively. The transmission function of each FGEQ is Fðl1 Þ ¼ 1 and Fðl2 Þ ¼ F. The SNR at the link output can be calculated as in the previous section: with X ¼ g m F and A ¼ ð1 g m Þ=ð1 gÞ, we obtain: MP 1 1 XM 1 k m SNRðl1 Þ ¼ K ðm þ AX2 ðg FÞ Þ ¼ K N þ AX2 1X k¼0 MP 1 1 X M ðm þ X21 Ag 1m ðg m FÞk Þ ¼ K N þ X21 Ag 1m SNRðl2 Þ1 ¼ K 1 X 1 k¼0 ð24Þ

The equalization of the SNR leads to: pffiffiffiffiffiffiffiffiffiffipffiffiffiffiffiffiffiffiffiffiffiffi X2 ¼ g1m X 1M SNR0 SNR ¼ 2 1 1 gm 1 1 X M 1 þ X2 m 1g M 1X

ð25Þ ð26Þ

where SNR0 is the maximum SNR obtained in the case of perfectly flat gain amplifiers with two wavelengths [see Eq. (23)]. Actually, the SNR calculation should also include the noise degradation due to the FGEQ loss. The mean loss of the FGEQ (in decibels) is close to 5 logðFÞ and the span averaged FGEQ loss is therefore 5 logðFÞ=m. It appears that the FGEQ spectral response that maximizes the SNR is different from the one that minimizes the preemphasis:

The SNR isffi maximum for F ¼ g m. In that case, the preemphasis is pffiffiffiffiffiffiffiffiffi 1m X2 ¼ g and SNR ¼ 2

SNR0 X 1 gm 1þ 2 m 1g

ð27Þ

The preemphasis is minimum for F ¼ g ðN1Þ=ð1M Þ. In that case, X2 ¼ 1 (0 dB preemphasis) and SNR ¼ 2

SNR0 G 1 gm 1þ m 1g

with

G¼

1 1 ðFg m ÞM M 1 Fgm

ð28Þ

Note that when N 1 and M 1, the value of F that maximizes the SNR and minimizes the preemphasis is the same and is equal to gm . This corresponds to the experimental case presented in the previous section: The FGEQ placed every 13 EDFAs exhibits a contrast of 3 dB, while each EDFA gain excursion is

184


FIGURE 16 SNR degradation and required preemphasis versus the number of FGEQs for N ¼ 150 and 0.3-dB gain distortion per amplifier: FGEQ 1 maximizes the SNR (F ¼ g m ) and FGEQ 2 minimizes the preemphasis (F ¼ gðN 1Þ=ð1MÞ ).

0.25 dB, leading to 3.25-dB gain distortion for the 13 EDFA chain composing the recirculating loop. Figure 16 represents the equalized SNR and the preemphasis versus the number of FGEQs. The amplifier count is 150 and the gain excursion over the wavelength range is 0.3 dB per amplifier. In Fig. 16, the SNR penalty versus the number of FGEQs includes the noise degradation due to the FGEQ insertion loss. To drop the SNR degradation below 0.5 dB and the preemphasis below 3 dB, the minimum number of FGEQs is 7 for a 150-amplifier chain with 0.3-dB gain excursion per amplifier. In that case, the contrast of each FGEQ is 150 0.3=7 ¼ 6.4 dB. C. Tunable Gain Equalizer Due to cable repairs and component aging, the average loss of the link increases during the life of the system. The cable aging and repair conditions of a long-haul transmission system were discussed in the first section of this chapter. For a 6000-km link length with 50-km span length including 1000 km of shallow water, the total loss increase is 57.5 dB shared as follows: 5 3 dB ¼ 15 dB (1000=20) 0.5 dB ¼ 12.5 dB 50 0.005 120 ¼ 30 dB

due to cable repairs in deep water due to cable repairs in shallow water due to the fiber loss increase


FIGURE 17

185

EDFA gain tilt due to span loss variation of 1 dB.

This corresponds to an average span loss increase of 0.5 dB. The resulting 0.5-dB EDFA gain increase leads to a shift of the gain peak wavelength to lower wavelength, thus inducing a negative spectral linear tilt (in decibels) of the EDFA gain. Figure 17 depicts the gain variation observed on one EDFA when the EDFA gain is increased or reduced by 1 dB. The EDFA gain tilt is typically 0.7 dB over 32 nm for a 1-dB change in EDFA gain (Fig. 17). Therefore, for a 6000-km link length including 120 EDFAs, the total expected gain tilt is 120 0.35 ¼ 42 dB over 32 nm. Such a gain tilt cannot be compensated for by a preemphasis adjustment since this would lead to a huge preemphasis value and prohibitive SNR degradation as discussed in a previous section. Therefore, it is necessary to insert in the link equipment whose spectral transmission response can be changed during the life of the system by remote control from the terminal station. Such equipment is called a tunable gain equalizer (TGEQ). Such a function can be obtained by the periodical insertion along the link of a tunable optical filter [23, 24]. Another way consists of periodically inserting Raman amplifiers. In the case of the Raman amplifier-based equipment, the tunable tilt function is achieved through remote control of the Raman pump power [25]. For example, when switching a 1480-nm Raman pump power from 0 to 50 mW into a NZDS fiber, a 2-dB gain tilt is obtained over the 1535- to 1565-nm spectral range (Fig. 18, right hand). This 2-dB tilt results from the 0.8-dB Raman amplification gain slope (Fig. 18, left hand) but also from the gain tilt (1.2 dB) of the first EDFA following the Raman amplifier. To demonstrate the efficiency of this technique in a transmission experiment, attenuation of 3 dB has been included in span 9 of a 513-km-long recirculating loop. The total bandwidth is 32 nm and one Raman pump has been inserted in

186


FIGURE 18 Tunable gain tilt equalizer based on Raman amplification inserted in an EDFA chain.

one span of the loop (span 5). A 32-wavelength transmission over 6700 km (13 loop orbits) has been carried out in three configurations: Case a: the nominal case Case b: with 3 dB of extra loss (in span 9) every 513 km Case c: with 3 dB of extra loss and one Raman pump turned on to 50 mW every 513 km Figure 19 depicts the optical spectrum recorded at the link output in the three configurations with a flat launched optical spectrum at the link input. It appears that in the nominal condition, the gain tilt is 4 dB. Then, after insertion of the total 42-dB loss in the transmission, the measured gain tilt is 20 dB; the tilt induced by this extra loss is expected to be 2.1 dB per orbit, thus leading to a 29-dB total gain tilt. However, due to spectral hole burning, the measured gain tilt is only 20 dB at the end of the link. Finally, when switching the Raman pump from 0 to 50 mW, the gain tilt is reduced to 5 dB.

D. Impact of Nonoptimal Gain Equalization One FGEQ or TGEQ aims at compensating for the residual gain distortion of a group of optical amplifiers. Note also that each group of optical amplifiers does not necessarily exhibit the same gain distortion. For example, due to cable repairs,


187

FIGURE 19 Optical spectrum at the 6700-km transmission output over a 32-nm bandwidth in three cases: Case a: in the nominal case; case b: with 3 dB of extra loss (in span 9) every 513 km; and case c: with 3 dB of extra loss and one Raman pump turned on to 50 mW every 513 km.

the loss increase does not occur in all spans and therefore only the TGEQ placed close to the cable repair has to be adjusted. To illustrate the impact of the spectral matching between the gain equalizer and the group of amplifiers associated with this equalizer, SNR calculations have been carried out for a 16-wavelength (32nm total wavelength range) transmission over 6000 km. The link is composed of 120 EDFAs and also includes 10 tunable gain equalizers (one TGEQ for every 12 EDFAs) to compensate for the EDFA gain tilt due to fiber aging and cable repairs. The optical SNR as well as the required preemphasis are calculated in the following system configurations:

In the nominal conditions, all optical amplifiers as well as all TGEQs are supposed to feature a flat spectral response. In a second configuration, cable repairs are included, distributed along the link as follows: spans 1–10 and 36–45: þ0:6-dB loss per span; spans 66– 68 and 90–92: þ3-dB loss per span.

In total, the extra loss due to cable repairs is 30 dB, thus leading to a total negative link gain tilt of 30 0.7 ¼ 21 dB over the 32-nm spectral range. This tilt is, of course, visible from the link output with an optical spectrum analyzer.

188


TABLE II SNR Degradation and Preemphasis Increased Due to Cable Repairs for Different TGEQ Settings

Without cable repairs; all TGEQs at 0-dB tilt With cable repairs; all TGEQs at 0-dB tilt With cable repairs; all TGEQs at þ2:1-dB tilt With cable repairs; TGEQs 1 and 4 at þ4:4 dB tilt and TGEQs 6 and 8 at þ6:3-dB tilt

SNR degradation (dB)

Preemphasis (dB)

0 2.4 0.4 0.3

0 16.8 6.1 1.8

Therefore, a first reaction is to modify all TGEQs equally by tuning each TGEQ to a þ2:1-dB tilt. However, a more appropriate gain equalization process is to move the TGEQ placed close to the cable repairs, which means: TGEQs 1 and 4 with a positive tilt equal to þ4:4-dB tilt and TGEQs 6 and 8 with a positive tilt equal to 6.3 dB. The SNR degradation as well as the preemphasis is calculated in the two cases: average tilt of 2.1 dB for all TGEQs or appropriate TGEQ adjustment: the results are depicted in Table II. The SNR degradation due to the extra span loss only can be calculated from Eq. (7) and is equal to 0.3 dB. Therefore, when the TGEQs are kept unchanged, the SNR degradation due to the gain tilt is 2.1 dB and the preemphasis has to be increased by 16.8 dB. When all the TGEQs are equally adjusted to a þ2:1-dB tilt, the required preemphasis increase is 6 dB and the total SNR degradation drops to 0.4 dB. The high level of preemphasis increase would enhance the impact of nonlinear effects since the power distribution of the wavelength multiplex would become strongly nonuniform along the link. When the appropriate TGEQs are tuned to the optimum tilt, the preemphasis increase is dropped to 1.8 dB. In conclusion, to reduce the required preemphasis, the spectral response of each gain equalizer has to be adjusted to the local gain distortion rather than setting all gain equalizers to an identical average value.

IV. CHROMATIC DISPERSION AND NONLINEAR EFFECTS The propagation impairment is induced by the interplay between the fiber chromatic dispersion and nonlinear effects such as SRS and Kerr-induced effects.

A. Nonlinear Kerr-Type Effects The Kerr effect consists of the variation of the fiber refractive index with the light intensity and leads to the following phenomena:


189

Modulation of the phase of each channel resulting from modulation of the fiber index by the light intensity. When the phase modulation is induced by the channel intensity itself, the effect is called self-phase modulation (SPM). When the phase modulation is induced by other channels, the effect is called cross-phase modulation (CPM) [26]. When combined with nonzero chromatic dispersion, the phase modulation due to SPM or CPM leads to a pulse distortion. However, the amount of phase modulation induced through the CPM process is reduced when the interacting wavelengths do not propagate at the same group velocity, which is the case if the fiber chromatic dispersion is not zero. Generation of a fourth wavelength from the propagation of three other wavelengths through the four-wave mixing (FWM) process. When generated at the same wavelength as one data channel, this spurious optical wave induces in-band crosstalk which can lead to significant data transmission degradation. To reduce the boost of the signal created by FWM, it is necessary to avoid phase matching between the transmitted channels through the use of nonzero fiber chromatic dispersion [27].

From the above remarks, it follows that, to reduce the impact of nonlinear Kerr-type effects, it is essential to have a fiber with a nonzero chromatic dispersion at all points of the link to reduce FWM and CPM effects, and to zero the chromatic dispersion at regular intervals along the link to reduce the pulse distortion due to SPM or CPM. This is why today’s submarine links developed for current 2.5- and 10-Gbps WDM transmission use two types of fiber [28]: One, called NZDSF (for nonzero dispersion-shifted fiber), has a chromatic dispersion of 2 ps=nmkm, and the second, NDSF (for nondispersion-shifted fiber) has a dispersion of þ18 ps=nmkm. So, over 10 fiber sections, 9 are NZDSF and 1 is NDSF, which means that the cumulative chromatic dispersion is reduced to zero every 10 sections although the second-order (or ‘‘local’’) chromatic dispersion is never zero. However, given that the chromatic dispersion of the fiber varies linearly with the wavelength, the accumulated chromatic dispersion cannot be reduced to zero at regular intervals for all wavelengths simultaneously. This spectral variation of the chromatic dispersion is typically þ0:08 ps=(nm2 km) and is called the third-order chromatic dispersion (or ‘‘the chromatic dispersion slope’’). For example, if the chromatic dispersion is compensated periodically for the center channel, then the accumulated chromatic dispersion of the two extreme channels is 8000 ps=nm at the end of a 6400-km link for a 32-nm wavelength multiplex. To reduce this cumulated chromatic dispersion, pre- and postchromatic dispersion are implemented in the transmit and receive terminal, respectively. With this technique, the maximum cumulated chromatic dispersion is divided by 2 (Fig. 20). With this type of fiber map, 105 10- and 68 10-Gbps transmissions over 6700 and 8700 km, respectively, have been reported [15]. Nevertheless, even with pre- and postchromatic dispersion compensation, the accumulated dispersion is

190


FIGURE 20 NZDSF chromatic dispersion map including pre- and postchromatic dispersion compensation.

not negligible and for very long systems using very broad bandwidth amplifiers, the transmission degradation of the outer wavelengths of the multiplex is significant. To overcome this problem, fiber suppliers have developed a new type of fiber called RDF (reverse dispersion fiber) that exhibits a second- and third-order chromatic dispersion opposite to those of the NDSF. The idea is then to combine the RDF with the NDSF in each repeater section, thus enabling us to nullify the accumulated chromatic dispersion for all wavelengths simultaneously [29]. This fiber combination is called dispersion managed fiber (DMF). Figure 21 depicts a DMF map where the NDSF=RDF length ratio per span is 1 : 1 and where the span-averaged third-order chromatic dispersion is 0.006 ps=nm2 km. In addition, the use of a DMF configuration is required for C þ L-band transmission [30, 31] because the second-order chromatic dispersion of the NDSF and of the RDF is never zero within the 1.5-mm window, thus eliminating the FWM (unlike the NZDSF for which the chromatic dispersion is zero at around 1580 nm). The DMF configuration can also benefit from the large effective area of the NDSF. That means that the light intensity can be reduced at constant optical power, along with nonlinear effects. Indeed, the NDSF has a core area of 110 mm2, whereas that of the NZDSF fiber is no more than 70 mm2. To exploit the benefit of the greater NDSF area, the section portion including the NDSF must be placed at the repeater output where the optical power is at a maximum. Nevertheless, the effective area of the RDF is usually much smaller than the NDSF and is about only 20 mm2 [32]; this counterbalances the benefit of the large effective area of the NDSF.


FIGURE 21

191

Example of DMF chromatic dispersion map.

B. Stimulated Raman Scattering SRS leads to optical amplification of the upper wavelengths by the lower wavelengths of the transmit multiplex [7]. This results in a power decrease at the lower wavelengths and a power increase at the upper wavelengths and this process is called SRS induced crosstalk. Since the Raman amplification frequency cutoff is much higher than the data bit rate, the Raman gain experienced by the individual pulses of the amplified channel depends on the pulse power of the pumping channels. In other words, the SRS induced crosstalk is characterized by its average value (Z) and standard deviation (s) as follows: Z is the average Raman gain (or depletion) experienced by the amplified channel (pumping channel respectively). This corresponds to the static SRS induced crosstalk. s is the standard deviation of the pulse power fluctuations due to SRS. This corresponds to the dynamic SRS induced crosstalk. The static SRS-induced crosstalk can be easily experimentally observed. Figure 22 represents the spectral response of a 45-km NZDSF fiber spool for 1- and 30-mW launched power into the fiber (50-mm2 effective area). With 1-mW input power, the static SRS induced crosstalk is negligible and the spectral response is the one of fiber attenuation. From Fig. 22 (upper diagram), we see that the fiber attenuation spectral variation is equal to 2 104 dB=nmkm. Looking at the differential gain between the two spectral responses (Fig. 22, lower diagram), we see that the spectral gain tilt induced by the static SRS crosstalk is about 0.7 dB over 40 nm for 30-mW total launch power in the fiber spool. This tilt can be compensated for by the insertion of an optical gain flattening filter in each amplifier. However, these gain flattening filters compensate for a static SRS-

192


FIGURE 22

Spectral response of a 45-km fiber spool with 1- and 30-mW total input power spread over 40 nm (upper diagram). Difference between the two responses (lower diagram).

induced tilt directly linked to the repeater output power. This means that the repeater output power cannot be changed during the life of the system without impacting significantly the link gain flatness. For example, when a transmission system is underequipped with only half of its full capacity, it is necessary to launch loading wavelengths into the link in order to reduce the actual data channel power by 3 dB (to avoid nonlinear Kerr-type interactions), instead of decreasing the repeater output power. Concerning the dynamic SRS-induced crosstalk, the gain flattening filter is not efficient since it is a dynamic process that leads to a random variation of the different pulses of the amplified channel due to the random distribution of the pumping wavelength pulse power. Note that the random gain for the upper wavelengths corresponds to a random depletion of the lower wavelengths. To evaluate the amplitude of these fluctuations, a simple relationship between Z and s for one repeater section can be used [33]: s 1 ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Z N BDaDl

ð29Þ

where B is the bit rate, D the chromatic dispersion, a the fiber attenuation, N the number of wavelengths, and Dl the wavelength spacing. Typically, with NDSF, 0.5-nm wavelength spacing, and 0.2 dB=km fiber attenuation, s=Z ranges from 0.1 to 0.01 when N ranges from 10 to 100.


193

Note that if the chromatic dispersion is compensated to zero at the end of each span, s increases linearly with the repeater count. On the other hand, if the chromatic dispersion is not compensated to zero, s2 increases linearly with the repeater count. Therefore, for a 100-amplifier chain, and a 100 10-Gbps transmission over a 32-nm bandwidth with þ15-dBm repeater output power, we have s ¼ 0:07 dB if the chromatic dispersion is not compensated to zero at the end of each span, and s ¼ 0:7 dB if the chromatic dispersion is compensated to zero at the end of each span. Therefore, the management of the fiber chromatic dispersion plays an important role in the reduction of the dynamic SRS-induced crosstalk. Actually, the higher the number of wavelengths and the chromatic dispersion, the lower the ratio s=Z.

C. Transmission Experiments 1. Experimental Setup The transmission experiments are usually carried out on a recirculating loop setup [34], which can easily be reconfigured since the number of pieces of equipment (optical amplifiers, fiber spools) is very low compared to a deployed testbed. However, the deployed testbed offers a configuration that is closer to the installed system and system performance can be investigated with a higher accuracy [35]. The setup of a recirculating loop is depicted in Fig. 23. Note that the Q-factor recorded per wavelength in laboratory experiments is the mean Q-factor corresponding to the time-averaged Q-factor. Therefore, in order to demonstrate the industrial feasibility of a transmission system, the

FIGURE 23

Recirculating loop setup.

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minimum mean Q-factor measured over the wavelength range in the laboratory should exhibit about a 2.4-dB margin compared to the industrial Q limit given by the FEC. The 2.4-dB margin corresponds to the industrial impairment not taken into account in the laboratory mean Q-factor measurement: 2:4 dB ¼ 1 dB ðsystem marginÞ þ 1:2 dB ðTVSPÞ þ 0:2 dB ðsupervisory impairmentÞ

In the case where a concatenated code featuring about an 8-dB net coding gain is used in the industrial transmission system, the minimum Q-factor to be demonstrated in the laboratory experiment is about 11.5 dB. The following transmission experiments illustrate the efficiency of the chromatic dispersion map in long-haul 10-Gbps WDM transmission systems carried out over the C-band amplification (1530–1565 nm). 2. Transmission Experiments over NZDSF The transmission experiments detailed in Table III have been carried out on NZDSF. The transmission is carried out on a 513-km long recirculating loop composed of eleven 46.6-km-spaced optical amplifiers (10.25-dB average span loss). The optical amplifier noise figure is 4.5 dB. The amplifier design is based on a 980-nm codirectional-pumping scheme and the amplifier output power is þ15, þ14:5, and þ14 dBm for the 105-, 80-, and 68-wavelength transmission, respectively. Each amplifier includes a fiber Bragg grating that compensates for the nonuniform gain response of the amplifier. This amplifier gain equalization technique is sufficient to guarantee an overall gain excursion lower than 2 dB per loop orbit over 32 nm. One optical gain equalizer is included in the loop to improve the loop gain flatness. As a result, a gain excursion of 6 dB over the 6668-km link is obtained over the 32-nm bandwidth ranging from 1534 to 1566 nm. The optical spectra recorded for the two 80 10-Gbps configurations at the link input and output are depicted in Fig. 24. In the 80 10-Gbps transmission with 0.25-nm wavelength spacing, four loading wavelengths have been placed on the edge of the amplification bandwidth in order to avoid a gain distortion of the amplifier and ASE noise growth. TABLE III NZDSF Capacity (10 Gbps) 68 80 80 105

Transmission Experiments Carried Out on

Length (km)

Wavelength spacing (nm)

8700 6700 6700 6700

0.35 within 1542–1558 nm and 0.6 outside 0.4 0.25 0.3


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FIGURE 24 80 10 Gbps over 6700 km with 0.4- and 0.25-nm wavelength spacing; optical spectrum at the link input and link output.

The mean chromatic dispersion of the NZDSF is 2 ps=nmkm and the chromatic dispersion slope is 0.08 ps=nm2 km. One span consists of NDSF (þ18 ps=nmkm). The loop average zero dispersion wavelength is 1549.8 nm. The transmitter consists of 105 laser sources separated in four groups passing through four modulation chains. Each chain is composed of a return-to-zero (RZ) amplitude modulation followed by a bit-synchronous phase modulation stage. The modulation format is therefore of CRZ type. The data consist of a 10-Gbps 223 1 bit sequence passing through a single Reed–Solomon FEC code, thus leading to a line bit rate of 10.7 Gbps. The Q-factor has been recorded for all wavelengths in the four transmission configurations. Figure 25 gives the minimum, average, and maximum Q-factors. Note that in all cases, the minimum Q-factor is above 11.9 dB, thus demonstrating that these system configurations exhibit sufficient performance margin for an industrial application. From the above figure, it also follows that the reduction of the wavelength spacing leads to a performance degradation: actually, CPM and FWM are enhanced by a wavelength spacing reduction. For example, in the 80 10-Gbps transmission over 6700 km, the reduction from 0.4 to 0.25 nm of the wavelength spacing leads to a 0.5-dB degradation of the average Q-factor. In all cases, the average Q-factor is close or above 12.5 dB, which corresponds to a BER of 1.2E 7 5 and the worst channel performance is a Q-factor of 11.9 dB, which corresponds to a BER of 3E 7 5. When the FEC code is turned on, errorfree behavior is observed (BER < 1E 7 13) on all wavelengths. Note that although a nonnegligible accumulated chromatic dispersion (4300 ps=nm for

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FIGURE 25 Transmission experiments over NZDSF: minimum, average, and maximum Q-factor recorded over the wavelength multiplex for four different transmission configurations.

105 channels and 4900 ps=nm for 68 channels) is experienced by the outer wavelengths, the Q-factor of these wavelengths is not worse than the center wavelengths. In the case of the 68 10-Gbps experiment, the 0.6-nm channel spacing applied to the outer wavelengths has permitted an increase in the phase modulation level, thus reducing the pulse distortion due to the interplay between the chromatic dispersion and the nonlinear dispersion. Figure 26 depicts the typical optical spectrum of a center (left side) and an outer (right side) wavelength, respectively. The broader spectral width observed for the outer wavelength is due to the larger amount of phase modulation applied onto this wavelength to counterbalance the pulse distortion due to the high level of accumulated chromatic dispersion. These experiments demonstrate that high-capacity C-band transmissions such as 105 10 and 68 10 Gbps can be transmitted over long distances (6700 and 8700 km, respectively) with a NZDSF map. The measured Q-factors are compliant with industrial implementation if a FEC code featuring at least 7.5 dB net coding gain is used. This experiment also demonstrates the high efficiency of the CRZ modulation format with NZDSF map. The SNR-based Q-factor calculated for the two transmission experiments is given in Table IV. Therefore, the propagation impairment due to nonlinear effects is 2.6 dB for the 105 10-Gbps, 6700-km experiment and 2.3 dB for the 68 10Gbps, 8700-km experiment. 3. Transmission Experiments with DMF A first study consists of evaluating the benefit of the DMF compared to the NZDSF in the case of the 105 10-Gbps transmission experiment over 6700 km.


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FIGURE 26 Typical optical spectrum of a center wavelength (left side) and an outer wavelength (right side) in a 68 10-Gbps, 8700-km transmission.

Therefore, the 105 10-Gbps transmission experiment has also been carried out over 6700 km of DMF [36]. Each span is composed of a 30-km large core NDSF (110-mm2 effective area) followed by a 15-km RDF (19-mm2 effective area). The mean chromatic dispersion of the NDSF and RDF, respectively, is þ19 and 40 ps=nmkm, respectively, leading to an average chromatic dispersion per span of 2 ps=nmkm. The chromatic dispersion slope of the NDSF=RDF combination is 0.025 ps=nm2 km. One span consists of NDSF (þ18 ps=nmkm) and the loop average zero dispersion wavelength is 1550 nm. The result is that the accumulated chromatic dispersion for each wavelength is divided by four compared to the case of the NZDSF map presented in the previous section. TABLE IV Main Parameters of the 68 3 10-Gbps, 8700-km and the 105 3 10-Gbps, 6700-km Transmission Experiments 105 10 Gbps, 6700 km

68 10 Gbps, 8732 km

Span loss Amplifier count Amplifier noise figure Amplifier output power Wavelength count Pin SNR ¼ kNf hnBopt

10.3 dB 169 4.5 dB þ15 dBm 105

10.3 dB 221 4.5 dB þ14 dBm 68

5.4 dB=nm

5.1 dB=nm

Electrical receiver bandwidth Extinction ratio Optical receiver bandwidth SNR-based Q-factor Minimum measured Q

6 GHz 0.1 30 GHz 14.6 dB 12 dB

6 GHz 0.1 30 GHz 14.3 dB 12 dB

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The Q-factors recorded for all wavelengths before error correction with the DMF are depicted in Fig. 27. For comparison, the Q-factors obtained with the NZDSF are also included in the figure. The average Q-factor is 12.7 dB, which corresponds to a BER of 8E 7 6. The worst channel Q-factor is 11.8 dB with the DMF. When the FEC code is turned on, error-free behavior is observed for all channels. Therefore, we see that the transmission performances with both fiber maps are very similar and, therefore, no performance improvement is observed when replacing the NZDSF with the DMF for 1-Tbps transmission over 6700 km. This can be explained by the two following reasons: First, note that although a nonnegligible accumulated chromatic dispersion (4300 ps=nm) is experienced by the outer wavelengths with the NZDSF, the Q-factor of these wavelengths is not worse than that for the center wavelengths. Therefore, there is no improvement to expect from reducing the accumulated chromatic dispersion. The other reason is the low effective area of the RDF (19 mm2), which drastically reduces the benefit of the 110-mm2 effective area of the NDSF. As a result, the equivalent effective area of the DMF is only 63 mm2, which is close to the NZDSF effective area (57 mm2). It follows that no reduction of the nonlinear interactions is expected when replacing the NZDSF by the DMF. The advantage of the DMF is only to reduce the amount of pre- and postchromatic dispersion compensation to be inserted in the transmit and receive terminal, respectively. A second comparison between the two fiber maps has been carried out for very long distance ( > 8500 km) transmission and for a very broad bandwidth multiplex range (32 nm). The NZDSF system configuration consists of a 52 10Gbps transmission experiment carried out over 8700 km with 0.6-nm wavelength spacing. The DMF system configuration consists of a 80 10-Gbps transmission experiment carried out over 9200 km with a 0.4-nm wavelength spacing. Figure 28 depicts the Q-factor recorded for all wavelengths in the NZDSF configuration.

FIGURE 27 105 10-Gbps transmission over 6700 km. Q-factor obtained with DMF (black circles) and NZDSF (white squares).


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FIGURE 28 Q-factor recorded for a 52 10-Gbps transmission with a 0.6-nm wavelength spacing over 8700 km NZDSF.

This experiment demonstrates the limit of NZDSF when a large amount of accumulated chromatic dispersion is experienced by the outer wavelength of the multiplex. It clearly appears that, with the NZDSF map, the extreme wavelengths suffer from the high level (5600 ps=nm) of accumulated chromatic dispersion at the link output: The Q-factor of channel 1 drops to 11 dB, whereas the Q-factor of the center wavelengths is 14 dB. In contrast, with the DMF, the Q-factor is uniform over the spectral multiplex and ranges from 12 to 13.5 dB. Figure 29 depicts the Q-factor recorded for all wavelengths in the DMF configuration. Note that the Q-factor is above 11.8 dB, thus ensuring sufficient system margin for an industrial application. Although a lower wavelength spacing and a longer transmission length are used, the transmission quality is much better than in the 52 10-Gbps transmission over 8700 km of NZDSF. This experiment

FIGURE 29 Q-factor recorded for an 80 10-Gbps transmission with a 0.4-nm wavelength spacing over 9200 km DMF.

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demonstrates the efficiency of the third-order chromatic dispersion compensation achieved by the combination of NDSF and RDF per amplifier section. Other C-band transmission experiments over DMF have been carried out such as 1 Tbps over 7750 km with a minimum Q-factor of 12 dB and an average Q-factor of 14 dB [37]. A 1.8-Tbps transmission experiment over 7000 km DMF has also been reported. The transmission is error free after error correction but the laboratory experiment does not exhibit sufficient margin for an industrial application [38]. Recently, a 1-Tbps transmission over 9000 km of DMF has been demonstrated with a 3.2-dB system margin [39] including FEC. In summary, the use of a DMF map gives better results than the NZDSF when the accumulated chromatic dispersion experienced by the outer wavelengths of the comb is above 5000 ps=nm. This is the case for 1-Tbps transmission over more than 8000 km.

V. FORWARD ERROR CORRECTING CODES A. Performance Requirement in Submarine Systems The performance requirement for submarine transmission systems is deduced from the G826 ITU recommendation [40]. A new recommendation called G828 is in preparation and is dedicated to synchronous digital paths. The quality of the transmission is assessed through the measurement of two rates: the background block error rate (BBER) and the severely errored second ratio (SESR). A severely errored second is a 1-s period that contains more than 30% errored blocks. An errored block is a block in which one or more bits are in error. A background block error is an errored block not occurring as part of an SES. An errored block (EB) is a block that includes at least one errored bit. According to the G828 recommendation, the number of blocks per second for a 10-Gbps bit rate is 8000. The performance requirements are defined for a 27,500-km digital section called the hypothetical reference path (HRP), as follows: SESR < 2 103

BBER < 103

For a link length below 27,500 km, the calculation has to be done as follows: The terminal should comply with 1% of the above figures. Each portion of 500 km of the link should comply with 1% of the above figures. If the overall percentage is below 6%, then 6% of the above figures have to be met.


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For example, for a 2000-km link, the total percentage is 1% þ 4 1% þ 1% ¼ 6% and the following performances have to be met: SESR < 1:2 104

BBER < 6 105

For an 8000-km link, the total percentage is 1% þ 16 1% þ 1% ¼ 18% and the following performances have to be met: SESR < 3:6 104

BBER < 1:8 104

In addition, submarine system operators usually request a performance 10 times better than the G826 recommendation. Therefore, for a 5000-km link, the performance requirements are typically: SESR < 2:4 105

BBER < 1:2 105

The BBER can be translated in a BER requirement through the following relationship: In the worst case of error distribution, each errored block includes only one error. Therefore, a BBER lower than 1:2 105 is ensured if the BER is below 1:2 105 8000=1010 ¼ 9:6 1012. Typically, the submarine transmission systems are designed to meet a BER lower than 1012 . B. Introduction to Forward Error Correction Forward error correction (channel coding) is a powerful technique for increasing the transmission system margin. For example, with the current FEC used in submarine systems, a BER of lower than 1013 (17.3-dB Q-factor) can be obtained for a BER before correction of only 104, thus providing a 5.8-dB system margin. Figure 30 shows a basic model of a digital transmission system using FEC techniques. The channel encoder introduces, in a controlled manner, some redundancy in the binary information sequence that can be used at the receive side to check and correct errors. More precisely, the channel encoder transforms a sequence of k information symbols into a unique n-symbol sequence, called a code word. The ratio k=n is called the code rate. The inverse of the code rate, namely, n=k, is a measure of the redundancy introduced by the encoding process. Two major types of decoding, hard and soft decision decoding, can be used to recover the information bits at the receive side. In hard decoding strategy, received samples are first compared at the output of the demodulator to the optimal threshold; then, hard decisions are taken and fed to the decoder where the errors are corrected. In the case of soft decoding strategy, the receiver does not take any decision; the received samples are quantized in a q-bit word and then are

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FIGURE 30

Block diagram of a typical digital data transmission using channel coding.

fed to the decoder. The decoder would make use of the information coming from the channel in order to perform better decoding than in the hard decoding case. Soft decision decoding allows an additional coding gain between 2 and 3 dB when compared to hard decision decoding. The theoretical foundations of FEC were introduced by Claude E. Shannon in 1948 in his landmark paper [41]. Most of the theoretical work on coding was done in the 1950s and 1960s where the research on coding was devoted to developing the theory of efficient encoders and decoders. Since the 1970s coding research has shifted from theoretical to practical applications. Recently, useful progress in microelectronics device technology has opened the way for the implementation of a more powerful and complex FEC scheme. Indeed, FEC techniques are widely used today for digital transmissions and data storage systems. FEC was introduced in submarine transmission systems in the early 1990s [42]. This late introduction comes from the fact that fiber optics is one of the most predictable and stable communications channels and allows very good transmission with a very low BER. However, with the explosion in demand for greater submarine transmission capacity, FEC is now a key function for the new generation of DWDM submarine transmission systems in order to achieve highcapacity transoceanic transmissions. The main constraint in submarine transmission systems is the high-bit-rate transmission. As a result, a low-redundancy FEC scheme should be considered (less than 25%). The purpose of this section is to present briefly some FEC schemes used or to be used in submarine transmission systems. For more theoretical detailed aspects, the reader should refer to [43–45].

C. Channel Model and Fundamental Limits Most submarine optical fiber transmission systems are intensity modulation systems with direct detection. It can be represented as OOK (on–off keying) modulation with the particularity that bits 0 and 1 do not have the same noise level. This is due to the predominance of the signal–ASE beat noise, which is larger for bit 1. With hard decision decoding, most of optical fiber channels can


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be modeled as binary symmetrical channels (BSCs; Fig. 31) with a crossover probability of 1 Q p ¼ erfc pffiffiffi 2 2 Shannon demonstrated that by properly encoding the information, we can transmit it reliably over a noisy channel under the condition that R 4 C, where R is the information rate and C the channel capacity. The channel capacity C is the maximum information quantity in bits per symbol that any system can transmit reliably over this channel. In the hard decision case, the capacity of the BSC is well known [44]: Chard ¼ 1 þ p log2 p þ ð1 pÞ log2 ð1 pÞ

ð30Þ

The channel capacity is the absolute performance limit that is very hard to achieve with a real coding scheme. Therefore, a second quantity Ro, called the cutoff rate, is usually used as a performance reference for the efficiency evaluation of any practical FEC coding system. Ro performance is approachable by implementing coding=decoding techniques and recently, coding systems with performance better than Ro have been demonstrated using a sophisticated decoding technique [46]. In hard decision decoding, the cutoff rate of the BSC is: pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi Ro ¼ 1 log2 b1 þ 2 pð1 pÞc ð31Þ

Figure 32 depicts a plot of the capacity and the cutoff rate of the BSC for hard decision decoding as a function of the Q-factor per information bit (Qb ). FEC coding systems should be compared to these curves. If their performance is close to that of Ro , they can be fairly considered to be efficient. For example, for a system designed at 0.8 bits=symbol, say, 25% of redundancy, it will not be possible to achieve error-free transmission with a Qb factor before correction of less than 6.4 dB. For good performance, at a reasonable cost, the system could work at a Qb factor before correction of about 9.5 dB. To achieve the ultimate capacity of most communication systems, soft decision decoding must be used. Soft decision decoding has been widely applied

FIGURE 31

Binary symmetrical channel.

