Table Of ContentQUANTUM 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
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London Sydney Tokyo Toronto
This book is printed on acid-free paper. (3)
Copyright (Γ) 1992 by Academic Press, Inc.
All rights reserved.
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ACADEMIC PRESS, INC.
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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], stimu-
lated Raman scattering [7], and parametric amplification [8]. Bloembergen's
book [9], published in 1965, summarized the intense theoretical and experi-
mental 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 cov-
ered 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 quan-
tum 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 num-
ber 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; photorefrac-
tives are partially covered in chapters on optical phase conjugation and neu-
ral networks.
Chapter 1 presents a description of the field of nonlinear guided-wave
optics. This field is concerned with the investigation and utilization of non-
linear 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 de-
scribed. 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 technolog-
ical 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 soli-
tons, 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 chap-
ter 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 ampli-
fication, 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 pro-
cesses, 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 empha-
sis 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 con-
sidering both copropagating and counterpropagating configurations for the
xiv Preface
pump and probe beams. Particular attention is paid to the nonlinear phe-
nomena 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 op-
tics 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
