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QUANTUM ELECTRONICS — PRINCIPLES AND APPLICATIONS EDITED BY PAUL F. LIAO Bell Communications Research, Inc. Red Bank, New Jersey PAUL L. KELLEY Lincoln Laboratory Massachusetts Institute of Technology Lexington, Massachusetts A complete list of titles in this series appears at the end of this volume. CONTEMPORARY NONLINEAR OPTICS Edited by Govind P. Agrawal and Robert W. Boyd The Institute of Optics University of Rochester Rochester, New York ACADEMIC PRESS, INC. Harcourt Brace Jovanovich, Publishers Boston San Diego New York London Sydney Tokyo Toronto This book is printed on acid-free paper. (3) Copyright (Γ) 1992 by Academic Press, Inc. 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. ACADEMIC PRESS, INC. 1250 Sixth Avenue, San Diego, CA 92101 United Kingdom Edition published by ACADEMIC PRESS LIMITED 24-28 Oval Road, London NW1 7DX Library of Congress Cataloging-in-Publication Data: Contemporary nonlinear optics/[edited by] G. P. Agrawal and R. W. Boyd, p. cm.—(Quantum electronics—principles and applications) Includes bibliographical references and index. ISBN 0-12-045135-2 (alk. paper) 1. Nonlinear optics. I. Agrawal, G. P. (Govind P.), date. II. Boyd, Robert W., date. III. Series. QC446.2.C66 1992 535.2—dc20 91-32809 CIP Printed in the United States of America 92 93 94 95 9 8 7 6 5 4 3 2 1 Contributors Numbers in parentheses indicate the pages on which the authors' con- tributions begin. Ν. B. Abraham (413), Department of Physics, Bryn Mawr College, Bryn Mawr, PA 19010-2899 Govind P. Agrawal (41), The Institute of Optics, University of Rochester, Rochester, NY 14627 Robert W. Boyd (85), The Institute of Optics, University of Rochester, Rochester, NY 14627 V. P. Chebotayev (367), Institute of Thermal Physics, Siberian Branch, Academy of Sciences of the USSR, 630090 Novosibirsk, USSR C. Flytzanis (297), Laboratoire d'Optique Quantique du C.N.R.S., Ecole Polytechnique, 91128 Palaiseau Cedex, France Gilbert Grynberg (85), Laboratoire de Spectroscopic Hertzienne de l'Ecole Normale Supérieure, Université Pierre et Marie Curie, 75252 Paris Cedex 05, France John H. Hong (235), Rockwell International Science Center, Thousand Oaks, CA 91360 J. Hutter (297), Laboratoire d'Optique Quantique du C.N.R.S., Ecole Polytechnique, 91128 Palaiseau Cedex, France James D. Kafka (119), Spectra-Physics Lasers, Inc., 1250 West Middlefield Road, Mountain View, CA 94039 J. Mostowski (187), Institute of Physics, Polish Academy of Sciences, Aleja Lotnikow, 32102-668, Warsaw, Poland Paras N. Prasad (265), Photonics Research Laboratory, Department of Chemistry, State University of New York at Buffalo, Buffalo, NY 14214 Demetri Psaltis (235), California Institute of Technology, Department of Engineering, Pasadena, CA 91125 M. G. Raymer (187), Department of Physics and Chemical Physics Institute, University of Oregon, Eugene, OR 97403 ix χ Contributors George I. Stegeman (1), Center for Research in Electro-Optics and Lasers (CREOL), University of Central Florida, 12424 Research Parkway, Orlando, FL 32826 Ian A. Walmsley (119), The Institute of Optics, University of Rochester, Rochester, NY 14627 Preface Nonlinear optics is a continuously evolving branch of optics. Although the nonlinear phenomenon of two-photon absorption [1] was discussed theo- retically as early as 1931, the field of nonlinear optics was not born until the advent of the laser [2,3]. In fact, the first experiment [4] demonstrating the generation of the second harmonic of the frequency of an incident light beam was carried out within a year after the operation of the first laser [3] was demonstrated. It was soon followed by the study of many nonlinear optical effects such as sum-frequency generation [5], optical rectification [6], stimulated Raman scattering [7], and parametric amplification [8]. Bloembergen's book [9], published in 1965, summarized the intense theoretical and experimental activity occurring during the early years of nonlinear optics. Many new nonlinear optical phenomena were discovered during the 1970s. They have led to new branches of nonlinear optics such as optical bistability [10] and phase conjugation [11,12]. Several books on nonlinear optics have