Erbium-Doped Fiber Amplifiers Fundamentals and Technology OPTICS AND PHOTONICS (formerly Quantum Electronics) EDITED BY PAUL L. KELLY Tufts University Medford, Massachusetts IVAN KAMINOW AT&T Bell Laboratories Holmdel, New Jersey GOVINDAGRAWAL University of Rochester Rochester, New York A complete list of titles in this series appears at the end of this volume. Erbium-Doped Fiber Amplifiers Fundamentals and Technology P. C. BECKER Passive Optical Networks Group Switching and Access Group Lucent Technologies Tokyo, Japan N. A. OLSSON Passive Optical Networks Group Switching and Access Group Lucent Technologies Murray Hill, New Jersey J. R. SIMPSON Ciena Corporation Linthicum, Maryland ACADEMIC PRESS San Diego London Boston New York Sydney Tokyo Toronto This book is printed on acid-free paper. © Copyright © 1999 by Lucent Technologies 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. All brand names and product names mentioned in this book are trademarks or registered trademarks of their respective companies. Academic Press A Harcourt Science and Technology Company 525 B Street, Suite 1900, San Diego, CA 92101-4495, USA http://www.academicpress.com Academic Press Harcourt Place, 32 Jamestown Rd., London NW1 7BY, UK http://www.academicpress.com Library of Congress Cataloging-in-Publication Data Becker, P. C. Erbium-Doped Fiber Amplifiers: Fundamentals and Technology / P. C. Becker, N. A. Olsson, J. R. Simpson. p. cm. — (Optics and Photonics) Includes bibliographical references and index. ISBN 0-12-084590-3—ISBN 0-12-084591-1 (Diskette) 1. Optical communications — Equipment and supplies 2. Optical amplifiers. 3. Optical fibers I. Olsson, N. A. II. Simpson, J. R. III. Title IV. Series. TK5103.59.B43 1997 621.382'75~-DC21 97-29070 CIP Printed in the United States of America 00 01 02 03 IP 9 8 7 6 5 4 3 2 Disclaimer: This eBook does not include the ancillary media that was packaged with the original printed version of the book. h Foreword x Preface xiii Acknowledgements xv 1 INTRODUCTION 1 1.1 Long Haul Fiber Networks 1 1.2 Historical Development of Erbium-Doped Fiber Amplifiers 5 1.3 From Glass to Systems Outline 9 2 OPTICAL FIBER FABRICATION 13 2.1 Introduction 13 2.2 Conventional Communication Fiber . 14 2.3 Rare Earth Doped Fibers 16 2.3.1 Rare Earth Vapor Phase Delivery Methods . 16 2.3.2 Rare Earth Solution-Doping Methods 21 2.3.3 Rod and Tube Methods 23 2.4 Pump-Signal Interaction Methods 25 2.4.1 Evanescent Field 25 2.4.2 Double Clad Fiber Design 26 2.5 Compositions 27 2.6 Physical Properties . 29 2.6.1 Fiber Refractive Index and Composition Profile . 29 2.6.2 Strength and Reliability , 30 2.6.3 Alternate Glass Host Fabrication . 30 3 COMPONENTS AND INTEGRATION 43 3.1 Introduction 43 3.2 Fiber Connectors 43 3.3 Fusion Splicing . 48 3.4 Pump and Signal Combiners 50 3.5 Isolators 52 v vi CONTENTS 3.6 Circulators 53 3.7 Filters 55 3.8 Fiber Gratings 55 3.8.1 Introduction 55 3.8.2 Applications of Bragg Gratings 57 3.8.3 Long Period Gratings 59 3.9 Signal Multiplexers and Demultiplexers 61 3.10 Signal Add/Drop Components 62 3.11 Dispersion Compensation Components 63 3.12 Integrated Components 66 3.13 Pump Lasers 66 4 RARE EARTH IONS INTRODUCTORY SURVEY 87 4.1 Introduction , . 