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FIGURE 32

C and Ro of a direct detection optical fiber system using hard decision decoding.

in the wireless communication system since the 1970s. It has been shown that soft decisions can provide up to 3 dB of additional coding gain. In practice, 2 dB of coding gain can be acheived. D. Practical Forward Error Correction Schemes in Submarine Transmission Systems FEC techniques can be classified into two categories: block codes and convolutional codes. In block coding, n k parity check symbols (n > k) are added onto k information symbols to form a code word of n symbols where n stands for code word length and k for the number of information symbols. In convolutional coding [43] the encoding of k information bits generates n binary symbols. One difference compared to the block codes is that each group of n binary symbols from a convolutional encoder is a function of not only the k input bits, but also of the m previous input blocks. The quantity (m þ 1) is called the constraint length of the code. Another difference compared to block codes is that the encoding and decoding of convolutional code are continuously performed. Viterbi decoding [47] is the most popular decoding algorithm for convolutional codes and a common convolutional code using Viterbi decoding is a 12 rate with constraint length equal to 7. However, the implementation of this decoding scheme is too complicated at very high bit rates (10 Gbps) and requires 100% redundancy, which is not acceptable for submarine transmission systems. Puncturing the coded data can reduce the redundancy of 12 rate convolutional code, but in this case the coding gain decreases significantly. For a high-capacity transmission


205

system, block codes are more adapted than convolutional codes and block codes can be divided into the following classes: 1. BCH (Bose–Chaudhuri–Hocquenghem) codes, decodable by the algebraic decoding, including the Reed–Solomon codes (RS) as a nonbinary subclass of the BCH codes 2. Cyclic codes used for error detection 3. Simple codes such as Hamming codes, Reed–Muller codes, etc. The most successful application of block codes is the Reed–Solomon codes, which have been widely used in several applications, including wireless and satellite communications and magnetic and optical recording. The first FEC scheme introduced in a submarine transmission system was the RS(255,239). In fact, RS codes are a good solution for high bit rates due to their nonbinary structures (at each clock top an m-bit symbol is processed by the RS encoder= decoder). Moreover, the RS encoder=decoder implementation can be relatively simple. The RS(255,239) has been adopted by the ITU G975 Recommendation as the standard FEC code for undersea optical fiber transmission systems and is starting also to be a standard for terrestrial optical transmission systems (ITU G709). E. Reed–Solomon Codes RS codes are BCH codes with nonbinary elements belonging to a Galois field GF (q ¼ 2m ). Each q-ary symbol of the Galois field can be mapped to m binary elements. The main parameters of RS code are (n, k, d), where n is the code length, k is the number of information symbols, and d stands for the minimum Hamming distance of the code. For a given redundancy, RS codes offer the largest d because RS codes are maximum distance separable (MDS) codes. The error correcting capability t of an RS code is t ¼ ðn kÞ=2 with d ¼ 2t þ 1. To achieve a high bit rate transmission, parallelism of the codec (encoder or decoder) is needed. MUX and DMUX are used to divide the overall bit rate into substreams, each being encoded and decoded by an elementary codec (Fig. 33). The performance of RS code can be evaluated easily using the following formula [44]: Pb

Ps 2

! n n i 1 P Ps ¼ p ð1 pni s Þ n i¼tþ1 i s m

ps ¼ 1 ð1 pÞ 1 Q p ¼ erfc pffiffiffi 2 2

ð32Þ

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FIGURE 33

Block chart of optical transmission system using FEC.

The transmission channel is supposed to be a memoryless binary channel with an error rate p; ps is the erroneous symbol rate before RS decoding, while Ps and Pb are, respectively, the erroneous symbol rate and the BER after RS decoding. The RS(255,239) adds about 7% of redundancy and can correct up to 8 erroneous symbols from among 255. The net coding gain obtained at 1013 BER after correction is about 5.8 dB. However, this coding gain becomes insufficient for the new generation of submarine transmission systems using 10-Gbps DWDM techniques, which will require a powerful coding scheme in order to achieve a higher capacity transmission. The performance of a single RS code can be improved by increasing the code length n and the error correcting capability t. However, increasing these two parameters (n and t) leads to a highly complex decoder. An easy and simple way to construct powerful codes with low decoding complexity was proposed first by Forney [48] and consists of the concatenation of two or more codes. F. Concatenated Codes Today, concatenated coding schemes are considered to be the best solutions for achieving powerful FEC codes. Concatenation is a specific method of constructing long codes achieving higher net coding gain by associating two or more shorter codes featuring a lower decoding complexity (Fig. 34). In practical applications, the number of codes used in a concatenated coding scheme is limited to two or three. Concatenated codes can be divided into two categories. The first one consists of the serially concatenated FEC codes while the second one concerns FEC codes

FIGURE 34

Transmission system using concatenated codes.


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concatenated in parallel. For serial concatenation, an outer encoder encodes the incoming data first. Then the encoded data (information and redundancy coming from the outer encoder) are interleaved before being encoded by an inner encoder and transmitted through the channel to the receiver. At the receiver end, inner decoding is performed first, and then the decoded data are fed to the outer decoder after de-interleaving. When parallel concatenation is used, after outer encoding the information symbols only are interleaved and encoded by the inner code; then, the information plus redundancy symbols delivered by the two encoders are sent through the channel. Serial concatenation gives the best results in terms of coding gain for a reasonable complexity of the decoder. Interleaving is an important function. The errors at the output of the inner decoder are dispersed uniformly on different code words that could be corrected by the outer decoder. The performance and the complexity of the concatenated coding scheme depend on its elementary codes and the interleaving design. Furthermore, the performance of concatenated codes can be improved by using an iterative decoding algorithm [49]. This technique offers the advantage of increasing the net coding gain without increasing the line bit rate since no modification of the FEC encoder is required. Indeed, after the first decoding process (which means at the output of the outer decoder), the decoded data are reinterleaved and fed again into the dual-stage decoder. The decoding can then be iterated as shown in Fig. 35. Targeting higher net coding gain, a recent study mentioned the combination of concatenated codes with interleaving and iterative decoding based on soft input decoding and soft output decision to achieve a performance very close to the Shannon limit [46, 50, 51]. This coding scheme is commonly called turbo code. For a system requiring a high coding rate of transmission, like submarine transmission systems, block turbo codes (called also turbo product codes) are very attractive.

FIGURE 35

Iterative decoding of concatenated codes.

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G. Turbo Product Codes Product codes are concatenated codes and their concept is very simple as illustrated in Fig. 36. In this figure, a two-dimensional product code P is considered using two block codes C1 and C2 having, respectively, parameters (n1 , k1 , d1 ) and (n2 , k2 , d2 ). The product code P ¼ C1 C2 is obtained by 1. Placing (k1 k2 ) information symbols in an array of k2 rows and k1 columns 2. Coding the k2 rows using code C1 3. Coding the n1 columns using C2 It can be shown that the last (n2 k2 ) rows are code words of C1 and the (n1 k1 ) last columns are code words of C2 by construction. The parameters (n, k, d) of the product code P are obtained by the product of the elementary codes parameters: n ¼ n1 n2 , k ¼ k1 k2 , d ¼ d1 d2 , and the code rate of P is R ¼ R1 R2 . Pyndiah et al. first introduced the turbo product code (TPC) in 1994 [52]. TPC is a product code decoded by an iterative decoding algorithm based on soft decoding of the component codes (rows and columns) and soft output decisions (representing the reliability of the decoded bits). The key success of the turbo codes is the correct combination of the reliability information delivered by the demodulator and the decoder. Several iterative soft input=soft output algorithms for TPC have been proposed [53, 54] and it has been shown that TPCs are very efficient for a high coding rate: More than 10-dB net coding gain could even be expected for submarine transmission [55]. H. Examples of FEC Scheme Performances for Submarine Transmission Systems This subsection is dedicated to experimental and simulation results where three FEC schemes are considered:

FIGURE 36 Construction of product code principle.


209

1. The first one is the standard RS(255,239), which adds about 7% of redundancy. 2. The second one is based on concatenated RS(255,239) þ RS(255,239) codes having 14% of redundancy. This choice is based on the fact that most of the new FEC generation schemes for DWDM submarine systems are based on concatenated RS code. These two codes (standard and concatenated RS codes) use hard decision decoding. 3. The third FEC coding scheme, turbo product code BCH(128,113,6)2, is based on soft input=soft output decoding. The performance of this scheme has been evaluated using unquantized and quantized soft received data from the demodulator. Figure 37 depicts a plot of the BER versus normalized Q-factor per information bit (Qb ) for those different FEC schemes. In this figure, the performance of standard RS(255,239) is given as experimental results while the performances of the RS(255,239) þ RS(255,239) and TPC BCH(128,113,6)2 solutions have been evaluated using Monte Carlo (MC) simulations. Note that it is not possible to process the calculation for a BER after correction lower than 109 because of the length of time required for such a simulation. Nevertheless the extrapolation of the BER curves gives a good estimation for low BER (1013 ), provided that the coding scheme has a lower asymptotically theoretical BER floor. As illustrated in Fig. 37, the RS(255,239) (dotted line) allows a net coding gain of about 5.8 dB at 1013 BER after correction. Concatenated RS(255,239) þ RS(255,239) code exhibits about 1.4- and 2.2-dB additional

FIGURE 37 Performances of FEC solutions for optical submarine transmission system.

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coding gain after one and two iterations, respectively, when compared to the RS(255,239) solution. The TPC BCH(128,113,6)2, after five iterations of decoding, achieves about 10.4- and 10-dB net coding gain when using, respectively, unquantized (optimal case) and quantized received data (4 bits of quantization). This represents up to 4.6-dB additional coding gain when compared to RS(255,239).

VI. TECHNOLOGY EVOLUTION The purpose of this section is to present new technologies that may be able to increase the capacity per fiber above 1 Tbps.

A. Modulation Format In currently designed 10-Gbps WDM systems, the amplitude modulation format is RZ followed by a 10-GHz bit-synchronous phase modulation; this is the socalled CRZ format [56]. The aim of the phase modulation is to compensate for the pulse distortion resulting from the combination of the nonzero accumulated chromatic dispersion (CD) and the nonlinear effects. Indeed, in current installed WDM systems, the transmission is based on NZDSF for which third-order CD is not zero. This means that when the fiber map is designed to nullify periodically (about every 500 km) the accumulated CD for the center wavelength of the comb, the outer wavelengths of the multiplex experience a large amount of accumulated CD at the link output. The amount of phase modulation applied at the transmit side depends therefore on the channel wavelength and on the system length. The drawback of this modulation format is the broad spectral width due to the phase modulation, which limits the spectral efficiency (wavelength spacing=bit rate) to relatively low values. Thanks to the development of the DMF which is third-order CD is close to zero per span, phase modulation is no longer required and other modulation formats such as CS-RZ, SSB-RZ, and simply NRZ enabling higher spectral efficiency can be considered. The CS-RZ (carrier-suppressed RZ) consists of an RZ amplitude modulation stage followed by a 180-deg phase modulation stage. The frequency of the phase modulation is half of the bit-rate clock, thus ensuring that two consecutive bits feature a phase shift of 180-deg. This technique has been tested for 30 20-Gbps WDM 6200km transmission where a 0.6-dB Q-factor improvement has been obtained compared to the standard CRZ format [57]. Other formats such as SSB-RZ (single-sideband RZ) or simply NRZ are now considered good candidates to increase the spectral efficiency. Figure 38 depicts the optical modulation spectrum of the five main formats considered in long-haul submarine transmission systems: NRZ, RZ, CRZ, CS-RZ, and SSB-RZ. It appears that the spectral width observed with the NRZ and SSB-RZ formats is


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about half of the spectral width obtained with a RZ or CS-RZ format. In Fig. 38, the CRZ spectrum is very broad since a 360-deg phase modulation amplitude is applied. The amount of phase modulation required for the outer wavelength transmitted in the 68 10-Gbps experiment carried out over 8700 km of NZDSF was described in a previous section. The NRZ format has been demonstrated as very efficient in 300 10-Gbps, 7380-km transmission experiment with a wavelength spacing of only 25 GHz [58]. A 200 10-Gbps transmission with 20-GHz wavelength spacing over 9000 km has also been demonstrated with a SSB-RZ format [59]. In this experiment, DMF and C-band amplification were used. The implementation of the SSB-RZ format requires the insertion of a narrow optical filtering to suppress half of the RZ modulation spectrum. We found that high spectral stability is requested to avoid any detuning between the channel and the filter wavelength that would lead to transmission impairment. The technology required for the implementation of a NRZ format appears easier to implement and more promising if also ensuring a high level of transmission quality. Note that in the two above-mentioned experiments [58, 59], the worst Q-factor obtained is 8.7 and 9 dB, respectively, which does not demonstrate the industrial feasibility of these transmission systems with such high capacity. However, high margin has been measured on the transmission setup used by Vareille et al. [58] with a lower

FIGURE 38 Optical spectrum of the main modulation formats used in long-haul WDM transmissions: NRZ, RZ, CRZ (with 360-deg phase modulation), CS-RZ, and SSB-RZ.

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FIGURE 39

Recorded Q-factors of a 112 10-Gbps, 6300-km transmission with NRZ format.

capacity. The experiment consists of a 112 10-Gbps transmission experiment over 6300-km DMF using NRZ modulation with a 25-GHz wavelength spacing in the C-band. The Q values recorded over the wavelength multiplex range from 12 to 14 dB (Fig. 39). This experiment demonstrates the industrial feasibility of the NRZ format associated with a DMF map and a 25-GHz wavelength spacing for a 10-Gbps WDM transatlantic system. The reduction of the wavelength spacing also leads to the increase of nonlinear interactions such as CPM and FWM. To reduce these interchannel interactions, one solution is to use the dependence of the CPM and FWM on the state of polarization (SOP) of the interacting wavelengths. Actually, the CPM and the FWM are reduced when the interacting wavelengths feature orthogonal SOP. Thus, CPM and FWM induced impairment can be reduced if the SOPs of two adjacent wavelengths are orthogonal. This is obtained by grouping the odd wavelengths in one SOP and the even wavelengths in the orthogonal SOP, thus leading to interleaved cross-polarization multiplexing. It has been demonstrated that with this terminal configuration, the Q-factor can be increased by about 1 dB compared to the case where all SOPs are parallel [60]. This technique, however, requires that all optical components and fibers in the transmit terminal maintain the wavelength SOP.

B. C 1 L-Band Erbium-Doped Fiber Amplifier To increase the transmission capacity per fiber, one solution consists of doubling the available optical bandwidth by introducing a new amplification spectral range called the L-band (1570–1610 nm) in addition to the current C-band (1530– 1570 nm). This L-band amplification can be obtained with an appropriate design


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of an EDFA. Then, by placing two EDFAs in parallel, one dedicated to the Cband amplification and the other one to L-band amplification, a C þ L-band amplifier is obtained [31]. This C þ L-band amplifier includes an optical demultiplexer (at the input) and an optical multiplexer (at the output) to separate and then recombine the two bands. With this technique, 210 10-Gbps transmission over 7221 km of DMF has been reported [61]. With this very broad bandwidth transmission, DMF is required to avoid the growth of FWM products in the center of the multiplex. Moreover, the DMF map enables the use of the NRZ modulation format, thus opening the door to lower wavelength spacing than with the CRZ modulation format. Through the combination of a DMF map with a NRZ modulation format, a 300 10-Gbps C þ Lband transmission experiment over 7380-km DMF has been demonstrated. The transmitter wavelength multiplex ranges from 1529.94 to 1560.00 nm for the 152 C-band channels and from 1573.92 to 1604.88 nm for the 148 L-band channels (Fig. 40). The 300 wavelengths are combined into 10 different NRZ modulation paths driven by 10 decorrelated data generators: Six modulation paths are used for the C-band and four modulation paths for the L-band. The 527-km-long recirculating loop is composed of 10 fiber sections and 11 C þ L-band EDFAs. The span-averaged second-order chromatic dispersion is 3 ps=nmkm and is compensated in one span to set the loop-averaged dispersion close to zero. The span averaged third-order chromatic dispersion is, respectively, 0.0037 ps= nm2 km for the C-band and 0:0093 ps=nm2 km for the L-band. The C þ Lband EDFA total output power is þ18:5 dBm and the noise figure is lower than 5.7 dB. The average Q-factor has been recorded for all wavelengths. The average Qfactor is 10.2 dB and the worst Q-factor is 8.7 dB (Fig. 41). This experiment demonstrates the capacity of C þ L-band EDFAs to extend the optical bandwidth above 60 nm. In addition, the combination of the NRZ format and the DMF map enables high spectral efficiency (0.4 bit=s=Hz for a 25-GHz wavelength spacing at 10 Gbps) for long-haul transmissions. The SNR-based Q-factor for this transmission experiment is calculated from Table V. From Table V, it follows that the propagation impairment is 3.3 dB for the channel featuring the worst performance. Very recently, the same testbed has been used to increase the capacity up to 365 10 Gbps for a transmission length equal to 6850 km [62]; in this later experiment, the wavelength spacing is reduced to 22.2 GHz. C. Transmission Systems with Distributed Raman Amplifiers Multiwavelength pumped distributed Raman amplifiers (DRAs) can provide broad bandwidth amplification [63] as well as a lower ASE level compared to EDFA-based systems. However, the calculation of the SNR of a system including DRAs should include another noise source called double Rayleigh scattering [64, 65]. In a first step, the SNR calculation is carried out without taking into account

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FIGURE 40

300 10-Gbps, 7380-km transmission experiment: C- and L-band optical spectrum.

FIGURE 41

300 10-Gbps, 7380-km transmission experiment: BER over the wavelength range.


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TABLE V Main Parameters of the 300 3 10-Gbps, 7380-km Transmission Experiment Span loss Amplifier count Amplifier noise figure Amplifier output power Wavelength count

9.9 dB 154 5.7 dB þ18:5 dBm 300

Pin kNf hnBopt SNR including the noise contribution from the transmitter (coupling loss) Electrical receiver bandwidth Optical receiver bandwidth SNR-based calculated Q-factor Worst measured Q-factor

4.0 dB=nm

SNR ¼

3.5 dB=nm 7 GHz 20 GHz 12.0 dB 8.7 dB

the DRS. In a second step, the SNR degradation induced by DRS is evaluated. This degradation actually depends on the signal spectral width and therefore on the modulation format. 1. SNR Calculation without Double Rayleigh Scattering The purpose of this section is to calculate and compare the optical SNR obtained for three types of optical amplified transmission systems:

EDFA transmission system Codirectionally pumped DRA transmission system Contradirectionally pumped DRA transmission system

The SNR of a transmission system is clearly related to the repeater output power, which has a maximum value limited by the transmission impairment due to nonlinear effects. Therefore, to compare the SNR obtained in different system configurations, the calculation has to be carried out with a repeater output power leading to the same amount of nonlinear effects. Because nonlinear effects depend on the optical intensity, the usual parameter used to quantify the nonlinear effects is the path averaged intensity (PAI) defined as ð 1 L Peaz PAI ¼ dz L 0 Aeff where P is the optical amplifier output power per wavelength, L the link length, a the fiber attenuation, and Aeff the fiber effective area. When the fiber effective area and attenuation are constant along the link, PAI ¼ P

1 eal alAeff

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where l is the span length. Note that the higher the fiber effective area, the lower the PAI. From the recent laboratory transmission experiments, it can be deduced that for a transoceanic 10-Gbps WDM transmission system, the PAI leading to the highest Q-factor is 2.8 MW=m2 per wavelength: in other words, for a 64 10Gbps experiment, the optimum EDFA output power is þ13 dBm with a 50-mm2 fiber effective area and a 40-km span length. In Fig. 42, the signal attenuation is 0.2 dB=km, the Raman pump attenuation is 0.24 dB=km, and the EDFA noise figure is 6 dB. In addition, the insertion loss of the passive components (optical multiplexer, isolator, gain flattening filter) included in the DRA is equal to 3 dB. In this section, the SNR calculations are carried out with a fixed PAI of 2.8 MW=m2 per wavelength and the noise calculation only includes the ASE. The line fiber is a DMF composed of two types of fiber per span: the NDSF, which has an effective area of 100 mm2, and the RDF, which has an effective area of 20 mm2. The length ratio NDSF=RDF is 2 : 1 per section. This nonuniform distribution of the effective area along the DMF span will induce a performance difference between contra- and codirectional pumping schemes for the DRA. The optical SNR obtained with an EDFA and contra- and codirectionally pumped DRA versus the span length is depicted in Fig. 42. The results of the calculation show the following:

The best performance is obtained with codirectionally pumped DRA since the SNR remains almost unchanged when the span length ranges from 40 to 100 km, the highest SNR being met for a 70-km span length. Nevertheless, the copumping scheme requires prohibitive pump power for submarine applications (more than 1 W of pump power!), since the pump power is launched into a large fiber effective area (100 mm2). Therefore, practical implementation of DRAs is based on a contradirec-

FIGURE 42

SNR (dB=nm) versus the span length with DMF for EDFA and DRA-based system for co- and contradirectional pumping schemes.


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tional pumping scheme where the pump power is launched into a 20-mm2 fiber effective area. In the case of contradirectionally pumped DRA, the SNR decreases with the span length but less quickly than in the EDFA configuration. The SNR improvement obtained when replacing EDFAs by a contradirectionally pumped DRAs is 1.1 dB for a 40-km span length and 3 dB for a 100-km span length. (The EDFA noise figure in this comparison is equal to 6 dB.) This improvement is reduced, however, by the impact of double Rayleigh scattering as discussed in a later section [66].

Laboratory experiments have been carried out with contradirectional pumped DRA. A 10 10-Gbps transmission over 7000 km [67] and later, a 105 10Gbps WDM transmission experiment in the C-band over 8000 km [68] have demonstrated the feasibility of this DRA technique for long-haul systems. A 32 40-Gbps transmission experiment has been recently demonstrated over 2400-km DMF including contradirectionally pumped DRA [69]. Finally, very recently, 2.4-Tbps (240 10-Gbps) transmission has been carried out over 7400 km with contradirectionally pumped DRAs enabling a 74-nm bandwidth [70]. The BER before correction over the wavelength multiplex ranges from 1:7 103 to 3:6 105 . The span length is 40 km and the modulation format is RZ. Besides the use of either EDFA or DRA, another technique consists of mixing both types of amplification schemes (EDFA and DRA) in each amplifier [25]. This type of hybrid optical amplifier has been used in a C þ L-band transmission experiment featuring an 80-km span length for a total capacity of 210 10-Gbps [61]. The same technique has been employed for a 40 42.7Gbps transmission over 2000 km with a 100-km span length [71]. 2. SNR Degradation Due to Double Rayleigh Scattering The purpose of this section is to evaluate the electrical SNR degradation due to double Rayleigh scattering (DRS) in a contradirectionally pumped DRA based system. The principle of the DRS occurring in a fiber span is depicted in Fig. 43 where Pm is the mean signal power launched into the span, L the span length, gðzÞ the signal variation along the link at the distance z from the span input, and b and b0 are Rayleigh backscatter coefficients at distance z and y, respectively. The backscatter coefficient depends on the fiber type and, in particular, increases when the fiber effective area is reduced. The spectral width of the DRS optical stream is the same as the transmit signal spectral width. As a result, this leads to an electrical beat noise after detection that exhibits a single-sided total bandwidth equal to the signal optical spectral width. This electrical beat noise is proportional to P2 , where P is the signal optical level, and behaves therefore as a relative intensity noise with one feature of providing a BER floor when increasing P to an infinite value. The purpose of the following calculation is to evaluate the electrical SNR degradation

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FIGURE 43

Principle of double Rayleigh scattering.

when including the DRS in the noise calculation. In amplified systems, since both the signal–ASE and signal–DRS beat noises are proportional to the repeater count, the electrical SNR degradation due to the DRS is independent of the repeater count and is given by: N ð33Þ SNR degradation ¼ 10 log 1 þ DRS N ASE where NDRS and NASE are optical spectral densities generated by one repeater section only: ð z¼L ð z gðzÞ2 1 dy dz ð34Þ bb0 NDRS ¼ P 2 m Dn gðyÞ y¼0 z¼0 where Dn is the spectral width of the launched signal and NASE ¼ Nf hn where NF is the DRA noise figure. Therefore, Pm DRS SNR degradation ¼ 10 log 1 þ DnNASE where DRS ¼

ð z¼L ð z z¼0

y¼0

bb0

gðzÞ2 dy dz gðyÞ2

ð35Þ

From the above formula, note that the SNR degradation should not depend on the line bit rate. Indeed, the repeater output power Pm should increase linearly with the bit rate in order to meet the system performance (SNR) requirement. Because Dn also varies obviously linearly with the bit rate, the ratio Pm =Dn should remain unchanged.


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FIGURE 44 SNR degradation due to DRS versus the span length for different modulation formats.

In Fig. 44, the following hypotheses are used: Fiber composed of 23 NDSF þ 13 RDF with 0.2 dB=km fiber loss Rayleigh backscattering coefficient: 5:8 108 =m with the NDSF and 2 107 =m with the RDF Raman gain coefficient: 0.30=(kmW) for the NDSF and 2.8=(kmW) for the RDF DRA passive component loss: 3 dB Path average intensity: 2.78 mW=mm2 Dn ¼ 20 GHz (NRZ), 40 GHz (RZ), 80 GHz (CRZ) Figure 44 depicts the electrical SNR degradation due to DRS with the above hypotheses. In summary, DRS-induced degradation is not negligible for long-haul DRAbased transmission systems and increases with the span length. SNR degradation also increases when the signal spectral width is narrow, which is the case for the modulation format enabling dense wavelength multiplexing. This degradation is, for example, 0.8 dB for a 40-km span length and NRZ format. Because the SNR improvement when replacing EDFA by contradirectionally pumped DRA was only 1.1 dB without including the DRS, we see that there is little benefit, from a SNR point of view, to employing DRA instead of EDFA in submarine systems. D. 40-Gbps Wavelength-Division Multiplexed Transmission Experiments 1. Nonregenerated 40-Gbps Wavelength-Division Multiplexed Transmission One usual way to increase the transmission capacity is to increase the bit rate per wavelength, as demonstrated by the market evolution moving from 2.5- to 10Gbps WDM transmission systems in the recent past few years. It is therefore

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logical to look further in this direction to increase the total transmitted capacity per fiber. Following the trend of the terrestrial network, 40-Gbps WDM transmissions have been studied in research laboratories. Now, if the bit rate is multiplied by four, so too is the noise band of the optical receiver and it then becomes necessary to increase the optical power per channel in the same ratio to keep the SNR unchanged. This means that the nonlinear effects will be intensified and therefore prohibitively degrade the transmission. As a result, the WDM 40Gbps transmission experiments carried out without in-line optical regeneration are limited to medium haul. Recently, a 32 40-Gbps transmission experiment has been achieved over 1704-km dispersion managed fiber [72]. In this experiment, the wavelength spacing is 100 GHz and the modulation chains are composed of a full ETDM (electrical time-domain multiplexing) amplitude modulator fed by NRZ 40-Gbps 29 1 bit sequence. The DMF span length is 45 km and the amplifier output power is þ14 dBm. The average Q-factor is 13.4 dB, which corresponds to a BER of 106 . The worst channel performance is a Q-factor of 12.8 dB, corresponding to a BER of 6 106 . Therefore, the transmission quality exhibits a 1.5-dB margin above the Q limit required with a standard Reed–Solomon correction code. Note also that complex coding schemes leading to higher overhead than 7% [overhead of the standard RS(255,239 code)] and would not be implemented due to the complexity of the electronics at such a bit rate. A 32 40-Gbps transmission over 2400 km has also been recently demonstrated using DRAs [69]. This later experiment has been carried out on a particular fiber map called a TeraLightTM=Reverse TeraLight map. The management of the chromatic dispersion as well as the interest in using Raman amplification in 40-Gbps WDM transmission has been reported by Wabnitz et al. [73]. The TeraLightTM (TL) fiber exhibits a þ8 ps=nmkm chromatic dispersion and the reverse TL features a 16 ps=nmkm while still compensating for the third-order chromatic dispersion of the TL. In the fiber map, the span averaged chromatic dispersion is 0:1 ps=nmkm whereas the loop-averaged dispersion is þ0:07 ps=nmkm. The span length is 40 km. Four Raman pumps are used to provide a 25.6-nm bandwidth and the pump power ranges from 45 to 173 mW. At the transmit side, two independent RZ modulation chains ensure the 40-Gbps modulation of the odd and even channels, respectively. (Orthogonal polarization is ensured between the odd and the even wavelengths.) The BER and the optical spectrum at the link output over the wavelength range are depicted in Fig. 45. The BERs are lower than 2E 7 4, which is the limit to get error-free behavior after correction using a standard single-stage Reed–Solomon (255,239) code. Other WDM 40-Gbps transmission experiments have been reported [71, 74, 75] with the same range of magnitude of the transmission length (1000– 2000 km). Very recently, a 32 40-Gbps transmission over 4500 km has been reported [76]; the modulation format is RZ, the wavelength spacing is 1.15 nm, and the worst Q-factor before correction over the spectral range is equal to 11 dB. This experiment also demonstrates that more than 2 dB of Q-factor degradation is


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FIGURE 45 BER (left side) and optical spectrum (right side) of a 32 40-Gbps, 2400-km transmission with DRAs and TeraLightTM=Reverse TeraLight fiber.

observed when reducing the wavelength spacing to 80 GHz. This illustrates the fact that the spectral efficiency for a medium-haul 40-Gbps WDM system is presently limited to 30%, which is much lower than the value achieved with 10Gbps WDM transmissions. In summary, the reported experiments show that conventional transmission techniques do not enable the propagation of 40-Gbps WDM signals over transoceanic distances with industrial margins. One solution is to consider 20Gbps instead of 40-Gbps WDM transmission [77–80]. Recently, a 6300-km 120 20-Gbps transmission has been reported [81], thus demonstrating that very high capacity based on a 20-Gbps WDM signal can be transmitted over a transatlantic distance. The propagation of a 20-Gbps WDM signal over a transpacific distance has also been considered since a recent 1.12-Tbps (56 20-Gbps) transmission over 9170 km has been reported [82]. The modulation format is RZ and the wavelength spacing is equal to 50 GHz, corresponding to 40% spectral efficiency. The worst Q-factor over the spectral range is 9.2 dB. To perform transoceanic distance transmission in a 40-Gbps WDM configuration, new techniques are being tested in laboratories, such as synchronous optical regeneration.

2. Optical Regeneration in 40-Gbps Wavelength-Division Multiplexed Transmission Indeed, periodic insertion of SM (synchronous modulation)-based modulators along the transmission link provides efficient jitter reduction [83] and limitation of the ASE noise growth. With this technique, it is possible to transmit optical pulses over 1 million kilometers [84]. To reduce the number of modulators in WDM transmission, a single modulator can be shared by several wavelengths. This technique requires that all bits be synchronous with the modulation, and also requests a WDM crosstalk-free modulator [85]. WDM synchronicity can be achieved, for example, by inserting appropriate time-delay lines within the

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DMux=Mux function of the optical regenerator. The 3R regeneration is obtained through synchronous intensity=phase modulation optical narrow-band filtering (NP) [86]. Note that this regenerator scheme only requires narrowband electronics, resulting in significantly lower power consumption compared to full electronic data regeneration. Although regeneration by SM requests nonlinear pulses [87], soliton transmission through the system is not required; in fact, nonsoliton-tosoliton conversion at the regenerator input is achieved through the combination of a high-output-power EDFA followed by a piece of NDSF. This makes it possible to apply the regeneration technique to an RZ data type [88]. A regenerated 10,000-km error-free 4 40-Gbps loop transmission using a Mach–Zehnder modulator based on 3R regeneration has been reported [89] and the 3R regenerator scheme is depicted in Fig. 46. The recirculating loop consists of four spans comprising 40 km of reduced dispersion-slope dispersion-shifted fiber featuring a þ2:25 ps=nmkm chromatic dispersion compensated at 96% by five compensating fiber modules. At the input of the optical regenerator, the WDM channels are demultiplexed and each wavelength passes though a soliton conversion stage followed by narrowband optical filtering. The four WDM channels are then recombined through a 200-GHz multiplexer to be simultaneously fed in the Mach–Zehnder modulator. The modulator is electrically driven by a 40-GHz clock extracted from channel 2 transmitted data. Optical delay lines are inserted to control the optical paths of channels 1, 3, and 4 and hence to ensure that the pulses from all four channels are synchronous with the modulation. The Q-factors for all four channels were measured at higher than 14.5 dB (5 108 BER) for 231 1 bit sequence. This experiment demonstrates the high efficiency of optical 3R regeneration for ultra-long-haul WDM 40-Gbps transmission.

FIGURE 46 3R optical regenerator used in the 4 40-Gbps transmission over 10,000 km.


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VII. CONCLUSION In summary, current WDM submarine transmission systems are designed to offer the maximum capacity with the minimum number of repeaters, knowing that the transmission length can range from 1000 to 9000 km for transpacific links. For that purpose, the following key technologies are employed:

Nonzero-dispersion-shifted fiber for the reduction of nonlinear wavelengths interactions Broad bandwidth optical erbium-doped fiber amplifier chains including optical gain equalizers 10-Gbps chirp return-to-zero modulation Forward error correction codes, which enable up to 8-dB net coding gain with concatenated codes and iterative decoding

With such techniques, 105 10-Gbps transmission over 7000 km or 68 10-Gbps over 9000 km are possible. Larger capacities require new technologies, whose feasibility has been already demonstrated in laboratory experiments:

Dispersion managed fiber composed of reverse dispersion fiber and nondispersion shifted fiber in one span. The purpose of this fiber management is to compensate the chromatic dispersion of all wavelengths at the output of each span. A new optical amplification bandwidth called the L-band (1570–1610 nm) can be added to the current C-band (1530–1570 nm), thus enabling close to a 70-nm amplification range. This has been demonstrated by placing in parallel two EDFAs, one for the C-band and one for the L-band. Other amplifier types based on multiwavelengths pumped Raman amplification are also good candidates for very broad bandwidth amplification. A new modulation format such as nonreturn to zero or single sideband return to zero enable very low wavelength spacing. Spectral efficiencies (channel spacing=bit rate) higher than 0.4 have been reported. New FEC codes based on soft decision coding such as block turbo codes can provide up to 10-dB net coding gain.

Note also that bit rates higher than 10 Gbps such as 20 and 40 Gbps are under study. However, the reported experiments with a 40-Gbps bit rate do not exhibit better performance than 10-Gbps WDM transmission systems due to nonlineareffect-induced degradation. Nevertheless, with the insertion of optical regenerators along the link, a 4 40-Gbps error-free transmission over 10,000 km has been reported. This technology is however not yet mature for practical submerged implementation. A 20-Gbps WDM transmission system could be an alternative but this bit rate is not currently in line with the trend of the terrestrial network. Finally, keep in mind that the final goal of transmission systems is to provide data channels at the lowest cost to the customer. For that purpose, the capacity per fiber has been multiplied by 200 since the first 5-Gbps amplified transatlantic

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transmission system. As a result, the submarine terminal represents the largest part of the total system cost and increasing the capacity per fiber above 1 Tbps raises the issue of the submarine terminal cost reduction.

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6 UNREPEATERED TRANSMISSION E. BRANDON AND J.-P. BLONDEL Alcatel Optics Group, Nozay Cedex, France

I. II. III. IV. V.

INTRODUCTION RECENT DEVELOPMENTS APPLICATIONS SYSTEM CONFIGURATIONS UNREPEATERED SYSTEM TECHNOLOGIES A. Line Fiber B. Postamplification C. Preamplification D. Raman Amplification E. Remote Amplification VI. LIMITATIONS INDUCED BY NONLINEAR EFFECTS A. Stimulated Brillouin Scattering B. Kerr Effect C. Stimulated Raman Scattering VII. POWER BUDGET CALCULATION VIII. MAIN LABORATORY ACHIEVEMENTS IX. INSTALLED UNREPEATERED SYSTEMS A. Deployed Unrepeatered Systems B. Safety Aspects References

I. INTRODUCTION Submarine fiber optic systems are used to create telecommunication backbones with very high capacities per cable. These networks consist of a combination of long-distance repeatered systems and of shorter distance unrepeatered systems. Very long repeatered submarine systems have been discussed in Chapter 5. This kind of system is designed to cross transoceanic distances by means of


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periodical optical amplification. In this chapter, unrepeatered submarine systems, also called repeaterless systems, are described. By definition, unrepeatered systems do not involve in-line repeaters, therefore they do not require electrical power feeding of the cable nor submerged electrically active components. Because of the absence of periodical optical amplification, unrepeatered systems are mainly loss-limited systems, which means achievable spans can be derived most often from cable loss. Typical covered distances are of a few hundred kilometers and may vary significantly depending on the capacity to be transmitted. Section II relates the fantastic capacity growth and the emergence of new techniques in the period covering the 1990s. Network applications and system configurations are described in Sections III and IV, respectively, and available system technologies are detailed in Section V. Usually, unrepeatered systems work at the edge of the optical power limitation induced by nonlinear effects, which are analyzed in Section VI, and power budget calculations are discussed in Section VII. Finally, the main laboratory achievements and already deployed unrepeatered systems are presented in Sections VIII and IX, respectively.

II. RECENT DEVELOPMENTS During the 1990s, progress made in research laboratories and development of new technologies led to fantastic improvements in the field of unrepeatered systems. At the beginning of the 1990s the system capacity obtained in the laboratory went from 622 Mbps to 2.5 Gbps (SDH STM-16 or SONET OC-48). This capacity increased again by a factor of four in the mid-1990s when 10-Gbps component technology reached its maturity. Then, system performances were continuously and rapidly improved thanks to fiber optimization and optical interface improvements. At the beginning of the 2000s, the first long-distance transmissions based on a 40-Gbps channel bit rate were demonstrated in the laboratory and in the field [1, 2]. In the meantime wavelength-division multiplexing (WDM) technology came into force by the mid-1990s. This technology allows for simultaneous transmission in the same optical fiber of several channels, each one at a different wavelength. The first generation of WDM laboratory systems operated with just a few channels, typically eight or less [3–5]. Successive system design improvements, such as fiber mapping optimization or perfecting of the broadband optical amplifiers, allowed us to reduce interactions between the transmitted channels and to extend the available optical bandwidth. It therefore became possible to reduce the wavelength spacing between each channel and to cover wider optical bandwidths. Thus, channel

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counts grew year after year, reaching 80 at the end of the 1990s and covering the conventional 1530- to 1560-nm optical bandwidth [6, 7]. Further extension of the transmission bandwidth has been already demonstrated in the laboratory by means of three adjacent optical bands, each covering more than 30 nm and leading to channel spread over 1495 to 1600 nm [8]. The fantastic growth in transmission capacity obtained in laboratory demonstrations is summarized in Fig. 1 for the 1991–2001 decade. During this period, three bit-rate generations combined with the introduction of WDM technique allowed progress from 2.5 Gbps toward 10 Tbps per fiber pair, as detailed in Section VIII. The network capacity is also directly proportional to the fiber count. In the early 1990s, unrepeatered cables were typically designed to support 12 fibers at maximum and the capacity was mainly achieved by the extensive use of high-bitrate terminal equipment. Gradually, with increasing capacity demand, the need for more fibers emerged in order to carry the continuously growing amount of traffic. Thus, 48-fiber submarine cables had been deployed all around the world by the mid-1990s. An additional demand coming from new players in the unrepeatered area was observed at the end of the same decade. This demand comes from companies that are carriers’ carriers and their core business is to sell installed fibers to other companies. This further increased the fiber count demand for repeaterless submarine cables and since then, cables incorporating 192 fibers have been developed and deployed [9]. Increases in transmission capacity are led by market requirements and are mainly a result of the increase in Internet traffic. There are no signs to predict a slowdown of this capacity growth in the near future.