covered the resulting growth in this ever expanding branch of optics [13-15]. Nonlinear optics has experienced considerable change during the decade of the 1980s. On the one hand, it has added to fundamental understanding in diverse fields such as optical chaos [16], squeezing [17], and optical solitons [18]. On the other hand, it has brought many technological advances through the study of nonlinear optics in new materials such as organic polymers [19] and photorefractive crystals [20] as well as in new structures such as quantum wells [21] and optical fibers [22]. Indeed, the growth of nonlinear optics has been so rapid during the 1980s that each of these fields is regarded as a branch of nonlinear optics and whole books have been devoted to each of them [15-22]. Contemporary nonlinear optics appears to have quite a different character because of the addition of so many subfields. The objective of this book is to provide a flavor of the current activities in the field of nonlinear optics. For this purpose, we have selected 10 topics, each described in individual chapters written by leading researchers. It was difficult to select the topics covered here since any choice would necessarily exclude several deserving topics. The guiding criterion was that each chapter should be broad in scope, so that it covers an entire branch of nonlinear optics rather than covering a small part of it. Even then, the necessary number of chapters was too large to fit into a single book of reasonable size. The secondary criterion used to select the topics was to avoid those that have xi xii Preface appeared in recent books. Thus, a chapter dealing with nonlinear fiber optics was not included because of a recently published monograph [22]. Similarly, a separate chapter on photorefractives [20] was not included; photorefractives are partially covered in chapters on optical phase conjugation and neural networks. Chapter 1 presents a description of the field of nonlinear guided-wave optics. This field is concerned with the investigation and utilization of nonlinear optical interactions in waveguide geometries. The chapter begins with a brief review of the principles of the propagation of light through dielectric waveguides. It then describes recent progress in second harmonic generation in nonlinear waveguides. The theory of the nonlinear refractive index is then briefly reviewed and the utilization of this effect for the construction of all- optical switching devices, such as the nonlinear directional coupler, is described. The chapter concludes with a discussion of effects that can occur in highly nonlinear waveguides, such as the propagation of spatial solitons. Chapter 2 surveys a new branch of nonlinear optics under the heading optical solitons. The field of optical solitons has seen tremendous growth during the 1980s motivated in part by the possibility of their technological applications in the fields of optical fiber communications and photonic switching. A major portion of the chapter is devoted to the discussion of fiber solitons that result from a balance between self-phase modulation and group- velocity dispersion when ultrashort optical pulses propagate inside optical fibers. Other kinds of optical solitons discussed in the chapter include self- induced transparency solitons, Raman solitons, multiple-wave mixing solitons, amplifier solitons, Bragg solitons, spatial solitons, and bistable solitons. Chapter 3 reviews recent progress in the field of optical phase conjugation. The chapter begins with a brief introduction that defines phase conjugation and describes how phase conjugation can be used to correct for the presence of aberrations in optical systems. The chapter then presents detailed descriptions of the processes of degenerate four-wave mixing and stimulated Brillouin scattering, which are the two nonlinear optical processes most often used to generate a phase conjugate signal. It then describes the photorefractive effect, and describes a number of ways in which this effect can be used to generate a phase conjugate signal. Finally, several applications of phase conjugation are described. Chapter 4 is devoted to ultrafast nonlinear optics, a field that is growing rapidly with