Table Of ContentAcademic Press Rapid Manuscript Reproduction
QUANTUM ELECTRONICS - PRINCIPLES AND APPLICATIONS
A Series of Monographs
EDITED BY
PAUL F. LIAO PAUL KELLEY
Bell Telephon,e Laboratories Lincoln Laboratory
Murray Hill New Jersey Massachusetts Institute of Technology
Lexingtont Massachusetts
A list of books in this series is available from the publisher on request.
Optical Bistability:
Controlling Light with Light
Hyatt M. Gibbs
Optical Sciences Center
University of Arizona
Tucson, Arizona
1985
ACADEMIC PRESS, INC.
Harcourt Brace Jovanovich, Publishers
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Copyright © 1985 by Academic Press, inc.
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United Kingdom Edition published by
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LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA
Gibbs, Hyatt M.
Optical bistability.
Bibliography: p.
Includes index.
1. Optical bistability. I. Title.
QC446.3.065G55 1985 535'.2 85-48069
ISBN 0-12-281940-3 (alk. paper)
PRINTED IN THE UNITED STATES OF AMERICA
85 86 87 88 9876 5 4321
To
Pip and Maa
Lethia, Alex, and Vanetta
and all of my bistability friends
PREFACE
This is a research book intended for new entrants and active workers in the
field of optical bistability. The treatment interprets optical bistability broadly to
include all of the steady-state and transient characteristics of nonlinear optical
systems which exhibit bistability under some operating conditions. It is restrictive
in placing the emphasis on passive (non-laser) systems which exhibit reversible
bistability with input intensity as the hysteresis variable. The book is motivated
by the desire to summarize the beauty of the physics and to describe the potential
applications of such systems for nonlinear optical signal processing.
This book may even be useful as a reference for advanced specialized courses.
The first draft was written in the fall of 1981 as the author taught what may have
been the only course on optical bistability. Parts of it were used again in the
spring of 1984 as part of a course on the semiclassical description of coherent
optical phenomena.
The history of optical bistability in lasers and passive systems is summarized in
Chapter 1. Steady-state theories of optical bistability are presented in Chapter 2.
Both intrinsic and hybrid experiments are described in some detail in Chapters 3
and 4, respectively. Light-by-light control is the focus of Chapter 5 which treats
pulse reshaping and external switching. In contrast, the transient phenomena of
Chapter 6 occur with a steady input, i.e., they are intrinsic instabilities. Consid
erations important for applications to optical signal processing and computing are
discussed in Chapter 7.
This is a research book about a very rapidly expanding field. This fact has
made it difficult to decide when to publish. Much of the underlying physics of the
behavior of these nonlinear optical systems is now understood, even though intense
studies on instabilities, transverse effects, and nonlinearity mechanisms will surely
result in many new breakthroughs. Work on applications to very-high-speed
switching and to massively parallel processing has just begun. Hopefully this book
captures the beautiful and diverse behavior of nonlinear optical systems in a
manner that will serve both as a basis for further physics research and as a ready
reference for nonlinear optical signal processing.
The author has had many rewarding collaborations in twelve years of working
on optical bistability. Thanks to Sam McCall for introducing the possibility of
seeing bistability to me and convincing me that collaborating with him was essen
tial to avoid a catastrophic explosion during one of his sodium-oven cleaning oper
ations! Thanks to Dick Slusher for earlier laser technology transfer and fruitful
collaborations on coherent optical phenomena. To Sam, Venky Venkatesan,
George Churchill, and AI Passner for sharing the excitement of those first Bell
Labs experiments in Na, ruby, and GaAs; somehow 2 a.m. data are special! And
without the beautiful GaAs samples of Art Gossard and Bill Wiegmann, I would
have never made the gas-to-solid transition. In 1980 the Justice Department
frightened me into establishing "Bell Labs West" at the Optical Sciences Center,
resulting in a greatly expanded effort with the help of a fantastic group of gradu
ate students: Shin-Sheng Tarng, Jack Jewell, Ed Watson, David Kaplan, Doreen
xi
xii Preface
Weinberger, Mike Rushford, Kuo-Chou Tai, Shlomo Ovadia, Lois Hoffer, Matt Der-
stine, Mial Warren, Yong Lee, Greg Olbright, Arturo Chavez, John Valley, Hans
Kulcke, George Gigioli, Lon Wong, Ruxiang Jin. Thanks to Professors Fred Hopf,
Jerry Moloney, Dror Sarid, and Rick Shoemaker for bistability collaborations and to
them, George Stegeman, and many others for helping in the formation of the Opti
cal Circuitry Cooperative. A special thanks to Assistant Professor Nasser Peyg-
hambarian for his hard work and close friendship during the last three years.