FIGURE 1

Evolution of capacity during 1991–2001.

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For years, another research direction has been to look at an increase in the achievable distance between the terminal equipment. Improvement of the capacity together with the distance to be covered is somewhat contradictory for unrepeatered systems because they are loss-limited systems. Both parameters are strongly linked and when one is increased, the second must logically be reduced to keep constant the system performance. For repeaterless systems, the relevant performance parameter is given by the sum of the link budget and of the logarithm of the capacity transported, as defined in Eq. (1). System performance parameter ¼ Link budget þ 10 logðCapacityÞ

ð1Þ

where the system performance parameter and the link budget are expressed in decibels and capacity is expressed in gigabits per second. We can deduce from Eq. (1) that doubling the capacity can be obtained by a 3-dB reduction of the link budget without a significant increase in transmission difficulty. Figure 2 plots the system performance parameter of laboratory records obtained over the 1991–2001 decade. From these data, we first observe a considerable improvement of about 40 dB in system performance during this 10-year period. Increase in the distance can be explained by the following technical advances: —The incredible progress in optical amplifier development. The output power of optical amplifiers has been considerably increased thanks to more and more powerful semiconductor laser diodes, which pump an erbium-doped fiber [10]. With the introduction of wavelength and polar-

FIGURE 2 Evolution of the system performance parameters during 1991–2001.


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ization multiplexing, it was possible to combine several diodes and to reach output powers of a few hundred milliwatts. The next step came with fiber lasers that are likely to deliver unlimited power. These lasers are based on a multitude of 980-nm multimode semiconductor diodes that pump a ytterbium fiber laser. The 1.06-mm beam coming out is converted into 1.48 mm owing to successive wavelength conversions induced by the Raman effect in a dedicated fiber. By amplifying the incoming signal, it is possible to reach several watts of output power at 1.55 mm thanks to the high output power of multimode diodes and to the high efficiency of Raman conversion. —The introduction of forward error correction (FEC). This feature consists of adding some information to the transmitted digital signal and using this information to correct errors in the received signal. In submarine systems, error can be created by a degradation of the optical signal-to-noise (SNR) ratio along the link, or by transmission impairments induced by linear effects such as polarization mode dispersion. In addition, nonlinear effects occurring when large powers are transmitted can strongly affect the system performance, especially for point-to-point repeaterless systems. Introduction of FEC in submarine networks has considerably improved the tolerance to these effects and link budgets are increased by about 7 dB using the 239=255 Reed–Solomon code, which is already implemented in industrial STM-16 and STM-64 systems [11]. The first unrepeatered laboratory experiments using this FEC code were reported in 1992 at 2.5 Gbps [12] and in 1999 at 10 Gbps [13]. —The introduction of remote optically pumped amplifiers (ROPAs). Remote amplification consists of pumping from one end of the link a piece of erbium-doped fiber inserted into the line fiber. The piece of erbium can be located either near the receiving side or near the transmitting side, or both, at a few tens of kilometers away from one end in each case. Pumping can be done through the line fiber itself or through a dedicated fiber within the same cable. Despite the presence of optical in-line amplifiers, systems using this scheme are still considered to be unrepeatered, due to the fact that this technique does not involve active electrical components. Early use of a remote amplifier in a laboratory record experiment at 1.8 Gbps was reported in 1989 [14], while the first implementation in an installed system at 2.5 Gbps occurred in 1995 with the RIOJA system. Since then, the distance between the ROPA and the end of the link has been increased year after year thanks to progress made in laser sources at 1.48 mm. With the introduction of fiber lasers based on Raman wavelength conversion, pumps with output powers in excess of 1 W have been implemented either in laboratory experiments or in industrial systems, allowing remote amplifiers to be located more than 100 km away from the terminal equipment. An additional improvement of the distance between the ROPA and the terminal has been obtained by an in-line filtering technique

234


[15, 16], which consists of placing some optical filters along the pump in order to cancel the wavelength conversion due to Raman effect in the line fiber. Using this technique, the pump power launched into the pumping fiber can be significantly increased, therefore allowing us to extend the distance between the ROPA and the terminal equipment. —The introduction of Raman amplification. When a signal beam is sent to the optical fiber, molecular vibrations of the medium induce a Stokes wave and amplification at longer wavelengths. A Raman effect occurs in any optical fiber and the maximum of amplification is observed for a shift of 440 cm1 , corresponding to an approximate 100-nm shift in the 1.5-mm transmission window. Despite the Raman effect having been studied for several decades since the early 1960s, the first laboratory experiments reporting its use for long unrepeatered transmissions were published in 1996 [3, 17]. This corresponds to the introduction of pump lasers with an output power in excess of 300 mW, which is the minimal power required to benefit from Raman amplification in standard fibers. With the perfection of fiber lasers and with the availability of large amounts of power, unrepeatered systems benefited greatly from this amplification scheme. The first industrial implementation of the Raman amplification technique was realized in early 2000, in the Hydro-Quebec cable system. One common aspect between the technical advances that allowed for strong capacity growth together with significant improvements in the link length is that each of them was implemented in a deployed network only a few years after its discovery in the laboratory. For instance, the first use of a ROPA in a laboratory record was reported in 1992, and the first submerged ROPA was laid in 1995. The same kind of delay applies to FEC, WDM technology, Raman amplification, and bit-rate increases. To illustrate this, Table I presents the major laboratory achievements together with some details on typical repeaterless submarine systems already installed. TABLE I Major Laboratory Achievements and Representative Unrepeatered Systems Already Installed Laboratory unrepeatered demonstrations

Installed unrepeatered systems

Length (km)

Capacity

Year

Name

Capacity

Installation

531 529 427 357 450 350 230

622 Mbps 2.5 Gbps 16 2:5 Gbps 8 10 Gbps 32 10 Gbps 100 10 Gbps 64 40 Gbps

1994 1995 1995 1995 1999 2000 2001

Germany-Sweden 4&5 RIOJA Alaska United Rembrandt Korea Domestic Cook Straight Pangea

622 Mbps 2.5 Gbps 4 2:5 Gbps 16 2:5 Gbps 32 2:5 Gbps 16 10 Gbps 32 10 Gbps

1993 1995 1999 1999 2000 2000 2000


235

III. APPLICATIONS Unrepeatered submarine systems can cover a significant range of network applications as depicted in Fig. 3. In addition to the obvious applications such as linking an island to the mainland (Fig. 3a) or a group of islands (Fig. 3b), repeaterless systems are very popular in coastal festoons (Fig. 3c). The reason is that in most of the world, population centers are located near to the ocean, often at the end of historical maritime trade routes. Many of these cities are within the range of unrepeatered spans and many are being linked using either a point-topoint cable or a coastal festoon. For this latter application, the telecommunication system can cover distances of several thousands of kilometers with a few regenerating stations where regional or domestic traffic is potentially added or dropped. In that case, submarine systems lead to fewer problems with civil works and rights of way than terrestrial cable systems, therefore resulting in short and cost-effective implementation. Undersea repeaterless systems can also be used in combination with very long-haul submarine systems to increase the network connectivity or to offer traffic protection. Figure 3d represents some unrepeatered links used to complete a long-haul repeatered network. Typical distances are a few hundred kilometers

FIGURE 3 Network applications offered by unrepeatered submarine systems.

236


for unrepeatered links and several thousand kilometers for the long haul. The flexibility of repeaterless systems allows these different cities to be linked with the capacity required by the customer—either a regional traffic capacity or the long-haul network total capacity. The same kind of mixing can be realized with terrestrial networks, where unrepeatered submarine links permit the crossing of wet sections (Fig. 3e). The benefits of repeaterless systems are not limited to the large capacity or to the high connectivity they can provide. They can also be very attractive from a cost viewpoint compared to long-haul repeatered systems. Indeed, for short distances unrepeatered systems use standard transmission techniques and lowcost terminal equipment. However, they require the most advanced technologies in optical amplification and transmission for significantly long distances. From this, it turns out that the cost of repeaterless submarine systems grows very quickly with distance, while in long-haul systems the cost increases nearly linearly. Depending on the capacity to be transmitted, the crossing point between the cost of both kinds of systems is in the range 300–400 kilometers. In practice, already installed unrepeatered systems are shorter than this limit, and are significantly cheaper than long-haul systems since they do not involve the ultimate technology.

IV. SYSTEM CONFIGURATIONS Typical configurations of repeaterless system are depicted in Fig. 4 versus the length of the link. Each step corresponds to an improvement of the transmission distance while increasing the complexity of the system. Associated technologies are detailed in Section V. Obviously, achievable spans depend on the fiber type, on the system capacity, and on the system margin required for aging and repairs.

FIGURE 4 Unrepeatered system configurations.


237

The first configuration is composed of a submarine terminal that includes forward error correction, which allows the system to operate virtually error free, postamplification to increase the signal power and preamplification to improve the system sensitivity (Fig. 4a). In that case, the span limit is determined by the power launched into the fiber and by the system sensitivity. The submarine terminal is usually associated with add and drop multiplexers (ADM), which are used to distribute the traffic toward complementary transmission equipment. To extend the distance, an optical pump power is launched into the line from the receiving side to provide Raman distributed preamplification (Fig. 4b). That allows us to increase by about 35 km the span length of the first configuration. It is also possible to implement this pump source after the installation of the system to make possible a WDM upgrade or a bit-rate improvement. In the third configuration (Fig. 4c), a piece of erbium-doped fiber is inserted into the cable, which allows for an increase in the span length by about 90 km with respect to the first configuration. As explained in Section II, this is still considered to be a repeaterless system because the ROPA is activated from the receiving terminal and does not require electrical power-feeding as opposed to conventional repeaters. Pumping of the erbium-doped fiber can be done through the line fiber itself or can involve an additional fiber in the same cable, thus increasing the potential pump power and the ROPA efficiency. The final step is represented in the last configuration (Fig. 4d) where a remote postamplifier is introduced into the line. In this case, the remote postamplifier acts as a second booster and allows the power of the first booster to be relaxed, therefore reducing the nonlinear effect of impairments. Typical commercial spans for each configuration are given in Table II versus the system capacity, taking into account 4-dB standard margins allocated to system aging and cable repairs. It also assumes the use of G.654 pure silica core fiber, which is beneficial to reach long distances thanks to its low loss.

V. UNREPEATERED SYSTEM TECHNOLOGIES The following sections describe the technologies used in unrepeatered systems to improve the transmission distance between two regenerating points. Despite the TABLE II

Typical Commercial Spans for Unrepeatered Systems

Configuration

1 2:5 Gbps (km)

8 2:5 Gbps (km)

32 2:5 Gbps (km)

80 2:5 Gbps (km)

8 10 Gbps (km)

32 10 Gbps (km)

80 10 Gbps (km)

a b c d

315 345 390 435

280 315 360 375

250 285 330 340

215 250 280 290

240 275 315 345

225 260 300 315

195 230 255 265

238


continuous progress being obtained in the laboratory, these technologies encounter physical limitations due to linear and nonlinear impairments that occur during the transmission of the signal through the optical fiber. Limitations due to these impairments will be discussed in Section VI.

A. Line Fiber Due to their loss-limited characteristic, attenuation of the line fiber is of first importance for unrepeatered systems, because it determines the maximum transmission distance. For that reason, standard fiber (NDSF for nondispersionshifted fiber) and pure silica core fiber (PSCF) are the preferred fibers for longdistance repeaterless systems. For moderate distances, however, dispersionshifted fiber (DSF) and non-zero dispersion-shifted fiber can also be employed but these fibers will reduce the possibility of a WDM upgrade due to their low chromatic dispersion. Indeed, the WDM nonlinear effect threshold is lower for moderate chromatic dispersion than for large dispersion as explained in Section VI. Therefore, it is beneficial to propagate the signals over a large local dispersion even if this dispersion induces the broadening of the channel optical spectrum. As a matter of fact, chromatic dispersion of NDSF and of PSCF can be supported for 2.5-Gbps signals over distances in excess of 500 km. For 10-Gbps or higher bitrate signals however, the line chromatic dispersion must be compensated in the receiving or transmitting terminal. This can be realized by dispersion compensating fiber or Bragg gratings, and very long distances can be achieved without experiencing a significant transmission penalty. Also preponderant is the effective core area of the fiber. As indicated in Table III, NDSF and PSCF have a larger effective area than DSF, which allows for a reduction in the impact of nonlinear effects, whose threshold is proportional to the inverse of the effective core area. Transmission experiments over 115- and 170-mm2 effective core area fibers have already demonstrated the benefit of a TABLE III Characteristics of Most Representative Line Fibers Parameter ITU standard Loss at 1550 nm Zero-dispersion wavelength Chromatic dispersion at 1550 nm Effective core area

Symbol Unit

NDSF DSF

PSCF NZDSF NZDSFþ NZDSFþþ

a

dB=km

G.652 G.653 0.2 0.21

G.654 G.655 0.18 0.21

l0

nm

1310

D

ps=nm=km þ17

Aeff

mm

G.655 0.21

G.655.B 0.21

1530–1570 1300 1560–1590 1470–1515 1420 0

75–80 50

þ18

2

75–80 55

þ4

þ8

55–70

65


239

large core, allowing a significant increase in the launched signal power with respect to standard fibers [7, 18].

B. Postamplification Postamplification is the simplest application of optical amplifiers in repeaterless systems. The principle is depicted in Fig. 5a: The transmitter source, which carries the information, has a typical output power of 0 dBm (1 mW). Insertion of an erbium-doped fiber amplifier (EDFA) between the transmitter and the line fiber allows the signal to be amplified by several orders of magnitude. This principle applies to single-wavelength transmitters as well as WDM transmitters owing to the use of wavelength multiplexers before amplification. The use of 1.48-mm semiconductor diodes to activate the erbium-doped fiber makes possible output powers of more than 20 dBm (100 mW). Taking advantage of the 1.48-mm high-power laser sources that use a Raman effect, the postamplifier output power can reach several watts. The same kind of power can be obtained from erbium fiber with a ytterbium co-dopant that can be activated with 0.975-mm semiconductor diodes [10]. Erbium-doped fiber amplifiers can also deliver power of several watts when based on a double-clad structure. In this approach, the pump power of multimode diodes is launched into a multimode guide around the erbium-doped guide where signals are traveling. This allows for high power levels and also high reliability if redundant semiconductor pumps are implemented.

FIGURE 5

Principle of (a) postamplification and (b) preamplification.

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Owing to the significantly high signal power at its input, the optical SNR at the postamplifier output is high enough to neglect the noise penalty on the receiver. In addition, the postamplifier does not cause any distortion of the highfrequency signal because of the slow response time of the saturation mechanism of the erbium-doped fiber. Therefore, the gain of the postamplifier can be considered to be a net gain on the link budget. For example, a system using a 20-dB gain amplifier at the transmitting side can cover a link loss 20 dB higher than a system without a postamplifier. Actually, achievable output powers of optical postamplifiers are limited by nonlinear effects that occur during the transmission of the signal over the line fiber. Nonlinear transmission impairments can be divided into three categories: (1) Brillouin effect, (2) Kerr effect, and (3) Raman effect. Due to these effects, which are described in Section VI, only a few unrepeatered experiments have demonstrated launch powers in excess of 1 W or so [4, 5, 19, 20]. C. Preamplification Preamplification of the signal is a technique that is used in all modern unrepeatered systems. Practical implementation is shown in Fig. 5b for singlechannel and WDM applications. The aim of the preamplifier is to provide optical gain to the signal prior to photodetection in order to change the balance of receiver noise terms. At the preamplifier output, the optical SNR can be expressed by the following relation: OSNR ¼ where

2 G2 Pin Nth þ hn NF Bo G2 Pin

ð2Þ

G ¼ amplifier gain Pin ¼ signal power at the input of the amplifier Nth ¼ receiver thermal noise hn ¼ photon energy NF¼ preamplifier noise figure Bo ¼ optical bandwidth considered When the receiver thermal noise (Nth ) becomes negligible compared to the signal-spontaneous beat noise (hn NF Bo G2 Pin ) generated by the amplifier, the receiver reaches a greatly improved sensitivity. To achieve this mode of operation, a high optical gain (typically in excess of 25 dB) and a narrow optical filter (typically 3 to 4 times the bit rate) are required. Then, the preamplified receiver sensitivity, that is, the power Pin to obtain a given bit error ratio, is only determined by the amplifier noise figure: 2nsp NF ¼ ð3Þ C1 where nsp is the amplifier inversion factor, and C1 is the amplifier input loss.


241

Compared to a standard avalanche photodiode (APD) receiver, a typical sensitivity improvement of 10 dB can be obtained with preamplified receivers. In the case of WDM systems, this power budget gain applies to each channel. D. Raman Amplification The Raman effect occurs in any optical fiber and can be described as follows: When a signal beam is sent into the optical fiber, molecular vibrations of the medium induce a Stokes wave and amplification at longer wavelengths. The maximum of amplification occurs for a shift of 440 cm1 , which corresponds to about 100 nm in the 1.5-mm wavelength range. Figure 6 shows the Raman gain spectrum obtained with a pump at 1455 nm launched into pure silica fiber. For this pump wavelength, the maximum gain is obtained for signals in the 1550- to 1560-nm range. For single-span optical communications, Raman amplification is usually implemented in the following way: A signal is launched at the point z ¼ 0 of the fiber section of length L and the pump is sent from the end of this section, that is, from the point z ¼ L. Equation (4) represents the way the signal grows in the medium: The first term is relative to the Raman amplification and the second term refers to the fiber loss. For a given fiber type, the power transferred to the amplified signal is proportional to the pump and also to the signal. As a consequence, the Raman gain grows exponentially with the pump power. In addition, the energy transferred from pump to signal is proportional to the pump and also to the Raman gain coefficient CR . Since the pump power and this coefficient play the same role

FIGURE 6 fiber.

Raman gain spectrum obtained with a 1455-nm pump launched into pure silica core

242


in the equation, this means that a relevant parameter for Raman efficiency is the product of the pump by the Raman gain coefficient. Pump evolution along the fiber is described by Eq. (5). In this equation, the first term depicts pump depletion by signal while the second term refers to the fiber loss. Note that the pump grows from z ¼ 0 to z ¼ L because it is counterpropagative. Equation (6) represents the noise evolution along the fiber section. There, the noise is amplified by Raman effect as described by the first term and attenuated in the fiber as depicted by the second term. Third part of Eq. (6) is relative to the quantum noise generated by the Raman amplifier, which may take into account a thermal effect. dIs ¼ CR Is Ip as Is dz dIp ls ¼ C I s I p þ ap I p dz lp R dN ¼ CR Ip N as N þ 2hn CR Ip dz

ð4Þ ð5Þ ð6Þ

where Is ¼ signal intensity Ip ¼ pump intensity N ¼ noise intensity CR ¼ Raman gain coefficient as ¼ fiber loss at signal wavelength ap ¼ fiber loss at pump wavelength ls ¼ signal wavelength lp ¼ pump wavelength n ¼ signal frequency Equations (4), (5), and (6) can be easily solved analytically assuming that pump depletion by the signal is neglected, which can be done because the signal and pump powers are usually not of the same order of magnitude. Solutions are given by the following formulas: Ip ðzÞ ¼ Ip ðLÞ expbap ðz LÞc " # ! 1 eap z Is ðzÞ ¼ Is ð0Þ exp CR Ip ðzÞ as z ap

ð7Þ ð8Þ

From Eq. (8), it is possible to calculate the on=off Raman gain on a signal at the end of the fiber section: ! 1 eap L on=off GRaman ¼ CR Ip ðLÞ ð9Þ ap


243

For silica-based fibers, the Raman gain coefficient depends mainly on the effective core area. It also depends slightly on the medium chemical composition, and fibers with a germanium-doped core, such as NZDSF or DSF have a higher Raman gain coefficient than PSCFs. In addition, fibers with a smaller effective area, such as NZDSF or DSF (about 50 mm2 against 80 mm2 for PSCF) also have a larger coefficient. Typical values for the Raman gain coefficient are given in Table IV for commonly used fibers. According to these values and as explained above, what happens in PSCF for a given pump power happens in DSF for almost half of this pump power. Unrepeatered systems can benefit from distributed Raman amplification that is realized either at the transmitting end or the receiving end. Interest in Raman amplification at the transmitting side (postamplification) is very low [21] because large power boosters are already available that reach the power limitation due to nonlinear interactions as explained in Section V.B. However, a significant power budget improvement can be expected with Raman preamplification, where the pump beam is multiplexed to the signal at the receive end of the unrepeatered system. In such a configuration, signal and pump are counterpropagative, which prevents noise copying from the pump to the signal. Figure 7 shows the Raman gain and the system power budget improvement given by Raman preamplification versus the launched pump power for the pure silica core fiber case. The Raman gain grows exponentially with pump as explained previously. The evolution of the power budget improvement is different: For a small launch pump power, the Raman gain is not sufficient to mask the multiplexer unit loss and the power budget improvement is low. However, for large pump powers, the power budget improvement (in decibels) grows linearly versus the pump power (in dBm) and with a slope equal to the ratio between the signal loss and the pump loss (around 0.85 for PSCF). This evolution of the power budget improvement versus the pump power can be explained as follows: Let us consider the Raman preamplifier to be equivalent to a preamplifier that extends from the terminal to a point where the remaining pump is just enough to create some gain. When the launched pump power is increased by X dB, this reference point is shifted by a distance equal to X dB divided by the pump loss (ap ). Then, the power budget improvement equals this distance multiplied by the signal loss (as ). Therefore, the improvement slope of the power budget in decibels versus pump increase in decibels is as =ap . TABLE IV Raman Gain Coefficient for Various Fiber Types Fiber type PSCF NDSF DSF

CR coefficient (m1 W1 ) 0:37 103 0:38 103 0:6 103

244


FIGURE 7

Raman gain and power budget improvement versus pump power.

Increasing the pump power is therefore of interest for the optical power budget of unrepeatered systems. However, the maximum pump power that can be launched in the line is limited by the combination of the Raman gain and of the intrinsic Rayleigh backscattering of the line fiber. Indeed, when increasing the Raman gain, double Rayleigh scattering causes some transmission impairments and induces a sensitivity penalty on the receiver. To illustrate this phenomenon, the Raman amplifier can be considered as a discrete amplifier of gain G and length L, and composed of two mirrors having a reflectance equal to the Rayleigh backscattering coefficient of the line fiber R. At the output of the amplifier, the signal power is: Pout ¼ G Pin þ G3 R2 Pin þ G5 R3 Pin þ

ð10Þ

The second term, called double Rayleigh scattering (DRS), is time delayed with respect to the first term due to its longer time of propagation through the fiber. As a result, the superposition of the main signal and of the double scattered signal at the receiver input creates a penalty on the system sensitivity. This penalty increases as the Raman gain of the amplifier increases, up to a point where the system can oscillate if the condition G R 1 is satisfied. For silica-based fibers, the Rayleigh scattering coefficient is of about 32 dB and the oscillation condition occurs for a pump power of 1.3 W in the case of


245

PSCF. The penalty due to DRS can be observed for Raman gain in excess of 25 dB, which corresponds to more than 1 W of pump power launched into the PSCF. When combined with local preamplification, the resulting optical SNR with distributed Raman preamplification is given by Eq. (11): 1 hn NFRaman Bo hn NFEDFA Bo ¼ þ Pin Pin GRaman A OSNR

ð11Þ

where A ¼ loss of the section where Raman amplification occurs (typically 50 km) Pin ¼ power at the input of the above mentioned section NRRaman ¼ noise figure of the distributed Raman amplifier GRaman ¼ gain of the distributed Raman amplifier NFEDFA ¼ noise figure of the local preamplifier Figure 8 presents experimental results obtained over PSCF for various pump powers in a Raman preamplification configuration. Bit error rate (BER) curves are plotted versus the 2.5-Gbps single-channel power reaching the local preamplifier which has a noise figure of 4 dB. When there is no pumping (0 mW), the curve corresponds to a baseline sensitivity plotted at the input of the preamplifier. When pump is launched, the BER is plotted versus the power that would reach the preamplifier if the pump was off. Therefore, the sensitivity read on the graph represents the baseline sensitivity improved by the power budget increase. At the nominal pump power of 1.1 W, which gives some margin with respect to the

FIGURE 8

Experimental power budget improvement with Raman preamplification.

246


1.3-W limit, the practical power budget improvement is about 7 dB. This corresponds to 35- to 40-km distance increase with conventional PSCF attenuation. The Raman preamplification principle can be applied to broadband WDM systems owing to the use of several pump sources, each at a different wavelength. In the transmission experiment from Boubal et al. [8], a mean Raman gain of 25 dB has been demonstrated over a seamless total bandwidth of 104 nm (1492– 1596 nm) with four pump sources, respectively, at 1390, 1425, 1455, and 1485 nm.

E. Remote Amplification Remote amplification consists of pumping a piece of erbium-doped fiber inserted into the line fiber and located a few tens of kilometers from the terminal equipment. To maintain the ‘‘unrepeatered’’ quality of the system, which means ‘‘no electrically active element underwater,’’ the pumping source is placed in the terminal station, either at the transmitting end, receiving end, or both. The higher the pump power, the further the amplifier can be placed while still featuring sufficiently high gain and low noise. However, as for the Raman amplification technique, the pump power launched into the fiber is limited by the double Rayleigh scattering effect, which induces laser oscillation when the Raman gain generated by the pump is greater than the Rayleigh backscattering coefficient. An oscillation condition occurs for a pump power of 1.3 W in the case of PSCF, and typical 1-W powers are used in systems to allow some margin on pump power fluctuation over the lifetime of the transmission system. The erbium-doped fiber can be activated by a pump wavelength of 980 or 1480 nm but only the second one is used in repeaterless systems due to the lower fiber loss at 1.48 mm with respect to the loss at 0.98 mm. This allows the distance between the terminal and the remote amplifier to be increased. To further increase this distance, it is possible to implement the following techniques which are depicted in Fig. 9: —Use of pump reflectors inside the ROPA. Such components allow a double pass of the residual pump power that is not absorbed into the erbiumdoped fiber. This slightly improves the gain and the noise figure of the ROPA, provided the insertion loss of the pump reflector is low enough. —Use of an additional dedicated pumping fiber. This allows more pump power to be provided to the remote amplifier thanks to a second pump source. The dedicated fiber is then combined with the main fiber thanks to a WDM signal and pump coupler located inside the ROPA box. This principle allows us to nearly double the pump power into the erbiumdoped fiber and therefore leads to higher gain and lower noise figure, which significantly improves system performance. However, this requires more fibers in the cable and increases the cost of the system.


Possible implementation of remote optically pumped amplifiers.

247

FIGURE 9

248


—Use of an in-line filtering technique. This principle, which was demonstrated in 1999 [15], applies only to the dedicated pumping fibers and allows us to exceed the launch power limitation induced by the Raman effect. The aim of this technique is to reduce the Raman gain generated at 1580 nm by the pump. This can be done by inserting wavelength-selective filters or WDM couplers at relevant locations in the pumping fiber, these components having a large attenuation at 1580 nm and a low insertion loss at pump wavelength. A typical distance improvement of 20 km can be obtained as a result of this technique. In most of the unrepeatered systems already deployed with that technology, remote amplification is provided from the receiving end only. The reason is that remote preamplification provides larger budget improvements than remote postamplification due to the availability of high-power local postamplifiers. The power budget improvement obtained using the remote preamplifier, with respect to the one achieved with local preamplification, is defined as follows: Budget improvement ¼ ðS 0 R0 þ D as Þ ðS 0 RÞ ¼ D as þ R R0 ð12Þ where S 0 ¼ launched power R ¼ local preamplifier sensitivity R0 ¼ remote preamplifier sensitivity D ¼ distance between the ROPA and the local preamplifier as ¼ fiber loss of the remote section at signal wavelength Sensitivity at the input of the remote amplifier can be obtained from the calculation of the optical SNR resulting from the cascade of remote amplification, Raman amplification and local amplification [22]. The contribution of each amplification scheme is developed in Eq. (13): 1 hn NFROPA Bo hn NFRaman Bo ¼ þ Pin ROPA Pin ROPA GROPA OSNR þ

hn NFEDFA Bo Pin ROPA GROPA GRaman A

ð13Þ

where Pin ROPA ¼ power at the input of the ROPA NFROPA ¼ noise figure of the ROPA GROPA ¼ gain of the ROPA A ¼ loss of the remote section

In practice, the sensitivities R and R0 are close together and the power budget improvement is close to the line fiber loss of the remote section (the section between the receiving terminal and the remote amplifier). Figure 10 presents the


249

FIGURE 10

Experimental budget improvement obtained with the remote preamplification technique versus the length of the remote section. The dashed curve represents the budget gain obtained for the 1.5-dB repair margin allocated in the remote section.

budget improvement versus the remote section length D obtained over pure silica core fiber. This simulation result assumes a fiber loss of 0.18 dB=km, a local preamplifier noise figure of 6 dB, and an optimum pump power launched toward the ROPA of 1 W. This typical example shows the influence of repair margin, 1.5 dB in this practical example. The potential degradation induced by cable repairs must be taken into account in the design of the system, because it yields a different optimum distance between the ROPA and the terminal. VI. LIMITATIONS INDUCED BY NONLINEAR EFFECTS Above a given optical power threshold, physical properties of optical fibers can be modified due to nonlinear effects occurring during beam propagation [23–25]. This applies either to the signal beam that carries the information to be transmitted or to the pump beams that may be used to improve the signal transmission owing to remote or Raman amplification. For both kinds of beams, unrepeatered system usually involve very large optical powers that are at the edge of the nonlinear effects limitation. These nonlinear interactions can be divided into three main categories: (1) Brillouin effect, (2) Kerr effect, and (3) Raman effect. A. Stimulated Brillouin Scattering Stimulated Brillouin scattering (SBS) is an inelastic phenomenon resulting from the scattering of an incoming photon inside the optical fiber. The scattered photon

250


FIGURE 11

Experimental reduction of stimulated Brillouin scattering.

is slightly frequency downshifted compared to the initial photon, the energy difference being transferred to an acoustic phonon. When increasing the launch power, the optical fiber practically acts as a mirror whose reflectance coefficient increases. As a result, the corresponding fiber loss can significantly grow and the induced reflections can degrade the system performance. Figure 11 shows the power reflected by a pure silica core fiber line versus launch power. When low power is injected into the fiber, only intrinsic Rayleigh back-reflections occur and the level of reflections is very low (32 dB). When high power is launched in the fiber, the backscattered power increases because of the stimulated Brillouin scattering. Then, the level of reflections increases very rapidly with the launch power. The system can operate properly for reflections level lower than 15 dB. Because the Brillouin effect acts as a narrowband resonator (< 100 MHz), the reflections can be reduced by dithering the laser linewidth. The usual, simple method consists of modulating the laser current with a small amplitude and low frequency, which induces laser chirp and permits launch powers up to about 20 dBm with moderate overmodulation amplitude. Launching of higher powers requires the use of phase modulation, which splits the power among three lines. The combination of both techniques has been already demonstrated [19] and allows very high powers up to 30 dBm to be launched. B. Kerr Effect In the case of a single-channel transmission, the refractive index of the waveguide is modulated by the fluctuations of the channel intensity via the Kerr effect. The


251

amplitude of this phenomenon is increased by a high launch power and small effective area inside the optical fiber. This nonlinear effect can broaden the channel spectrum and therefore interplay with the chromatic dispersion, resulting in pulse distortion and broadening. The basic physical phenomenon is relative to the dependence of the fiber refractive index on the intensity of the optical beam in the fiber core and can be described by the following relation: n ¼ n0 þ

n2 P Aeff

ð14Þ

where n ¼ fiber refractive index n0 ¼ linear part of the fiber refractive index n2 ¼ nonlinear index coefficient Aeff ¼ fiber core effective area P ¼ optical power The Kerr effect is usually decomposed in three different contributions that are actually closely related. When a signal travels alone through the fiber, its modulated power induces a self-phase modulation (SPM). By contrast, the presence of several channels in a WDM transmission generates on each signal a cross-phase modulation. For the particular case of well-phase-matched WDM signals (i.e. moderate fiber chromatic dispersion), the Kerr effect produces fourwave mixing (FWM). Each of these contributions is described in the following paragraphs. 1. Self-Phase Modulation According to Eq. (14) and assuming that n2 is positive, light travels more slowly when the optical power is high, leading to a phase difference compared to light traveling at a low optical power. The result of the propagation of an amplitude-modulated signal is presented in Fig. 12a for a linear regime, that is,

FIGURE 12 Experimental eye diagrams obtained after propagation in (a) the linear regime and (b) the nonlinear regime.

252


for low peak powers. Figure 12b illustrates the distortions generated by the SPM effect for high launch powers. Self-phase modulation becomes significant as soon as the launch power is typically larger than 12 dBm.

2. Cross-Phase Modulation In the case of several high-power channels propagating simultaneously within the same fiber, the refractive index modulation experienced by one given channel is not only caused by the intensity modulation of this specific channel (SPM) but also by the intensity modulation brought by the copropagating channels [26]. This cross-refractive index modulation is called cross-phase modulation (XPM) and can be described as a process through which the intensity fluctuations in a particular channel are converted to phase fluctuations in the other channels. Figure 13 illustrates the experimental transmission penalty induced by XPM on WDM 10-Gbps systems over pure silica core fiber. The penalty on the receiver sensitivity for a BER of 105 , assuming the use of FEC, is plotted versus the launched power per channel for several channel spacings. Curves are plotted with respect to the receiver sensitivity obtained without fiber (back-to-back). This experimentally demonstrates that the lower the channel spacing, the higher the transmission impairments induced by cross-phase modulation. Also noticeable is the slight performance improvement that can be obtained with respect to the back-to-back configuration under a moderate nonlinear transmission regime. The resulting negative penalty can be explained by a pulse compression in the

FIGURE 13

Experimental influence of cross-phase modulation on 10-Gbps system performance for various channel spacings.


253

temporal domain induced by the nonlinear regime propagation through the standard fiber, which has a large chromatic dispersion. 3. Four-Wave Mixing When several carriers at different wavelengths are launched into the fiber and are closed to be phase-matched, new waves can be generated by four-wave mixing via third-order intermodulation process. The optical frequencies of these FWM-generated waves are given by ni þ nj nk where ni ; nj , and nk are the frequencies of the launched initial channels (i.e., the signal channels). Four-wave mixing can transfer a fraction of the channel powers to the frequency of the other channels through the generation of FWM waves. The efficiency of the four-wave mixing, that is, the level of the FWM waves, depends on various parameters. The FWM efficiency is favored by high launch power, low chromatic dispersion, low channel spacing and identical states of polarization for all channels. FWM waves can impair system performance through homodyne crosstalk leading to large amplitude interferences during the quadratic detection at the photodiode level. It is worth noting that FWM waves are generated at the expense of the signal channels, therefore strong FWM effects will degrade WDM system performance by crosstalk or excess attenuation via depletion of the signal channels. Allocating the channel frequencies on a nonregular spacing grid allows impairments induced by four-wave mixing to be reduced [27]. Indeed, if the frequency separation of any two channels of a WDM system is different from that of any other pair of channels, no FWM waves will be generated at any of the channel frequencies, thereby suppressing FWM crosstalk. Figure 14 illustrates the experimental distortion induced by FWM on the optical spectrum and on the receiving eye diagrams of an unequally spaced channel system. In this experiment, eight channels at 10 Gbps are transmitted over 100 km of DSF whose zero-dispersion wavelength is 1554.4 nm. Channel wavelengths are 1533.08, 1533.86, 1536.22, 1540.17, 1544.93, 1550.52, 1558.58, and 1560.2 nm, respectively. The receiving eye diagrams presented in Fig. 14 are relative to the 1550.52-nm channel, which experiences the highest degradation from FWM. Using this optimized nonregular spacing allows us to launch more than 6 dBm per channel, whereas a maximum power of 0 dBm would have been achieved with a regular spacing. C. Stimulated Raman Scattering Like SBS, stimulated Raman scattering (SRS) is an inelastic phenomenon resulting from the scattering of an incoming photon inside the optical fiber. The scattered photon is frequency downshifted compared to the initial photon, the energy difference being transferred to an optical phonon. When several beams propagate through the fiber at different wavelengths, the maximum energy transfer occurs for a 13.2-THz separation between the channels, as described in Section V.D.

254


FIGURE 14

Experimental influence of four-wave mixing on optical spectrum and on a 10-Gbps eye diagram after propagation over 100 km of DSF.

Channel interaction due to Raman scattering is not maximal for channel spacing lower than 13.2 THz, which is the case for WDM systems; nevertheless, it can still be significant for high-power, wideband systems. If we approximate the Raman gain spectrum by a triangular profile such that gr ðnÞ increases linearly versus the frequency from 0 to 13.2 THz, then the tilt


255

induced by SRS is expressed in decibels by [28]: SRStilt ¼ 2:17

Leff @gR P Dl Aeff @l out

ð15Þ

where gR ¼ Raman gain Leff ¼ effective length of the fiber Aeff ¼ effective area Pout ¼ total input power in the fiber (W) Dl ¼ wavelength bandwidth (nm) For a given fiber type, Eq. (15) demonstrates that the tilt induced by stimulated Raman scattering depends only on the total launched power and on the wavelength bandwidth. Figure 15 presents the spectrum tilt resulting from Raman depletion over standard fiber versus the launched power. Curves are plotted for three different spectrum bandwidths: 2 THz, which corresponds to half of the C-band and can for example accommodate 40 channels spaced by 50 GHz; 4 THz, which is relative to the C-band; and 9 THz, which corresponds to C and Lbands. For the latter case, launch powers in excess of 20 dBm yield to significant tilts that should be taken into account in the optical power budget. Part of this depletion tilt can be compensated for, thanks to linear channel preemphasis with the reverse slope.

