Table Of ContentCambridge University Press
978-0-521-42424-0 - The Elements of Nonlinear Optics
Paul N. Butcher and David Cotter
Table of Contents
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© Cambridge University Press www.cambridge.org
Cambridge University Press
978-0-521-42424-0 - The Elements of Nonlinear Optics
Paul N. Butcher and David Cotter
Table of Contents
More information
© Cambridge University Press www.cambridge.org
Cambridge University Press
978-0-521-42424-0 - The Elements of Nonlinear Optics
Paul N. Butcher and David Cotter
Table of Contents
More information
© Cambridge University Press www.cambridge.org
Cambridge University Press
978-0-521-42424-0 - The Elements of Nonlinear Optics
Paul N. Butcher and David Cotter
Table of Contents
More information
© Cambridge University Press www.cambridge.org
Cambridge University Press
978-0-521-42424-0 - The Elements of Nonlinear Optics
Paul N. Butcher and David Cotter
Table of Contents
More information
© Cambridge University Press www.cambridge.org
Preface
In recent years there has been a rapid expansion of activity in the field of
nonlinear optics. Judging by the proliferation of published papers,
conferences, international collaborations and enterprises, more people
than ever before are now involved in research and applications of
nonlinear optics. This intense activity has been stimulated largely by the
increasing interest in applying optics and laser technology in tele-
communications and information processing, and has been propelled by
significant advances in nonlinear-optical materials.
The origins of these recent developments can be traced through
three decades of work since the invention of the laser and the first
observations of nonlinear-optical phenomena by Franken et al (1961).
From the earliest days it was recognised that such phenomena can have
useful practical applications; for example, effects such as optical-
frequency doubling allow the generation of coherent radiation at
wavelengths different from those of the available lasers. In the 1960s
many of the most fundamental discoveries and investigations were made.
Work was then mainly concerned with the interaction of high-power
lasers with inorganic dielectric crystals, gases and liquids. Effects such as
parametric wave-mixing, stimulated Raman scattering and self-focusing
of laser beams were investigated intensively. The invention of the
wavelength-tunable dye laser paved the way for the development during
the 1970s of many tunable sources utilising nonlinear effects, such as
harmonic generation, sum- and difference-frequency mixing, and
stimulated Raman scattering. In this way tunable coherent radiation
became available in a wide spectral range from the far infrared to vacuum
ultraviolet. Some of these sources used dielectric crystals as the
nonlinear medium, whilst others used atomic and molecular gases; in the
latter cases the efficiency was increased by tuning the input radiation
close to the resonant frequencies of the medium. These new tunable light
sources were used increasingly for spectroscopy, and numerous
spectroscopic techniques were developed which themselves relied on
nonlinear-optical processes, such as coherent anti-Stokes Raman
scattering, and multi-photon absorption and ionisation. Mode-locked
lasers capable of generating pulses of sub-nanosecond duration became
more widely available during the 1970s, allowing time-resolved nonlinear
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xii Preface
spectroscopy and coherent transient effects to be studied.
The mid- to late-1970s also saw the advent of telecommunications
using optical fibres, and this has been the most important stimulus for the
explosion of effort in nonlinear optics during the last decade. By the late
1980s and early 1990s it is common to find information carried on a laser
beam in the process of communication, storage, retrieval, printing or
sensing, and there is increasing effort to achieve ever greater data-
processing capabilities, by using ultrafast optoelectronic interactions and
by harnessing the properties of laser light for highly-parallel manipulation
and interconnection of signals. Nonlinear optics provides the key to many
of these future developments, and exploits the properties of new
materials (such as multiple-quantum-well semiconductors, fibre wave-
guides, organic polymers and photorefractive materials). New effects
(such as optical bistability, phase conjugation and optical solitons) have
been discovered which can make use of these nonlinearities for signal
processing. In summary, the field of nonlinear optics has become
enormously diverse, with applications in many branches of science and
engineering.
In writing this book our objective was not to review this vast range
of activity. Several excellent books have already appeared which cover
specialised aspects and, most notably, the recent book by Shen (1984)
provides a broad review. However, the diversity of the field has meant
that, especially for the newcomer, the underlying principles often lie
hidden in the technical literature amongst a wealth of detail. Therefore,
this book is intended to fulfil the need for a self-contained account of the
most important principles and theory of nonlinear optics, fully developed
from basic concepts. The book is written for graduate students of physics
and electrical engineering, as well as for the increasing numbers of
scientists and engineers entering the field. The book is also directed to
established researchers who need a source reference for the derivation of
fundamental formulae, with confidence that the notation, vexing
numerical factors and units are treated consistently. No prior knowledge
of quantum mechanics, apart from the most simple notions, is required of
the reader. All the essential quantum-mechanical apparatus is derived
fully and explained. Only a familiarity with simple calculus, vectors and
electromagnetic theory is assumed.
In 1965 one of us (PNB) published a monograph Nonlinear
Optical Phenomena, based on a series of lectures at Ohio State University
during 1963-4; this work has been out of print for many years. Those
readers familiar with the monograph may recognise some sections and
passages in the earlier chapters of this book. The original material has
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Preface xiii
been revised extensively to bring it into line with modern conventions and
practice, and represents not quite one-quarter of the present book.
