Table Of ContentSelf-Organization in Optical Systems
and Applications in Information Technology
Springer
Berlin
Heidelberg
New York
Barcelona
Budapest
Hong Kong
London
Milan
Paris
Santa Clara
Singapore
Tokyo
Springer Series in Synergetics Editor: Hermann Haken
An ever increasing number of scientific disciplines deal with complex systems. These are systems that
are composed of many parts which interact with one another in a more or less complicated manner. One
of the most striking features of many such systems is their ability to spontaneously form spatial or
temporal structures. A great variety of these structures are found, in both the inanimate and the living
world. In the inanimate world of physics and chemistry, examples include the growth of crystals,
coherent oscillations oflaser light, and the spiral structures formed in fluids and chemical reactions. In
biology we encounter the growth of plants and animals (morphogenesis) and the evolution of species.
In medicine we observe, for instance, the electromagnetic activity of the brain with its pronounced
spatio-temporal structures. Psychology deals with characteristic features of human behavior ranging
from simple pattern recognition tasks to complex patterns of social behavior. Examples from sociology
include the formation of public opinion and cooperation or competition between social groups.
In recent decades, it has become increasingly evident that all these seemingly quite different kinds
of structure formation have a number of important features in common. The task of studying analogies
as well as differences between structure formation in these different fields has proved to be an ambitious
but highly rewarding endeavor. The Springer Series in Synergetics provides a forum for interdisciplinary
research and discussions on this fascinating new scientific challenge. It deals with both experimental and
theoretical aspects. The scientific community and the interested layman are becoming ever more
conscious 0 f concepts such as self-organization, instabilities, deterministic chaos, nonlinearity, dynamical
systems, stochastic processes, and complexity. All of these concepts are facets of a field that tackles
complex systems, namely synergetics. Students, research workers, university teachers, and interested
laymen can find the details and latest developments in the Springer Series in Synergetics, which
publishes textbooks, monographs and, occasionally, proceedings. As witnessed by the previously
published volumes, this series has always been at the forefront of modern research in the above
mentioned fields. It includes textbooks on all aspects of this rapidly growing field, books which provide
a sound basis for the study of complex systems.
A selection of volumes in the Springer Series in Synergetics:
Synergetics An Introduction 3rd Edition Nonlinear Nonequilibrium Thermodynamics I
ByH. Haken Linear and Nonlinear Fluctuation-Dissipation
Handbook of Stochastic Methods for Physics, Theorems By R. Stratonovich
Chemistry, and the Natural Sciences Nonlinear Nonequilibrium Thermodynamics II
2nd Edition By C. W. Gardiner Advanced Theory By R. Stratonovich
Dynamics of Hierarchical Systems An
Limits of Predictability
Evolutionary Approach By J. S. Nicolis Editor: Yu. A. Kravtsov
Dimensions and Entropies in Chaotic Systems
Interdisciplinary Approaches to Nonlinear
Quantification of Complex Behavior
Complex Systems Editors: H. Haken,
Editor: G. Mayer-Kress
A. Mikhailov
Information and Self-Organization
Inside Versus Outside Endo- and Exo-
A Macroscopic Approach to Complex Systems
Concepts of Observation and Knowledge in
ByH.Haken
Physics, Philosophy and Cognitive Science
Synergetics of Cognition
Editors: H. Atmanspacher, G. J. DaIenoort
Editors: H. Haken, M. Stadler
Modelling the Dynamics of Biological Systems
Foundations of Synergetics I
Editors: E. Mosekilde, O. G. Mouritsen
Distributed Active Systems 2nd Edition
By A. S. Mikhailov Self-Organization in Optical Systems and
Applications in Information Technology
Foundations of Synergetics II
2nd Edition Editors: M. A. Vorontsov,
Complex Patterns 2nd Edition
W. B. Miller
By A.S. Mikhailov, A.Yu. Loskutov
Quantum Signatures of Chaos
ByF. Haake
Mikhail A. Vorontsov
Walter B. Miller (Eds.)
Self-Organization
in Optical Systems
and Applications
in Information Technology
Second Edition
With 105 Figures
Springer
Professor Mikhail A. Vorontsov
M.V. Lomonosov Moscow State University,
International Laser Center, Vorob'evy Gory,
Moscow 119 899, Russia
,,'
New Mexico State University,
Las Cruces, New Mexico 88003, USA
Dr. Walter 8. Miller
U.S. Army Research Laboratory, Battlefield Environment Directorate,
White Sands Missile Range, New Mexico 88002, USA
Series Editor:
Professor Dr. Dr. h.c.mult. Hermann Haken
Institut fUr Theoretische Physik und Synergetik der Universititt StUitgart,
0-70550 StuHgart, Germany
'C"en' ter for Complex Systems, Florida Atlantic University,
Boca Raton, Fl3343t, USA
The first edition appeared in the series as Volume 66.