FIGURE 15 bandwidths.

SRS tilt induced over standard fiber versus total launched power for various signal

256

TABLE V

Power Budget Calculation of Unrepeatered Systems

Equipment power budget Launch power at point S0 Section loss of remote postamplification Section loss of remote preamplification Receiver sensitivity at point R0 Transmission impairments Equipment aging SOL equipment power budget EOL equipment power budget Cable power budget Cable length SOL cable attenuation SOL cable loss EOL cable attenuation EOL cable loss Installation loss Repair margin SOL total cable loss EOL total cable loss SOL system margin EOL system margin

Unit

Configuration 1

Configuration 2

Calculation

dBm dB dB dBm dB dB dB dB

17.5 0.0 0.0 46.0 0.5 1.0 62.0 61.0

14.0 11.0 18.0 43.0 0.5 1.0 84.5 83.5

A1 A2 A3 A4 A5 A6 A7 ¼ A1 þ A2 þ A3 A4 A5 A8 ¼ A7 A6

km dB=km

300.0 0.181 54.3 0.186 55.8 1.0 3.0 55.3 59.8 5.7 1.2

420.0 0.181 76.0 0.186 78.1 1.0 3.0 77.0 82.1 6.5 1.4

B1 B2 B3 ¼ B1 B2 B4 B5 ¼ B1 B4 B6 B7 B8 ¼ B3 þ B6 B9 ¼ B4 þ B6 þ B7 C1 ¼ A7 B8 C2 ¼ A8 B9

dB=km dB dB dB dB dB dB dB


Item


257

FIGURE 16 Unrepeatered system configuration and definition of reference points for transmit power and sensitivity. TX, transmitter; RX, receiver.

VII. POWER BUDGET CALCULATION The basic principle of power budget calculation is illustrated on Table V and Fig. 16 for two different unrepeatered configurations. The first configuration corresponds to a basic repeaterless system involving only local postamplification and local preamplification. The calculation applies to single-channel transmission as well as WDM transmission as long as the launched power is expressed on a perchannel basis. The equipment power budget is given by the difference between the transmitted power and the receiver sensitivity, which should take into account some impairments induced by, for example, nonlinear interactions. The terminal equipment performance can also be degraded by component aging over the lifetime of the system. The cable power budget is defined as the sum of the fiber loss, of the cable installation loss, and of the repairs allowed. Repairs and cable aging should be taken into account for the end-of-life conditions only. The second configuration corresponds to a repeaterless system involving remote amplification at the transmitting and receiving sides. In that case, the relevant launched power is defined at the output of the remote postamplifier, whereas the relevant sensitivity is defined at the input of the remote preamplifier. Then, remote section losses can be added to the equipment power budget since they can be considered transparent. For both configurations, it is important to calculate the start-of-life (SOL) and end-of-life (EOL) system margins. Indeed, the SOL margin allows us to check that the system works as expected just after its installation, whereas a positive EOL margin should guarantee good performances over the lifetime of the system.

VIII. MAIN LABORATORY ACHIEVEMENTS Many unrepeatered transmissions were demonstrated in laboratories during the 1990s and some of these experiments established world records in terms of distance achieved for a given capacity. Table VI lists the most representative laboratory achievements over this period with the corresponding techniques employed, and the following section describes one of these experimental results. Reference [48] describes the unrepeatered transmission of 160 channels, each carrying a 10-Gbps capacity over 380 km. In that experiment, the most

258


TABLE VI

Main Unrepeatered Laboratory Achievements

System configuration Capacity Distance Year (Gbps) (km) FEC Raman Post-ROPA Pre-ROPA Company

Reference

1991 1992 1994 1994 1994 1994 1994 1995 1995 1995 1995 1996 1996 1996 1996 1996 1997 1997 1998 1998 1998 1999

29 12 30 31 32 33 34 35 36 37 38 17 39 40 41 3 4 5 19 20 42 43

1 2:5 1 2:5 1 2:5 1 2:5 1 2:5 1 2:5 1 40 1 2:5 1 2:5 1 2:5 16 2:5 1 2:5 1 2:5 1 10 1 10 8 10 8 2:5 8 2:5 1 2:5 16 10 1 40 4 10

318 357 374 407 410 423 80 481 511 529 427 415 490 412 442 352 377 461 453 340 240 235

1999 16 10 430 1999 32 10 450 1999 1 2:5 570 2000 64 10 305 2000 100 10 350 2000 32 40 250 2001 32 40 202 2001 1 40 252 2001 2001 2001 2001 2001

104 40 256 40 64 40 160 10 160 10

135 100 230 321 380

x

x

x x x x x

x x x x

x x x x

x x x

x x x x

x

x x x x x x

x x x

x

x x

x x x

x x x x x

x x

x x x x x x x x x x x x x

x x

x x x x x

x

AT&T Alcatel ATT Alcatel STC AT&T BT Alcatel Alcatel AT&T Alcatel Alcatel AT&T Alcatel AT&T AT&T Alcatel Alcatel Alcatel NEC NTT US Naval Research Lab. Alcatel Alcatel Alcatel Alcatel Alcatel Alcatel Mitsubishi Heinrich Hertz Institut Alcatel Alcatel KDD Alcatel Alcatel

13 15 16 6 7 1 44 45 8 46 18 47 48

advanced unrepeatered technologies have been implemented to establish a world record performance: FEC encoding=decoding [12], use of a large power booster [19], implementation of a remote amplifier [14], in-line filtering of the pump sent to the ROPA [15], and second-order pumping Raman amplification [47].


259

Figure 17 presents the experimental setup, which consists of a transmit terminal, a receive terminal, and a remotely pumped preamplifier in between the two. The line fiber consists of pure silica core fiber having an 80 mm2 effective core area, except in the sections where optical power is very large. Indeed, some 110mm2 PSCF lengths are inserted at the transmit side in order to reduce nonlinear interactions between the channels. The same enlarged fiber is also implemented at the receiving side to allow the injection of higher pump powers than those limited by the Raman effect over the standard effective core area. Thus, the ratio of core areas represents the practical gain on the maximum launched power for signals and pumps and corresponds to about 1.5 dB at each side of the system. In this experiment, the remote optically pumped amplifier involves a dedicated pumping fiber, whereas Raman preamplification is realized on the main fiber. Located 125 km away from the receiver, the ROPA demonstrates a mean gain of 18 dB and a noise figure lower than 7 dB over the signal wavelength range. To overcome the limitation coming from oscillations induced by Raman gain and Rayleigh backscattering, fused WDM couplers are inserted in the dedicated pumping fiber. These couplers act like filters, with low loss at pump wavelength, but high loss in the region of Raman gain. It is therefore possible to send to the ROPA more than the usual 1.8-W maximum pump power and to increase the budget gain. As far as Raman amplification is concerned, a second-order pumping scheme is implemented, involving three pumps launched in the direction opposite to the signals. The principle is that the second-order Raman pump, centered at 1367 nm, provides gain for the first-order Raman pumps, respectively, at 1425 and 1455 nm. This scheme pushes the Raman distributed gain farther from the end of the link and thereby improves the equivalent noise figure by about 1.5 dB as compared to a conventional first-order pumping Raman amplification. In this experiment, 160 laser sources are spaced by 25 GHz and cover a 32nm bandwidth in the wavelength range from 1530.73 to 1562.44 nm. These sources are separately modulated by eight different LiNbO3 Mach–Zehnder external modulators driven by a 10.6-Gbps pseudo-random sequence of 223 1 length. This sequence is FEC encoded using a standard 239=255 Reed–Solomon coding. Implementation of a significant number of amplitude modulators at the transmitting side is required for such experiments to be representative of a real communication system. It ensures that nonlinear interactions between two adjacent channels are representative of the reality since these channels are not carrying the same information as that carried for commercial systems. Modulator outputs are multiplexed and then amplified owing to a 29.5-dBm power booster before being launched into the line fiber. A linear channel preemphasis of 11 dB is applied at the transmitting side to compensate for the amplitude tilt induced by stimulated Raman scattering and by the wavelengthdependent loss of the line fiber. Although a small amount of dispersion is introduced at the transmitting side (500 ps=nm), chromatic dispersion of the line fiber is mainly compensated at

260 E. BRANDON AND J.-P. BLONDEL

FIGURE 17

Experimental test setup of 1.6-Tbps transmission demonstration over 380 km.


261

the receiving side, using dispersion compensating fiber (DCF) modules. These modules also compensate for the slope of the line chromatic dispersion and the positive resulting dispersion is about 700 ps=nm for all channels. In this demonstration all channels are measured with a BER lower than 2 104 when the FEC correction is disabled and are lower than 1012 when the correction is enabled. Therefore, error-free operation has been demonstrated for this dense-WDM 1.6-Tbps transmission capability over 380 km.

IX. INSTALLED UNREPEATERED SYSTEMS A. Deployed Unrepeatered Systems Table VII presents a quasi-exhaustive list of the repeaterless systems deployed all around the world during the 1990–2000 period that had a capacity larger than 560 Mbps. Note that some links have been upgraded several times over this period, either in terms of bit rate or wavelength count. In addition, the incredible growth in capacity described in Section II becomes obvious while glancing through the list. TABLE VII

Deployed Unrepeatered Systems during the 1990–2000 Period

Year

Project name

1990 1991 1991 1992 1992 1992 1992 1992 1992 1992 1992 1993 1993 1993 1993 1993 1993 1993 1993 1993 1993

Italian Festoon APOCS 1 UK–France 4 Canada Dom (Vancouver) Denmark–Norway 5 Locri–Catanzaro Taino–Carib TAT 10 Thai Festoon UK Dom. Porthsmouth–Ryde UK–Ireland 1 BT–TE 1 Batam–Singapore Cios (Israel–Cyprus) Denmark–Germany 1 Germany–Sweden 4 & 5 Iceland Dom. Japan Dom. (Miyuzaki–Chikura) Lanveoc 2 Lemnos–Thassos–Kavala Marianna Islands (Kwajalein) UK Dom. Brean–Swansea

Capacity per fiber pair 1 560 Mbps 1 560 Mbps 1 560 Mbps 1 560 Mbps 1 560 Mbps 1 560 Mbps 1 560 Mbps 1 2:5 Gbps 1 560 Mbps 1 560 Mbps 1 560 Mbps 1 560 Mbps 1 622 Mbps 1 2:5 Gbps 1 622 Mbps 1 560 Mbps 1 1:8 Gbps 1 622 Mbps 1 560 Mbps 1 560 Mbps 1 2:5 Gbps

Fiber pairs

Project capacity (Gbps)

6 6 6

3.4 3.4 3.4

6 6 6 2 6

3.4 3.4 3.4 5.0 3.4

2

1.1

6 4

15 2.5

2

3.6

6 6

3.4 15

262


TABLE VII

(continued )

Year

Project name

1993 1994 1994

UK–France 3 Cyprus Domestic (Kinyras) Girvan–Larne 1 (Scotland–N. Ireland) Hawaii Network No. 2 Norway Dom. 01 SF–S-5–Finland–Sweden Tefkros (Cyprus Dom) Tunisia–Italy (Kelibia–Trapani) UK–Ireland 3 (Celtic) APOCS 2 CC5 Denmark–Germany 2 ECFS EES 1 (Sweden–Estonia) France–Italy (Monaco, Savonna) Greece–Creta (Lagonisi=Chania) Guernsey–Jersey 4 Kattegat 1 Lanis (Mercury) Latvia–Sweden Malaysia Dom. (Southern Link) Mallorca–Menorca North Sea Cable 1 Odin Penbal 5 Rioja 2 Spain–Morocco 1993 (Estepona– Tetouan) St. Thomas–St. Croix (US) Syracusa–Malta Tasmania (Bass Strait) Tenerife–La Palma Ugarit (Syria–Cyprus) UK–Channel Isl. No. 8 US Navy San Diego (Focus) Zirku–Ruwais Abu Dhabi Dubai Adria 1 Bahamas 2 Baltica Brazilian Festoon Cape Verde Dom. Cayman–Jamaica (CFJS) China Dom. 1996 Colombian Festoon

1994 1994 1994 1994 1994 1994 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1995 1996 1996 1996 1996 1996 1996 1996 1996 1996

Capacity per fiber pair 1 2:5 Gbps 1 560 Mbps 1 560 Mbps 1 2:5 Gbps 1 560 Mbps 1 622 Mbps 1 622 Mbps 1 560 Mbps 1 2:5 Gbps 1 2:5 Gbps 1 622 Mbps 1 2:5 Gbps 1 622 Mbps 1 622 Mbps 1 622 Mbps 1 622 Mbps 1 560 Mbps 1 2:5 Gbps 1 560 Mbps 1 622 Mbps 1 5 Gbps 1 622 Mbps 1 560 Mbps 1 2:5 Gbps 1 622 Mbps 1 2:5 Gbps 1 622 Mbps 1 622 Mbps 1 622 Mbps 1 622 Mbps 1 560 Mbps 1 560 Mbps 1 560 Mbps 1 560 Mbps 1 622 Mbps 1 622 Mbps 1 622 Mbps 1 2:5 Gbps 1 2:5 Gbps 1 622 Mbps 1 622 Mbps 1 2:5 Gbps 1 2:5 Gbps 1 622 Mbps

Fiber pairs


3 6

7.5 3.4

4

2.5

6

15

6 2 4 6 12

3.7 5.0 2.5 3.7 7.5

6 6 4 12 2 6

3.4 15 2.2 7.5 10 3.7

6 6 6 2

15 3.7 15 1.2

6

3.7

3 6

1.7 3.4

6 6

3.7 3.7

2 3

5.0 1.9

2

5.0


TABLE VII

(continued )

Year

Project name

1996 1996 1996 1996 1996

Denmark–Sweden 18 Indonesia Dom. (2 segments) Italian Festoon Kafos Korea Dom. 1996 (2nd Mainland– Cheju-Do) Lebanon–Cyprus (Cadmos) Malaysia Festoon (Telkom) Thailand West (Jasmine)(Cab) UK–Netherlands 14 Antillas 1 Baltic Cable System Berytar China Dom. 1997=1 (Shanghai–Chongming) China Festoon (Unicom) GST–Hawaii (HI Fibernet) GSTR Fibernet Hermes 1 Hermes 2 Indonesia Dom. (Packet 1) Italy–Albany Italy Dom. 1996=1 (Ischia, Capri) Italy–Greece 1 Nigeria Festoon Palau Festoon Network (14 segments) Philippines Dom. Telicphil Russia Dom. (Novorossyisk, Sotchi) SFL–2 Tafiks Ulysses 1 Ulysses 2 Acores Submarine System Brazil Festoon Extension 1998 (Rio de Janeiro, Santos) Brazilian Festoon Corfu–Bar Greece Dom. 1997 Mexicom GST (Sea of Cortez) Northstar Norway Dom. 1997 Penbal 4 Petrobras Sesimbra–Lagos Sirius Solas

1996 1996 1996 1996 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1997 1998 1998 1998 1998 1998 1998 1998 1998 1998 1998 1998 1998 1998

263

Capacity per fiber pair 1 2:5 Gbps 1 622 Mbps 1 622 Mbps 1 622 Mbps 1 2:5 Gbps 1 622 Mbps 1 622 Mbps 1 2:5 Gbps 1 2:5 Gbps 1 622 Mbps 1 2:5 Gbps 1 622 Mbps 1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 1 560 Mbps 1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 1 622 Mbps 1 622 Mbps 1 622 Mbps 1 622 Mbps 1 622 Mbps 1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 1 622 Mbps 1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps

Fiber pairs 6

Project capacity (Gbps) 15

12 2 3

7.5 1.2 7.5

2 2 6 2

1.2 1.2 15 5.0

2 6 24

5.0 3.7 60

12

30

12 12

30 30

6 15 6

3.7 9.3 3.7

6 4 12 6 24 24 8 24

15 10 30 15 60 60 20 60

3 4 12 6 6 2 6 12 24 6

7.5 10 30 15 15 5.0 3.7 30 60 15

264


TABLE VII

(continued )

Year

Project name

1998 1999 1999 1999 1999 1999 1999 1999 1999

Venfoins Alaska United Candalta Circe Curacao–Aruba ESAT I ESAT II Farland (UK–France) Flag Extension Saudi Arabia–Sudan (Jeddah–Port Sudan) Norway Dom. 1998 Penbal 5 Pencan 5 Petrocom Rembrandt (Ex UK–Netherlands 15–16) Sochi–Poti Taiwan Dom. TPKM2 Transcan 3 Americas 2 Bahamas Cable (Bahamas–Miami) Cook Strait ECFS Ireland–UK Crossing Jamaica South Coast Korea Dom. 1999 (3rd Mainland–Cheju-Do) Pangea Baltic Ring Pangea One Thailand Dom. Cat Festoon Transgulf-1

1999 1999 1999 1999 1999 1999 1999 1999 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000 2000

Capacity per fiber pair

Fiber pairs


1 2:5 Gbps 4 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 4 2:5 Gbps 4 2:5 Gbps 1 2:5 Gbps 16 10 Gbps

12 2 6 24 6 12 12 12 4

30 20 15 60 15 120 120 30 640

1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 1 10 Gbps 16 2:5 Gbps

6 1 1 6 24

15 2.5 2.5 60 960

1 2:5 Gbps 1 2:5 Gbps 1 2:5 Gbps 4 2:5 Gbps 16 2:5 Gbps 16 10 Gbps 3 2:5 Gbps 16 10 Gbps 1 622 Mbps 32 2:5 Gbps

4 6 3 4 24 8 4 12 4 6

10 15 7.5 40 960 1280 30 1920 2.5 480

16 10 Gbps 32 10 Gbps 1 2:5 Gbps 1 2:5 Gbps

24 24 4 24

3840 14400 10 60

B. Safety Aspects Above 500 mW in the 1400- to 1600-nm wavelength range, laser sources are Class 4 radiation hazards. The major consideration in a system carrying such optical power, which is commonly deployed within unrepeatered systems, is the risk of exposure following a cable break at any point in the system. The danger of this eventuality is normally overcome in commercial equipment by using automatic power reduction mechanisms: —Figure 18 presents the basic shutdown mechanisms that can be implemented in deployed unrepeatered systems. For most of these systems, a jointing box, which protects the splice between the land cable and the


FIGURE 18

265

Potential shutdown mechanisms in deployed unrepeatered systems.

submerged cable, is implemented on the beach. Adding a tap coupler in this jointing box allows for a dedicated fiber in the land section to be used for monitoring the returned power. Then, if the pump detection circuit does not receive some power, a cable is assumed to be broken in the receiving terminal–beach joint section and the pump will be shut down. —Detection of amplified spontaneous emission (ASE) noise can be potentially used for shutdown control. This detection can be realized in the pump source unit or in the local preamplifier. —Some EDFAs are using optical tracking filters to suppress ASE noise. In the case of a cable break, the loss of a locking signal can provide useful information to the pump source. —Finally, the receiver can potentially send a loss-of-frame alarm for the pump to be shut down. Combining several of these mechanisms, radiation hazards are fully prevented in modern unrepeatered communication systems [49].

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6. F. Boubal, E. Brandon, L. Buet, V. Havard, L. Labrunie, P. Le Roux, and J.-P. Blondel. Broadband (32 nm) 640 Gbit=s unrepeatered transmission over 300 km with distributed dual wavelength Raman preamplification. In OAA Technical Digest, postdeadline paper PDP8 (2000). 7. L. Buet, F. Boubal, V. Havard, L. Labrunie, P. Le Roux, and E. Brandon. Error-free 100 10 Gbit=s unrepeatered transmission over 350 km. in OFC Technical Digest, Paper TuU5 (2001). 8. F. Boubal, E. Brandon, L. Buet, S. Chernikov, V. Havard, C. Heerdt, A. Hugbart, W. Idler, L. Labrunie, P. Le Roux, S. A. E. Lewis, A. Pham, L. Piriou, R. Uhel, and J.-P. Blondel. 4.16 Tbit=s (104 40 Gbit=s) unrepeatered transmission over 135 km in SþCþL bands with 104 nm total bandwidth. In ECOC Technical Digest (2001). 9. I. Vintermyr, R. Vogt, and J. S. Andreassen. High fibre count submarine cable for unrepeatered systems. In IWSC Technical Digest (1999). 10. P. C. Becker, N. A. Olsson, and J. R. Simpson. Erbium-Doped Fiber Amplifiers, Fundamentals and Technology. Academic Press (1999). 11. O. Ait Sab and J. Fang. Concatenated forward error correction schemes for long-haul DWDM optical transmission systems. In ECOC Technical Digest, paper ThC2.4 (1999). 12. P. M. Gabla, J.-L. Pamart, R. Uhel, E. Leclerc, J. O. Frorud, F. X. Ollivier, and S. Borderieux. 401 km, 622 Mb=s and 357 km, 2.488 Gb=s IM=DD repeaterless transmission experiments using erbium-doped fiber amplifiers and error correcting code. IEEE Photon. Technol. Lett. 4(10) (October 1992). 13. E. Brandon, J.-P. Blondel, P. Le Roux, D. Toullier, and M. Mesic. Error-free 16 10 Gbit=s unrepeatered transmission over 430 km. In ECOC Technical Digest, paper WeC4.2 (1999). 14. K. Aida, S. Nishi, Y. Sato, K. Hagimoto, and K. Nakagawa. 1.8 Gb=s 310 km fiber transmission without outdoor repeater equipment using a remotely pumped in-line Er-doped fiber amplifier in an IM=direct-detection system. In ECOC Technical Digest, postdeadline paper PDA-7 (1989). 15. J.-P. Blondel, E. Brandon, L. Labrunie, P. Le Roux, D. Toullier, and G. Zarris. Error-free 32 10 Gbit=s unrepeatered transmission over 450 km. In ECOC Technical Digest, postdeadline paper PD6 (1999). 16. P. Le Roux, E. Brandon, J.-P. Blondel, L. Labrunie, D. Toullier, and G. Zarris. Error-free 2.5 Gbit=s unrepeatered transmission over 570 km. In ECOC Technical Digest, Paper Th10.3.2 (2000). 17. K. M. Guild, S. M. Webb, and S. S. Sian. Unrepeatered transmission over 415 km at 2.5 Gbit=s with Raman gain and þ26:5 dBm launch power. Electron. Lett. 32(22) (October 1996). 18. T. Miyakawa, I. Morita, K. Tanaka, H. Sakata, and N. Edagawa. 2.56 Tbit=s (40 Gbit=s64 WDM) unrepeatered 230 km transmission with 0.8 bit=s=Hz spectral efficiency using low-noise fiber Raman amplifier and 170 mm2 Aeff fiber. In OFC Technical Digest, postdeadline paper PD26-1 (2001). 19. E. Brandon and J.-P. Blondel. Raman limited, truly unrepeatered transmission at 2.5 Gbit=s over 453 km with þ30 dBm launch signal power. In ECOC Technical Digest, paper WdC28 (1998). 20. T. Koga, T. Ogata, and Y. Aoki. 10 Gb=s, 16 channels unrepeatered WDM transmission over 340 km of standard single mode fiber with very high power amplifier. In ECOC Technical Digest (1998). 21. J.-P. Blondel. Raman amplification and remotely pumped postamplification at transmit side of 622 Mbit=s and 2.5 Gbit=s repeaterless systems. IEEE Photon. Technol. Lett. 7(1) (January 1995). 22. J.-P. Blondel, F. Misk, and P. M. Gabla. Theoretical evaluation and record experimental demonstration of budget improvement with remotely pumped erbium-doped fiber amplification. IEEE Photon. Technol. Lett. 5(12) (December 1993). 23. G. A. Agrawal. Nonlinear Fiber Optics. Academic Press (1995). 24. A. Hadjifotiou and N. Jolley. The performance limits of unrepeatered systems. In SubOptic Technical Digest, Paper 7.3 (1993). 25. A. R. Chraplyvy. Limitations on lightwave communications imposed by optical-fiber nonlinearities. J. Lightwave Technol. 8(10) (October 1990).


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26. D. Marcuse. Dependence of cross-phase modulation on channel number in fiber WDM systems. J. Lightwave Technol. 12(5) (May 1994). 27. F. Forghieri, R. W. Tkach, and A. R. Chraplyvy. WDM Systems with unequally spaced channels. J. Lightwave Technol. 13(5) (May 1995). 28. S. Bigo, S. Gauchard, A. Bertaina, and J.-P. Hamaide. Experimental investigation of stimulated Raman scattering limitation on WDM transmission over various types of fiber infrastructures. IEEE Photon. Technol. Lett. 11(6) (June 1999). 29. Y. K. Park, S. W. Granlund, T. W. Cline, L. D. Tzeng, J. S. French, J.-M. P. Delavaux, R. E. Tench, S. K. Korotky, J. J. Veselka, and D. J. DiGiovanni. 2.488 Gb=s–318 km repeaterless transmission using erbium-doped fiber amplifiers in a direct-detection system. IEEE Photon. Technol. Lett. 4(2) (February 1992). 30. P. B. Hansen, V. L. Da Silva, G. Nykolak, J. R. Simpson, D. L. Wilson, J. E. J. Alphonsus, and D. J. DiGiovanni. 374-km, 2.4888-Gb=s repeaterless transmission system with a remotely pumped erbium-doped fiber amplifier. In ECOC Technical Digest, Paper We.B.1.3 (1994). 31. O. Gautheron, G. Grandpierre, P. M. Gabla, J.-P. Blondel, E. Brandon, P. Bousselet, P. Garabe´dian, and V. Havard. 407 km, 2.5 Gbit=s repeaterless transmission using an electroabsorption modulator and remotely pumped erbium-doped fiber post and preamplifiers. In ECOC Technical Digest, postdeadline paper (1994). 32. M. S. Chaudhry, S. S. Sian, K. Guild, P. R. Morkel, and C. D. Stark. Single span transmission of 2.5 Gbit=s over 410 km with remote amplification and dispersion compensation. In ECOC Technical Digest, postdeadline paper (1994). 33. P. B. Hansen, V. L. Da Silva, L. Eskilsen, S. G. Grubb, V. Mizrahi, W. Y. Cheung, T. Erdogan, T. A. Strasser, J. E. J. Alphonsus, G. Nykolak, D. L. Wilson, D. J. DiGiovanni, D. Truxal, A. M. Vengsarkar, S. G. Kosinski, P. F. Wysocki, J. R. Simpson, and J. D. Evankow. 423-km Repeaterless transmission at 2.488 Gb=s using remotely pumped post and preamplifiers. In ECOC Technical Digest, postdeadline paper (1994). 34. A. D. Ellis and D. M. Spirit. Unrepeatered transmission over 80 km standard fibre at 40 Gbit=s. Electron. Lett. 3(1) (January 1994). 35. O. Gautheron, S. S. Sian, G. Grandpierre, M. S. Chaudhry, J.-L. Pamart, T. Barbier, E. Bertin, P. Bonno, E. Brandon, M. Genot, P. Marmier, M. Mesic, P. M. Gabla, and P. Bousselet. 481 km, 2.5 Gbit=s and 501 km, 622 Mbit=s unrepeatered transmission using forward error correction and remotely pumped post and preamplifiers. Electron. Lett. 31(5) (March 1995). 36. S. S. Sian, O. Gautheron, M. S. Chaudhry, C. D. Stark, S. M. Webb, K. M. Guild, M. Mesic, J. M. Dryland, J. R. Chapman, A. R. Docker, E. Brandon, T. Barbier, P. Garabe´dian, and P. Bousselet. 511 km at 2.5 Gbit=s and 531 km at 622 Mbit=s—unrepeatered transmission with remote pumped amplifiers, forward error correction and dispersion compensation. In OFC Technical Digest, postdeadline paper PD26 (1995). 37. P. B. Hansen, L. Eskilsen, S. G. Grubb, A. M. Vengsarkar, S. K. Korotky, T. A. Strasser, J. E. J. Alphonsus, J. J. Veselka, D. J. DiGiovanni, D. W. Peckham, E. C. Beck, D. Truxal, W. Y. Cheung, S. G. Kosinski, D. Gasper, P. F. Wysocki, V. L. Da Silva, and J. R. Simpson. 2.488-Gb=s unrepeatered transmission over 529 km using remotely pumped post and preamplifiers, forward error correction, and dispersion compensation. In OFC Technical Digest, postdeadline paper PD25 (1995). 38. S. S. Sian, K. M. Webb, and K. M. Guild. 16 2:5 Gbit=s WDM unrepeatered transmission over 427 km (402 km without forward error correction). In ECOC Technical Digest, postdeadline paper Th.A.3.3(1995). 39. L. Eskilden, P. B. Hansen, S. G. Grubb, A. M. Vengsarkar, S. K. Korotky, T. A. Strasser, J. J. Veselka, J. E. J. Alphonsus, D. Truxal, and D. J. DiGiovanni. Single fibre repeaterless transmission over 490 km at 2.488 Gbit=s using a remote preamplifier and dispersion compensation. Electron. Lett. 32(18) (August 1996). 40. S. M. Webb, K. M. Guild, and S. S. Sian. 337 km unrepeatered transmission at 10 Gbit=s with Raman amplification and clock prechirp. Electron. Lett. 32(9) (April 1996).

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41. P. B. Hansen, L. Eskilden, S. G. Grubb, A. M. Vengsarkar, S. K. Korotky, T. A. Strasser, J. E. J. Alphonsus, J. J. Veselka, D. J. DiGiovanni, D. W. Peckham, and D. Truxal. 442 km repeaterless transmission in a 10 Gbit=s system experiment. Electron. Lett. 32(11) (May 1996). 42. K. I. Suzuki, N. Ohkawa, M. Murakami, and K. Aida. Unrepeatered 40 Gbit=s RZ signal transmission over 240 km conventional singlemode fibre. Electron. Lett. 34(8) (April 1998). 43. M. L. Dennis, W. I. Kaechele, L. Goldberg, T. F. Carruthers, and I. N. Duling. Wavelengthdivision-multiplexed 4 10 Gb=s adiabatic soliton transmission over 235 km. IEEE Photon. Technol. Lett. 11(12) (December 1999). 44. K. Shimizu, K. Kinjo, N. Suzuki, K. Ishida, S. Kajiya, K. Motoshima, and Y. Kobayashi. Fibereffective-area managed fiber lines with distributed Raman amplification in 1.28-Tb=s (32 40 Gb=s), 202-km unrepeatered transmission. In OFC Technical Digest, Paper TuU2-1 (2001). 45. M. Gunkel, F. Ku¨ppers, J. Berger, U. Feiste, R. Ludwig, C. Schubert, C. Schmidt, and H. G. Weber. 40 Gb=s RZ unrepeatered transmission over 252 km SMF using Raman amplification. In OFC Technical Digest, Paper TuU3-1 (2001). 46. S. Bigo, Y. Frignac, G. Charlet, W. Idler, S. Borne, H. Gross, R. Dischler, W. Poehlmann, P. Tran, C. Simonneau, D. Bayart, G. Veith, A. Jourdan, and J.-P. Hamaide. 10.2 Tbit=s (256 42:7 Gbit=s PDM=WDM) transmission over 100 km Teralight2 fiber with 1.28 bit=s=Hz spectral efficiency. In OFC Technical Digest, postdeadline paper PD25-1 (2001). 47. L. Labrunie, F. Boubal, E. Brandon, L. Buet, N. Darbois, D. Dufournet, V. Havard, P. Le Roux, M. Mesic, L. Piriou, A. Tran, and J.-P. Blondel. 1.6 Terabit=s (160 10:66 Gbit=s) unrepeatered transmission over 321 km using second order pumping distributed Raman amplification. In OAA Technical Digest, postdeadline paper PD3 (2001). 48. P. Le Roux, F. Boubal, E. Brandon, L. Buet, N. Darbois, V. Havard, L. Labrunie, L. Piriou, A. Tran, and J.-P. Blondel. 25 GHz spaced DWDM 160 10:66 Gbit=s (1.6 Tbit=s) unrepeatered transmission over 380 km. In ECOC Technical Digest, Postdeadline Paper PD.M.1.5 (2001). 49. J. Dryland, R. Oberland, and A. Shelton. High power amplifier design and system safety considerations for long distance unrepeatered links. In SubOptic Technical Digest, paper P.4.2.7 (2001).

7 POLARIZATION EFFECTS IN LONG-HAUL UNDERSEA SYSTEMS C. R. MENYUK University of Maryland, Baltimore County, Department of Computer Science and Electrical Engineering, Baltimore, Maryland; and Photonex Corporation, Maynard, Massachusetts

B. S. MARKS University of Maryland, Baltimore County, Department of Computer Science and Electrical Engineering, Baltimore, Maryland; and The Laboratory for Physical Sciences, College Park, Maryland

I. T. LIMA, JR., J. ZWECK AND Y. SUN University of Maryland, Baltimore County, Department of Computer Science and Electrical Engineering, Baltimore, Maryland

G. M. CARTER University of Maryland, Baltimore County, Department of Computer Science and Electrical Engineering, Baltimore, Maryland; and The Laboratory for Physical Sciences, College Park, Maryland

D. WANG Chorum Technologies, Richardson, Texas

I. INTRODUCTION II. PROPAGATION OF POLARIZED LIGHT IN AN OPTICAL FIBER TRANSMISSION SYSTEM A. Fiber Propagation B. Polarization Mode Dispersion C. Polarization-Dependent Loss and Gain D. Comments on Notation and Nomenclature


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III. REDUCED STOKES PARAMETER MODEL A. Model Formulation B. Theoretical Validation C. Experimental Validation D. Applications to Transoceanic Systems Acknowledgments References

I. INTRODUCTION It has long been known that single-mode optical fibers are actually bimodal due to the presence of randomly varying birefringence along their length [1, 2]. From a physical standpoint, one can view the HE11 mode, which is the only mode that exists in single-mode optical fibers, as behaving like a weakly confined vacuum mode propagating along the fiber axis [3]. In the absence of birefringence, the HE11 mode has two degenerate polarization states, just like vacuum modes. However, slight ellipticity in the core and stress that is induced by material inhomogeneities lead to a slight birefringence. This birefringence is very small indeed. In communications fibers, one finds that Dn 107 , corresponding to a beat length of 30 m. Although the beat length is small, its effect is large. In optical fibers, the magnitude of an effect is inversely proportional to its length scale. Thus, compared to chromatic dispersion, which has a typical length scale of tens of kilometers or more, or the Kerr nonlinearity, which has a typical length scale of hundreds or even thousands of kilometers, the birefringence must be considered large. Indeed, if the orientation of the birefringence were fixed, it would lead to a walkoff of the two polarizations dominating the pulse evolution, and it would ultimately tear apart pulses that consist of more than one polarization. However, the orientation of the fiber’s axes of birefringence varies on a scale of centimeters to around 100 m in communications fibers. Thus, compared to the nonlinear and dispersive length scales, the orientation is rapidly changing. These rapid changes almost cancel the effects of birefringence, but the residual effects lead to a random accumulation of walkoff and pulse spreading, which is referred to as polarization mode dispersion (PMD) [4]. When analyzing optical communications systems, it is essential to keep in mind the length scales that play a role [5]. As shown in Fig. 1, these length scales span 13 orders of magnitude and divide into three broad groups. The shortest length scale corresponds to the wavelength of light and the radius of the optical fiber core. One must use the full set of Maxwell’s equations to describe phenomena on this length scale; for example, to calculate the dispersion relation bðoÞ and the transverse mode profile. The intermediate length scale corresponds to the pulse duration, the birefringence beat length, and the fiber correlation length. The fiber correlation length is the length scale on which an ensemble

7. POLARIZATION EFFECTS IN LONG-HAUL SYSTEMS

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FIGURE 1 Illustration of the key length scales in optical fiber communications systems.

of fibers with the same statistical properties loses memory of the axes of birefringence. The variation of an optical fiber’s orientation is ergodic [6]; so, this length is also the average length over which the axes of birefringence change their orientation in a single member of the ensemble. To describe phenomena on this length scale, one makes the slowly varying envelope approximation, which averages over the transverse profile and the rapid wavelength variations, to obtain the coupled nonlinear Schro¨dinger equation [7, 8]. The third and final length scale corresponds to the scales for fiber attenuation, dispersion, nonlinearity, and PMD in communications systems—as well as the lengths of the systems themselves. On this length scale, one averages over the randomly and rapidly varying birefringence to obtain the Manakov-PMD equation [5, 9, 10]. When PMD can be ignored, and the signal is launched in a single polarization state, then one obtains the nonlinear Schro¨dinger equation and its variants [5]. In addition to the rapid variations in the polarization state in the optical fibers and the consequent PMD, one must account for the polarization effects in the amplifiers. First, the amplifiers can contribute an additional differential group delay (DGD), which adds to the overall PMD of the transmission line. We note parenthetically that in the present-day scientific literature considerable confusion surrounds the terms PMD and DGD. PMD is usually used to refer to a statistical property of a long length of optical fiber, in which case it is measured in units of (time)=(length)1=2 , typically ps=km1=2 . On some occasions, PMD is used interchangeably with DGD and is thus a property of a particular length of fiber or a particular component. In this case, PMD is measured in units of time, typically picoseconds, just like the DGD. Some of the confusion may stem from the techniques for measuring PMD, most of which actually measure the average DGD for some frequency range over a given length of fiber, from which one must infer the PMD [4]. In this chapter, we will always use PMD to refer to a statistical property of the fiber, and it will always be measured in units of ps=km1=2 .