the ability of generating and controlling femtosecond optical pulses. The chapter is divided into two major sections. Section 1 discusses the use of nonlinear optical techniques for the generation of ultrashort optical pulses. Section 2 describes the application of ultrashort optical pulses for the measurement of subpicosecond dynamics by using nonlinear phenomena such as four-wave mixing and time-resolved fluorescence. A separate sub- section considers a new branch of nonlinear optics referred to as strong-field ultrafast nonlinear optics. Preface xiii Chapter 5 is devoted to a branch of nonlinear optics that may be termed nonlinear quantum optics. When an intense optical beam propagates through a nonlinear optical medium, it can initiate novel quantum effects. The chapter focuses on two nonlinear phenomena where quantum effects play an im- portant role. In the case of stimulated Raman scattering, the intense pump beam generates a new Stokes beam from quantum noise whose frequency is downshifted from the pump frequency by an amount that corresponds to a medium resonance. Microscopic quantum fluctuations give rise to large macroscopic fluctuations in the Stokes beam, which can be observed experi- mentally. In another nonlinear process, known as optical parametric amplification, quantum fluctuations generate the so-called squeezed light, whose statistical behavior is essentially nonclassical. The chapter discusses squeezing with emphasis on the recent experimental results. Chapter 6 reviews the new field of photorefractive adaptive neural networks. It describes how highly parallel optical computing machines can be constructed in a manner that mimics the functions performed by biological neural networks. It also presents some new ideas regarding computing machines that can "learn" in the sense that the programming of the machine is updated in real time in response to the changing input stimuli. This chapter also presents a description of how the photorefractive effect can be exploited for the construction of optical neural networks and presents a description of the construction of holographic interconnects for use in computing. Chapter 7 presents a discussion of recent successes in the development of nonlinear optical media based on organic materials. Such materials offer a very versatile system whose properties can be tailored to specific needs. The chapter describes the microscopic theory of optical nonlinearities of organic materials, and describes how these theories can be used to deduce bulk nonlinear optical properties. Also included are discussions of techniques for the measurement of optical nonlinearities, of the dynamics of nonlinear processes, of the results of some specific measurements, and of the role of car- riers in determining the nonlinear optical properties of organic materials. Chapter 8 reviews the field of nonlinear optics in quantum confined structures. The relationship between dielectric and quantum confinement is briefly described. The effects of quantum confinement in one, two, and three dimensions is then explored, and the role of broadening mechanisms in determining the optical response is elucidated. A description of light-induced effects such as optical saturation, the optical Kerr effect, and the optical Stark effect together with a description of parametric nonlinear effects is presented. Chapter 9 reviews the field of nonlinear laser spectroscopy, with emphasis on advances made during the 1980s. It begins with the discussion of satu- rated absorption spectroscopy and includes topics such as the second-order Doppler effects. A separate section discusses probe wave spectroscopy by considering both copropagating and counterpropagating configurations for the xiv Preface pump and probe beams. Particular attention is paid to the nonlinear phenomena associated with the optical Stark effect and the anomalous Zeeman effect. Chapter 10 reviews the field of nonlinear optical dynamics by considering nonlinear optical systems that exhibit temporal, spatial, or spatio-temporal instabilities. It describes the basic procedure for finding the stability of the steady state and then discusses the evolution of the system toward periodic, quasiperiodic, or chaotic states in the instability domain. The generic behavior is illustrated by considering specific examples of nonlinear optical systems such as multimode lasers, optical ring resonators, and electrooptic or acousto- optic systems with feedback. Particular attention is paid to the formation of spontaneous spatial patterns for nonlinear optical systems that exhibit spatio- temporal instabilities. References 1. M. Göppert-Mayer, Ann. Physik 9, 273 (1931). 