87 4.2 Atomic Physics of the Rare Earths 87 4.2.1 Introduction The 4f Electron Shell 87 4.2.2 The "Puzzle" of 4f Electron Optical Spectra 91 4.2.3 Semiempirical Atomic and Crystal Field Hamiltonians ... 92 4.2.4 Energy Level Fitting 94 4.3 Optical Spectra of Rare Earth Ions 95 4.3.1 The Character of 4fN 4fN Optical Transitions 95 4.3.2 Intensities of One-Photon Transitions Judd-Ofelt Theory . 96 4.4 Fundamental Properties 99 4.4.1 Transition Cross Sections 99 4.4.2 Lifetimes 105 4.4.3 Linewidths and Broadening 108 4.5 Spectroscopy of the Er3 Ion 110 4.5.1 Lifetimes 111 4.5.2 Er3 Spectra, Cross Sections, and Linewidths 114 4.6 Er3 -Er3 Interaction Effects 120 5 ERBIUM-DOPED FIBER AMPLIFIERS AMPLIFIER BASICS 131 5.1 Introduction 131 5.2 Amplification in Three-Level Systems Basics 131 5.2.1 Three-Level Rate Equations 131 5.2.2 The Overlap Factor 140 5.3 Reduction of the Three-Level System to the Two-Level System ... 144 5.3.1 Validity of the Two-Level Approach 144 5.3.2 Generalized Rate Equations 146 5.4 Amplified Spontaneous Emission 147 5.5 Analytical Solutions to the Two-Level System 149 6 ERBIUM-DOPED FIBER AMPLIFIERS - MODELING AND COM- PLEX EFFECTS 153 6.1 Introduction 153 6.2 Absorption and Emission Cross Sections 153 CONTENTS vii 6.3 Gain and ASE Modeling 156 6.3.1 Model Equations - Homogeneous Broadening 156 6.3.2 Average Inversion Relationship , 158 6.3.3 Inhomogeneous Broadening 159 6.4 Amplifier Simulations 161 6.4.1 Signal Gain, ASE Generation, and Population Inversion . . , 161 6.4.2 Gain as a Function of Fiber Length 169 6.4.3 Spectral Profile of the ASE . 169 6.4.4 Small Signal Spectral Gain and Noise Modeling . . . . . .. 171 6.4.5 Saturation Modeling Signal Gain and Noise Figure . . .. 173 6.4.6 Power Amplifier Modeling 175 6.4.7 Effective Parameter Modeling 178 6.5 Transverse Mode Models Erbium Confinement Effect 180 6.6 Excited State Absorption Effects 186 6.6.1 Model Equations , 186 6.6.2 Modeling Results in the Presence of ESA 188 6.6.3 800 nm Band Pumping 188 6.7 Er3 -Er3 Interaction Effects 191 6.7.1 Upconversion Effects on Amplifier Performance 193 6.7.2 Pair Induced Quenching 195 7 OPTICAL AMPLIFIERS IN FIBER OPTIC COMMUNICATION SYS- TEMS - THEORY 201 7.1 Introduction 201 7.2 Optical Noise: Device Aspects 202 7.2.1 Classical Derivation of Optical Amplifier Noise . . . . . .. 202 7.2.2 Noise at the Output of an Optical Amplifier . 205 7.2.3 Comparison of Optical Amplifier Devices 210 7.3 Optical Noise: System Aspects 212 7.3.1 Receivers , 213 7.3.2 Bit Error Rate Calculations - Direct Detection 214 7.3.3 Optical Preamplifiers - Noise Figure and Sensitivity . . . .. 