Although Sam McCall never found time to coauthor this book as first planned,
much of what I know about bistability has come from him and I hope I have cap
tured much of his insight. Thanks to David Holm and Jerry Moloney for writing
Appendices F and G, respectively. Thanks to Jeannette Gerl and Lisa DuBois for
early versions of the book and to Kathy Seeley and Norma Laguna for the tedious
and seemingly endless preparation of the camera-ready manuscript. Thanks for
helpful comments on the manuscript from Professors Howard Carmichael, Luigi
Lugiato, Pierre Meystre, Des Smith, and Doreen Weinberger and from Drs. Martine
LeBerre, Elisabeth Ressayre, and Andree Tallet.
CHAPTER 1
INTRODUCTION TO OPTICAL BISTABILITY
Optical bistability is a rapidly expanding field of current research because of
its potential application to all-optical logic and because of the interesting phe
nomena it encompasses. Since the first observation of optical bistability in a pas
sive, unexcited medium of sodium (Na) vapor in 1974 (McCall, Gibbs, Churchill,
and Venkatesan, 1975), bistability has been observed in many different materials
including tiny semiconductor etalons. Current applied research is focused on opti
mizing these devices by decreasing their size, switching times, and operating
power, and operating them at room temperature. Both improved nonlinear materi
als and more efficient device configurations are being sought. Current fundamen
tal research centers on the interesting physical behavior of simple bistable sys
tems. Many bistable devices consist of a nonlinear medium within an optical reso
nator, just as do lasers, except the passive bistable devices are excited only by the
incident coherent light. The counterparts of many of the phenomena studied in
lasers, such as fluctuations, regenerative pulsations, and optical turbulence, can be
observed in passive bistable systems, often under better controlled conditions.
Optical bistability in lasers, which was seen prior to passive bistability, is treated
briefly in Section 1.3 although it is not the main subject of this book.
1.1. DEFINITION AND TYPES OF OPTICAL BISTABILITY
A system is said to be optically bistable if it has two output states Ij for the
same value of the input Ιχ over some range of input values. Thus a system having
the transmission curve of Fig. 1.1-1 is said to be bistable between I* and If.
Such a system is clearly nonlinear, i.e., Iy is not just a multiplicative constant
times Ιχ. In fact, if Ιχ is between I4, and If, knowing Ιχ does not reveal Ij. Non-
linearity alone is insufficient to assure bistability. It is feedback that permits the
nonlinear transmission to be multivalued, i.e., bistable. It is this restricted defini
tion of optical bistability defined by Fig. 1.1-1, with the nonlinear medium unex
cited, that is adopted here. This definition implies that the bistable system can be
cycled completely and repeatedly by varying the input intensity. Systems that
exhibit hysteresis as a function of some other parameter but not light intensity are
not of interest here. This restricted definition rules out "bistable" optical systems
that cannot be reset merely by reducing the input intensity, such as a burglar
alarm or a card in a laser beam powerful enough to burn through the card. Even
an optical damage device that can be restored by irradiation with light of a dif
ferent wavelength is not in the spirit here of an all-optical completely recyclable
passive system.
1
2 [1.1]
INPUT INTENSITY Ij
Fig. 1.1-1. Characteristic curve for an optical bistable system.
An example of a system exhibiting optical bistability is a Fabry-Perot inter
ferometer containing a saturable absorber; see Fig. 1.1-2. A simple analysis of
such a nonlinear etalon reveals the possibility of bistability. For weak input in
tensity, Ιχ, the intracavity absorption spoils the finesse of the cavity even though
the laser frequency v and cavity frequency vpp of peak transmission are coinci
dent. Therefore the intracavity intensity Iq at z = 0 is simply Ιχ times the input
mirror transmission T. At the cell exit
led) = e"“*- Tl! (1.1-1)
and the transmitted intensity is
IT = β-β ίτ*ΐχ. (1.1-2)
ETALON
Ii 0 Ic L It
Fig. 1.1-2. Etalon intensities for an intracavity intensity much less
than the saturation intensity.
Introduction 3
Equation (1.1-2) holds as long as the saturation intensity Ig of the medium is large
compared with the intracavity intensity, i.e., if
Is > ΤΙχ (1.1-3)
is satisfied sufficiently. Figure 1.1-3 depicts the case of strong input intensity in
which the medium is bleached, the finesse is high, and the etalon transmits per
fectly; i.e., Tj s and « Ij/T. This clearly holds for I^· » I$, i.e., if
II > TIS (1.1-4)
is satisfied sufficiently. The possibility of bistability is suggested by noting that
both Eqs. (1.1-3,4) can be satisfied by the same input intensity. For example,
take Ij = Is, then both inequalities require that T be lesst han 1 as it always is.
This physical argument iss ubstantiated by the morer igorous deriivnaS teiocnti on
. .