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Besides adding DGD to the transmission line, the amplifiers also add polarization-dependent loss (PDL) and polarization-dependent gain (PDG). It has long been known that these two effects when acting together can seriously degrade the transmission in single-channel systems [11–13]. PDL is a result of a signal-independent sensitivity of amplifier components, particularly isolators and wavelength couplers. By contrast, PDG is a result of polarization hole burning in erbium-doped fiber amplifiers (EDFAs), and it is sensitive to the signal. The gain in the signal polarization is slightly less than the gain in the orthogonal polarization, so that noise that is orthogonal to the signal can grow exponentially. This effect can be controlled by scrambling the signal’s polarization to reduce the signal’s degree of polarization and thus reduce the polarization hole burning [14]. However, one then has to contend with the PDL, which tends to repolarize a polarization-scrambled signal [15]. Thus, the combination of these two effects is far more troublesome than either effect acting alone. It has recently been discovered that the dynamic behavior in a wavelengthdivision multiplexed (WDM) system with 10 or more channels is quite different [16, 17]. In this case a small amount of PMD—an amount that is insufficient to degrade a single channel—is still sufficient to randomize the polarization states of the different channels with respect to each other. As a consequence, the effects of PDG become negligible. The effect of PMD here is analogous to the effect of chromatic dispersion in a nonlinear system, which by mixing the relative phases of the different channels helps avoid deleterious effects from four-wave mixing. However, the PDL in the amplifiers, along with the variation in the polarization states from channel to channel, causes different channels to undergo different gains in the amplifiers. Because the amplifiers operate in saturation or are gain clamped in order to keep the total power nearly constant as the signal propagates from amplifier to amplifier, some channels will effectively gain power at the expense of others. Thus, the power in each channel undergoes a kind of random walk, and, as a consequence, a finite probability exists that any given channel will fade. This mechanism is the dominant source of fading in long-haul, WDM systems [16, 17]. There are significant differences between undersea systems and long-haul terrestrial systems [18]. Terrestrial systems typically make use of legacy fibers when the number of channels and the data rates per channel are upgraded. The reason is that it is far more expensive in a terrestrial system to replace the fiber than it is to replace the transmitters, receivers, and amplifiers. By contrast, it is not really possible to replace the amplifiers in an undersea system without replacing the fiber as well, and it is far simpler just to lay a new cable line—fibers, amplifiers, and all. As a consequence, high-data-rate undersea systems use the best available fiber. At present, it is possible to obtain PMD values as low as 0.02 ps=km1=2 , so that intrachannel PMD is not a serious problem in undersea systems. Moreover, undersea amplifiers are typically significantly more reliable than terrestrial amplifiers since repairs are significantly more expensive. A mean time to failure of 20 years is not exceptional for undersea systems.


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Transoceanic systems, as opposed to shorter haul undersea systems, are even more specialized. The PDLs in transoceanic amplifiers are significantly lower than in terrestrial amplifiers. One normally specifies values of 0.1 dB or less per amplifier, while values as high as 0.5 dB are not uncommon in terrestrial amplifiers. Amplifier spacings are typically around 50 km, which allows signal power to be held low while still maintaining a good signal-to-noise ratio (SNR). Consequently, a transoceanic transmission line will typically have in excess of 100 amplifiers; by contrast, terrestrial systems rarely have more than 10. Thus, we are led to consider systems with small values of PMD, PDL, and PDG, in which these effects accumulate over many amplifiers and long distances. In this limit, the polarization effects do not lead to much pulse distortion. Instead, they raise and lower the signal and noise power levels and rotate the polarization state of each wavelength channel as a whole [19, 20]. As a consequence, the polarization effects do not interact much with nonlinearity and chromatic dispersion, so that it is possible to calculate the penalties due to polarization effects separately from other penalties [16, 17, 19, 20]. The separability of polarization effects is fortunate because in practice one wants to specify an allowed margin for the polarization effects, for example, 3 dB, and one wants to ensure that the probability that the actual penalty will exceed this allowed margin, the outage probability, is less than some small number such as 106 . It is not possible experimentally or through full time-domain simulations to observe enough fiber realizations to calculate whether a design’s outage probability is lower than the required specification or not. However, it is possible to use a reduced model in which one just follows the Stokes parameters of the signal and the noise of each wavelength channel (eight numbers per wavelength channel) to calculate the polarization penalties [16, 17]. One can easily calculate 105 realizations from this approach, from which one can extrapolate to obtain the outage probability at the allowed margin. In the near future, we anticipate that the importance sampling technique, which has recently been applied to calculating the penalties due to PMD in a high-PMD system, will allow us to accurately calculate the outage probability at the allowed margin. In Section II of this chapter, we review our notation and the basic equations that govern light propagation in optical fibers with rapidly and randomly varying birefringence. In Section III, we derive the Stokes parameter model and present the theoretical and experimental results that validate it. We conclude with a discussion of applications to undersea systems. II. PROPAGATION OF POLARIZED LIGHT IN AN OPTICAL FIBER TRANSMISSION SYSTEM A. Fiber Propagation Our starting point is to write the electric field in a single-mode optical fiber in the form

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Eðx; y; z; tÞ ¼

1=2 o0 ½U1 ðz; tÞR1 ðx; y; o0 Þ þ U2 ðz; tÞR2 ðx; y; o0 Þ 2e0 c2 bðo0 Þ

exp½ibðo0 Þz io0 t

ð1Þ

which is valid in the slowly varying envelope approximation [5]. We have chosen the z direction to be the propagation direction along the fiber. The dispersion relation bðoÞ is evaluated at the carrier frequency o ¼ o0. The quantity t corresponds to physical time, while x and y indicate the transverse dimensions, chosen so that ðx; y; zÞ form a right-handed system. The vector field R1 is the transverse mode profile of the HE11 mode, which includes a small component in the z direction. In the weak-guiding approximation, which is an excellent approximation for optical fibers, we may choose R1 so that it is primarily oriented in the x direction [3]. In that case, designating the unit vector in the z direction as e^ z , we find that R2 ¼ e^ z R1 is oriented primarily in the y direction. The coefficients U1 ðz; tÞ and U2 ðz; tÞ, which are the principal objects of our study, contain all the effects of birefringence. Although, in principle, the birefringence will lead to slight variations in the fields R1 and R2, in practice, these variations are too small to have any observable effects. The factor ½o0 =2e0 c2 bðo0 Þ1=2 has been chosen so that jU1 j2 þ jU2 j2 corresponds to the optical power in the weak guiding approximation, where e0 is the vacuum dielectric permittivity and c is the speed of light in the vacuum. A key point that merits some emphasis is that we are using a negative carrier frequency, that is, the factor exp½ibðo0 Þz io0 t appears in Eq. (1), rather than the factor exp½io0 t ibðo0 Þz that corresponds to a positive carrier frequency. As Gordon and Kogelnik [21] have pointed out, there is considerable confusion of notation and nomenclature among researchers studying polarization effects in optical fibers. Much of this confusion can be traced back to the widespread use of both positive and negative carrier frequencies among these researchers. Later in this section, we carefully discuss the current conventions in nomenclature and notation and how our own choices compare. For the moment, we note that our nomenclature is completely consistent with Born and Wolf [22]. Like them, we use a negative carrier frequency, and we define right and left circular polarization, the Stokes parameters, and the Poincare´ sphere in precisely the same way. One reason for our choice of a negative carrier frequency is that this convention is overwhelmingly used among researchers who are studying the impacts of nonlinearity and chromatic dispersion on optical fiber transmission systems. Ultimately, it will be important to study polarization effects in combination with other impairments, rather than in isolation, as is the case with the majority of present-day work. The use of a common convention for the carrier frequency will help to eliminate misunderstandings. We now define the Stokes vector U ¼ ðU1 ; U2 Þz, where the superscript z indicates the transpose so that U is interpreted as a column vector. We also define


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the retarded time t ¼ t b0 ðo0 Þz, where b0 ðo0 Þ ¼ dbðoÞ=dojo¼o0 . The equation governing the z evolution of U now becomes [5] @U 1 00 @2 U 1 y 0 @U 2 i þ g jUj U ðU s2 UÞs2 U ¼ 0 iGU þ DBU þ iDB b @z @t 2 @t 2 3 ð2Þ where y indicates the conjugate transpose and DB ¼ Dbðs3 cos y þ s1 sin yÞ The sj are the standard Pauli matrices 0 0 1 ; s2 ¼ s1 ¼ i 1 0

i ; 0

s3 ¼

ð3Þ

1 0

0 1

ð4Þ

Primes indicate derivatives with respect to o, evaluated at the carrier frequency o ¼ o0 , so that b00 ¼ d 2 b=do2 jo¼o0 . The parameter G accounts for the fiber loss, which is polarization independent. The parameter g ¼ o0 n2 =cAeff , where n2 is the Kerr coefficient and Aeff is the fiber’s effective area, accounts for the Kerr nonlinearity. The quantity Db indicates the birefringence strength, while y indicates its orientation, which is rapidly and randomly varying with z. We stress that the physical orientation of the axes of birefringence inside the fiber is actually given by y=2, not y [10]. It is useful to define the angle the way that we have because this angle appears naturally in the Stokes and Poincare´ sphere representations in which the physical angular separations are multiplied by two. We are assuming that y is o independent so that DB0 ¼ Db0 ðs3 cos y þ s1 sin yÞ. We are also assuming that birefringence does not contribute to the chromatic dispersion. Both assumptions are completely consistent with the experimental evidence to date. We are also neglecting higher order dispersion and nonlinearities other than the Kerr nonlinearity. It is not difficult to modify Eq. (2) to include these effects when appropriate [5], and we take into account higher order dispersion in some of the system modeling that we present in Section III. A key assumption that is implicit in Eq. (2) is that the local birefringence contains no intrinsic helicity. Intrinsic helicity would appear as a term that is proportional to s2 . This assumption is well justified by the experimental data to date even in moderately twisted fibers. Rashleigh [23] showed that the helicity coefficient is quite small, and attempts to induce intrinsic helicity by twisting the fiber as it is drawn have not proved successful [24]. By contrast, twisting fiber once it has been drawn on a scale comparable to the beat length will lead to a fiber evolution that in many ways mimics the behavior that is expected in a fiber with intrinsic helicity even though the local birefringence is linear [25]. One can also infer that the intrinsic helicity must be small from the measured ratio of cross- to self-phase modulation. In a fiber with linear birefringence, the ratio is 2=3. In a fiber with circular birefringence, the ratio is 2. In a fiber with arbitrary birefringence, this ratio is somewhere in between [26]. Experiments by Botineau

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and Stolen [27] and by Stolen, Botineau, and Ashkin [28] demonstrated the 2=3 ratio that is expected for linearly birefringent fibers. Later theoretical work showed that the Kerr coefficient in a fiber with randomly varying birefringence is expected to be 8=9 as strong in a fiber with fixed birefringence when the intrinsic birefringence is linear [29, 30]. The 8=9 factor has been verified experimentally by Buckland and Boyd [31] and by Chernikov and Taylor [32]. To visualize the evolution of the polarization state of light as it propagates in the fiber, it is useful to define the Stokes parameters, S0 ¼ Uy U;

S1 ¼ Uy s3 U;

S2 ¼ Uy s1 U;

S3 ¼ Uy s2 U

ð5Þ

The last three parameters together define the Stokes vector S ¼ ðS1 ; S2 ; S3 Þ. We note that S02 ¼ S S, so that we can define a unit Stokes vector s ¼ S=S0. The set of normalized Stokes vectors defines a sphere, referred to as the Poincare´ sphere, shown in Fig. 2. The equator corresponds to linearly polarized light at various orientation angles; the þs1 axis corresponds to horizontal polarization; the s1 axis corresponds to vertical polarization; the þs2 axis corresponds to a 45

orientation; the s2 axis corresponds to a 135 orientation. As the latitude increases on the sphere, the ellipticity increases. In the upper hemisphere, the light appears to rotate clockwise as the observor faces an oncoming beam, while, in the lower hemisphere, the light appears to rotate counterclockwise. The þs3 axis corresponds to right circular polarization, while the s3 axis corresponds to left circular polarization.

FIGURE 2

The Poincare´ sphere.


277

When light propagates through a medium with fixed birefringence, its polarization state at a single frequency traces a circle on the Poincare´ sphere around the eigenstates of the fiber, that is, the two polarization states that propagate without changing in the medium. (Note that every circle on a sphere has two centers.) Optical fibers are nearly linearly birefringent, so that the eigenstates are close to the equator of the Poincare´ sphere. In the case of polarization-preserving fiber, in which the birefringence is nearly fixed, the circle traced on the sphere resembles Fig. 3a. However, the random variations of the axes of birefringence that occur in communications fibers move the eigenstates randomly on the equator of the Poincare´ sphere. As a consequence, the polarization state moves randomly over the entire Poincare´ sphere and eventually covers it uniformly, as shown in Fig. 3b. It is often naively supposed that the polarization state undergoes a random walk on the sphere, but the reality is more complex. The diffusion lengths in the equatorial and azimuthal directions are not equal in general and depend on both the beat length LB and the fiber correlation length hfiber . This dependence is intricate and differs depending on whether we consider a local frame that is tied to the local axes of birefringence or a fixed laboratory frame [9]. It turns out that the usual linear PMD only depends on the equatorial diffusion coefficient in the local frame [9], which explains why the existence of several different diffusion lengths has not been much noted to date. However, the other diffusion coefficients impact the interaction of nonlinearity with polarization effects [9, 10] and have been experimentally observed [33]. We note as well that the longest length scale for the polarization state to randomize on the Poincare´ sphere is several kilometers at most, which is short compared to the length scales of interest in communication systems. Thus, it is typically correct to assume that the polarization states rapidly randomize on the Poincare´ sphere.

B. Polarization Mode Dispersion Thus far, in our discussion of the polarization evolution, we have focused on the evolution of a single frequency. The differential evolution of nearby frequencies is what leads to PMD. To study the evolution due to PMD, we rewrite Eq. (2) in the frequency domain, neglecting chromatic dispersion and nonlinearity, to obtain [5] i

~ @U ~ þ Db þ Db0 $ s3 cos y þ s1 sin y U ~ ¼0 iGU @z

ð6Þ

where $ ¼ o o0 is the angular frequency measured with respect to the carrier frequency, and ð1 ~ ðz; $Þ ¼ U dt expði$t ÞUðz; tÞ ð7Þ 1

is the Fourier transform of Uðz; tÞ. Writing the 2 2 identity matrix as I, we now

Ð ~ , where R ¼ cosðy=2ÞIþ i sinðy=2Þs2 is the ~ ¼ exp z Gðz1 Þ dz1 R1 U define V 0

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FIGURE 3 Evolution of the polarization state of a single frequency of light in a medium with (a) fixed birefringence and (b) randomly varying birefringence.

~ , were it not for the z variation of matrix that would diagonalize the evolution of U y. We thus obtain i

~ @V ~ ¼0 þ ½ Db þ Db0 $ s3 þ ðyz =2Þs2 V @z

ð8Þ


279

~ ðz; $Þ ¼ T1 ðzÞV ~ ðz; $Þ, where T satisfies where yz ¼ dy=dz. We now write W the equation i

@T þ ½Dbs3 þ ðyz =2Þs2 T ¼ 0 @z

ð9Þ

~ ðz; $ ¼ 0Þ is constant which corresponds to Eq. (8) at $ ¼ 0. It follows that W 1 1 ~ ~ and the transformation Wðz; $Þ ¼ T R Uðz; $Þ measures the relatively slow evolution of other frequencies relative to o0 . Explicitly, we now find i

~ @W ~ ¼0 þ Db0 $ s 3 W @z

ð10Þ

where s 3 ¼ T1 s3 T. In undersea systems, the differential changes in the polarization states in different wavelength channels are more important than the time spread that occurs in a single wavelength channel. However, PMD is defined in terms of this spread. ~ ðz; $Þ, where ~ ðz; $Þ ¼ að$ÞA So, we now calculate it. To do so, we first write W 2 ~ jAj ¼ 1 and a is real. We now define a matrix Fðz; $Þ such that i

~ @A ~ ¼0 þ FA @$

ð11Þ

From Eqs. (10) and (11), we infer that @F ¼ iDb0 $ðs 3 F Fs 3 Þ þ Db0 s 3 @z

ð12Þ

so that the trace of F is constant as a function of z. Since the transformation ~ ðz; $Þ at different values of $ is unitary, the matrix F is Hermitian. relating A Thus, its eigenvalues are real and its eigenvectors are orthogonal. We designate the eigenvectors as Toff TPMD . The eigenvectors are conventionally referred to as the principal states, while the difference between the eigenvalues, 2TPMD , is referred to as the differential group delay. Physically, the DGD corresponds to the delay that appears between the components of light that are launched along the principal states. To relate the DGD to the pulse spreading, we now define a new set of frequency-dependent Stokes parameters ~ y s3 A ~; s~ 1 ¼ A

~ y s1 A ~; s~ 2 ¼ A

~ y s2 A ~ s~ 3 ¼ A

ð13Þ

which in turn allows us to define a new unit Stokes vector s~ ¼ ð~s1 ; s~ 2 ; s~ 3 Þ in the frequency domain and hence a new Poincare´ sphere. We have used a to distinguish s~ from the time-domain quantities S or s that we defined earlier in Eq. (5) et seq., but we stress that s~ is not the Fourier transform of either S or s. The relationship between s~ and either S or s is not simple, although s~ becomes equal to s in the case of a single frequency corresponding to $ ¼ 0. Because all three quantities are referred to in the literature as ‘‘S,’’ the readerÐ must pay careful 1 attention. Defining the mean signal time T ðzÞ ¼ 1 tjWðz; tÞj2 dt=

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Ð1 Ð1 jWðz; tÞj2 dt and the mean square signal time T 2 ðzÞ ¼ 1 t 2 jWðz; tÞj2 dt= Ð1 1 2 2 1 jWðz; tÞj

dt,2 we may define the squared signal spread S ðzÞ ¼ T 2 ðzÞ T ðzÞ . By analogy with the Stokes vector, it is conventional to write 1 FðzÞ ¼ Toff I þ ðO1 s3 þ O2 s1 O3 s2 Þ 2

ð14Þ

which defines a vector V ¼ ðO1 ; O2 ; O3 Þ, whose magnitude equals the DGD and that is referred to as the polarization dispersion vector. The general expression for the spreading due to PMD is complex [5], but when the variation of O and s~ can be ignored over the bandwidth of the signal, one finds that [5, 34, 35] 1 S2 ðzÞ S2 ðz ¼ 0Þ ¼ jVðz; o0 Þ s~ ðz; o0 Þj2 4

ð15Þ

To determine the length scale on which spreading occurs, we may first write cos ys sin ys expðifs Þ ð16Þ s 3 ¼ sin ys expðifs Þ cos ys which defines the angles ys and fs . Calculating O21 ðzÞ at o ¼ o0 , we find ðz ð z1 0 2 O1 ðzÞ ¼ 8 dz1 fDb ðz1 Þ cos½ys ðz1 Þg dz2 fDb0 ðz2 Þ cos½ys ðz2 Þg ð17Þ 0

0

To make further progress, one must know the autocorrelation function Cðz1 ; z2 Þ ¼ hDb0 ðz1 Þ cos½ys ðz1 ÞDb0 ðz2 Þ cos½ys ðz2 Þi, where hi indicates the average over an ensemble of fibers. A wide variety of fiber models all imply [4, 5, 9] that Cðz1 ; z2 Þ ¼ 13 h½Db0 ðzÞ2 i expðjz1 z2 j=hfiber Þ. Using this autocorrelation function in Eq. (17) and noting that hO21 i ¼ hO22 i ¼ hO23 i, we conclude hO2 i ¼ 8h½Db0 ðzÞ2 ifhfiber z þ h2fiber ½expðz=hfiber Þ 1g

ð18Þ

which is Poole’s classic result [4, 36]. To determine the effects of randomly varying birefringence on a full timedomain signal, one must solve Eq. (2) using a model for the variation of DBðzÞ. Wai and Menyuk [9] studied two different physical models of the random variation, one of which took both Db cos y and Db sin y to be Maxwellian distributed and the other of which held Db fixed and with y uniformly distributed. Both models yield nearly identical statistical behavior for the evolution of the field’s polarization properties. However, both of these models—referred to as fine step models—require resolving the y variations on a length scale that is small compared to the fiber autocorrelation length. These step sizes are too small to be useful. In practice, one must take step sizes that are on the order of kilometers. Marcuse et al. [10] showed that a coarse step procedure in which one fixes the birefringence for a length that is long compared to the maximum diffusion length on the Poincare´ sphere and then scrambles the polarization uniformly on the sphere for all frequencies will yield the correct PMD statistics if one artificially lowers Db0 by a factor ð2hfiber =zÞ1=2, where z is the step size. They also showed


281

that this approach does not yield the correct statistics for the nonlinear fluctuations, but these fluctuations are too small to matter in communication systems to date. In Section III of this chapter, we describe a reduced model that just follows one set of Stokes parameters for the signal and the noise in each of the channels. To determine the effect of PMD on each set of Stokes parameters, one must adapt the coarse step procedure that we just described in the preceding paragraph. We begin by defining h i N P Uðz; tÞ ¼ UðmÞ ðz; tÞ exp ibðmÞ z ioðmÞ t ð19Þ m¼1

where U is the wave envelope of the mth channel and bðmÞ and oðmÞ are its corresponding wavenumber and frequency with bðo0 Þ and o0 subtracted, respectively. We now define the average Stokes parameters for each channel, writing ð i 1 t2 h ðmÞ 2 S0ðmÞ ¼ jU1 ðtÞj þ jU2ðmÞ ðtÞj2 dt T t1 ð i 1 t2 h ðmÞ 2 ðmÞ S1 ¼ jU1 ðtÞj jU2ðmÞ ðtÞj2 dt T t1 ð i 2 t2 h ðmÞ S2ðmÞ ¼ Re U1 ðtÞU2ðmÞ* ðtÞ dt T t1 ð i 2 t2 h ðmÞ Im U1 ðtÞU2ðmÞ* ðtÞ dt S3ðmÞ ¼ T t1 ðmÞ

where T ¼ t2 t1 is assumed to be large enough that the channel becomes statistically stationary. We next define the average Stokes vector of the mth ðmÞ channel as SðmÞ ¼ ðS1ðmÞ ; S2ðmÞ ; S3ðmÞ Þ, and we denote its magnitude by Spol . The degree of polarization of the mth channel ðmÞ ðmÞ ¼ Spol =S0ðmÞ dpol

ð21Þ

is between 0 and 1. To apply the coarse step method in an optical fiber with PMD, we proceed by first noting that PMD induces no change in the total power so that S0ðmÞ ðz þ zÞ ¼ S0ðmÞ ðzÞ, where z is the step size. We also find that [16, 17], ðmÞ ðmÞ SðmÞ ðz þ zÞ ¼ MðmÞ R ðzÞMj ðzÞS ðzÞ

ð22Þ

where the subscript j indicates the jth z step in the algorithm. The matrix 0 1 1 0 0 B 0 ðmÞ 0 ðmÞ C ð23Þ MðmÞ R ¼ @ 0 cosðDb o zÞ sinðDb o zÞ A 0 ðmÞ 0 ðmÞ 0 sinðDb o zÞ cosðDb o zÞ

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accounts for the channel-dependent rotation due to the fiber birefringence and differs for each channel but is the same at each step. The matrix 0 cos yj sin yj cos cj B sin y cos f cos y cos f cos c sin f sin c ðmÞ Mj ¼ @ j j j j j j j sin yj sin fj cos yj sin fj cos cj þ cos fj sin cj sin yj sin cj

1

cos yj cos fj sin cj sin fj cos cj C A cos yj sin fj sin cj þ cos fj cos cj

ð24Þ

induces the random rotation at the end of each step that is required by the coarse step method. We note that it is the same as the well-known Euler angle rotation matrix [37]. It is the same for each wavelength channel but differs at each step. At each step, the cos yj are chosen randomly from a uniform distribution between 1 and 1, while the fj and cj are chosen randomly from a uniform distribution between 0 and 2p. The quantity Db0 that one must use in Eq. (23) is related to the measured PMD as follows: First, we note that the PMD is defined as hOi=z1=2 , and, assuming distribution of the DGD, hO2 i ¼ ð3p=8ÞhOi2 , so that pffiffiffiffiffiffi a Maxwellian 0 1=2 Db ¼ ð 3p=8Þð1=hfiber Þ hOi=z1=2 from Eq. (18). Recalling that Db0 must be reduced in the coarse step method by the factor ð2hfiber =zÞ1=2, we use pffiffiffiffiffiffi ð25Þ Db0 ¼ ð 3p=8Þð2=zÞ1=2 PMD C. Polarization-Dependent Loss and Gain In addition to PMD, polarization effects due to polarization-dependent loss and gain play a major role in undersea systems. They interact with the PMD in a complex way, and it is not possible to accurately treat any of these effects in isolation from the others. PDL and PDG are contributed by the amplifiers, in contrast to PMD, which is mostly contributed by the optical fiber transmission line. Amplifiers in optical communication systems typically operate with gain saturation and=or active gain control elements in order to keep the total output power nearly constant after every amplifier stage. At the same time, amplifiers have polarization-sensitive elements like isolators and WDM couplers that induce polarization-dependent loss. We are not concerned with the overall polarizationindependent loss in amplifiers because we can assume that the amplifiers leave the overall gain constant. Thus, in the Jones representation for each channel m, we may model the effect of the PDL as ! ! ! 1 0 U1ðmÞ U1ðmÞ ð26Þ ¼ 0 a U2ðmÞ before U2ðmÞ after where the second component is in the direction of maximum loss, and a is related to xPDL , with PDL in decibels, through the relationship xPDL ¼ 20 log10 a.


283

Typical values of xPDL in undersea systems are on the order of 0.1 dB per amplifier, and it is important to keep this value low [15]. Converting to the Stokes representation using Eq. (20), we obtain ðmÞ S0;after ¼

1 þ a2 ðmÞ 1 a2 ðmÞ S0;before þ S1;before 2 2

ðmÞ S1;after ¼

1 a2 ðmÞ 1 þ a2 ðmÞ S0;before þ S1;before 2 2

ð27Þ

ðmÞ ðS2 þ iS3 ÞðmÞ after ¼ aðS2 þ iS3 Þbefore

where we recall that the Stokes parameters are averaged over time. PDG is due to polarization hole burning induced by the incoming signal to an EDFA. The incoming signal saturates the amplifier, lowering its gain. While the gain in both the signal’s polarization and in the polarization orthogonal to the signal are lowered, the gain in the signal’s polarization is reduced slightly more. Thus, the gain in the polarization orthogonal to the incoming signal is slightly larger than the gain in the polarization of the incoming signal. The amount of PDG in a single amplifier is only about 0.07 dB for an EDFA with 3 dB of gain compression, that is, an amplifier in which the gain is reduced by a factor of 2 by gain saturation relative to the small signal gain. The PDG becomes larger as the amplifier goes deeper into gain compression. The magnitude of the polarization hole burning is proportional to the degree of polarization dpol of the incoming signal. We may model PDG much like PDL, except that the direction of maximum gain is determined by the existing signal in a given system. Thus, writing S0ðtotalÞ ¼

N P

m¼1

S0ðmÞ ;

SðtotalÞ ¼

N P

SðmÞ

m¼1

ð28Þ

we find that the total degree of polarization is dpol ¼ jSðtotalÞ j=S0ðtotalÞ and the total state of polarization is s ¼ SðtotalÞ =jSðtotalÞ j. We now write U1ðmÞ ðtÞ

U2ðmÞ ðtÞ

!

after

¼R

1

0

0

g

!

1

R

U1ðmÞ ðtÞ

U2ðmÞ ðtÞ

!

before

ð29Þ

where g is the polarization-dependent gain, normalized to the gain in the polarization state of the input signal. The value of g is related to xPDG , with PDG measured in decibels, through the relationship xPDG dpol ¼ 20 log10 g [12]. The rotation matrix R is determined by the overall polarization state of the incoming light since it is this polarization state that determines the polarization state with reduced gain due to PDG, while R1 is the inverse of R. The elements of R are related to s through the relationships s1 ¼ jr11 j2 jr12 j2 and

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* . Transforming once again from the Jones representation to the s2 þ is3 ¼ 2r11 r12 Stokes representation, we obtain

SðmÞ after ¼ ðmÞ S0;after ¼

g2 1 ðmÞ g2 þ 1 ðmÞ ðg 1Þ2 s ðs SðmÞ S0;before s þ Sbefore þ before Þ 2 2 2

g2 þ 1 ðmÞ g2 1 S0;before s SðmÞ before 2 2

ð30Þ

where s in Eq. (30) is the unit vector of the total polarization state before the light passes through the PDG element. In systems with a small number of channels, PDG is a pernicious effect because it leads to excess noise and channel outage [11–13]. We can reduce this effect by scrambling the polarization state of the incoming signal to make the degree of polarization, dpol as small as possible. However, PDL tends to repolarize polarization-scrambled signals, which then become susceptible to PDG. To study the repolarization due to PDL, we consider a simple example in which there is only a single channel. In the case, it is possible to calculate the evolution of the probability distribution function of the degree of polarization, f ðdpol Þ, analytically using the methods of stochastic differential equations. These methods have become an important tool in the analysis of optical fibers with randomly varying birefringence since their introduction by Gisin [38] and by Foschini and Poole [39]. They are often considered difficult, but in our view they are simply an extension of the standard tools of calculus. The currently available textbooks on this subject are written at the level of rigor that is common among mathematicians, which makes them difficult to penetrate for some applied physicists and engineers and may account for some of the perceived difficulty. Wai and Menyuk [9] have given an elementary derivation of the basic approach at the level of rigor common among applied physicists and engineers. There are two versions of stochastic differential calculus that apply in different physical contexts [40]. Both contexts appear in optical fiber transmission problems. The first context is one in which the source of the randomness is varying continually along with the dynamic variables. An example is the evolution of the polarization dispersion vector in an optical fiber, the problem that was considered by Gisin [38] and by Foschini and Poole [39]. In this case, Stratonovich calculus is appropriate. The second context is when the dynamic evolution is physically separated from the randomization. In the example that we consider here, in which we study the evolution of dpol , the randomization of the Stokes parameters, which occurs in the optical fibers, is separate from the evolution of dpol , which occurs in the amplifiers. In this case, Itoˆ calculus is appropriate.


285

We start by combining Eq. (24) and Eq. (27) to obtain S0; jþ1 ¼

1 þ a2 1 a2 S0; j þ Spol; j cos yj 2 2

S1; jþ1 ¼

1 a2 1 þ a2 S0; j þ Spol; j cos yj 2 2

ð31Þ

ðS2 þ iS3 Þjþ1 ¼ aSpol; j expðifj Þ where the cos yj are independent and identically distributed (i.i.d.) random variables uniformly distributed in the range ½1; 1 so that hcos2 yj i ¼ 1=3. Similarly, the fj are i.i.d. random variables that are independent of the cos yj and are uniformly distributed in the range ½0; 2p. The goal is to calculate f ðdpol; j Þ, where dpol; j ¼ Spol; j =S0; j . Only the ratio dpol; j is meaningful since the difference equations, Eqs. (31), do not take into account the polarizationindependent gain and loss. We will consider the initial condition dpol;0 ¼ 0, corresponding to a polarization-scrambled channel. We first note that 2 2 2 2 2 2ðjþ1Þ S0; , which motivates one to replace jþ1 Spol; jþ1 ¼ a ðS0; j Spol; j Þ ¼ a j S0; j and Spol; j with xj ¼ S0; j =a and yj ¼ Spol; j =aj, which satisfy x2j y2j ¼ 1. One then obtains the difference equation xjþ1 ¼

1 þ a2 1 a2 2 xj þ ðxj 1Þ1=2 cos yj 2a 2a

ð32Þ

Since a is small, this difference equation can be approximated by the stochastic differential equation dx ¼ rx þ ðx2 1Þ1=2 g dj

ð33Þ

where j is now treated as a continuous variable, r ¼ ð1 aÞ2 =2a and s2g ¼ ð1 a2 Þ2 =12a2 . We note that Eq. (32) is a forward difference equation, which follows physically from the separation of the random variation of cos yj and fj in the optical fibers and x in the amplifiers. Consequently, Eq. (33) should be interpreted in the sense of Itoˆ, which implies that the evolution of the probability distribution function of x; fx ðxÞ, is governed by the Fokker–Planck equation [40] s2g @2 2 @fx @ þ r xfx ðx 1Þ fx ¼ 0 @x 2 @x2 @j

ð34Þ

It is useful now to change variables from x to g, where x ¼ cosh g. It follows that dpol ¼ tanh g. One then finds that fg ðgÞ ¼ fx ½xðgÞ dx=dg ¼ fx ½xðgÞ= sinh g is governed by the Fokker–Planck equation @fg 1 2 @1 1 @2 fg fg s2g 2 ¼ 0 þ r sg ð35Þ 2 @g g 2 @g @j

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which has the solution 2 g2 fg ðgÞ ¼ 1=2 ð2s2g jÞ Gðb=s2g Þ 2s2g j

!ðr=s2g Þð1=2Þ

g2 g2 exp ’ 1=2 p ð2s2g jÞ3=2 2s2g j 4

!

g2 exp 2 2sg j

! ð36Þ

where Gð Þ indicates the usual Gamma function. Using f ðdpol Þ ¼ fg ðgÞdg=dðdpol Þ, one may compare Eq. (36) to a direct solution of original difference equations, Eq. (32). We show this comparison in Fig. 4, where Eq. (32) was solved with 106 different realizations. We see that the analytical theory yields results that are indistinguishable from those yielded by the original difference equations. The original difference equations do not have an analytical solution and so could not have yielded the analytical result directly. Thus, our results show the power of the methods of stochastic differential equations. A thorough discussion of the impact that repolarization has on undersea systems is given in Section III. However, some simple conclusions may already be drawn from the simple results that we have obtained here. Assuming that repolarization of 15% is acceptable, and allowing an outage probability of 5 106 , one finds upon integrating Eq. (36) at j ¼ 300 that xPDL < 0:025, which is about a quarter of the best current value [15]. While this sort of reduction of xPDL is difficult to obtain, it is worth striving for. D. Comments on Notation and Nomenclature As Gordon and Kogelnik [21] have pointed out, there is little uniformity of notation and nomenclature among researchers studying polarization effects in optical fibers. Indeed, the same authors (including us) will switch notation and nomenclature from paper to paper. Since it has been averred [41] that this lack of uniformity is an impediment to at least experimental progress, some discussion of our own notation and nomenclature, as well as its relationship to the notation and

FIGURE 4 Comparison of the distribution f ðdpol Þ obtained by Monte Carlo simulation of the original difference equations to the theoretically calculated function. The parameters are xPDL ¼ 0:1 dB. (a) j ¼ 100. (b) j ¼ 300. The two approaches yield indistinguishable results.


287

nomenclature of others, is appropriate. First, as noted previously, we use negative carrier frequencies. By contrast, Gordon and Kogelnik [21] use positive carrier frequencies, as do Poole and Giles [42]. As noted previously, our choice of negative carrier frequencies is dictated by a desire to be consistent with nearly all the theoretical literature that is focused on dispersive and nonlinear effects in optical fibers. This choice is consistent with Agrawal [7] as well as with Born and Wolf [22]. We find that if we define the Stokes parameters in the traditional way, as done in this chapter, then s3 ¼ þ1 corresponds to right circular polarization, and s3 ¼ 1 corresponds to left circular polarization. For clarity, we note that right circular polarization implies that the electric field vector of the light appears to rotate in a clockwise fashion when heading toward the observer. However, if one uses positive carrier frequencies and defines the Stokes parameters in the traditional way, then s3 ¼ 1 corresponds to right circular polarization. Poole made this choice implicitly since he uses the traditional Stokes parameters. There is significant historical precedent for this choice, which coincides with the choice of Shurcliff and Ballard [43], a standard reference on polarized light. By contrast, Gordon and Kogelnik [21] redefine s3 so that s3 ¼ þ1 corresponds to right circular polarization. This choice appears to be unprecedented. We note that most of the literature on polarization effects in optical fibers is indefinite about both the definition of the Stokes parameters and the sign of the carrier frequencies. For most applications, it does not matter; however, it can be quite important when making careful comparisons between theory and experiment [41]. In another notational innovation, Gordon and Kogelnik redefined the standard Pauli matrices. Doing so simplifies the transformation between the Stokes and Jones vectors, allowing them to replace the last three components in our Eq. (5) with the expression sj ¼ Uy sj U. We have not adopted this notation in this chapter, and it is our view that in most cases it is not worth the confusion that it might lead to, given the long history of the Pauli representation. In most applications, one picks either the Stokes or the Jones representation, and it is not necessary to do much transformation back and forth. However, this notation is a real computational convenience if one is making many transformations between the two representations. Finally, we turn to the question of PMD-related notation and nomenclature. We write the polarization dispersion vector as V. This choice is consistent with Poole [4], Gisin [38], and most of the rest of the literature in this field. By contrast, Gordon and Kogelnik use t. We have used V in this chapter in order to conform with what appears to be the consensus and to avoid adding to the notational confusion. There is no consensus as to what this vector is called. Poole has historically referred to it as the ‘‘polarization dispersion vector’’; Gordon and Kogelnik refer to it as the ‘‘PMD vector.’’ We have used Poole’s nomenclature. Since he first described the concept, there is some precedent for following his naming convention. Moreover, we dislike the term ‘‘PMD vector’’ because, as noted earlier, PMD is often confused with DGD. The magnitude of the polarization dispersion vector has units of time and is a DGD, not a PMD. In closing, we

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note that our polarization dispersion vector, like that of Gordon and Kogelnik but in contrast to that of Poole, points toward the slow axis.