Die Deutsche Bibliothek - CIP-Einheitsaufnahme
Self-organization in optical systems and applications in
information technology/Mikhail A. Vorontsov; Walter B. Miller
(ed.). - Berlin; Heidelberg; New York; Barcelona; Budapest; Hong
Kong; london; Milan; Paris; Santa Clara; Singapore; Tokyo:
Springer, t998
(Springer series in synergetics)
ISBN-'3' WS-3-540-64l~~-4 ~-[SBN-'3: 978-3-64~-603'~-(>
DOl: 10.1007/9~3-64~-6031S'"
ISSN Ol72-nBg
This work is subjecl 10 copyright. All righls ar~ reserved, whether lhe whole or pari of th. material is
concerned, specifically th. rights of tr~nsl~tion, reprinling, reuSe of illustrations, recilation, broadcasling;
reproduction On microfilm or in any Olher way, and .lOuge in data banb. Duplication of this publication or
parIS lhereofis permitted only under lhe provisionsofthe German Copyright LawofSeptember 9, 1965, in its
current version, and permission for use must always be oblained from Springer-Verlag. Violations are liable
for prosecution under the German Copyright Law.
C Spring~r.V"'lag Berlin Heidelberg 1995. 1998
The uSc of general descriptive names , registered names, trademarks, elC. in this publication does nol imply,
cyen in lhe absence of a spedfic Slatement, that such Mmes are exempl from lhe rel evanl prolective laws and
regulations and lherefore free for general us •.
TypeseUing: Camera· ready copy from lh. editors using a Springer T EX macro pac kage
SPIN 10669)27 }SIJIH - S 4 3 2 1 0 • Printed on add·frce paper
Preface
After the laser came into existence in 1960, basic experimental and theoretical
research was focused on its behavior in the time domain. In this way, single and
multimode operation and the effect of frequency locking as well as various kinds
of spiking and ultrashort pulses were studied. Later, laser-light chaos was pre-
dicted and discovered. Sophisticated investigations concentrated on the study
of the line width and of photon statistics. Though it was known from the very
beginning that cavity modes may show different kinds of spatial patterns, in par-
ticular in the transverse direction, it was not until more recently that transverse
spatial patterns caused by laser-light dynamics were discovered. Since laser ac-
tion can be maintained only if the laser is continuously pumped from the outside,
it is an open system. It is by now well known that there are a number of open
systems in physics that may show spontaneous formation of spatial or temporal
or spatio-temporal patterns. An important example is provided by fluid dynam-
ics where a liquid layer heated from below may suddenly form hexagonal cells.
In the center of each cell the fluid rises and sinks down at the borders. Also other
patterns are observed such as rolls and stripe structures showing various kinds
of defects. Similarly, certain chemical reactions can develop large-scale patterns
such as concentric rings, spirals or, as was shown more recently, hexagonal and
stripe patterns.
As I have shown a number of years ago, the occurence of such patterns,
irrespective of the physical substratum, can be traced back to general principles
of self-organization that are explored in the field of synergetics. More technically
speaking, they can be explained by specific kinds of equations that I derived and
called the generalized Ginzburg-Landau equations.
The discovery of spatial transverse patterns in lasers is of great importance
in several ways. First of all, we discover that pattern formation is a wide-spread
phenomenon in open systems. As will become more obvious from the articles in
this book, lasers provide us with a wonderful means with which to study general
phenomena of self-organization that are not so easily obtainable in chemical
reactions or in fluid dynamics. One reason is the much shorter time scale in
lasers, another one is the possibility to manipulate the individual modes in a
sophisticated manner. Furthermore a number of technical applications become
possible. As it seems, we are at the beginning of what may be called optical
computers, including the optical synergetic computer.
VI Preface
This book, written by several pioneers of this new field, gives an excellent
survey of the present state of the art and provides the reader with deep insights
into the mechanisms by which patterns in lasers and in passive optical devices
are formed.
I wish to congratulate Professor Mikhail Vorontsov, who himself has made
a fundamental contribution to this field, for the excellent selection of authors
and articles, and to both he and Dr. Miller for their editing work. I am sure
that this book will be of great help to all scientists and engineers working on
fundamental problems in optics or looking for important new applications. The
book concludes with an excellent article by Professor Yuri Klimontovich on the
general problem of self-organization.
Stuttgart, February 1995 H. Haken
To Professor Sergey Akhmanov
who had a profound impact on the development of nonlinear optics. Per-
haps more profound was the impact of his personality on colleagues and
students at Moscow State University.
Acknowledgments
Behind the publication of every book lies a separate and somewhat dra-
matic story. For our own particular case, we wish to take a moment and
recognize several of the lead participants and acknowledge their roles.