2 1
ETALON
Fig. 1.1-3. Etalon intensities for an intracavity intensity much larger
than the saturation intensity.
There are two useful classifications of bistable systems. A system may be
absorptive or dispersive, and it may be intrinsic or hybrid. For example, the nonli
near Fabry-Perot interferometer just discussed is an absorptive intrinsic system.
A system is absorptive or dispersive depending on whether the feedback occurs by
way of an intensity-dependent absorption or refractive index. Clearly this dis
tinction is not sharp, since both absorptive and refractive mechanisms may be sig
nificant simultaneously. The distinction between intrinsic (all-optical) and hybrid
(mixed optics and electronics) i£ sharp. In an intrinsic system the intensity de
pendence arises from a direct interaction of the light with matter. In a hybrid
system the intensity dependence arises from an electrical signal from a detector
monitoring the transmitted intensity, usually applied to an intracavity phase
shifter. Experimental embodiments of intrinsic and hybrid systems are described in
Chapters 3 and 4, respectively.
For further reading: a simple introduction to optical bistability is Gibbs,
McCall, and Venkatesan (1979) and recent collections of papers are: Bowden,
Ciftan, and Robl (1981); Bowden, Gibbs, and McCall (1984); and A. Miller, Smith,
and Wherrett (1984). Apart from this book, the most extensive review of optical
4 [1.2]
bistability, both theory and experiment, is Abraham and Smith (1982a)· Lugiato
(1984) gives a more recent and thorough review of the theory of optical bistabil
ity. Goldstone (1984) is a good introduction, especially for dynamic effects.
1.2. OPTICAL LOGIC WTTH BISTABLE DEVICES
The transmission of information as signals impressed on light beams traveling
through optical fibers is replacing electrical transmission over wires. The low cost
and inertness of the basic materials of fibers and the small size and low loss of the
finished fibers are important factors in this evolution. Furthermore, for the very
fast transmission systems, for example, for transmitting a multiplexed composite of
many slow signals, optical pulses are best. This is because it is far easier to gen
erate (Höchstrasser, Kaiser, and Shank, 1980; Shank, Ippen, and Shapiro, 1978) and
propagate (Bloom, Mollenauer, Lin, Taylor, and DelGaudio, 1979) picosecond opti
cal pulses than electrical pulses. With optical pulses and optical transmission a
reality, the missing component of an all-optical signal processing system is an op
tical logic element in which one light beam or pulse controls another. The optical
bistable systems described in this book have many desirable properties of an all-
optical logic element. Hopefully they are the forerunners of tiny, low-energy,
subpicosecond, room-temperature devices. The high frequencies of optical elec
tromagnetic radiation give optical devices a potential for subpicosecond switching
and room-temperature operation unavailable to Josephson junctions or electronics.
The fact that electrical charges are not used or are used only in tiny beam-inter
acting regions makes an all-optical system much more immune to electromagnetic
interference from electrically noisy industrial environments or the electromagnetic
pulses from a nuclear explosion. If this book aids and accelerates the understand
ing and development of such all-optical systems, it will have served its purpose.
Bistable devices have already performed a host of logic functions. Both two-
state (Fig. 1.2-1) and many-state (Fig. 1.2-2) optical memories have been demon
strated. The amount of transmitted light reveals the past history of the input
light; i.e., the system "remembers" whether or not the input ever exceeded a par
ticular threshold value. By modifying the operating conditions, an optical transis
tor or transphasor mode of operation is achieved as in Fig. 1.2-3. A small modu
lation on the input (or on a second signal beam) is amplified. An optical discrimi
nator (Fig. 1.2-4) transmits pulses with intensities above the threshold and
suppresses those below. An optical limiter (Fig. 1.2-5) shows little change in the
transmitted power. This function could serve to limit the power reaching some
thing or someone or to decrease the percentage noise level. Figure 1.2-6 illus
trates optical discrimination in which a signal is faithfully transmitted whenever it
exceeds the threshold level. Changes in pulse shape can be accomplished with
nonlinear etalons. For example, in Fig. 1.2-7 the etalon initially transmits the
light well, but the energy absorbed from the pulse heats the etalon, detunes it
from the laser frequency, and terminates the transmission long before the input
pulse turns off. Sometimes the transmitted signal oscillates when the input is per
fectly constant, resulting in an optical oscillator (Fig. 1.2-8). Or an etalon placed
in a continuous wave (cw) beam and initially detuned from the laser frequency can
be swept using a pulse from a second laser to gate out a short pulse from the cw
beam (Fig. 1.2-9). These examples illustrate that existing bistable optical devices
have the desired characteristics of many all-optical operations. Nonetheless,
smaller, faster, cheaper, room-temperature, efficient devices are needed.