III. REDUCED STOKES PARAMETER MODEL A. Model Formulation In Sections II.B and II.C, we obtained equations that govern the evolution of the Stokes parameters in an optical fiber transmission system with PMD, PDL, and PDG. In this section, we develop these equations into a system model that will enable us to predict the penalties due to these effects. In addition to modeling the PMD, PDL, and PDG, we must account for the effects of amplified spontaneous emission (ASE) noise. We begin by introducing ðmÞ a new set of Stokes parameters for the noise ðS0;noise ; SðmÞ noise Þ. We must track these parameters separately from the signal Stokes parameters so that we can compute the SNR and ultimately a Q-factor for each wavelength channel. Because the ASE noise is unpolarized, each amplifier will cause the following change in the Stokes parameters, ðmÞ ðmÞ S0;noise;after ¼ S0;noise;before þ 2nsp ðG 1ÞBðmÞ hn ðmÞ SðmÞ noise;after ¼ Snoise;before

ð37Þ

where nsp is the spontaneous emission factor, G is the amplifier gain, hn is the energy of a single photon, and BðmÞ is the bandwidth of the mth channel. These Stokes parameters are affected by the PMD, PDL, and PDG in exactly the same way as the signal Stokes parameters and participate in determining the degree of polarization and the total Stokes parameters. Additionally, if any part of the gain bandwidth of the EDFA is not included in one of the optical channels, then this noise energy will participate in the total energy balance. We may write for this additional portion, ðaddÞ ðaddÞ S0;noise;after ¼ S0;noise;before þ 2nsp ðG 1ÞBðaddÞ hn

ð38Þ

and we assume that this contribution is unpolarized. This portion is not included in the example WDM systems that we will present later in this chapter, but it could be present in some practical systems. We now write S0ðtotalÞ ¼ SðtotalÞ ¼

n P

m¼1 n P

m¼1

S0ðmÞ þ SðmÞ þ

n P

m¼1 n P

m¼1

ðaddÞ S0;noise þ S0;noise

SðmÞ noise

ð39Þ

and the degree of polarization becomes dpol ¼ jSðtotalÞ j=S0ðtotalÞ . The final step is to take into account the effect of gain saturation or gain clamping by assuming that


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the total power at the output of the amplifier is fixed at a value S. We then ðmÞ ðaddÞ renormalize S0ðmÞ ; SðmÞ ; S0;noise ; SðmÞ by the factor S=S0ðtotalÞ. noise , and S0 We summarize the complete procedure schematically in Fig. 5. This procedure is repeated iteratively from amplifier to amplifier. From the calculated signal and noise Stokes parameters, it is possible to determine QðmÞ —the so-called Q-factor—for each channel m and from that to infer the penalty due to PDL and PDG in combination with PMD. To calculate this penalty, we first note that a QðmÞ that we calculate from this model is not meaningful by itself because the model does not take into account degradation due to nonlinearity and chromatic dispersion. What is meaningful is the difference DQðmÞ between the QðmÞ values that we calculate when PDL and PDG are present and when they are absent for a specific realization of fiber PMD. To calculate QðmÞ for a particular choice of PMD, PDL, and PDG, we must obtain the effective signal-to-noise ratio (ESNR) of channel m after detection in the receiver. The optical signal-to-noise ratio (OSNR) equals S0ðmÞ =S0;noise , but there is no simple, universal relationship between the ESNR and the OSNR. It depends on the modulation format, the signal distortion during transmission, and the details of the receiver. In the receiver, the signal will typically pass through a photodiode detector, an electrical filter, and a time-domain sampler with a narrow

FIGURE 5 Schematic illustration of the modeling procedure.

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window. There is often a nonlinear limiter in the receiver as well. These factors combine to determine the receiver enhancement factor Z that relates the ESNR and the OSNR for channel m through the relationship ESNRðmÞ ¼ Z OSNRðmÞ . For standard NRZ transmission, it is usual to approximate Z ¼ 2. This value is exact for ideal square NRZ pulses and ideal integrate-and-dump receivers [44, 45]. In the full simulations that we compared to the reduced model, we used an ideal square law detector to model the photodiode, we used a 10th-order Bessel filter whose bandwidth equaled the data rate (5 or 10 GHz), and we assume that there is an ideal instantaneous sampler in the center of the timing window. Because it is only possible to keep a limited number of bits in the full simulations, there is too much statistical variation if we numerically implement an ideal sampler to obtain accurate results. So, instead we numerically calculate the SNR after the electrical Bessel filter, and we multiply that by the enhancement factor Z. In the work reported in this chapter, we approximated Z ¼ Ppeak =Pave, the ratio of the peak power to the average power in the optical signal channel just prior to the receiver. For the standard nonreturn-to-zero (NRZ) modulation format, this ratio is 2; for the standard return-to-zero (RZ) modulation format, this ratio is 4; for the chirped return-to-zero (CRZ) of Bergano et al. [46], in which the pulses reach their minimum duration just prior to detection, this ratio is approximately 5.3. We recently used noise-free simulations to find that the actual efficiency factor for the RZ modulation format and our electrical filter is in the range Z ¼ 3:2–3.4, depending on the propagation distance. We note that in commercial systems, where the bandwidth of the electrical filter is 70–80% of the data rate, we would expect Z to be somewhat lower. We also expect that the actual enhancement factor for the CRZ format is somewhat less than 5.3. Because we are calculating DQðmÞ in decibels, the results are insensitive to the choice of Z. We may now use a formula relating the Q-factor to the ESNR, assuming that the noise is Gaussian distributed [44, 45],

ðmÞ

Q

sffiffiffiffiffiffiffiffiffiffi 2Bopt ESNRðmÞ ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2ESNRðmÞ þ 1 þ 1 Belec

ð40Þ

where Bopt is the optical bandwidth and Belec is the electrical bandwidth. We are assuming that the receiver is insensitive to polarization and that there is no signal power in the spaces, so that there is an infinite extinction ratio. Physically, the electrical detector at the end of the transmission line receives 2Bopt =Belec noise modes. Therefore, the signal–spontaneous beat noise power S0;sigspon is given by ðPpeak =Pave Þ1=2 ðS0 S0;noise Þ1=2 ðBelec =2Bopt Þ1=2 , while the spontaneous–spontaneous beat noise power S0;sponspon just equals S0;noise . The noise power in the marks is given by S0;sigspon þ S0;sponspon, while the noise power in the spaces is just given by S0;sponspon.


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B. Theoretical Validation 1. Separability of Polarization Penalties In order for the penalties due to PDL and PDG to be separable from the penalties due to nonlinearity and chromatic dispersion, the nonlinearity and chromatic dispersion must not be allowed to affect the degree of polarization. In this subsection, we investigate the conditions under which the impact of nonlinearity and chromatic dispersion on the degree of polarization of individual channels can safely be ignored. Our starting point is the Manakov equation, written in the form [9, 10] i

@U 1 00 @2 U 8 b þ gjUj2 U ¼ 0 @z 2 @t 2 9

ð41Þ

This equation may be derived from Eq. (2) by averaging over the rapidly and randomly varying birefringence and neglecting all fluctuating terms. Physically, Eq. (41) holds in the limit of low PMD. We also neglect the polarizationindependent gain and loss since it has no effect on our results except to effectively renormalize the distance over which nonlinearity acts [16, 19, 20]. We will also assume that the dispersion between channels is large since we anticipate that the effect of nonlinearity and chromatic dispersion on the degree of polarization of individual channels will be negligible in this limit. Substituting Eq. (19) into Eq. (41), we obtain i

n P @UðmÞ 1 00 @2 UðmÞ 8 8 b þ gjUðmÞ j2 UðmÞ þ g jUðqÞ j2 UðmÞ ¼ 0 2 2 9 9 q¼1;6¼m @z @t

ð42Þ

where we have neglected the four-wave mixing terms, consistent with our assumption that the dispersion between the channels is large. We now find that dS0 =dz ¼ 0 and that dS1ðmÞ 8g ¼i 9T dz

ð t2 t1

½U1ðmÞ U2ðmÞ* þ U1ðmÞ* U2ðmÞ

½U1ðmÞ U2ðmÞ*

U1ðm*Þ U2ðmÞ

i P n

q¼1;6¼m

n P

½U1ðqÞ U2ðqÞ* U1ðqÞ* U2ðqÞ

q¼1;6¼m

½U1ðqÞ U2ðqÞ*

þ

U1ðqÞ* U2ðqÞ

dt

ð43Þ

where we have used the definitions of the Stokes parameters in Eq. (20). In a highly dispersive system, the channels with q 6¼ m rapidly pass through channel m in the time domain. Consequently, the evolution of the mth channel is only affected by the average variation in the other channels. So, we can effectively treat these other channels as continuous waves. We thus make the substitution ð 1 t2 ðqÞ ðqÞ* ½U U U1ðqÞ* U2ðqÞ dt ð44Þ U1ðqÞ U2ðqÞ* U1ðqÞ* U2ðqÞ ! T t1 1 2

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from which we conclude n dS1ðmÞ 8 P ¼ g ½S2ðmÞ S3ðqÞ S3ðmÞ S2ðqÞ 9 q¼1 dz

ð45Þ

n dSðmÞ 8 ðmÞ P ¼ gS SðqÞ 9 dz q¼1

ð46Þ

We can find similar expressions for dS2ðmÞ =dz, and dS3ðmÞ =dz, so that we finally obtain

The effect of dispersion does not appear in Eq. (46); only the nonlinearity appears, and the equations are analogous to the equations that govern nonlinear rotation of continuous-wave beams [47]. However, the large local dispersion is critical because it must be large enough so that each channel appears as a continuous-wave background to its neighbors. It is an immediate consequence of Eq. (46), referred to as the mean field model, that the Stokes parameters of a single-channel system do not evolve. Moreover, regardless of the number of channels, the polarization of each channel simply rotates, so that the degree of polarization is not changed. Although the mean field model is nonlinear, a complete analytical solution can be found. This result is intrinsically significant because the number of largedimensional nonlinear systems for which exact solutions can be found is limited. However, the form is somewhat cumbersome and is not presented here. It may be found elsewhere [16, 20]. The mean field model has been validated by simulating NRZ signal transmission with dispersion management [16, 19, 20]. The NRZ signal was polarization scrambled using synchronous phase modulation, as described by Bergano and Davidson [48]. Polarization scrambling of the optical carrier is achieved by differential modulation of the optical phases of two polarization states with a sinusoidal signal, U1ðmÞ ðtÞ ¼ A1 ðtÞ exp½if1 ðtÞ and U2ðmÞ ðtÞ ¼ A2 ðtÞ exp½if2 ðtÞ, where f1 ðtÞ ¼ d1 þ a1 cosðoph t þ c1 þ p=2Þ and f2 ðtÞ ¼ d2 þ a2 cosðoph t þ c2 þ p=2Þ. Here, one lets A1 ðtÞ ¼ c1 HðtÞ and A2 ðtÞ ¼ c2 HðtÞ, where c1 and c2 are constant coefficients. One sets HðtÞ ¼ 1 in the time slots of the marks and HðtÞ ¼ 0 in the time slots of the spaces, except when making a transition from a space to a mark or a mark to a space, in which case the transition is smoothed over 5% of the pulse rise and fall times using a hyperbolic tangent function. Choosing a1 ¼ 3:307 and a2 ¼ 0:903, one finds that the difference nearly equals j0;1 , the first zero of the zeroth Bessel function. With this choice and setting c1 ¼ c2 , an ideal square pulse is depolarized. The sum a1 þ a2 was chosen to be consistent with Bergano and Davidson [48]. The phase modulation frequency oph corresponds to the bit rate, c1 and c2 describe the relative phases between the phase modulation and the data bits, and d1 and d2 denote arbitrary offsets. By varying c1 ; c2 ; d1 ; d2 ; c1 , and c2, one can adjust the initial degree of polarization to any desired value.


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In Fig. 6, we show the evolution of the Stokes parameters of two channels spaced 1 nm apart. In Fig. 6a, we show the prediction of the mean field model. In Fig. 6b, we show the evolution in a dispersion map that uses a span of normal dispersion fiber at D1 ¼ 2 ps=nm-km, followed by a span of anomalous dispersion fiber at D2 ¼ 17 ps=nm-km, where the dispersions are at a central wavelength of 1.58 mm. The third-order dispersion was 0.07 ps=nm2 -km in both spans, from which the dispersion at any particular wavelength could be determined. The length of the map was 1000 km, the bit rate was 5 Gb=s, and the power in each channel was approximately 0.4 mW. In Fig. 6c, the dispersions were multiplied by 10. Comparing Figs. 6a and 6b, one finds that visible quantitative differences exist between the predictions of the Manakov model, Eq. (41), and the mean field model, Eq. (46), that only disappear when the dispersion becomes quite large as shown in Fig. 6c. Nonetheless, the Stokes parameters still oscillate around their

FIGURE 6 Evolution of the Stokes vector components as a function of distance in a 5-Gbps system. The dispersion map length is 1000 km, and the channel spacing is 0.5 nm. The solid lines are the Stokes components of channel 1; the dashed lines are the Stokes components of channel 2. (a) Stokes model result. (b) Manakov model result, D1 ¼ 2 ps=nm-km, D2 ¼ 17 ps=nm-km. (c) Manakov model result, D1 ¼ 20 ps=nm=km, D2 ¼ 170 ps=nm-km. Other simulation parameters are l ¼ 1550 nm for channel 1, l ¼ 1550:5 nm for channel 2; c1 ¼ 0 and c2 ¼ 0:7p for channel 1, c1 ¼ 0 and c2 ¼ 0:7p for channel 2; the peak power in the 1-polarization is 0.24 mW for channel 1 and 0.2 mW for channel 2; the peak power in the 2-polarization is 0.2 mW for channel 1 and 0.24 mW for channel 2.

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initial values in Fig. 6b, although with somewhat different frequencies and amplitudes than in Fig. 6a. There are no long-term drifts in the Stokes parameters from the predictions of the Manakov model. Thus, we would anticipate that there is little change in the degree of polarization, and this prediction is borne out in Fig. 7, where we show dpol for each channel over 10,000 km. The change is only about 0.02. In particular, one finds that if dpol ¼ 0 initially for both channels, which is obtained by setting A1 ¼ A2 , then the channels undergo little repolarization. Wang [16] and Wang and Menyuk [20] carried out extensive parameter studies to determine the limits of validity of the mean field model. They found that as they increase the number of channels, the predictions of the mean field model agree better with the Manakov model because the presence of multiple channels leads to better averaging over the different channels. As the data rate increases, the predictions of the mean field model again agree better with the Manakov model assuming that the channel spacing scales proportionately. As noted earlier, adding realistic polarization-independent gain and loss makes no difference because it merely rescales the equations. One also finds that adding amplitude modulation so that the equations are RZ rather than NRZ makes no significant difference. When the channel spacing increases, the predictions of the mean field model agree better with the Manakov model and when the channel spacing decreases, the predictions deteriorate. At a channel spacing of about 0.3 nm for the 5-Gbps system that Wang and Menyuk considered, the predictions become unacceptably poor. Similarly, reducing the map length leads to worse averaging and deterioration of the predictions of the mean field model. Below about 200 km, the discrepancies become unacceptable. In any real system, it is important to carry out a validation effort like the one just described here prior to validating the full Stokes model presented in Section III.A by comparing it to full system simulations including PDL and PDG. In order for the Stokes model to yield useful results, the changes in any channel’s degree of polarization induced by nonlinearity, chromatic dispersion, and intrachannel PMD must be negligible.

FIGURE 7 Evolution of the degree of polarization as a function of distance. Parameters are the same as those in Fig. 6b.


295

2. Stokes Model Validation We now present a validation of the Stokes model described in Section III.A. We compare the Stokes model to a full model that includes the effects of PDL and PDG as well as PMD for both single-channel and eight-channel WDM systems at a data rate of 10 Gbps per channel. In the WDM studies, a channel spacing of 1 nm was used. All the results presented in this subsection used an RZ format. Additional work that uses a data rate of 5 Gbps per channel and studies the NRZ and CRZ formats may be found in [16]. The results are similar. The full model is based on Eq. (2). These studies [16, 17] used a periodic dispersion map that consisted of one section of a single-mode fiber whose dispersion D1 at l0 ¼ 1:55 mm is 16 ps=nm-km and whose length is 264 km, and another section of dispersion-shifted fiber whose dispersion D2 at l0 ¼ 1:55 mm is 2 ps=nm-km and whose length is 33 km. In both sections, the dispersion slope was 0.07 ps=nm2 -km. Channels for which l 6¼ l0 had pre- and post-dispersion compensation, split equally, to compensate for the excess dispersion. In the WDM simulations, each channel was filtered using a 10th-order, 60-GHz optical Bessel filter at the end of the transmission line. All simulations included squaring in the photodetector and a 10th-order, 10 GHz electrical filter. The simulations used the standard coarse step method [9], described in Section II.B, to include PMD, and used Eqs. (27) and (30), presented in Section II.C, to include PDL and PDG. The simulations used standard Monte Carlo methods to include ASE noise [16]. Each set of parameters was studied using 20 different realizations of the ASE noise and the fiber. However, the bit string was the same in all 20 cases in order to avoid Q-variations due to the pattern dependences in the limited strings of 64 bits per channel that it was possible to keep in the simulations. For each set of parameters, the decision level in the full model simulations was empirically set to obtain the best OSNR. The OSNR was computed in the time domain, after the Bessel filter, by calculating ðI1 I0 Þ=I0 , where I1 is the average current in the marks and I0 is the average current in the spaces. After determining the OSNR for each of the 20 realizations, Wang [16] and Wang and Menyuk [20] found the corresponding Q values using Eq. (40) after multiplying the OSNR by Z to obtain the ESNR. The choice of Z was the same as for the reduced model. From the Q values, Wang and Menyuk could then calculate the mean hDQðmÞ i and the standard deviation sðmÞ Q for comparison to the Stokes model. Given the large random variation of the the signal–spontaneous beat noise from realization to realization, which leads to significant variations in DQðmÞ from realization to realization, 20 realizations is not really sufficient. Moreover, with only 64 bits per channel, significant pattern dependences arose. The number 20 was chosen due to computational limitations that make running a significantly larger number of cases impractical [16, 20]. Thus, a comparison of the Stokes model to the full model should be viewed as a demonstration of consistency, not a complete check of the Stokes model.

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The Stokes model does not suffer from these computational limitations, which is why it was developed in the first place. In the comparisons with the full model, Wang [16] and Wang and Menyuk [20] used 2000 realizations. The applications presented in Section III.D used as many as 105 realizations. For this reason, it is our view that the Stokes model is at least as reliable as full simulations for determining the combined effects of PMD, PDL, and PDG. We first compare the full model to the Stokes model in the simple case when the pulse modulation format is RZ. The pulses are the same as in Section III.B.1, and U2ðmÞ ðtÞ ¼ A2 ðtÞ except that U1ðmÞ ðtÞ ¼ A1 ðtÞ cosðoph t=2 þ p=2Þ cosðoph t=2 þ p=2Þ, so that the pulses are amplitude modulated but unchirped. We show the results for DQ as a function of the PDL in Figs. 8 and 9 for a single channel system, setting the PMD¼ 0:1 ps=km1=2 and the PDG¼ 0:0 and 0.06 dB, respectively. The agreement between the two models is quite good. The PDL values that were compared are 0.1, 0.2, . . . ; 0.6 dB. We note that when sQ ¼ 1, the expected deviation of the Q-factor from its mean in the full simulation model pffiffiffiffiffi is approximately 1= 19 ¼ 0:23 because there are only 20 realizations at each value of PDL. Thus, the deviation between the full model and the Stokes model lies within the expected statistical error of the full model. We note that the difference between the two models is systematic rather than random because the full model yielded either higher or lower values than the Stokes model for both

FIGURE 8

Comparison of the signal degradation as a function of PDL in the Stokes model and in the full simulation model, where PMD¼ 0:1 ps=km1=2 and PDG¼ 0:0 dB: (a) hDQi. (b) sQ . Solid lines indicate the Stokes model and dashed lines indicate the average of the full simulation model.


297

FIGURE 9 Comparison of the signal degradation as a function of PDL in the Stokes model and in the full simulation model, where PMD¼ 0:1 ps=km1=2 and PDG¼ 0:06 dB: (a) hDQi. (b) sQ . Solid lines indicate the Stokes model and dashed lines indicate the average of the full simulation model.

hDQi and sQ in every plot as we varied the PDL. This systematic deviation is due to the use of the same fiber realizations and the same bit pattern for all 20 realizations. Wang [16] and Wang and Menyuk [20] found that the choice of the fiber realization is more significant than the pattern dependences for both the RZ simulations presented here and NRZ simulations. However, they also found that pattern dependences become more important for CRZ simulations. Comparing Figs. 8 and 9, it is apparent that PDG adds a substantial penalty to the single-channel systems almost independent of the PDL. When the PDL is 0.6 dB but the PDG is 0 dB, hDQi is under 2 dB. By contrast, when the PDG is 0.06 dB, hDQi is consistently above 2 dB regardless of the PDL and almost reaches 4 dB when the PDL is 0.6 dB. However, sQ increases only slightly with nonzero PDG. One finds similar results with the NRZ format; however, polarization scrambling substantially reduces the effect of the PDG, as expected [16]. We turn next to a comparison of the Stokes and full models with an eightchannel RZ system. We show the comparison in Fig. 10 when the PDG is 0 dB. Comparison to Fig. 8 shows that the degradation hDQðmÞ i is almost the same as with a single channel, but the sðmÞ Q values are larger. With PDG included, we show the comparison in Fig. 11. In contrast to the single-channel system, the effect of PDG is negligible. Again, an NRZ system yields similar results [16].

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FIGURE 10


FIGURE 11



299

C. Experimental Validation We now compare the Stokes model to experiments that were carried out in a recirculating loop configuration described by Carter et al. [49]. The recirculating loop is a little over 100 km long. Recirculating loops are a simple and efficient way to study long-haul transmission systems. However, it has long been known that the behavior of recirculating loops that are shorter than about 500 km can differ significantly from real transmission systems. Yet, this behavior has only recently been characterized [16]. In this section, we compare the evolution of the degree of polarization in the experimental system to the predictions of the Stokes model. We present cases in which a single-channel 10-Gbps pseudo-random signal is propagating and cases in which there is no initial signal, and the light in the recirculating loop grows from ASE noise. The work presented in this section not only serves to validate the Stokes model, but it also gives insight into the polarization evolution in short recirculating loops. In more detail, the experimental system is a dispersion-managed recirculating loop that contains 100 km of dispersion-shifted fiber with a normal dispersion of 1:1 ps=nm-km at 1551 nm and ’ 7 km of standard fiber with an anomalous dispersion 16.7 ps=nm-km at 1551 nm. The entire loop comprises one period of the dispersion map. The PMD of the fiber is below 0.1 ps=km1=2 . A single 2.8-nm bandwidth optical filter and five EDFAs are in the loop. The polarization evolution inside the loop was investigated using a commercial polarization analyzer, the HP 8509B [16]. By sampling the Stokes parameters as a function of the propagation, we can determine the degree of polarization as a function of the propagation time or, equivalently, distance. In Fig. 12, we show the evolution of the degree of polarization. The different curves correspond to different values of the BER measured at 20,000 km, and we obtained these different values of the final BER by using different settings of the polarization controllers. The polarization evolution inside the loop is closely correlated to the final BER. The signal is highly polarized when the BER is less than 1010 at 20,000 km. When the polarization controllers are set so that the final BER increases, the signal depolarizes increasingly with distance.

FIGURE 12 Evolution of the degree of polarization corresponding to different BERs. (a) BER¼ 109 . (b) BER¼ 106 . (c) BER¼ 102 .

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To measure the PDL in the loop, it was necessary to open the recirculating loop into a 107-km straight-line experiment and then measure the PDL of the entire line. Varying the polarization state of the input signal so that it covers the entire Poincare´ sphere, one measures the output power as a function of the output polarization state. The difference between the maximum and minimum power equals the PDL. In the experiments presented here, the total PDL of the loop equaled 0.35 dB. To compare the Stokes model to the experiments, one must first modify the model to take into account the periodicity of the loop. This periodicity is important because the PDL contributions are no longer random but repeat with the same period as the loop. Using the modified model, one finds that when the PDL equals 0.45 dB, the results of the model are in exact agreement with the experiments, as shown in Fig. 13. The agreement between the model and the experiment is acceptable because the error in measuring the PDL is expected to equal approximately 0.1 dB, and the open loop did not contain the switches and couplers that were used in the closed-loop experiments. In Fig. 13, we also show the effect of reducing the PDL, keeping the setting of the polarization controller in the Stokes model that yields the lowest BER. As the PDL becomes smaller, the noise plays an increasingly important role, leading to an increased depolarization. When the PDL equals 0.01 dB, the degree of polarization falls below 0.5. The repolarization of the noise when there is no signal also becomes smaller as the PDL decreases. When the PDL equals 0.01 dB, one finds that the degree of polarization after 27,000 km just equals 0.2, as shown in Fig. 13b.

FIGURE 13 Evolution of the degree of polarization with (a) signalþnoise and (b) noise only. The experimental results are shown as stars. The theoretical curves correspond, in order of decreasing degree of polarization, to PDLs of 0.45, 0.25, 0.15, 0.05, and 0.01 dB.


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D. Applications to Transoceanic Systems We now apply the Stokes model to the problem of calculating the outage probability in transoceanic systems assuming a system margin for polarization effects of either 2.5 or 3.0 dB. The calculations presented here used 105 realizations for each choice of parameters, and, when necessary to compute the outage probability, a Gaussian distribution was fitted to the tail of the numerically determined probability distribution function. Acceptable outage probabilities are typically around 106, corresponding to a little more than half a minute per year. The number of WDM channels in transoceanic systems has grown rapidly in recent years. While the effect of PMD on a single channel is typically small in undersea systems, where the PMD is usually quite low, the PMD does rotate the polarization states of the different channels with respect to one another. In other words, the PMD changes the angular separation of the channels on the Poincare´ sphere. As a consequence of the interaction of the PMD and the PDL, different channels will undergo different amounts of loss when they pass through a device with PDL. Because the gain saturation or gain clamping in the amplifiers is tuned to effectively restore the total signal power in all channels, some channels gain power at the expense of others. This effect leads to a random walk in the power of each channel and can cause one or more channels to fade. We present results here that show this mechanism is the primary cause of fading in systems with more than approximately 10 channels, in contrast to single-channel systems in which PDG is the primary cause of fading. We first consider a system in which the channel spacing and the optical filter bandwidth equal 0.6 nm, with other system parameters set as follows: PMD¼ 0:1 ps=km1=2 , PDL¼ 0:0 dB, and PDG¼ 0:06 dB. Figure 14 shows that as the number of channels increases, the importance of PDG decreases as expected from the argument in the preceding paragraph. Next, we consider a system in which the PDG equals zero, leaving only the effects of PMD and PDL in the model. In this example, the channel spacing is 1.0 nm, and the optical filter bandwidth is 0.5 nm. The PMD equals 0.1 ps=km1=2 , and the PDL equals 0.1 dB in each optical amplifier. By increasing the number of channels, one obtains the result shown in Fig. 15. If DQallowed , the allowed

FIGURE 14 channels.

The degradation and variance of the Q-factor as a function of the number of

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FIGURE 15 Outage probability as a function of the number of channels. The solid line is for DQallowed ¼ 2:5 dB; the dashed line is for DQallowed ¼ 3:0 dB.

degradation level for any single channel, is set equal to 2.5 dB, then the outage probability dramatically increases from 6:5 1013 in the case of a single channel to 3:0 104 when there are many channels. With only three channels, the outage probability already exceeds 105 . If we raise DQallowed to 3.0 dB, then the maximum outage probability falls to 2:3 106 , a decrease of more than 2 orders of magnitude. When the amplifier spacing increases from 33 to 45 km and then to 50 km, the average value of Q decreases due to the additional ASE noise that is added to the total signal. However, the outage probability decreases because the number of PDL elements along the transmission line is reduced, as shown in Fig. 16. When the number of channels is 40, the outage probability drops from 3:0 104 to 1:3 105 and 2:8 106, respectively. So, when one designs a WDM system and chooses the amplifier spacing, one has to take into account both noise-

FIGURE 16 Outage probability as a function of the number of channels. Amplifier spacing equals (a) 45 km and (b) 50 km. The solid line is for DQallowed ¼ 2:5 dB; the dashed line is for DQallowed ¼ 3:0 dB.


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induced and polarization-induced penalties. If the PDL is the same in each amplifier, then a short amplifier spacing will introduce less noise but will increase the outage probability. By contrast, a long amplifier spacing will introduce more noise but will decrease the outage probability. Figure 14 shows that the effect of PDG becomes insignificant when there are more than approximately 10 channels in a WDM system. To further investigate this issue, one may add a PDG of 0.07 dB to the case shown in Fig. 15. We show these results in Fig. 17. Instead of a small outage probability when the number of channels is small, one finds that the outage probability peaks at a small number of channels and then decreases to its final value. The dramatic increase in the outage probability when the number of channels is small is due to the faster growth of ASE noise that is induced. The outage probability then decreases as the number of channels becomes larger because the PMD between the channels leads to an averaging of the polarization states so that the degree of polarization for the total signal is nearly zero, and the PDG leads to nearly no excess noise growth. When the number of channels equals 40, the outage probability is 2:2 104 , which is actually smaller than the corresponding value of 3:0 104 when there is no PDG. The reason for this paradoxical decrease is that the PDG tends to compensate for the effects of PDL on channels that experience excess loss.

ACKNOWLEDGMENTS Sections II.B, II.C, and all of III are based on the Ph.D. dissertation of Dr. Ding Wang. One of us (CRM) is also grateful to Drs. H. Sunnerud and F. Bruye`re for making their Ph.D. dissertations available to him. The insights in both dissertations were useful. We are grateful for financial support from the Air Force Office of Scientific Research, the Defense Advanced Research Projects Agency, the Laboratories for Physical Sciences and Telecommunications Sciences at the Department of Defense, the Department of Energy, and the National Science Foundation. We are grateful to the submarine systems group, then at AT&T Bell Laboratories, for arranging for some early financial support for the development of the Stokes model. In particular, we thank Peter Runge and Frank Kerfoot for

FIGURE 17 Outage probability as a function of the number of channels, where PDG¼ 0:07 dB. The solid line is for DQallowed ¼ 2:5 dB; the dashed line is for DQallowed ¼ 3:0 dB.

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encouraging this model’s development. Finally, we are grateful to Ciena Corporation and Science Applications International Corporation for recent support that has allowed us to better validate the models presented here and broaden their range of applications.

REFERENCES 1. 2. 3. 4.

I. P. Kaminow. Polarization in fibers. Laser Focus 16(6), 80–84 (June 1980). I. P. Kaminow. Polarization in optical fibers. IEEE J. Quantum Electron. 17, 15–22 (1981). A. W. Snyder and J. D. Love. Optical Waveguide Theory. Chapman and Hall, London (1983). C. D. Poole and J. Nagel. Polarization effects in lightwave systems. In Optical Fiber Telecommunications, Vol. IIIA (I. P. Kaminow and T. L. Koch, Eds.), Chap. 6. Academic, San Diego (1997). 5. C. R. Menyuk. Application of multiple-length-scale methods to the study of optical fiber transmission. J. Eng. Math. 36, 113–136 (1999). 6. C. R. Menyuk and P. K. A. Wai. Polarization evolution and dispersion in fibers with spatially varying birefringence. J. Opt. Soc. Am. B 11, 1288–1296 (1994). 7. G. P. Agrawal. Nonlinear Fiber Optics. Academic, San Diego (1995). 8. A. Hasegawa and Y. Kodama. Solitons in Optical Communications. Clarendon, Oxford (1995). 9. P. K. A. Wai and C. R. Menyuk. Polarization mode dispersion, decorrelation, and diffusion in optical fibers with randomly varying birefringence. J. Lightwave Technol. 14, 148–157 (1996). 10. D. Marcuse, C. R. Menyuk, and P. K. A. Wai. Application of the Manakov-PMD equation to studies of signal propagation in optical fibers with randomly varying birefringence. J. Lightwave Technol. 15, 1735–1746 (1997). 11. F. Bruye`re and O. Audouin. Penalties in long-haul optical amplifier systems due to polarization dependent gain and loss. IEEE Photon. Technol. Lett. 6, 654–656 (1994). 12. E. Lichtman. Performance limitations imposed on all-optical ultralong lightwave systems at the zero-dispersion wavelength. J. Lightwave Technol. 13, 898–905 (1995). 13. E. Lichtman. Limitations imposed by polarization-dependent gain and loss on all-optical ultralong communication systems. J. Lightwave Technol. 13, 906–913 (1995). 14. N. S. Bergano. Undersea amplified lightwave systems design. In Optical Fiber Telecommunications, Vol. IIIA (I. P. Kaminow and T. L. Koch, Eds.), Chap. 10. Academic, San Diego (1997). 15. C. R. Menyuk, D. Wang, and A. N. Pilipetskii. Repolarization of polarization-scrambled optical signals due to polarization dependent loss. IEEE Photon. Technol. Lett. 9, 1247–1249 (1997). 16. D. Wang. Polarization Effects in Dense WDM Systems. Ph.D. dissertation, University of Maryland, Baltimore County (2000). 17. D. Wang and C. R. Menyuk. Calculation of penalties due to polarization effects in a long-haul WDM system using a Stokes parameter model. J. Lightwave Technol. 19, 487–494 (2001). 18. See, e.g., J. Schesser, S. M. Abbot, R. L. Easton, and M. S. Stix. Design requirements for the current generation of undersea cable systems. AT&T Technol. J. 74, 16–32 (1995). 19. D. Wang and C. R. Menyuk. Reduced model of the evolution of the polarization states in wavelength-division-multiplexed channels. Opt. Lett. 23, 1677–1679 (1998). 20. D. Wang and C. R. Menyuk. Polarization evolution due to the Kerr nonlinearity and chromatic dispersion. J. Lightwave Technol. 17, 2520–2529 (1999). 21. J. P. Gordon and H. Kogelnik. PMD fundamentals: Polarization mode dispersion in optical fibers. Proc. Natl. Acad. Sci. USA 97, 4541–4550 (2000). 22. M. Born and E. Wolf. Principles of Optics. Pergamon, Oxford, UK (1980). 23. S. C. Rashleigh. Origins and control of polarization effects in single-mode fibers. J. Lightwave Technol. 1, 312–331 (June 1983). 24. R. I. Laming and D. N. Payne. Electric current sensors employing spun highly birefringent optical fibers. J. Lightwave Technol. 7, 2084–2094 (1989).


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25. C. R. Menyuk and P. K. A. Wai. Elimination of nonlinear polarization rotation in twisted fibers. J. Opt. Soc. Am. B 11, 1307–1309 (1994). 26. C. R. Menyuk. Pulse propagation in an elliptically birefringent Kerr medium. IEEE J. Quantum Electron. 25, 2674–2682 (1989). 27. J. Botineau and R. H. Stolen. Effect of polarization on spectral broadening in optical fibers. J. Opt. Soc. Am. 72, 1592–1596 (1982). 28. R. H. Stolen, J. Botineau, and A. Ashkin. Intensity discrimination of optical pulses with birefringent fibers. Opt. Lett. 7, 512–514 (1982). 29. P. K. A. Wai, C. R. Menyuk, and H. H. Chen. Stability of solitons in randomly varying birefringent fibers. Opt. Lett. 16, 1231–1233 (1991). 30. S. G. Evangelides, Jr., L. F. Mollenauer, J. P. Gordon, and N. S. Bergano. Polarization multiplexing with solitons. J. Lightwave Technol. 10, 28–35 (1992). 31. E. L. Buckland and R. W. Boyd. Electrostrictive contribution to the intensity-dependent refractive index of optical fibers. Opt. Lett. 21, 1117–1119 (1996). 32. S. V. Chernikov and J. R. Taylor. Measurement of normalization factor of n2 for random polarization in fiber. Opt. Lett. 21, 1559–1661 (1996). 33. M. F. Arend, M. L. Dennis, I. N. Duling, E. A. Golovchenko, A. N. Pilipetskii, and C. R. Menyuk. Nonlinear-optical loop mirror demultiplexer using a random birefringence fiber: Comparisons between theory and experiments. Opt. Lett. 22, 886–888 (1997). 34. F. Bruye`re. Impact of first- and second-order PMD in optical digital transmission systems. Opt. Fiber Technol. 2, 269–280 (1996). 35. M. Karlsson. Polarization mode dispersion-induced pulse broadening in optical fibers. Opt. Lett. 23, 688–690 (1998). 36. C. D. Poole. Statistical treatment of polarization dispersion in single-mode fiber. Opt. Lett. 13, 687–689 (1988). 37. H. Goldstein. Classical Mechanics, pp. 143–158. Addison-Wesley, Reading, MA (1980). 38. N. Gisin. Solutions of the dynamical equation for polarization diffusion. Opt. Commun. 86, 371–373 (1991). 39. G. J. Foschini and C. D. Poole. Statistical theory of polarization mode dispersion. J. Lightwave Technol. 9, 1439–1456 (1991). 40. L. Arnold. Stochastic Differential Equations: Theory and Applications. Wiley, New York (1974). 41. H. Kogelnik, private communication. 42. See, e.g., C. D. Poole and C. R. Giles. Polarization-dependent pulse compression and broadening due to polarization dispersion in dispersion-shifted fiber. Opt. Lett. 13, 155–157 (1988). 43. W. A. Shurcliff and S. S. Ballard. Polarized Light. Van Nostrand, Princeton, NJ (1964). 44. D. Marcuse. Derivation of analytical expressions for the bit-error probability in lightwave systems with optical amplifiers. J. Lightwave Technol. 9, 1816–1823 (1990). 45. P. A. Humblet and M. Azizog˜lu. On the bit error rate of lightwave systems with optical amplifiers. J. Lightwave Technol. 9, 1576–1582 (1991). 46. N. S. Bergano, C. R. Davidson, M. Ma, A. N. Pilipetskii, S. G. Evangelides, H. D. Kidorf, J. M. Darcie, E. A. Golovchenko, K. Rottwitt, P. C. Corbett, R. Menges, M. A. Mills, B. Pedersen, D. Peckham, A. A. Abramov, and A. M. Vengsarkar. 320 Gb=s WDM transmission (64 5 Gb=s) over 7,200 km using large mode fiber spans and chirped return-to-zero signals. In OFC ’98 Technical Digest, postdeadline paper PD12. Optical Society of America, New York (1998). 47. P. D. Maker and R. W. Terhune. Study of optical effects due to an induced polarization third order in the electric field strength. Phys. Rev. 137, A801–A818 (1965). 48. N. S. Bergano and C. R. Davidson. Circulating loop transmission experiments for the study of long-haul transmission systems using erbium-doped fiber amplifiers. J. Lightwave Technol. 13, 879–888 (1995). 49. G. M. Carter, R. M. Mu, V. S. Grigoryan, C. R. Menyuk, T. F. Carruthers, M. L. Dennis, and I. N. Duling III. Transmission of dispersion-managed solitons at 20 Gbit=s over 20,000 km. Electron. Lett. 35, 233–234 (1999).