2. A. L. Schawlow and C. H. Townes, Phys. Rev. 112, 1940 (1958). 3. T. H. Maiman, Nature 187, 493 (1960). 4. P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinreich, Phys. Rev. Lett. 7, 118 (1961). 5. M. Bass, P. A. Franken, A. E. Hill, C. W. Peters, and G. Weinrich, Phys. Rev. Lett. 8, 18 (1962). 6. M. Bass, P. A. Franken, J. F. Ward, and G. Weinreich, Phys. Rev. Lett. 9, 446 (1962). 7. E. J. Woodbury and W. K. Ng, Proc. IRE 50, 2347 (1962). 8. J. A. Giordmaine and R. C. Miller, Phys. Rev. Lett. 14, 973 (1965). 9. N. Bloembergen, "Nonlinear Optics," Benjamin, Reading, Massachusetts, 1965. 10. H. M. Gibbs, "Optical Bistability: Controlling Light with Light," Academic Press, Orlando, 1985. 11. R. A. Fisher, ed., "Optical Phase Conjugation," Academic Press, New York, 1983. 12. B. Ya. Zel'dovich, N. F. Phiilipetsky, and V. V. Shkunov, "Principles of Phase Conjugation," Spinger-Verlag, Berlin, 1985. 13. Y. R. Shen, "The Principles of Nonlinear Optics," Wiley, New York, 1984. 14. M. Schubert and B. Wilhelmi, "Nonlinear Optics and Quantum Electronics," Wiley (Interscience), New York, 1986. 15. P. N. Butcher and D. Cotter, "The Elements of Nonlinear Optics," Cambridge University 16. R. W. Boyd, M. G. Raymer, and L. M. Narducci, eds., "Optical Instabilities," Cambridge University Press, Cambridge, 1986. 17. M. C. Teich and Β. E. A. Saleh, in "Progress in Optics," Vol. 26, E. Wolf, ed., North-Holland, Amsterdam, 1988. 18. A. Hasagawa, "Optical Solitons," Springer-Verlag, Berlin, 1989. 19. P. N. Prasad and D. J. Williams, "Introduction to Nonlinear Optical Effects in Molecules and Polymers," Wiley, New York, 1990. 20. P. Gunter and J.-P. Huignard, "Photorefractive Materials and their Applications," Springer- Verlag, Berlin, Vol. I (1988) and Vol. II (1989). 21. H. Haug, ed., "Optical Nonlinearities and Instabilities in Semiconductors," Academic Press, Boston, 1988. 22. G. P. Agrawal, "Nonlinear Fiber Optics," Academic Press, Boston, 1989. Chapter 1 NONLINEAR GUIDED WAVE OPTICS George I. Stegeman Center for Research in Electro-Optics and Lasers (CREOL) University of Central Florida Orlando, Florida 1. Introduction 1 2. Principles of Waveguiding 2 3. Second Order Nonlinear Phenomena 5 3.1. Second Harmonic Generation: Co-propagating Waves 6 3.2. Second Harmonic Generation: Contra-propagating Waves 13 3.3. Parametric Mixing 15 4. Intensity-Dependent Refractive Index 16 5. All-Optical Switching Devices 18 5.1. Nonlinear Directional Coupler 19 5.2. Other All-Optical Switching Devices 23 6. Highly Nonlinear Waveguides 25 6.1. Nonlinear Guided Waves 26 6.2. Spatial Solitons in the Plane of the Waveguide 33 7. Summary 36 References 37 1. INTRODUCTION Nonlinear integrated optics is the investigation and utilization of nonlinear optical interactions in waveguide geometries. It started in the early 1970s with the demonstration of second harmonic generation in planar integrated optics waveguides [1]. Subsequently, other second order interactions such as difference frequency mixing [2] and parametric interactions [3] were all demonstrated. In this initial phase, which lasted into the mid 1980s, this field was science rather than technology driven. Now there are well-defined needs for efficient conversion of semiconductor lasers into the blue for xerography and data storage, and these have led to rapid advances in waveguide second harmonic generation in channel and fiber waveguides. But why bother with the complexities of waveguide fabrication and design for achieving efficient harmonic generation in the first place? They key is that a waveguide such as a channel or a fiber allows electromagnetic waves to CONTEMPORARY NONLINEAR OPTICS 1 Copyright © 1992 by Academic Press, Inc. All rights of reproduction in any form reserved. ISBN 0-12-045135-2