Chapter 1 is a brief general introduction to nonlinear optics. The
starting point for the main development in Chapter 2 is the constitutive
relations between the polarisation and electric field. The chapter also
contains a representative catalogue of nonlinear-optical phenomena, and
particular attention is paid to conventions and the various numerical
factors. Chapter 3 on quantum mechanics serves two purposes: with the
unfamiliar reader in mind, we provide a self-contained tutorial review
starting from basic concepts; we also derive various formulae for later
use. Throughout the book, with a few simple exceptions, we use the
semiclassical approach in which the light is treated classically but the
nonlinear medium is treated quantum-mechanically. Chapter 4 is the
core of the first half of the book, in which the formulae for the linear and
nonlinear susceptibilities are derived Two different approaches are fully
developed: that using electric-dipole operators, and the alternative in
terms of momentum operators. The latter are of greatest value in the
discussion of systems, such as semiconductors, which contain mobile
charged particles. Topics such as resonance enhancement and local-field
factors are also discussed here. The various symmetry properties of the
susceptibilities are discussed in Chapter 5. In Chapter 6 we develop the
descriptions appropriate to resonant processes, which are of increasing
importance today. We place particular emphasis on the links between the
simple model for a two-level system and the susceptibility formalism, and
show how the two approaches complement each other. Chapter 7 is
concerned with propagation and wave-coupling processes in nonlinear
media. The object here is to provide practical descriptions of processes
such as harmonic generation, frequency mixing, parametric amplification
and stimulated scattering. More specialised topics, including phase
conjugation and soliton effects in optical fibres, are also discussed.
There are very many kinds of nonlinear-optical media of interest.
However, because of the need to keep the book to a reasonable size, we
have selected only one material system for detailed discussion (in
Chapter 8). We chose semiconductors for a number of reasons: first,
semiconductors provide useful illustrations of many aspects from earlier
chapters; second, in recent years there have been very significant
advances in semiconductor materials and these are likely to remain of the
greatest technological importance; and lastly, this reflects the current
research interests of the authors. Finally, in Chapter 9 we describe the
background to the present intense interest in new artificial materials for
nonlinear optics. Examples of applications of the general theory are
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xiv Preface
scattered throughout the book. We use SI units, and the relations
between alternative systems of units and definitions are given in
appendices.
Because of the vast scope of the subject and the limits of space,
the contents of the book are inevitably a compromise. We hope,
however, that the choice of topics will provide an understanding of the
broad principles. We consider that the material presented here
represents the minimum knowledge necessary for an appreciation of key
aspects of the current literature.
We are grateful to our many past and present colleagues who have
influenced the writing of this book; we are especially indebted to T.P.
McLean, R. Loudon, D.C. Hanna and M.A. Yuratich. Nonlinear optics
has developed through the efforts of countless researchers. For brevity,
however, references are limited to those which supplement the text. We
sincerely apologise to the many authors of important works whom we
have failed to cite by name. We acknowledge with thanks the permission
of those authors and publishers whose figures are reproduced or adapted
here.
This book was set in type by the authors using the eroff and eqn
text-formatting codes. Permission to use a UNIX system at British
Telecom Research Laboratories is gratefully acknowledged. We are
grateful to C.J. Todd for his support, and to the system administrators for
much invaluable help. Finally, we thank sincerely Freda Butcher and
Sarah Cotter, Colin, Kirsty and Simon, for their tolerance and
encouragement.
Coventry\ Warwickshire Paul Butcher
Wbodbridge, Suffolk David Cotter
January 1990
The reprinting of the book has provided an opportunity to make some
small corrections.
January 1991
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1
Introduction
'Nonlinear' optical phenomena are not part of our everyday experience.
Their discovery and development were possible only after the invention of
the laser.
In optics we are concerned with the interaction of light with
matter. At the relatively low light intensities that normally occur in
nature, the optical properties of materials are quite independent of the
intensity of illumination. If light waves are able to penetrate and pass
through a medium, this occurs without any interaction between the waves.
These are the optical properties of matter that are familiar to us through
our visual sense. However, if the illumination is made sufficiently
intense, the optical properties begin to depend on the intensity and other
characteristics of the light. The light waves may then interact with each
other as well as with the medium. This is the realm of nonlinear optics.
The intensities necessary to observe these effects can be obtained by
using the output from a coherent light source such as a laser. Such
behaviour provides insight into the structure and properties of matter. It
is also utilised to great effect in nonlinear-optical devices and techniques
which have important applications in many branches of science and
engineering.
Another effect of light on matter can sometimes be to induce
changes in the chemical composition; such 'photochemical' processes lie
outside the subject of this book.
1.1 Origins of optical nonlinearity
We now consider in a simple way how nonlinear-optical behaviour might
arise. The materials which concern us in optics can be thought of as a
collection of charged particles: electrons and ion cores. When an electric
field is applied the charges move; the positive charges tend to move in the
direction of the field, whilst negative ones move the opposite way. In
conductors, some of the charged particles are free to move through the
material for as long as the electric field is applied, giving rise to a flow of
electric current. In dielectric materials, on the other hand, the charged
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