SEMICONDUCTOR LASERS SEMICONDUCTOR LASERS Second Edition Govind P. Agrawal The Institute of Optics, University of Rochester Rochester, New York and Niloy K. Dutta AT&T Bell Laboratories Murray Hill, New Jersey . ., ~ KLUWER ACADEMIC PUBLISHERS BOSTONIDORDRECHTILONDON Distributors for North, Central and South America: Kluwer Academic Publishers 101 Philip Drive Assinippi Park Norwell, Massachusetts 02061 USA Telephone (781) 871-6600 Fax (781) 871-6528 E-Mail <[email protected]> Distributors for all other countries: Kluwer Academic Publishers Group Distribution Centre Post Office Box 322 3300 AH Dordrecht, THE NETHERLANDS Telephone 31 78 6392 392 Fax 31 78 6546474 E.-.M.. ail [email protected]> • , Electronic Services <http://www.wkap.nl> Library of Congress Cataloging-in-Publication Agrawal, G.P. (Govind P.), 1951-- Semiconductor lasers / Govind P. Agrawal and Niloy K. Dutta.--2nd ed. p. cm. First ed. published 1986 under title: Long-wavelength semiconductor lasers. Includes bibliographical references and index. ISBN-13: 978-1-4612-7579-4 e-ISBN-13: 978-1-4613-0481-4 001: 10.1007/978-1-4613-0481-4 1. Semiconductor lasers. I. Dutta, N.K. (Niloy K.), 1953-- II. Agrawal, G.P. (Govind P.), 1951--Long-wavelength semiconductor lasers. III. Title. TA1700.A37 1993 92-46782 621.36'61--dc20 eIP Copyright © 1993 by AT&T Third printing 2001 by Kluwer Academic Publishers Softcover reprint of the hardcover 2nd edition 2001 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system or transmitted in any form or by any means, mechanical, photo-copying, recording, or otherwise, without the prior written permission of the publisher, Kluwer Academic Publishers, 101 Philip Drive, Assinippi Park, Norwell, Massachusetts 02061 Printed on acid-free paper. This printing is a digital duplication of the original edition. CONTENTS Preface to the First Edition/xiii Preface to the Second Edition/xv 1. Introduction/1 1.1 Historical Perspective/1 1.2 Semiconductor Materials/5 1.3 Operating Principles/9 1.3.1 p-n Junction/9 1.3.2 Dielectric Waveguide/II 1.3.3 Recombination Mechanisms/12 1.3.4 Laser Threshold/13 1.4 Optical Fiber Communications/15 1.5 Overview /19 Problems / 21 References / 22 2. Basic Concepts/25 2.1 Introduction/25 2.2 Maxwell's Equations/26 2.3 Threshold Condition and Longitudinal Modes/30 2.4 Gain and Stimulated Emission/35 2.5 Waveguide Modes/39 2.5.1 Effective Index Approximation/41 2.5.2 Transverse Modes/44 2.5.3 Lateral Modes/49 2.6 Emission Characteristics/55 2.6.1 Light-Current Characteristics/55 2.6.2 Spatial-Mode Characteristics/64 2.6.3 Spectral Characteristics/67 2.6.4 Dynamic Characteristics/70 Problems/70 References/71 v vi CONTENTS 3. Recombination Mechanisms in Semiconductors/74 3.1 Introduction/74 3.2 Radiative Recombination/75 3.2.1 Absorption and Emission Rates for Discrete Levels/78 3.2.2 Absorption and Emission Rates in Semiconductors/81 3.2.3 Absorption Coefficient and Optical Gain/88 3.3 Nonradiative Recombination/98 3.3.1 Band-to-Band Auger Processes/99 3.3.2 Phonon-Assisted AugeJ;.. Processes/112 3.3.3 Defect and Surface Recombination/119 3.4 Experimental Results/120 3.5 Threshold Current Density /126 3.5.1 Carrier Leakage over the Heterojunctions/127 3.6 Temperature Dependence of Threshold Current/132 3.6.1 Carrier-Lifetime Measurements/134 3.6.2 Optical-Gain Measurements/136 3.6.3 External Differential Quantum Efficiency/136 3.6.4 Discussion/139 Problems/142 References/143 4. Epitaxy and Material Parameters of InGaAsP/ 147 4.1 Introduction/147 4.2 Liquid-Phase Epitaxy/148 4.2.1 LPE Apparatus/148 4.2.2 Growth Methods/150 4.2.3 LPE of InGaAsP/152 4.3 Vapor-Phase Epitaxy /156 4.4 Metal-Organic Vapor-Phase Epitaxy/158 4.5 Molecular-Beam Epitaxy/159 4.6 Lattice-Mismatch Effects/162 4.7 Material Parameters/165 4.7.1 Band-Structure Parameters/166 4.7.2 Mobility/170 4.7.3 Refractive Index/17l 4.8 Strained-Layer Epitaxy /174 Problems/176 References/176 5. Laser Structures and Their Performance/180 5.1 Introduction/180 5.2 Broad-Area Lasers/181 CONTENTS vii 5.3 Gain-Guided Lasers/185 5.4 Weakly Index-Guided Lasers/196 5.5 Strongly Index-Guided Lasers/201 5.6 Leakage Current/212 5.7 Laser Arrays/218 5.8 Surface-Normal Emitting Lasers/223 Problems/226 References/227 6. Rate Equations and Operating Characteristics/231 6.1 Introduction/231 6.2 Rate Equations/232 6.3 Steady-State Characteristics/238 6.3.1 Light-Current