8 NONLINEAR TRANSMISSION TECHNIQUES AND SOLITONS S. WABNITZ Xtera Communications, Allen, Texas

I. INTRODUCTION II. NONLINEAR PULSE PROPAGATION A. Periodic Loss Averaging B. Soliton Perturbation Theory C. Soliton–Noise Interactions D. Soliton 2-R Regeneration E. Soliton–Soliton Interactions F. Polarization Multiplexing G. Soliton 3-R Regeneration III. DISPERSION-MANAGED SOLITONS A. Variational Representation B. Dispersion-Managed Soliton–Noise Interactions C. Dispersion-Managed Soliton Example D. Self-Phase Modulation E. Dispersion-Managed Soliton 2-R Regeneration F. Cross-Phase Modulation G. Doubly Periodic Maps H. Nonlinear Chirped Return-to-Zero Pulse I. Dispersion-Managed Soliton 3-R Regeneration J. Dispersion-Managed Soliton Distributed Raman Amplification IV. CONCLUSIONS Acknowledgments References

I. INTRODUCTION In 1973, Hasegawa and Tappert proposed in a pioneering work to use the optical soliton concept for repeater-free all-optical communications, whereby fiber Undersea Fiber Communication Systems Copyright 2002, Elsevier Science (USA). All rights reserved.

307

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S. WABNITZ

dispersion is compensated by the auto-induced pulse chirp through the intensitydependent refractive index of the fiber [1]. This effect was experimentally confirmed by Mollenauer, Stolen, and Gordon to be in good agreement with the theory, using picosecond pulses from a color-center laser [2]. As discussed by Kodama and Hasegawa, optical solitons could provide the natural data format for high-bit-rate fiber-based optical communications, once the problem of compensating for fiber loss by periodic amplification was solved [3]. The natural technique for compensating fiber loss is the use of Raman gain in the fiber [4, 5], and the transmission of optical solitons over several thousands of kilometers was demonstrated using Raman amplification [6]. The advent of erbium-doped fiber amplifiers (EDFAs) in combination with dispersion-shifted fibers has permitted the demonstration of practical soliton transmission systems [7]. In spite of the periodic loss in the amplifier span, the soliton effect may still be exploited to compensate the action of fiber nonlinearity by means of the residual dispersion of the link [8, 9]. In recent years, the technique of wavelength-division multiplexing (WDM) has been established in order to multiply the fiber capacity by a large number of wavelength channels. In the case of soliton transmissions, the combination of WDM and periodic amplification may be prone to four-wave mixing and timing jitter instabilities [10] unless the fiber local dispersion is relatively large. This led to the development of the dispersion management (DM) technique, in which a large local dispersion is periodically compensated by means of specially designed fibers with reverse dispersion and dispersion slope. Although the detrimental effects of nonlinear interchannel interactions are largely suppressed in DM transmission systems, fiber nonlinearity is still a key factor that should be properly compensated for in ultra-long-haul and transoceanic links. Again, to properly design high-bit-rate (10 Gbps and higher) nonlinear transmissions it is necessary to extend the soliton concept to DM links [11, 12]. In this chapter, we do not attempt to provide complete and fully up-to-date coverage of the many theoretical and experimental works on the subject of optical fiber solitons. Rather, we would like to present a unified framework to describe the basic dynamic properties of nonlinear pulse propagation through either uniform or dispersion-managed fiber links. We provide several examples of applications of the theory to show how it may be helpful to complement extensive numerical experiments in the design of high-bit-rate return-to-zero WDM transmission systems.

II. NONLINEAR PULSE PROPAGATION By assuming, for simplicity, a single state of polarization in the fiber and a single guided mode, one can separate the transverse ðx; yÞ from the longitudinal z

8. NONLINEAR TRANSMISSION TECHNIQUES AND SOLITONS

309

variables, so that the fiber field reads as Eðx; y; z; tÞ ¼ Eðz; tÞFðx; yÞ, where F is the transverse profile of the mode. Moreover, ð E^ ðoÞ exp½ifkðoÞz otg do ð ^ ¼ Eðo0 þ DoÞ expði ½kðo0 þ DoÞ k0 z Dot Þ dðDoÞ exp½i k0 z o0 t þ c:c: ð1Þ where k is the propagation constant, and o0 is the mean frequency of the field. The intensity-dependent contribution to the refractive index of the fiber leads to the following expansion: 1 on2 jEj2 k k0 ¼ k 0 Do þ k 00 Do2 þ cAeff 2

ð2Þ

where n2 is the nonlinear index and Aeff is the effective area of the fiber mode. Equation (2) yields, in dimensionless units, the perturbed nonlinear Schro¨dinger (NLS) equation: i

@q 1 @2 q sgnðk 00 Þ þ jqj2 q ¼ iR½q; q* @Z 2 @T 2

ð3Þ

where we used the identities k k0 ¼ ið@=@zÞ; Do ¼ ið@=@tÞ, and t ¼ ðt k 0 zÞ. pffiffiffiffiffi Moreover, we have set q ¼ E= P0 with P0 ¼ cAeff =ðo0 n2 z0 Þ; Z ¼ z=z0 ; z0 ¼ t20 sgnðk 00 Þ=jk 00 j, and T ¼ t=t0, where t0 is a reference time. In Eq. (3), the term R represents the action of perturbations such as fiber loss, amplifier noise, pulse interactions, or higher order dispersion. In the unperturbed case (i.e., with R ¼ 0) for k 00 < 0, Eq. (3) admits so-called soliton solutions, which represent a balance between fiber nonlinearity and dispersion. The simplest soliton solution of Eq. (3) reads as follows: qðZ; T Þ ¼ Z sech½ZðT xðZÞÞ exp½ikT icðZÞ dx ¼ k dZ

ð4Þ

dc k2 Z2 ¼ dZ 2 A general solution of the NLS Eq. (3) can be obtained through the so-called inverse scattering transform (IST) method [13]. The power of the IST method is that it permits us to solve a nonlinear evolution equation in terms of the solution of a linear scattering problem. This technique is based on the observation that Eq. (3) is the compatibility condition of the set of linear partial differential equations: LðZÞC ¼ xC @C ¼ M ðZÞC @Z

ð5Þ ð6Þ

310

S. WABNITZ

where the differential operators L and M read as follows: 3 2 2 3 @ i 2 1 2 6 i @T q 7 6 ix þ 2 jqj iqx 2 qT 7 7 7; M ¼ 6 L¼6 4 4 @ 5 1 i 2 5 2 q* i iq*x þ q*T ix jqj @T 2 2

ð7Þ

The solution of the above scattering problem permits us to find a complete solution in terms of solitons and radiation, for any input condition qðZ ¼ 0; T Þ of Eq. (3) with R ¼ 0.

A. Periodic Loss Averaging In periodically amplified fiber links, the balance between dispersion and nonlinearity may still lead to optical solitons when the path-average pulses are considered [14]. To demonstrate that, let us consider nonlinear pulse propagation in the presence of fiber loss and periodic amplification by lumped EDFAs, spaced by a fixed distance, say, za . In this case, the perturbation term in Eq. (3) reads R ¼ iðG GðZÞÞq iG00 ðZÞqTT ¼ iFðZÞq iG00 ðZÞqTT , where G ¼ gz0 and g is a distributed loss coefficient, and G; G00 represent the periodic gain and bandwidth of the amplifiers, respectively. Whenever the dispersion of the fibers is relatively low, one has G 1 and, consequently, Za ¼ za =z0 1. This inequality permits us to decouple the ‘‘short’’ length scale over which fiber loss leads to significant signal attenuation, namely za, from the relatively long dispersion distance z0 , over which dispersion and nonlinearity act to reshape the signal in time. Formally, one can derive a new NLS equation, averaged over the amplifier spacing za . Setting qðZ; T Þ ¼ aðZÞuðZ; T Þ, where aðZÞ obeys i

M P da ¼ Ga þ ½expðGZa Þ 1 dðZ nZa Þa dZ n¼1

ð8Þ

and inserting Eq. (8) into Eq. (3) leads to a NLS equation with spatially varying nonlinearity: i

@u 1 @2 u þ aðZÞ2 juj2 u ¼ iP½u; u*; Z @Z 2 @T 2

ð9Þ

Here a2 ¼ a2 ðZÞ represents the periodic power variation and P is a perturbation term. Let us now average Eq. (9) over the amplification span Za . In the anomalous dispersion regime (i.e., for k 00 < 0), the resulting NLS equation reads as follows: i

@q 1 @2 q þ þ jqj2 q ¼ iR½q; q* @Z 2 @T 2

ð10Þ

Here we have set a2 ðZ ¼ 0Þ ¼ a20 ¼ 2GZa =ð1 expð2GZa ÞÞ ¼ G lnðGÞ=ðG 1Þ (G ¼ expð2GZa Þ is the amplifier gain), so that ha2 ðZÞi ¼ 1.


311

Note that for the validity of the averaging approximation, the condition Za 1 translates in real units into B2 za

1 r2 jk 00 j

ð11Þ

pffiffiffi where B is the bit rate, and r ¼ 200 ln ð1 þ 2Þ=D with D equal to the percentage ratio between the soliton full width and the bit time (duty cycle). Whenever Eq. (11) is not verified, radiative waves are generated as described by Midrio et al. [15].

B. Soliton Perturbation Theory Let us formulate the perturbation theory based on the integrable NLS equation, Eq. (10). The evolution of the field qðZ; T Þ can be seen as resulting from a variational principle, much in the same way as for a particle in classical mechanics. In the case of the NLS equation, the evolution of q is obtained in correspondence with an extremum of the action [16], which in this case is the time and space integral of the Lagrangian density L0. In the unperturbed (i.e., with R ¼ 0) case, L ¼ L0 , where i 1 L0 ðq; q*; . . .Þ ¼ ðqq*Z qZ q*Þ ðjqj4 jqT j2 Þ 2 2 The general variational principle reads as ðð dI ¼ d Lðq; q*; qZ ; q*Z ; qT ; q*T ; qTT ; . . .Þ dT dZ ¼ 0

ð12Þ

ð13Þ

Whenever the variation of the action dI in Eq. (13) upon a variation dq of the field q is computed, one obtains after an integration by parts 1 P

ð1Þn

n¼0

@n @L @ @L d L½q; q* ¼ 0 ¼ n @T @q*nT @Z @q*Z dq*

ð14Þ

where q*nT ¼ @n q*@T n , and we assumed that the variations dq and dq* are arbitrary and independent. Whenever the Lagrangian density [Eq. (12)] is inserted in Eq. (14), one obtains the NLS equation, Eq. (10), with R ¼ 0. In general, Eq. (10) can be written i

dL ½q; q* ¼ R½q; q* dq*

ð15Þ

The perturbation analysis based on the Lagrangian approach involves the solution of a reduced version of Eq. (10) based, for example, on the assumption

312

S. WABNITZ

that the one-soliton parameters of Eq. (4) are slowly evolving with distance Z. One obtains in this case for the time-averaged reduced Lagrangian L0 ð1 dx dd Z3 þ þ Zk2 L0 ¼ L0 ½q0 ; q*0 dT ¼ 2Z k ð16Þ dZ dZ 3 1 where we set c þ kx þ d ¼ 0 in Eq. (4). We now have two different ways to evaluate the variations of L0 with respect to the soliton parameters. One is to directly compute the Euler–Lagrange equations for each parameter from Eq. (16) to obtain dL0 @L0 d @L0 dx dd þ Z 2 þ k2 ð17Þ ¼ ¼2 k dZ dZ dZ @Z dZ @ðdZ=dZÞ In a similar way, one also obtains dL0 dx ¼ 2Z þ 2Zk dk dZ

ð18Þ

dL0 dZ dk 2Z ¼ 2k dZ dZ dx

ð19Þ

dL0 dZ ¼ 2 dd dZ

ð20Þ

With R ¼ 0 in Eq. (10), one again obtains the one-soliton solution, Eq. (4). In the general case where R 6¼ 0, we may also use the chain-rule expression for the variations of L0 , and write ð1 dL0 dL0 @q0 ðT Þ dL0 @q*0 ðT Þ þ ¼ dT ð21Þ dZ dq*0 ðT Þ @Z 1 dq0 ðT Þ @Z We can replace dL0 =dq* and its conjugate in this expression as determined by Eq. (15), and calculate the derivatives of the one-soliton ansatz (4) with respect to its parameters. This procedure leads to the following expressions for the evolution of the soliton parameters: ð1 dZ ¼ Re Reif sechðtÞ dt ð22Þ dZ 1 ð1 dk ¼ Im Reif sechðtÞtanhðtÞ dt ð23Þ dZ 1 ð dx 1 1 ¼ k þ 2 Re Reif tsechðtÞ dt ð24Þ dZ Z 1 ð dy Z2 k2 dk 1 1 ¼ þ þx Im Reif sechðtÞð1 tanhðtÞÞ dt ð25Þ dZ dZ Z 1 2


313

where t ¼ ZðT xÞ and f ¼ kT cðZÞ. Typical examples of perturbations R may be higher order dispersion [17] or noise. We discuss in some detail in the next section the action of noise on soliton propagation.

C. Soliton–Noise Interactions As a first example of application of soliton perturbation theory, we consider the case of noise from EDFA amplified spontaneous emission (ASE) [18]. As is well known, the spectral density of ASE noise reads as NASE ¼ nsp hnðG 1Þ

ð26Þ

where h is Planck’s constant, and nsp ¼ N2 =ðN2 N1 Þ is the population inversion of the amplifier, whose noise figure is F ¼ 2nsp ðG 1Þ=G ’ 2nsp 5 2. For a chain of N EDFAs, ASE introduces a random perturbation of the type RðZ; T Þ ¼

N P

n¼1

dðZ nZa ÞnðZ; T Þ expðiOT þ ifÞ

ð27Þ

where hRðT ÞijZ¼Za ¼ 0 and hRðT ÞR*ðT 0 ÞijZ¼Za ¼ NASE z0 =ðP0 t0 za ÞdðT T 0 Þ ¼ 2NASE dðT T 0 Þ=ða20 Es Þ, where Es is the unit amplitude NLS soliton energy Es ¼ 2P0 t0 . By inserting (27) into Eqs. (22) through (25), one obtains the following expressions for the variance of the soliton amplitude and frequency fluctuations: s2Z ¼

2NASE a20 Es

ð28Þ

s2k ¼

2NASE 3a20 Es

ð29Þ

The consequence of amplitude fluctuations is a degradation of the signal-to-noise ratio (SNR) at the receiver, whereas the frequency fluctuations introduce a more harmful timing jitter, which is known as the Gordon–Haus (GH) effect. Indeed, a small soliton frequency shift, say, dk, translates, through group-velocity dispersion, into a shift of the arrival time of the soliton after one amplifier span, namely, dx ¼ dkZa . By simply adding up all the timing shifts that result from frequency shifts at each individual amplifier, one obtains for N spans the total shift Dx ¼

N P

k¼1

dxk ¼ Za

N P k P

k¼1 j¼1

dkk

ð30Þ

In Eq. (30), we have a sum of N independent random variables with Gaussian distribution, which also has Gaussian distribution, with variance equal to the sum

314

S. WABNITZ

of the variances of the individual variables. Therefore, one obtains the GH timing jitter variance over a total distance Z ¼ NZa : s2GH ¼ s2k

N P

k¼1

ðkZa Þ2 ¼

s2k 3 Z 3Za

ð31Þ

where we replaced the sum in Eq. (31) by an integration. So as not to induce an error at the receiver, the average timing shift sGH t0 induced by the GH jitter should not exceed a small fraction, say, 10%, of the total bit slot, which sets a restriction on the maximum bit rate of a given soliton system.

D. Soliton 2-R Regeneration As we have seen, the fiber loss can be periodically compensated by EDFAs without affecting the stability properties of the path-averaged optical soliton pulses. On the other hand, the accumulation of noise and dispersive waves needs to be compensated for by means of some form of soliton control. Let us discuss first the amplification and reshaping of solitons (2-R regeneration) and the reduction of the noise-induced jitter by means of in-line bandpass filters [19, 20]. Because the solitons exhibit stable particle-like properties, in the presence of filters the soliton frequency will be effectively locked to the center of the filter bandpass so that the filter-induced loss is minimized, and ASE-induced frequency shifts will be suppressed. Indeed, with in-line filters one obtains s2GHf ¼

3s2GH 16d2 Z 2

ð32Þ

where d is the amplifier excess gain (see below). Hence the GH timing jitter grows only linearly with distance, instead of the cubic growth predicted by Eq. (31). By the same mechanism, filtering also reduces frequency shifts from soliton interactions [21] and collisions [22]. If the filters are relatively weak, the energy loss in the wings of the soliton spectrum can be compensated for by extra gain at the filter center wavelength. However, this extra gain unavoidably leads to the buildup of continuous-wave (cw) radiation at that center wavelength, which ultimately breaks up the soliton propagation. To reduce the cw growth, one may suitably shape the transfer function of the filter [23]. A more effective soliton control method involves continuously restoring the soliton amplitude, frequency, and shape by progressively shifting the center wavelength of the filters (sliding filter technique) [24], as demonstrated for 10- to 20-Gbps transmissions in [25]. Alternatively, one can use fixed filters and insert frequency shifting elements such as acousto-optic modulators [26]. With sliding filters, the perturbation term reads as R ¼ dq þ bð@T þ iof ðZÞÞ2 q

ð33Þ


315

Here d ¼ G=Za G > 0 is the excess gain per span, and b ¼ 2=ðB2 Za Þ, where B is the finite amplification bandwidth. In the case of a WDM system with channel spacing os , the simplest example of frequency-periodic filter is a Fabry–Perot etalon, whose complex transfer function reads as HF ðoÞ ¼

1R 1 R expfiðo of Þ2d=cg

ð34Þ

where R and d ¼ pc=os are the mirror reflectivity and spacing, respectively. By performing a Taylor expansion about os of the path-averaged filter transmission hF ¼ ln½HF ðoÞ=Za , one obtains b¼

2 ; Za jdjB2

B¼

os ð1 RÞ pffiffiffi p R

ð35Þ

where d is the path-averaged dispersion. The analysis of the action of sliding filters on soliton propagation is facilitated by rewriting the perturbed NLS equation, Eq. (10), into an accelerating frame, by setting qðZ; T Þ ¼ QðT þ a0 Z 2 =2; ZÞ exp½ia0 ZT ia20 Z 3 =3

ð36Þ

so that the perturbing term in a new NLS equation for Q reads as follows: RðQÞ ¼ dQ þ bQT 0 T 0 þ ia0 T 0 Q

ð37Þ

where T 0 ¼ T þ a0 Z 2 =2. The amplitude and frequency of a soliton evolve in the accelerating frame as 2 dZ Z 2 ¼ 2dZ 2bZ þk ð38Þ dZ 3 dk 4 ¼ a0 bkZ2 dZ 3 These equations have a stable solution with Z ¼ 1 for 2a 1 k ¼ 0 ; d ¼ b k2 þ 3 3b

ð39Þ

ð40Þ

provided the sliding rate does not exceed a maximum value equal to ac ¼ ð2=3Þ3=2 b

ð41Þ

The use of sliding filters is also very effective in suppressing the capacity limitations that arise, as discussed in the next section, from soliton–soliton interactions [27, 28]. Another passive technique to suppress ASE noise and dispersive perturbations is provided by the inclusion of fast-saturable absorbers or nonlinear-loop mirrors, in analogy with the case of fiber soliton lasers [29].

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S. WABNITZ

E. Soliton–Soliton Interactions The interaction between adjacent soliton pulses shifts away the information bits from their original relative positions and may lead to detection errors. This effect may be studied by means of the Lagrangian perturbation theory. By writing the total field as a linear superposition of the two interacting one-soliton pulses q ¼ q1 þ q2 , one arrives at jqj2 q ¼ ðjq1 j2 q1 þ q21 q*2 þ 2jq1 j2 q2 Þ þ ðjq2 j2 q2 þ q22 q*1 þ 2jq2 j2 q1 Þ. Because of the small tail overlap between the temporally separated solitons, only the first three terms in the above sum act on the first pulse, which leads to the following perturbed NLS equation: i

@q1 1 @2 q1 þ þ jq1 j2 q1 ¼ 2jq1 j2 q2 q21 q*2 @Z 2 @T 2

ð42Þ

From Eqs. (22) through (25) one obtains the following set of evolution equations for the soliton parameters: dp ¼ 4Z3 eZD sinðCÞ dZ dq ¼ 4Z3 eZD cosðCÞ dZ dD ¼ 2q dZ dC ¼ 2pZ dZ

ð43Þ ð44Þ ð45Þ ð46Þ

where Z ¼ ðZ1 þ Z2 Þ=2; p ¼ ðZ2 Z1 Þ=2; q ¼ ðk2 k1 Þ=2; D ¼ x1 x2 ; C ¼ y2 y1 kD, and k ¼ ðk1 þ k2 Þ=2. Moreover, dZ=dZ ¼ dk=dZ ¼ 0. The above equations are exactly integrable and permit us to represent well the collision behavior between adjacent soliton pulses. For example, one can obtain the collision distance between two pulses that are initially spaced by the time interval D0 as follows: p ð47Þ Zc ’ eD0 =2 4 Clearly Eq. (47) sets an upper limit to maximum transmission distance as the two adjacent soliton bits coalesce and the original information is lost. F. Polarization Multiplexing One interesting method to reduce soliton interactions is provided by polarization multiplexing, where adjacent bits in a given wavelength channel have orthogonal polarization states [30]. Although we have neglected the polarization degree of freedom thus far, as is well known, single-mode fibers support the propagation of two nearly degenerate orthogonal polarization modes [12]. The total electric field reads as Eðx; y; z; tÞ ¼ Ex ðz; tÞex Fx ðx; yÞ þ Ey ðz; tÞey Fy ðx; yÞ, where ex;y are


317

orthogonal unit vectors. The corresponding third-order nonlinear polarizability in anisotropic fibers reads as P3 ¼ w½ð1 BÞðE E*ÞE þ BðE EÞE*

ð48Þ

In the case of pure electronic nonlinearity (i.e., neglecting electrostriction), one has B ¼ 1=3 in Eq. (48), and the electric field components obey, in dimensionless units, the vector NLS equation i

@q @q 1 @2 q þ NðqÞ ¼ R þ K idp þ kq þ @Z @T 2 @T 2

ð49Þ

Here q ¼ ðqx ; qy ÞT ; dp and k represent the local polarization mode dispersion (PMD) and linear fiber birefringence, respectively; and R is a perturbation term. The terms K and N denote linear and nonlinear birefringence, respectively, and are read as follows:

cosð2cÞ K¼ sinð2cÞ

sinð2cÞ ; cosð2cÞ

N¼

"

ðjqx j2 þ ð1 BÞjqy j2 Þqx þ Bq2y q*x ðjqy j2 þ ð1 BÞjqx j2 Þqy þ Bq2x q*y

# ð50Þ

where c ¼ cðZÞ is the local angle of the fiber birefringence axes with respect to a fixed coordinate system. By rewriting Eq. (49) in a rotating reference frame, attached with the local birefringence axes, one obtains a simplified set of coupled NLS equations [31]: @Vx 1 @2 Vx þ þ sðZÞjVx j2 þ rðZÞjVy j2 Vx ¼ Rx 2 @Z 2 @T @Vy 1 @2 Vy þ i þ sðZÞjVy j2 þ rðZÞjVx j2 Vy ¼ Ry 2 @Z 2 @T i

ð51Þ

where Vx;y are the field components in the local birefringence axes basis, and we have assumed that the PMD dp can be averaged out. Indeed, it has been shown by numerical simulations and experiments that optical solitons are robust with respect to PMD [30–32]. Namely, the two polarization components of an optical soliton do not split under the action of PMD if the soliton power is above a certain threshold [32]. If the birefringence axes rotate over all possible polarization states over distances shorter than the dispersion distance z0 , then one can average s and r in Eq. (51) over the Poincare´ sphere and obtain s ¼ r ¼ 1. To consider the interaction between two adjacent, orthogonally polarized pulses, one can use the Lagrangian perturbation approach as in the previous

318

S. WABNITZ

section with the incoherent perturbation term jVy j2 Vx acting on the pulse amplitude Vx to obtain the set of coupled equations dq ¼ 2f 0 ðDÞ dZ

ð52Þ

dD ¼ 2q dZ

ð53Þ

where f 0 ðdÞ ¼ df =dD, and f ðDÞ ¼

D cothðDÞ 1 sinh2 ðDÞ

ð54Þ

By comparing the solutions of the above equations with the parallel case of Eqs. (43) through (46), one finds that the collision distance may be greatly increased by polarization multiplexing [31]. On the other hand, in the case of a WDM transmission system, the colliding pulses in different channels have different polarizations, which eventually leads to a depolarization of the signal over a few megameters (Mm) [33].

G. Soliton 3-R Regeneration To achieve a complete (3-R) all-optical regeneration of optical solitons, a retiming action must be introduced by means of synchronous modulation of the pulse intensity or phase [34, 35]. Let us consider the propagation of optical pulses in a long-distance fiber link with periodic inclusion of bandpass filters and synchronous periodic phase modulators [36]. By averaging the action of the control elements over one span of the map, one obtains a perturbation term of the type R ¼ dðZÞq þ bðZÞ

@2 q iaP cosðOT Þq @T 2

ð55Þ

Here the periodic synchronous phase modulation plays the role of an equivalent periodic potential in time. As a consequence, stable soliton propagation can only occur if the pulses are aligned with the minima of the potential function V ðT Þ ¼ aP cosðOT Þ. In fact, from the soliton perturbation theory one obtains for the parameters of two equal-amplitude (i.e., Z1 ¼ Z2 , so that p ¼ 0) adjacent solitons the equations dq 4 aP pO2 ¼ 4Z3 eZD cosðCÞ bqZ2 þ dZ 3 2Z sinhðOp=2ZÞ dD ¼ 2q dZ dZ 2 ¼ 2dZ bZ3 dZ 3

ð56Þ ð57Þ ð58Þ


319

where for simplicity we took k ¼ 0. One finds that soliton–soliton intrachannel interactions are fully suppressed as soon as the modulation amplitude exceeds a certain threshold (which depends on the initial pulse separation) and its frequency is such that O ¼ 2p=D, where D is the initial pulse separation in time, so that the two pulses sit at minima of the periodic potential [36]. Under such conditions one can effectively suppress by synchronous phase modulation not only the pulse position fluctuations that arise from nonlinear pulse interactions, but also any timing jitter fluctuations as noise-induced GH jitter, whose variance saturates to a fixed value for long distances. In a similar manner, if one considers a combination of in-line filtering and synchronous intensity modulation (IM), one obtains the perturbation term R ¼ dðZÞq þ bðZÞ

@2 q a cosðOT Þq @T 2 A

ð59Þ

and the evolution equation for the soliton energy 2 dZ 2aA m Z 2 þk ¼ cosðOxÞZ þ 2dZ 2bZ dZ sinhðmÞ 3

ð60Þ

where m ¼ pO=ð2ZÞ. By setting dZ=dZ ¼ 0, the above equation shows that a stable soliton transmission (with Z ¼ 1) is obtained whenever d þ aA m= ½sinhðmÞ ¼ b=3. Another interesting possibility of retiming a soliton train is given by the periodic coherent injection of a cw of suitable amplitude [37].

III. DISPERSION-MANAGED SOLITONS Because the GH effect translates frequency shift into timing jitter via fiber dispersion, Suzuki et al. [38] proposed to keep the path-averaged dispersion of a fiber link close to zero by means of periodic dispersion compensation. Whenever the local dispersion is much stronger than the path-averaged dispersion, the simulations show that a new type of pulse may form to represent a balance, on average, between residual dispersion and nonlinearity [39]. Moreover, periodic dispersion management has the advantage of suppressing four-wave mixing and strongly reducing XPM in dense WDM transmissions [40–44], thus opening the way for terabit transoceanic transmission capacities in a single fiber [45]. Let us rewrite NLS Eq. (9) by taking into account a spatially varying dispersion coefficient: i

@u dðZÞ @2 u þ þ aðZÞ2 juj2 u ¼ iP½u; u*; Z @Z 2 @T 2

ð61Þ

Here dðZÞ represents the dispersion variation. In the absence of perturbations (P ¼ 0), Eq. (61) is Hamiltonian in form and its approximate solution can be found again in terms of the variational principle [46, 47].

320

S. WABNITZ

A. Variational Representation Let us consider an approximate solution of Eq. (61) of the form u0 ðT ; ZÞ ¼ AðZÞf ðT ; ZÞ expðiCðZÞÞ

ð62Þ

where f ðT ; ZÞ ¼ exp½p2 ðZÞðT xðZÞÞ2 , and CðZÞ ¼ CðZÞðT xðZÞÞ2 kðZÞðT xðZÞÞ þ y0 ðZÞ. By integrating the corresponding Lagrangian density [Eq. (12)], one obtains LðZÞ ¼ ¼

ð1

1

L dT

EG a2 ðZÞpEG 1 dC C2 dk dy pffiffiffi 2 dðZÞ p2 þ 2 þ k2 þ 2x 2 2p dZ dZ dZ p 2 p

ð63Þ

pffiffiffiffiffiffiffiffi where we used the relationship A2 p=2 ¼ pEG between Ð pulse amplitude, width, and the unit-amplitude Gaussian pulse energy EG ¼ f 2 dT. By considering a vanishing perturbation (i.e., P ¼ 0) first, one can easily calculate from Eq. (63) the Euler–Lagrange equations for each pulse parameter, as in Eq. (17). One obtains for the pulse width and chirp the evolution equations dp ¼ 2dpC dZ

ð64Þ

dC E a2 p3 ¼ 2dð p4 C 2 Þ Gpffiffiffi dZ p

ð65Þ

In the case of nonvanishing perturbation P, by proceeding as in Eq. (21) one obtains dp ¼ 2dpC dZ

rffiffiffi !1=2 ð 1 2 p 2 RefPeif g½4t2 1et dt p EG 1

dC E a2 p3 ¼ 2dð p4 C 2 Þ Gpffiffiffi 2 dZ p 2

ð66Þ

!1=2 ð rffiffiffiffiffi 1 23 5 p EG RefPeif g 3 p 1

½4t2 1et dt !1=2 ð rffiffiffi 1 dk 2 1 2 ¼4 ½C ImfPeif g p2 RefPeif gtet dt dZ p EG p3 1

ð67Þ ð68Þ

where t ¼ pðT xÞ, and f ¼ CðT xÞ2 kðT xÞ þ y0 . In the next sections, we discuss some examples of DM soliton perturbations such as noise or in-line control devices.


321

B. Dispersion-Managed Soliton–Noise Interactions Let us consider first briefly how the interaction between ASE and solitons is affected by dispersion management [48]. By considering a perturbation as in Eq. (27) in Eqs. (66) through (68), one obtains the variance of the DM soliton frequency fluctuation as ! 2 ^ C 2N s2k ¼ 2 ASE p^ 2 þ 2 ð69Þ p^ a0 EG where C^ and p^ are calculated at the amplifier position. In comparing Eqs. (29) and (69), one notes that the GH jitter can be strongly reduced by dispersion management as long as EG Es , where Es is the energy of a hyperbolic secant soliton with the same pulse width in a fiber with a constant dispersion equal to the path-averaged value of the dispersion-managed line. The frequency shift that occurs at the mth amplifier leads to a time shift, hence a jitter of the arrival time of the DM soliton after N spans "ð #2 s2m ¼ s2k;m

NZa

dðZÞ dZ

mZa

ð70Þ

The resulting overall Gordon–Haus timing jitter variance is simply obtained from Eq. (70) by summing over the N amplifiers: s2T ¼

N P

s2m

m¼1

ð71Þ

C. Dispersion-Managed Soliton Example Let us consider an example of application of the DM soliton theory to the modeling of a 40-Gbps return-to-zero (RZ) nonlinear transmission system. We consider Za ¼ 50-km spans composed of about two-thirds positive dispersion (Dþ ¼ 8 ps=nm-km) fiber, followed by one-third negative or reverse dispersion fiber (D ¼ 25:4 ps=nm-km). The effective area and loss of these fibers are equal to Aþ ¼ 65 mm2 , A ¼ 25 mm2 , aþ ¼ 0:2 dB=km, and a ¼ 0:35 dB=km, respectively, whereas the nonlinear refractive index is n2 ¼ 2:5 1020 m2 =W. A DM soliton for this transmission link is defined as the particular RZ pulse that periodically returns back equal to itself after each span. For a given initial pulse energy E0, one can find such a pulse by solving Eqs. (64) and (65) and imposing pð0Þ ¼ pðZa Þ and Cð0Þ ¼ CðZa Þ. Figure 1 shows, for an input average power of 3 dBm of the 40-Gbps pseudo-random bit sequence (PRBS), the evolution of the DM soliton peak power, chirp, bandwidth, and time width over a single span. For better clarity, in Fig. 1 we have removed from the power variation the exponential loss over the span, and the chirp is expressed in terms of a cumulated dispersion in ps=nm. For a path-averaged dispersion of

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S. WABNITZ

FIGURE 1 Span evolution of DM soliton parameters.

d ¼ 0:01 ps=nm-km, it turns out that the chirp-free minimum pulse duration is equal to 15 ps, and the input chirp is 80 ps=nm. D. Self-Phase Modulation In a practical system, it may be difficult to precisely tune the signal power and RZ pulse width so that an exact DM soliton will be launched in the link. On the other hand, a given input chirp, say, Cð0Þ, can be quite easily selected by including a suitable length of pre-chirp fiber. In linear conditions, the action of an arbitrary pre-chirping fiber may be fully compensated for, as far as dispersive broadening is concerned, by the accumulated dispersion of the link of length L and a postchirp fiber that provides a chirp equal to, say, CðLÞ, at the receiver end. Indeed, linear compensation of the link dispersion is achieved whenever Cð0Þ þ CðLÞ þ dL ¼ 0, where d is the residual or path-averaged dispersion of the spans. The presence of fiber nonlinearity or self-phase modulation (SPM) does change this situation dramatically. Indeed, it turns out that whenever the signal power grows larger, SPM introduces a significant system penalty for all but a small range of pre-chirp values around, say, a certain C^ ð0Þ. Figure 2 shows the dependence of the system performance (as expressed in terms of the Q-factor) as a function of the pre- and post-chirp for the central channel of a 5 40 Gbps transmission with 100-GHz spacing. Note that, as far as the XPM impairment on the central channel is concerned, given the relatively large local dispersion of the


323

FIGURE 2 Numerical Q-factor for center channel at 2 Mm versus pre- and post-chip values for input power per channel of 3 dBm.

fibers, one can neglect the contribution of channels with more than 200-GHz spacing. The dispersion map is the same as in the case of Fig. 1, the input chirpfree RZ pulse duration is equal to 12.5 ps (50% duty cycle), and its average input power is equal to 3 dBm. The pre- and post-chirp are provided by means of the same positive or negative dispersion fibers that are employed in the transmission line. The error-free domain corresponds to the region in Fig. 2 where Q > 16 dB. As can be seen in Fig. 3, the stable region is aligned along the line Cð0Þ þ CðLÞ ¼ 0, which leaves a total residual uncompensated link dispersion of about 20 ps=nm. Moreover, the peak Q-value is obtained for a pre-chirp C^ ð0Þ ¼ 80 ps=nm, and system performance is rapidly degraded as the pre-chirp shifts away from this value. Note that, in the absence of SPM, system performance remains unchanged as long as Cð0Þ þ CðLÞ þ dL is a constant. On the other hand, as shown by Fig. 2 and by the comparison between the two eye diagrams of Fig. 3 (which should exhibit the same performance in linear conditions), the SPM leads to a relatively narrow error-free region around the optimal pre-chirp C^ ð0Þ. Figure 4 shows that the variational representation of the action of dispersion and SPM on a chirped RZ pulse in a dispersion-managed fiber link can be used to predict the optimal pre-chirp value with quite good accuracy. In Fig. 4, the closed circle represents the peak power of the input chirp-free pulse. Moreover, the diamonds of curve (a) indicate the output power and chirp of the RZ pulse after its propagation through a pre-chirp fiber, 2 Mm of transmission link, and a postchirp fiber, so that the linear condition Cð0Þ þ CðLÞ þ dL ¼ 0 is satisfied. The

324

S. WABNITZ

FIGURE 3 Output eye diagram at 2 Mm for pre-chirp of 80 ps=nm (left) or þ80 ps=nm (right). The post-chirp is equal to þ80 and 80 ps=nm, respectively.

pre-chirp is varied here between 440 and þ60 ps=nm when moving in a counterclockwise direction on curve a. As can be seen, the output pulse that is closest to the input value is obtained for a pre-chirp of 80 ps=nm. Curve (b) in Fig. 4 has been obtained by artificially reducing the fiber nonlinearity by a factor of 2, which clearly shows that the mismatch between input and output pulses is due to the action of SPM. Clearly, had we launched a DM soliton, the input and the output pulses would remain exactly the same for each and every span. In practice, this is a rather restrictive condition to achieve; a more practical way to compensate for the SPM-induced mismatch between the input and output RZ pulses is the use of a suitable prechirp C^ ð0Þ. As we have seen, the variational model may be helpful to determine such an optimal pre-chirp value.