First and foremost, we thank the authors, without whose energy, dedica-
tion, and enthusiasm this book would not exist. Both Janet Vasiliadis and
Boris Samson did a tremendous service to all by assisting as technical edi-
tors and providing moral support. Egor Degtiarev graciously prepared the
chapter by S. A. Akhmanov and helped with preparation of the camera-
ready manuscript. W. Firth's interest and support throughout the entire
process was greatly appreciated. Last, but not least, we acknowledge the
role played by all those at the Army Research Laboratory whose interest
allowed the completion of this book up to the final act. In particular, we
recognize the support of Don Veazey and Douglas Brown, and the ever-
present help provided by Jennifer Ricklin. To all of these players we offer
our sincerest thanks.
The Editors
Contents
INTRODUCTION
Self-Organization in Nonlinear Optics - Kaleidoscope of
Patterns - M.A. Vorontsov and W.B. Miller. 1
1 What Is This Book About? ............... 1
2 Nonlinear Optics: The Good Old Times. . . . . . . . . 3
3 The First Model- Kerr-Slice/Feedback Mirror System 3
4 Diffusion, Diffraction, and Spatial Scales . . . . . . . . 5
5 One More Scheme: The First Step Toward Optical Synergetics . 6
6 Nonlocal Interactions; Optical Kaleidoscope of Patterns. 7
7 OK-Equation and "Dry Hydrodynamics" . . . . . . . . . 9
8 One More Nonlinear Element: Two-Component Optical
Reaction-Diffusion Systems . . . . . 10
9 Diffraction at Last; Rolls and Hexagons. . . . . . . . 12
10 diffraction and Diffraction . . . . . . . . . . . . . . . 13
11 Far Away from Hexagons: Delay in Time and Space. 16
12 Diffusion + Diffraction + (Interference) + Nonlocal
Interactions = Akhseals 18
References 22
CHAPTER 1
Information Processing and Nonlinear Physics: From Video
Pulses to Waves and Structures - S.A. Akhmanov . . . . . .. 27
1 Information Encoding by Carrier Modulation and the Physics of
Nonlinear Oscillations and Waves .............. 27
2 Modulation of Light Waves and Information Encoding in Digital
Optical Computers. Optical Triggers . . . . . . . . . . .. 29
3 Strong Optical Nonlinearities. Nonlinear Materials. . . . . .. 35
4 Generation and Transformation of Femtosecond Light Pulses . 36
5 Control of Transverse Interactions in Nonlinear Optical
Resonators: Generation, Hysteresis, and Interaction of
Nonlinear Structures. . . . . . . . . . . . . . . . . . 38
6 Conclusion. Nonlinear Optics and Molecular Electronics 40
References . . . . . . . . . . . . . . . . . . . . . . . . . . 43
XII Contents
CHAPTER 2
Optical Design Kit of Nonlinear Spatial Dynamics -
E.V. Degtiarev and M.A. Vorontsov .. 45
1 Elementary Optical Synergetic Blocks. . . 46
1.1 Characteristics of a Synergetic Block . . . 46
1.2 Optical Synergetic Block Based on LCLV . 47
1.3 Main Mathematical Models ....... . 50
1.4 Optical Multistability and Switching Waves 52
2 Integral Transverse Interactions . . . . . . . 54
2.1 The Synergetic Optical Block with an Electronic
Feedback Circuit . . . . . . . . . . . . . . . . 54
3 Optical Counterparts of Two-Component Reaction-Diffusion
Systems .......................... . 56
3.1 Linear Stability Analysis and Bifurcation of Uniform States 60
4 Conclusion 64
References 66
CHAPTER 3
Pattern Formation in Passive Nonlinear Optical Systems -
W.J. Firth . . . . . . . . . . . . . . . . 69
1 Induced and Spontaneous Patterns 71
1.1 Materials and Geometries .... 72
2 Mirror Feedback Systems . . . . . . 73
2.1 Kerr Slice with Feedback Mirror. . 74
2.2 Basic Model and Stability Analysis 75
2.3 Liquid Crystal Light Valve Systems 81
3 Pattern Formation in Optical Cavities 82
3.1 Vector Kerr Model and Equations. . . 83
3.2 Spatial Stability of Symmetric Solutions 84
3.3 Pattern Formation in a Two-Level Optical Cavity 89
4 Conclusion 93
References 94
CHAPTER 4
Spatio-Temporal Instability Threshold Characteristics in Two-
Level Atom Devices - M. Le Berre, E. Ressayre, and
A. Tallet . . . . . . . . . . . . . . . . . . . . . . . . . . 97
1 Linear Stability Analysis of Stationary Solutions . 100
2 Feedback Mirror Experiment. 104
2.1 Experimental Results . . . . . . . 104
2.2 Linear Analysis . . . . . . . . . . 105
2.3 Static and Dynamical Thresholds 107
2.4 Role of the Longitudinal Grating 109