Curve/239 6.3.2 Longitudinal-Mode Spectrum/242 6.4 Transient Response/250 6.4.1 Dynamic Longitudinal-Mode Spectrum/250 6.4.2 Turn-On Delay/252 6.4.3 Relaxation Oscillations/255 6.5 Noise Characteristics/258 6.5.1 Langevin Formulation/259 6.5.2 Intensity Noise/261 6.5.3 Phase Noise and Line Width/269 6.6 Modulation Response/275 6.6.1 Small-Signal Analysis/276 6.6.2 Intensity Modulation/277 6.6.3 Frequency Chirping/284 6.6.4 Large-Signal Modulation/289 6.6.5 Ultrashort Pulse Generation/293 6.7 External Optical Feedback/297 6.7.1 Modified Rate Equations/298 6.7.2 Steady-State Behavior / 300 6.7.3 Dynamic Behavior/304 6.7.4 Noise Characteristics/306 Problems/309 References/311 7. Distributed-Feedback Semiconductor Lasers/319 7.1 Introduction/319 7.2 DFB Laser Structures/321 7.3 Theory /323 viii CONTENTS 7.3.1 Coupled-Wave Equations/324 7.3.2 Longitudinal Modes and Threshold Gain/329 7.3.3 Coupling Coefficient/336 7.3.4 Threshold Behavior/340 7.3.5 Light-Current Characteristics/344 7.4 Performance/345 7.4.1 CW Operation/346 7.4.2 Modulation Performance/351 7.4.3 Phase-Shifted DFB Lasers/354 7.4.4 Multiquantum-Well DFB Lasers/358 7.4.5 Gain-Coupled DFB Lasers/359 7.5 DBR Lasers/361 7.5.1 Design Issues/361 7.5.2 Theory/362 7.5.3 Emission Characteristics/366 7.6 Tunable Semiconductor Lasers/368 7.7 Transmission Experiments/371 Problems/376 References/378 8. Coupled-Cavity Semiconductor Lasers/385 8.1 Introduction/385 8.2 Coupled-Cavity Schemes/387 8.3 Theory /390 8.3.1 Coupling Constant /3 91 8.3.2 Longitudinal Modes and Threshold Gain/394 8.3.3 Side-Mode Suppression/398 8.3.4 Modulation Response/399 8.4 Operating Characteristics/401 8.4.1 Longitudinal-Mode Control/403 8.4.2 Optimum Biasing for Direct Modulation/406 8.4.3 Frequency Chirp/408 8.4.4 Transmission Experiments/410 8.4.5 External-Cavity Semiconductor Lasers/413 8.5 Diverse Applications/416 Problems/422 References/423 9. Quantum-Well Semiconductor Lasers/426 9.1 Energy Levels/426 9.2 Density of States/430 CONTENTS ix 9.3 Experimental Observation of Confined States/432 9.4 Radiative Recombination/434 9.5 Auger Recombination/443 9.6 Single Quantum-Well and Multiquantum-Well Lasers/450 9.7 MQW Laser Results/455 9.8 Modulation and Noise Characteristics/461 9.9 Strained Quantum-Well Lasers/462 Problems/468 References/469 10. Surface-Emitting Lasers/472 10.1 Introduction/472 10.2 Mirror Refiectivity/473 10.3 GaAs-AIGaAs and InGaAs-GaAs Surface-Emitting Lasers/477 10.4 InGaAsP-InP Surface-Emitting Lasers/482 10.5 Laser Arrays/484 Problems/485 References/485 11. Optical Amplifiers/487 11.1 Introduction/487 11.2 General Concepts/487 11.2.1 Gain Spectrum and Bandwidth/489 11.2.2 Gain Saturation/490 11.2.3 Amplifier Noise/491 11.2.4 Amplifier Applications/493 11.3 Semiconductor Laser Amplifiers/494 11.3.1 Impact of Facet Reflectivity/496 11.3.2 Amplifier Designs/498 11.3.3 Amplifier Characteristics/504 11.3.4 Multichannel Amplification/50B 11.3.5 Pulse Amplification/51O 11.3.6 System Applications/517 11.3.7 Multiquantum-Well Amplifiers/519 11.4 Fiber Amplifiers/520 11.4.1 Energy Levels/522 11.4.2 Fiber Amplifier Performance/524 Problems/526 References/527 x CONTENTS 12. Photonic and Optoelectronic Integrated Circuits/530 12.1 Introduction/530 12.2 Photonic Integrated Circuits/530 12.2.1 Arrays/530 12.2.2 Integrated Laser Detector/533 12.2.3 Integrated Laser Modulator/534 12.2.4 Integrated Laser Amplifier/537 12.2.5 Heterodyne Receiver/538 12.3 Optoelectronic Integrated Circuits (OEICs)/539 12.3.1 Receiver OEICs/539 12.3.2 Transmitter OEICs/539 12.3.3 Regenerator OEICs/542 12.3.4 Logic OEICs/543 References/546 13. Infrared and Visible Semiconductor Lasers/547 13.1 Lead-Salt Lasers/547 13.2 Materials and Physical Properties/547 13.3 Band Structure/550 13.4 Optical Gain/554 13.5 Auger Recombination/556 13.6 Laser Diode Fabrication/561 13.7 Laser Properties/563 13.8 Tuning Characteristics/570 13.9 Other Material Systems/573 13.9.1 Infrared Semiconductor Lasers/573 13.9.2 Visible Semiconductor Lasers/574 Problems/578 References/579 14. Degradation and Reliability /583 14.1 Introduction/583 14.2 Defect Formation in the Active Region/584 14.2.1 Experimental Techniques/585 14.2.2 Electroluminescence/585 14.2.3 Photoluminescence/587 14.2.4 Cathodoluminescence/589 14.2.5 Dark Defects under Accelerated Aging/591 14.3 Catastrophic Degradation/593 14.4 Degradation of Current-Confining Junctions/595