E. Dispersion-Managed Soliton 2-R Regeneration The frequency and amplitude fluctuations of DM solitons or chirped nonlinear RZ pulses may be controlled by means of in-line filtering [49] and nonlinear pulse reshaping elements. Let us consider in Eq. (61) the following perturbation term: P ¼ dðZÞu þ bðZÞ

@2 u þ g1 ðZÞjuj2 u þ g2 ðZÞjuj4 u @T 2

ð72Þ


325

FIGURE 4 Output pulse power and chirp at 2 Mm, for different pre-chirp values. (a) Input power 3 dBm. (b) Same as part (a), but with half as much fiber nonlinearity.

which includes the effect of bandwidth-limited gain (resulting, for example, from in-line bandpass filters) and nonlinear gain [as determined, for example, by a fast saturable absorber (FSA) such as a nonlinear-loop mirror] [50]. One finds by applying the variational perturbation theory the following evolution equations for the pulse energy E and frequency k: pffiffiffi pffiffiffi dE C2 2 2 g A4 E ¼ 2dE 2bk2 E b p2 þ 2 E þ 2g1 A2 E þ p dZ 3 2 dk C2 ¼ 4b p2 þ 2 dZ p

ð73Þ ð74Þ

These equations show that a stable or steady-state value for the DM soliton energy results whenever 1 1 d ¼ bB^ pffiffiffi g1 A^ 2 pffiffiffi g2 A^ 4 3 2

ð75Þ

with B^ ¼ p^ 2 þ C^ 2 =^p2 ; the hat denotes the value of a parameter calculated at the (supposedly common) position of the filter and nonlinear gain element. By calculating the fluctuations dE of energy around its steady-state value, say, E0 , one finds that FSA and filtering lead to a stable or attracting value of energy for the DM solitons. Without filtering and FSA, an instability of the DM soliton energy may result for relatively large pulse energies.

326

S. WABNITZ

F. Cross-Phase Modulation For the interaction between two WDM channels in a DM transmission link, we may again write u ¼ u1 þ u2 in Eq. (61) and obtain the perturbed equation for the field in, say, channel 1 i

@u1 dðZÞ @2 u1 þ þ aðZÞ2 ju1 j2 u1 ¼ 2a2 ðZÞju2 j2 u1 2 @T 2 @Z

ð76Þ

where we have retained as a perturbation the cross-phase modulation (XPM) term but we have neglected, owing to the large local dispersion, the four-wave mixing terms proportional to u21 u*2 . By setting p1 ¼ p2 ¼ p; C1 ¼ C2 ¼ C; Dk ¼ k1 k2 , and DT ¼ x1 x2, one obtains the coupled DM soliton evolution equations in the presence of XPM [51–53]: dp ¼ 2dpC dZ

ð77Þ

dC a2 p3 E 2a2 p3 E 2 2 ¼ 2dð p4 C 2 Þ pffiffiffi 0 pffiffiffi 0 ð2p2 DT 2 1Þep DT p p dZ

dDk 4 2 2 ¼ pffiffiffi a2 p3 E0 DTep DT dZ p

dDT ¼ dDk dZ

ð78Þ ð79Þ ð80Þ

These equations can be used to estimate the XPM-induced timing jitter that results from a large number of collisions of a RZ pulse with other pulses in adjacent channels [54, 55]. Let us denote with dTc the time shift of a given pulse at the receiver with respect to its nominal position, owing to a collision with a pulse in some adjacent channel at position Zc . The relative time shift between two pulses in a given channel, spaced by k consecutive bits, due to collisions with pulses (with an equal k bits spacing) in another channel may be written as DTk;c ¼ ðbcþk bc ÞdTc

ð81Þ

where bj ¼ 0; 1 represents the information in a given bit. By supposing that the channel wavelength spacing is such that a given pulse experiences N collisions with pulses in an adjacent channel over the transmission distance L, one obtains the total time shift between the two pulses as dTk ¼

N P

ðbcþk bc ÞdTc

c¼1

ð82Þ

The resulting XPM-induced time jitter reads as s2 ¼

1 P

k¼1

2k hðdTk Þ2 i

ð83Þ


327

where we took into account the pseudo-random statistical distribution of the bits bj and also that the probability of a bit pattern composed of k 1 consecutive zeroes is equal to 2k .

G. Doubly Periodic Maps For reducing the XPM impairments in high-bit-rate RZ transmissions, it proves convenient to design a dispersion map with a relatively large residual dispersion per span. So as not to accumulate through the link dispersion that is too large overall, which would require impractical lengths of precompensated and postcompensation fibers, a relatively simple solution is to adopt a doubly periodic map [56, 57]. As a result, the overall or path-averaged dispersion (PAD) of a series of N overcompensated spans of, say, SMF, can be reduced by periodically inserting an uncompensated span of SMF. As far as the nonlinear pulse interactions are concerned, an optimal span compensation fraction may be determined as a trade-off between intrachannel and interchannel collisions. In fact, whenever the span-averaged dispersion (SAD) grows larger, the interactions between pulses in the same channel are increased, whereas the effect of interchannel collisions is reduced. For a doubly periodic map, DM solitons can still be found. Figure 5 shows one period of the evolution of a DM soliton for a double map composed of five 34-km-long compensated spans of SMF (D ¼ þ17 ps=nm-km), plus a single

FIGURE 5

Span evolution of DM soliton in doubly periodic map with D ¼ 3 ps=nm-km and d ¼ 0:1 ps=nm-km.

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S. WABNITZ

span of uncompensated SMF, for a total map length of about 200 km. In this case, the SAD ¼ 3 ps=nm-km, whereas the PAD ¼ 0.1 ps=nm-km. As can be seen, for a pulse injected after the first compensated span the input chirp is close to zero. The input average power is equal to 4:5 dBm for a 20-Gbps PRBS. Figure 5 also shows that while the pulse width oscillates by 150% (from 35 to 55 ps) within the map, the spectral width of the pulses only changes by about 1%. The advantage of designing a map with a relatively high SAD is clearly shown by comparing Fig. 6 with Fig. 7. Here we consider a collision between two DM solitons with a frequency spacing of 50 GHz (0.4 nm), and we display the relative time separation and frequency difference as a function of distance for the worst case of two adjacent pulses that are fully overlapping in time at the system input (initial half-collision). As can be seen, with a small SAD (D ¼ 0:5 ps=nmkm) the pulse separation periodically returns close to zero after each span, which leads to a sequence of half-collisions and an accumulation of a large net negative frequency shift. This in turn entails a relatively large XPM-induced frequency jitter. On the other hand, with a SAD as large as D ¼ 3 ps=nm-km, the two pulses are shifted by 40 ps (about one pulsewidth) after each span so that a full decorrelation of the pulse sequences occurs. As a result, the accumulated net frequency shift periodically returns to zero after a whole period of the 200 km dispersion map, and the resulting timing jitter is basically suppressed. Note that in both Figs. 6 and 7, the PAD d ¼ 0:1 ps=nm-km.

FIGURE 6 Evolution of pulse separation and frequency difference between colliding pulses in doubly periodic dispersion managed link with SAD¼ 0:5 ps=nm-km.


FIGURE 7

329

Same as in Fig. 6, with SAD¼ 3 ps=nm-km.

H. Nonlinear Chirped Return-to-Zero Pulses As we have already observed in a previous section, the strict condition on the input pulse width that must be matched for a given dispersion map in order to launch a DM soliton may be relaxed by allowing the SPM and dispersive impairments to be compensated at a given system output distance by means of adjusting the signal pre-chirp only. This mode of transmission may be termed nonlinear chirped RZ or higher order soliton format. Let us consider, for example, the case of 10-Gbps transmission with 50% duty cycle, which means a 50-ps input chirp-free duration for the pulses. This value will not correspond, in general, to the DM soliton minimum pulse duration for a given dispersion map. Therefore, in the presence of SPM, the minimum and maximum pulse durations will not be preserved unchanged at each map period, but will slowly evolve along a periodic trajectory. Figure 8 shows, for a doubly periodic DM map as in Figs. 6 and 7, the long-term evolution of the maximum (dashed curves) and minimum (solid curves) pulse durations within each of the successive 200-km dispersion maps, for a total transmission distance up to 10 Mm. As can be seen, the period of the slow evolution of the pulse parameters is controlled by the signal power. On the other hand, one finds that a horizontal shift of the pulse trajectory can be obtained by changing the pre-chirp, so as to match the input and output pulse widths as closely as possible (see also Fig. 4), as recently demonstrated in a 32 10-Gbps transmission experiment over 6 Mm using a SMF-reverse dispersion fiber map [58].

330

S. WABNITZ

FIGURE 8 Evolution with distance of minimum (solid curve) and maximum pulse width for input average power (at 10 Gbps) of 5, and 2 dBm, respectively.

I. Dispersion-Managed Soliton 3-R Regeneration The techniques of dispersion management and all-optical regeneration can be combined to extend the reach of 40-Gbps systems over transoceanic distances [59, 60]. As we shall see, the stability of DM soliton propagation under the action of discrete control elements periodically placed within the dispersion map may be studied by means of standard results for the stability of ordinary differential equations with periodic coefficients [61, 62]. Indeed, the nonlinear chirped RZ pulse stability may be analyzed by combining the variational model for the periodic evolution of the pulse parameters with the discrete change of these parameters that occurs at the control element position. From the variational model, one obtains a transformation of the vector of soliton parameters, say, FL ðX Þ ¼ ½AðLÞ; pðLÞ; CðLÞ; kðLÞ; xðLÞ, which represents the evolution after a map of length L from the input pulse vector X ¼ ½Að0Þ; pð0Þ; Cð0Þ; kð0Þ; xð0Þ at z ¼ 0. The action of an in-line control element can also be defined in terms of the associated discrete change to the pulse parameters. For example, synchronous in-line IM can be described for convenience by a Gaussian intensity transfer function such that uðZþ ; T Þ ¼ uðZ ; T ÞM ðT Þ ¼ uðZ ; T Þ expðmT 2 Þ, whereas a bandpass filter can be represented by means of a spectral transfer function of the type u^ ðZþ ; oÞ ¼ u^ ðZ ; T ÞFðoÞ ¼ u^ ðZ ; T Þ expðbo2 Þ. In each case, the action of a discrete control element corresponds to a transformation of the type Xþ ¼ CðX Þ. The stabilizing action of the control element on the DM soliton parameters over a given periodic map can then be inferred from a linear stability analysis based on the eigenvalues of the Jacobian matrix of the overall transformation


331

[63]. In the case of pulse propagation over a finite distance, the Jacobian matrix JF is defined as @FZ ½X @X

ð84Þ

@CZ ½X jX @X

ð85Þ

JF ðZÞ ¼ Similarly, for a lumped device one has JD ¼

The resulting Jacobian, say, JT , for the whole map of length L is simply obtained by means of a matrix multiplication (in an order corresponding to the physical arrangement) of the different Jacobian matrices associated with either freepropagation or lumped devices. One obtains the maximum growth rate of a perturbation to the soliton parameters as G ¼ ð20= lnð10ÞÞ log jlMAX j=L [dB=km], where jlMAX j ¼ max½jli j and ½lj is the set of eigenvalues of JT . On the other hand, whenever G < 0, the control devices have a stabilizing action, so that any perturbation to the soliton parameters will be attenuated on propagation through the map. Figure 9 shows the instability gain G as a function of the position of a synchronous IM, placed inside a 40-km-long dispersion map. In this case, the map is composed of 20.5 km of positive dispersion fiber with Dþ ¼ þ2 ps=nmkm (effective area Aþ ¼ 50 mm2 ), followed by 19.5 km of negative dispersion fiber with D ¼ 2 ps=nm-km (A ¼ 30 mm2 ). The loss of both fibers is equal to 0.2 dB=km and the path-averaged dispersion d ¼ þ0:05 ps=nm-km. In Fig. 9, the

FIGURE 9 Stability of IM control (G < 0) versus IM position for pulse energies EG ¼ 50 fJ (solid thick curve), 100 fJ (dashed curve), or 200 fJ (solid thin curve).

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thick solid, dashed, and thin solid curves correspond to the case of 50-, 100-, and 200-fJ pulse energies, respectively. As can be seen, in every case the IM has a stabilizing action on the pulse fluctuations only if it is placed close to the middle of the dispersion map, near the splice between the positive and the negative fiber. Moreover, an increase of the pulse energy widens the pulse stability region around the middle of the map. In fact, Fig. 10 shows the result of a simulation for a single pulse propagation: The pulse intensity is displayed at intervals equal to multiples of the map period. Here the IM is placed after 14 km of Dþ fiber. As can be seen from the top panel of Fig. 10, the pulse experiences an amplitude instability for an input energy of 50 fJ, whereas the bottom panels show that if the pulse energy is increased up to 200 fJ, DM soliton propagation remains stable. The stabilizing action of an IM is strongly dependent on the arrangement of fibers in the dispersion map. Figure 11 compares, for a Gaussian pulse of energy EG ¼ 200 fJ, the stability regions (dashed areas, for G < 0) of the previously described map (a) with (b) a map with 10 km of D fiber, followed by 20.5 km of Dþ fiber and 9.5 km of D fiber; (c) a map with 19.5 km of D fiber followed by 20.5 km of Dþ fiber. As can be seen, in the last case one obtains the minimum G (hence, the strongest stabilization of the pulse parameters) in the practical arrangement of an IM placed at the amplifier site.

J. Dispersion-Managed Soliton Distributed Raman Amplification Recent experiments by Mollenauer et al. [64] have shown that distributed Raman amplification (DRA) can be combined with EDFAs and the DM soliton format to

FIGURE 10 DM soliton evolution for IM at 14 km. Top: pulse energy EG ¼ 50 fJ; bottom:

EG ¼ 200 fJ.


FIGURE 11

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Stable modulator positions (gray areas) for different dispersion maps.

enhance the transmission performance of ultra-long-haul and transoceanic WDM transmissions. In this section, let us compare the impact of fully replacing EDFAs with DRA on the propagation and interactions of 40-Gbps DM solitons [65]. Figure 12 compares the evolution across a 50-km span of the signal power PðZÞ and nonlinearity [i.e., PðZÞ=Aeff ðZÞ] for the case of EDFAs (dashed curves) and DRA with counterpropagating pumping (solid curves), respectively. Here we neglected for simplicity Raman pump saturation by the signal (small signal regime). In Fig. 12, left, the path-averaged signal power is the same in the two cases, whereas in Fig. 12, right, the path-averaged nonlinearity is equal with EDFAs and DRA. The fiber parameters are the same as in Fig. 1. As can be seen, although the signal power distribution is more uniform with DRA, the effective nonlinearity is more asymmetric with DRA, owing to the small effective area of the reverse dispersion fiber. Moreover, Fig. 12 shows that, to obtain an equal amount of effective nonlinearity, the input power with DRA should be reduced by about 2.5 dB with respect to the EDFA case. Figure 13 summarizes the nonlinear limitations on the maximum transmission distance, as set by either intrachannel or interchannel XPM as a function of the transmission fiber dispersion (the dispersion of the compensating fiber was fixed at 25.4 ps=nm-km, for a total 50-km span length), in the case of WDM 40Gbps transmissions with 100-GHz channel spacing. In Fig. 13 the input pulses did correspond in each case to a DM soliton; therefore, the input pulse chirp-free time width was changed from about 6 to 15 ps when the transmission fiber

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FIGURE 12 Span evolution of signal power (left) and nonlinearity (right) with EDFAs (dashed curves) or DRA (solid curves).

dispersion grew from 2 to 17 ps=nm-km. The results of Fig. 13 are qualitative but we understand from them that the optimum transmission fiber dispersion and maximum distance result from a trade-off between intrachannel and interchannel pulse interactions. In fact, intrachannel interactions increase as the transmission fiber dispersion grows larger, whereas XPM-induced impairments are reduced. Again, the results obtained with EDFAs are represented in Fig. 13 by means of

FIGURE 13

Distance limitations set by intrachannel XPM and interchannel XPM, for EDFA (dashed curves) or Raman-based (solid curves) transmission.


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dashed curves, whereas the case of DRA is shown by solid curves. The input power per channel was set to 1 dBm for EDFAs and 3 dBm for the DRA case, so that the path-averaged nonlinearity is about the same in the two cases. In Fig. 13, the intrachannel interaction distance was estimated by numerically considering the case of two-pulse interactions. The distance shown here leads to more than a 30% time shift of their initial 25-ps separation, whereas the XPM distance was calculated for the central channel of a 100-GHz spaced, five-channel group by means of the variational model. The corresponding statistical timing jitter reached 10% of the bit slot at the distances shown in Fig. 13. As can be seen, DRA reduces the intrachannel interactions, but increases the effect of WDM collisions, owing to the larger asymmetry in the nonlinearity profile of Fig. 12. For each type of amplification, the dots in Fig. 13 indicate the optimal dispersion values for the transmission fiber, namely, of þ8 ps=nm-km for EDFAs and around twice this value for DRA. Note that the effect of XPM is overestimated in Fig. 13 because all colliding pulses have the same polarization state, whereas in a real case neighboring channels tend to be depolarized. To assess the relative merit of the lumped EDFA and the DRA amplification schemes for N 40-Gbps transmissions, it is necessary to perform a full numerical simulation, as in the case summarized by Fig. 14. Here we show, for a total transmission distance of 2000 km, the dependence of the optimal Q-factor (by selecting the best pre- and post-chirp values) versus input average power for the central channel of a 100-GHz spaced, five-channel RZ transmission. The noise figure of the 50-km spans was equal to 17 dB with EDFAs and was 3 dB lower with DRA. The duty factor of the RZ modulation was 50%, for a 12.5-ps chirp-free pulse duration of the input pulses, whereas the PAD was equal to d ¼ 0:05 ps=nm-km. In Fig. 14 the optimal Q-factor results from a trade-off

FIGURE 14

Quality factor Q at 2 Mm using DRA (solid curve) or EDFAs (dashed curve).

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between the optical SNR, which improves as the signal power grows larger, and the nonlinear penalty from SPM and XPM that leads to a rapid performance degradation above a certain threshold power. As can be seen, the optimal input power with DRA is about 2.5 dB lower than with EDFAs, which, as pointed out by Fig. 12, leads to equal effective nonlinearity in the two cases. Nevertheless, thanks to the reduced noise figure, DRA leads to about a 1-dB improvement in the overall system performance. Note that for an input average power of 3 dBm, the DM soliton of the map has a chirp-free duration of 25 ps; hence, the input format corresponds to nonlinear chirped RZ pulses.

IV. CONCLUSIONS In this chapter we presented an overview of the theory of soliton and nonlinearitybased telecommunications. The propagation of a RZ pulse under the action of fiber dispersion, nonlinearity, and various sources of perturbation can be represented in terms of a simple set of evolution equations for its parameters. This approach is particularly effective in the context of presently deployed dispersion-managed fiber links, where the fiber nonlinearity is a small perturbation with respect to the relatively high local fiber dispersion. Therefore, the propagation of the RZ pulses is quasi-linear, and the generation of dispersive waves is negligible. In dispersion-managed links, SPM has a significant impact on system performance. We have discussed how the concept of a soliton-based transmission can be generalized to the case of a nonlinear chirped RZ system, where nonlinear distortion of the input pulse may be minimized at a given output distance by a suitable choice of a pre-chirp. In this situation, the main nonlinear system impairment is due to pulse-to-pulse interactions and collisions, which can in turn be reduced by properly designing the dispersion map. The remaining linear constraints to the overall transmission capacity, namely, the noise accumulation and the gain bandwidth, can be alleviated by the use of distributed Raman amplification, which should be properly combined with the nonlinear RZ, chirp-adjusted mode of transmission.

ACKNOWLEDGMENTS The author is grateful to Alcatel, who stimulated and supported this work in its early phase, and to the many colleagues who took part in the research that I have summarized here. In particular, I would like to thank Y. Kodama and T. Hirooka for the collaboration on soliton perturbation theory, as well as A. Tonello and A. Capobianco for the joint work on all-optical DM soliton control, and L. du Mouza, E. Seve, G. Le Meur, and J. P. Hamaide for work on DM solitons and Raman amplification.


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24. L. F. Mollenauer, J. P. Gordon, and S. G. Evangelides. The sliding frequency guiding filter: An improved form of soliton jitter control. Opt. Lett. 17, 1575–1577 (1992). 25. L. F. Mollenauer, E. Lichtman, M. J. Neubelt, and G. T. Harvey. Demonstration, using slidingfrequency guiding filters, of error-free soliton transmission over more than 20 Mm at 10 Gbit=s single channel and over more than 13 Mm at 20 Gbit=s in a two-channel WDM. Electron. Lett. 29, 910–911 (1993). 26. Y. Kodama, M. Romagnoli, and S. Wabnitz. Stabilization of optical solitons by an acousto-optic modulator and filter. Electron. Lett. 30, 261–262 (1994). 27. Y. Kodama and S. Wabnitz. Analysis of soliton stability and interactions with sliding filters. Opt. Lett. 19, 162–164 (1994). 28. S. Wabnitz. Effect of frequency sliding and filtering on the interactions of polarization division multiplexed solitons. Opt. Lett. 20, 261–263 (1995). 29. Y. Kodama, M. Romagnoli, and S. Wabnitz. Soliton stability and interactions in fiber lasers. Electron. Lett. 28, 1981–1983 (1992). 30. S. G. Evangelides, L. F. Mollenauer, J. P. Gordon, and N. S. Bergano. Polarization multiplexing with solitons. J. Lightwave Technol. 14, 28–35 (1992). 31. C. De Angelis and S. Wabnitz. Interactions of orthogonally polarized solitons in optical fibers. Opt. Commun. 125, 186–196 (1996). 32. L. F. Mollenauer, K. Smith, J. P. Gordon, and C. R. Menyuk. Resistance of solitons to the effects of polarization dispersion in optical fibers. Opt. Lett. 9, 1218–1221 (1998). 33. L. F. Mollenauer, J. P. Gordon, and F. Heismann. Polarization scattering by soliton–soliton collisions. Opt. Lett. 20, 2060–2062 (1995). 34. M. Nakazawa, E. Yamada, H. Kobota, and K. Suzuki. 10 Gbit=s soliton transmission over one million kilometers. Electron. Lett. 27, 1270–1272 (1991). 35. M. Nakazawa, K. Suzuki, E. Yamada, H. Kubota, Y. Kimura, and M. Takaya. Experimental demonstration of soliton data transmission over unlimited distances with soliton control in time and frequency domains. Electron. Lett. 29, 729–730 (1993). 36. S. Wabnitz. Suppression of soliton interactions by phase modulation. Electron. Lett. 29, 1711– 1712 (1993). 37. S. Wabnitz. Control of soliton train transmission, storage and clock recovery by CW injection. J. Opt. Soc. Am. B 13, 2739–2749 (1996). 38. M. Suzuki, I. Morita, N. Edagawa, S. Yamamoto, H. Taga, and S. Akiba. Reduction of Gordon– Haus timing jitter by periodic dispersion compensation in soliton transmission. Electron. Lett. 31, 2027–2028 (1995). 39. N. J. Smith, F. M. Knox, N. J. Doran, K. J. Blow, and I. Bennion. Enhanced power solitons in optical fibres with periodic dispersion management. Electron. Lett. 32, 54–55 (1996). 40. S. Wabnitz. Stabilization of sliding-filtered soliton WDM transmissions by dispersion compensating fibers. Opt. Lett. 21, 638–640 (1996). 41. F. Matera and S. Wabnitz. Periodic dispersion compensation of soliton wavelength division multiplexed transmissions with sliding filters. Opt. Fiber Technol. 3, 7–20 (1997). 42. H. Taga, M. Suzuki, N. Edagawa, S. Yamamoto, and S. Akiba. Long-distance WDM transmission experiments using the dispersion slope compensation. IEEE J. Quantum Electron. 34, 2055–2063 (1998). 43. D. Le Guen, A. O’Hare, S. Del Burgo, D. Grot, F. Favre, and T. Georges. Narrowband 640 Gbit=s soliton DWDM transmission over 1200 km of standard fibre with 100 km 21 dB amplifier spans. Electron. Lett. 34, 2345–2346 (1996). 44. L. F. Mollenauer and P. V. Mamyshev. Massive wavelength-division multiplexing with solitons. IEEE J. Quantum Electron. 34, 2089–2102 (1998). 45. T. Tsuritani, N. Takeda, K. Imai, K. Tanaka, A. Agata, I. Morita, H. Yamauchi, N. Edagawa, and M. Suzuki. 1 Tbit=s (100 10:7 Gbit=s) transoceanic transmission using 30 nm wide broadband optical repeaters with Aeff -enlarged positive dispersion fibre and slope-compensating DCF. Electron. Lett. 35, 2126–2128 (1999).


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PART

III

SUBMARINE EQUIPMENT


9 SUBMERGED PLANT NEVILLE J. HAZELL CHRISTOPHER E. LITTLE Alcatel Submarine Networks Ltd., Greenwich, United Kingdom

I. OVERVIEW OF SUBMERGED PLANT II. REPEATERS A. Optical Topology B. Drive and Control Electronics C. Supervisory Functionality D. Power Unit and Protection III. EQUALIZERS A. Passive Equalizers B. Active Tilt Equalizers IV. BRANCHING UNITS A. Full Fiber-Drop Branching Units B. Wavelength Add=Drop Branching Units C. Power Module V. MECHANICAL ENGINEERING OF SUBMARINE EQUIPMENT A. Internal Design Aspects B. External Aspects of Design VI. POWER-FEED EQUIPMENT FOR SUBMARINE EQUIPMENT A. Network Powering B. High-Voltage Generation C. Other Functions VII. RELIABILITY A. Quality Control and Qualification B. Reliability of Submerged Plant C. Reliability of Power-Feed Equipment VIII. FUTURE TRENDS IN SUBMARINE EQUIPMENT References


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NEVILLE J. HAZELL AND CHRISTOPHER E. LITTLE

I. OVERVIEW OF SUBMERGED PLANT Network terminal stations are electrically and optically linked by the submerged plant. As can be seen in Fig. 1, this plant comprises the cable for transmission, repeaters to amplify the signal at regular intervals, equalizers to maintain equal power in each signal channel, and branching units to enable network connectivity and flexibility. Associated with the submerged equipment is power-feed equipment, which is located at the terminal stations. Repeaters, equalizers, branching units, and power-feed equipment are described in this chapter. Data are transported in all-optical form via the silica fibers in the undersea cable at bit rates of up to 1–2 Tbps per fiber using DWDM transmission techniques. However, optical fibers possess inherent losses that cause signal degradation for transmission over long distances. A reduction in optical signal power occurs as the propagation distance increases so that for transmission across distances in excess of around 400 km, the signals must be amplified at regular intervals, or spans, of typically 40–60 km in order to be processed successfully at the receiving terminal station. Chains of repeaters can be seen in each segment of the network shown in Fig. 1. Current generation optical repeaters incorporate an erbium-doped fiber amplifier (Chapters 2 and 4) for each transmission fiber in the cable. This amplifier boosts the signal power in every channel carried by the fiber, independent of bit rate. Repeaters are described in Section II. Gain-flattening filters are used in each repeater to ensure that each optical channel is sent to the next repeater in the chain at the same power level. Repeater filters are not perfect, however, and small cumulative errors lead to deviations from signal spectrum flatness after transmission through many devices. Equalizers (Section III) are inserted in the network every block of typically 12 repeaters to ensure that the network channel power flatness, or ‘‘equalization,’’ requirement is met so as to ensure minimum errors are incurred on each channel upon reception.

FIGURE 1 Elements of a submarine telecommunications network.

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Together repeaters and equalizers enable long-haul submarine telecommunication to be achieved. But many networks need features that are supplementary to simple point-to-point transmission and which repeaters and equalizers cannot provide. For example, the diversion or rerouting of complete fibers or of individual signal channels (wavelengths) at nodes (where three cables meet) is a common requirement. As well, in the event of a break in a cable segment, reconfiguration of the network power feed may be needed to ensure that optical traffic in the undamaged segments of the network is maintained. The network optical connectivity and power-feed flexibility needed to satisfy these additional features are provided by branching units (BUs) at network nodes. The network in Fig. 1 has a single BU located at a node. Branching units are discussed in Section IV. The operating environment of the submerged plant places great demands on its mechanical design (Section V). Deployment depths for repeaters and equalizers can reach 8 km, where the hydrostatic pressure is around 800 atmospheres (80 MPa). In addition to the obvious requirement for mechanical strength against external water pressure, the equipment housing must protect the interior atmosphere against gas ingress (especially hydrogen). The plant needs to be operated at voltages of up to 15 kV more than the surrounding seawater potential, must be designed so that all critical electronic components are within thermal operating limits, and must be able to cope with the practicalities of laying cable in the ocean. The submerged plant must be powered from the terminal stations, where dedicated power-feed equipment (PFE) is installed (Section VI). The current necessary to power the repeaters, active equalizers, and BUs in a segment is delivered along the copper conductor that surrounds the optical fiber in the undersea cable. The power-feed equipment not only provides power to the submerged plant but is also used to terminate the terrestrial and submarine cables and to provide earth connections, power distribution, and monitoring of the electrical status of the network. The simple network in Fig. 1 can be powered in a number of ways. For all but the longest interterminal distances, the repeaters, equalizers, and BUs along the primary cable or trunk can be powered from either terminal A or B alone, although for redundancy purposes the provision of highvoltage DC power is normally shared between PFE in each terminal. The PFE then power each end at opposite polarity voltages and there is a virtual earth in the middle of the trunk or segment. High-voltage limitations make it mandatory to power very long trunks with power sharing between terminals. The secondary cable or spur that links the BU node to the third terminal station C in Fig. 1 is powered from that station, with a sea-earth at the BU and a sea current return. At any time, the BU may be instructed to reconfigure to make one of the routes A–C or B–C the trunk, perhaps while a cable fault is repaired on the A–B route. The industry standard for the design life of a submarine network is 25 years. The target for the reliability of the submarine plant is that no more than one ship repair should be needed during that lifetime per two fiber pairs on a transatlantic

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cable (7000 km or around 175 repeaters). Such high reliability is ensured by design, with the use of high-reliability electronics and application of redundancy for components that display higher failure rates, together with strict quality procedures in the selection, testing, burn-in, and documentation of components and the use of ultraclean fabrication facilities. Reliability issues are addressed in Section VII. Few people foresaw how quickly the need for capacity on submarine cables would grow with the arrival of the Internet in the early 1990s, or indeed how the submarine industry would meet the challenge in time, but in Section VIII we endeavor to predict some of the trends for the development of submarine plant during the next 10 years. II. REPEATERS Repeaters enable long-haul optical signal transmission to be achieved by using erbium-doped fiber amplifiers (EDFAs) to boost the powers of signals in channels in the C-band (1525–1565 nm) of the infrared transmission spectrum. The same technology can be applied to amplify the L-band (1570–1610 nm) channels. All submerged equipment is designed on a fiber-pair basis for bidirectional operation (one fiber for each direction), and amplifier pairs are the basic building blocks of repeaters. Although there is one EDFA per fiber, laser diode (LD) pumps, the control and the supervisory circuitry are shared between the two EDFAs of an amplifier pair. A single repeater can be used to amplify signals on up to 12 fiber pairs, although a typical network would comprise 4 or 6 fiber pairs. The external view of a repeater is shown in Fig. 2. Inside the central housing are the EDFAs and their associated power, control, and supervisory electronics. Here we consider the optical and electronic engineering of repeaters. The mechanical aspects are discussed in Section V. A. Optical Topology The optical topology of a typical implementation of EDFAs used in submarine repeaters is shown in Fig. 3 for a fiber pair. Laser diode pumps are provided in

FIGURE 2 External view of a repeater. The diameter and length of the central housing are typically 300 and 1000–1500 mm, respectively.

9. SUBMERGED PLANT

FIGURE 3 Optical scheme for a submarine repeater EDFA.

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348


either pairs or quadruplets (as shown) and have wavelengths of 1480 or 980 nm. Generally speaking, the earliest optical repeaters made use of 1480-nm LDs. When reliable high-power 980-nm devices became available later, they enabled more efficient pumping with lower output signal noise, and have now supplanted the earlier 1480-nm technology. Where both 980- and 1480-nm LDs have been used, the first provide copumping of the signal and the second provide counterpumping. This allows two simple pump=signal multiplexers to be used despite the presence of two pump wavelengths. Irrespective of pump wavelength, although the pump power needed could be provided by two LDs, four are used in a redundant configuration for reliability purposes. The redundancy is provided in a very simple and reliable way by sharing the pumps for the two directions using optical fiber couplers. The 980-nm LDs in Fig. 3 have their wavelengths grating stabilized and their outputs are combined in two steps, before being split and injected into the two erbium-doped fibers in the amplifier pair. In each EDFA, the pump radiation is injected into the signal fiber by a wavelength-division multiplexer (WDM) coupler that also allows the 1550-nm traffic signals to pass with minimal losses. The pump radiation then enters a 10- to 20-m-long coil of erbium-doped fiber, whose length and dopant concentration are selected on a network basis to amplify the signal wavelengths with the appropriate gain and power levels. After the erbium-doped fiber, a low-loss isolator is used to prevent the back reflection of signal light from subsequent optical components that remain in the signal line. This is necessary to minimize parasitic extraction of signal power in the opposite direction to traffic transmission. Gain flattening filters (GFFs) are used to impose equal powers on each output signal channel, and their use in each repeater is necessary to ensure that the bit error rate of the received signal meets the minimum requirement for all channels [1]. The main cause of channel power imbalance is the wavelength dependence of the EDF amplifier gain. Other factors include wavelength-dependent losses of other optical components in the amplifiers and of the transmission fiber. As well, stimulated Raman scattering in the transmission fiber transfers power from the shorter wavelengths to the longer ones generating a linear (in logarithmic terms) tilt across the bandwidth. The GFFs correct for the wavelength dependence of the gain shape of the EDF amplifier, and can impress a pretilt to oppose some of the tilt that will arise from propagation on the succeeding fiber span. Because the gain shape depends on the input power distribution and the pump power, and the tilt induced by stimulated Raman scattering on the fiber is signal power sensitive, the output power of each EDFA and the fiber span loss need to be carefully controlled if the GFFs are to be effective. The gain shape also depends on pump wavelength, temperature, and inhomogeneous processes such as spectral hole burning. The LD pump wavelength is usually controlled by the use of gratings as shown in Fig. 3. The EDFA gain profile needs to be measured under representative operational (power and temperature) conditions so that the GFFs can be correctly specified. Spectral hole burning is mitigated by ensuring that power is

9. SUBMERGED PLANT

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shared across all channels in the band—dummy wavelengths are used in networks which at the start of life are only partly loaded with traffic. The GFFs are typically comprised of in-line fiber gratings, tapered fiber filters, or multilayer dielectric layer (MDL) elements [2]. The filters should fit tight specifications with respect to wavelength (0.25 nm) and transmission loss (0.1 dB), and display wavelength stability against bending (losses

Undersea Fiber Communication Systems (Optics and Photonics)

Undersea Fiber Communication Systems (Optics and Photonics)

Undersea Fiber Communication Systems (Optics and Photonics)

Erbium-Doped Fiber Amplifiers (Optics and Photonics)

Fiber Bragg Gratings (Optics and Photonics)

Applications of Nonlinear Fiber Optics (Optics and Photonics Series)

Nonlinear Fiber Optics, Fourth Edition (Optics and Photonics)

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Fiber-Optic Communication Systems

Fiber-Optic Communication Systems

Fiber-Optic Communication Systems

Fiber-Optic Communication Systems

Elements of Photonics, For Fiber and Integrated Optics, Vol. 2

Fiber Bragg Gratings, Second Edition (Optics and Photonics Series)

Fiber optics handbook: fiber, devices, and systems for optical communications

Fiber Optics Handbook: Fiber, Devices, and Systems for Optical Communications

Photonics Rules of Thumb: Optics, Electro-Optics, Fiber Optics and Lasers

Introduction to Information Optics (Optics and Photonics)

Photonics Rules of Thumb: Optics, Electro-optics, Fiber Optics, and Lasers

Optics and photonics: an introduction

Optical Fiber Telecommunications V B, Fifth Edition: Systems and Networks (Optics and Photonics)

Optics and Photonics: An Introduction

Optical Fiber Telecommunications V B, Fifth Edition: Systems and Networks (Optics and Photonics)

Fiber Optics: Physics and Technology

Fiber Optics: Physics and Technology

Fiber Optics: Physics and Technology

Information Optics and Photonics: Algorithms, Systems, and Applications

Fiber Optics Handbook

Fiber Optics. Technican's Manual

Introduction To Fiber Optics

Raman Amplification in Fiber Optical Communication Systems

Undersea Fiber Communication Systems (Optics and Photonics)