220 7.3.4 Optical Inline Amplifiers - Amplifier Chains 226 7.3.5 Noise in Optical Power Amplifiers 235 7.3.6 Nonlinearity Issues 236 7.3.7 Analog Applications 240 8 AMPLIFIER CHARACTERIZATION AND DESIGN ISSUES 251 8.1 Introduction 251 8.2 Basic Amplifier Measurement Techniques 251 8.2.1 Gain Measurements 251 8.2.2 Power Conversion Efficiency 257 8.2.3 Noise Figure Measurements 258 8.3 Amplifier Design Issues 263 8.3.1 Copropagating and Counterpropagating Pumping Issues . . . 265 Viii CONTENTS 8.3.2 Choice of Fiber Lengths and Geometries for Various Applica- tions ... 268 8.3.3 Multistage Amplifiers 273 8.3.4 Bidirectional Amplifiers 277 8.3.5 Power Amplifiers 280 8.3.6 WDM Amplifier Design Issues . 284 8.3.7 Distributed Amplifiers 295 8.3.8 Waveguide Amplifiers 302 9 SYSTEM IMPLEMENTATIONS OF AMPLIFIERS 321 9.1 Introduction 321 9.2 System Demonstrations and Issues 323 9.2.1 Preamplifiers 323 9.2.2 Inline Amplifiers - Single Channel Transmission 327 9.2.3 Mine Amplifiers - WDM Transmission 335 9.2.4 Repeaterless Systems 345 9.2.5 Remote Pumping 346 9.2.6 Analog Applications 351 9.2.7 Gain Peaking and Self-Filtering 354 9.2.8 Polarization Issues 359 9.2.9 Transient Effects 363 9.3 Soliton Systems 367 9.3.1 Principles 367 9.3.2 System Results and Milestones 374 10 FOUR LEVEL FIBER AMPLIFIERS FOR 13 M AMPLIFICATION 401 10.1 Introduction 401 10.1.1 Gain in a Four-Level System 401 10.2 Pr3 -doped Fiber Amplifiers 404 10.2.1 Introduction 404 10.2.2 Spectroscopic Properties 405 10.2.3 Gain Results for Pr3 -doped Fiber Amplifiers 406 10.2.4 Modeling of the Pr3 -doped Fiber Amplifier Gain 412 10.2.5 System Results 416 10.3 Nd3 -Doped Fiber Amplifiers 418 10.3.1 Introduction 418 10.3.2 Gain Results for Nd3 -Doped Fiber Amplifiers 419 10.3.3 Modeling of the Nd3 -Doped Fiber Amplifier Gain 420 Appendix A 429 A.I OASIXR R Amplifier Simulation Software 429 A.2 Introduction 429 A.2.1 System Requirements 429 A.2.2 Installing OASIXR 430 A.2.3 Starting OASIXR 430 A.2.4 What to do next , . . , 430 CONTENTS ix A.3 A Quick Overview and Tour . . . . . . .. 430 A.3.1 Fibers and Modeling Parameters 430 A.3.2 Saving a Simulation Configuration 431 A.3.3 Device Types Simulated 431 A.3.4 Data Entry and Device Conventions . . . . . . . . . , . , ,. 432 A.3.5 Screens and Menus . . 432 A.3.6 Simulation Looping and Output Modes , , , , 433 A.4 Screen Contents and Simulation Methodology . . . . . . . . . . .. 434 A.4.1 Main/Entry Screen 434 A.4.2 Single-Stage Setup Screen 435 A.4.3 Additional Signals Screen 435 A.4.4 Output Setup Screen 436 A.4.5 Simulation Status Box 437 A.5 Simulation Looping Structure , . 438 A.5.1 Specifying Loop Parameters 438 A.5.2 Choosing Loop Order 438 A.5.3 Linear or Logarithmic Looping 439 A.5.4 Multiple Parameters Varied in a Loop 439 A.5.5 Influence on Output Format 440 A.5.6 Output Modes . 440 A.6 Sample Simulations 442 A.6.1 Single-Run, Single-Stage EDFA 442 A.6.2 Multiple-Run, Single-Stage EDFA 443 A.6.3 Other simulations to try 443 A.7 Computation of Signal Related Quantities , 443 A. 8 Computation of ASE Related Quantities 444 A.9 Basic Operating Principles 445 A.9.1 Simulation Speed and the Number of Waves 446 A.9.2 Causes and Remedies for Convergence Failure . . . . . . .. 447 A. 10 Comment on the treatment of losses 448 INDEX 451