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.
MOLECULAR
NONLINEAR OPTICS
MATERIALS, PHYSICS, AND DEVICES
Joseph Zyss
Centre National d'Etudes des Telecommunications
Laboratoire de Bagneux, Bagneux, France
ACADEMIC PRESS, INC.
Harcourt Brace & Company, Publishers
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Copyright © 1994 by Academic Press, Inc.
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No part of this publication may be reproduced or
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ACADEMIC PRESS, INC.
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United Kingdom Edition published by
ACADEMIC PRESS LIMITED
24-28 Oval Road, London NW1 7DX
Library of Congress Cataloging-in-Publication Data:
Zyss, J.
Molecular nonlinear optics : materials, physics, and devices /
Joseph Zyss.
p. cm. — (Quantum electronics—principles and applications)
Includes bibliographical references and index.
ISBN 0-12-784450-3
1. Nonlinear optics. 2. Quantum electronics. 3. Optoelectronics—
Materials. 4. Polymers. I. Title. II. Series.
QC446.2.79 1993
621.36'9-dc20 92-42976 CIP
Printed in the United States of America
93 94 95 96 BC 9 8 7 6 5 4 3 2 1
Contributors
Numbers in parentheses indicate the pages on which the authors' contribu
tions begin.
J. H. Andrews (245), Case Western Reserve University, Department of Physics,
Cleveland, OH 44106-7079
Gregory L. Baker (433), Michigan State University, East Lansing, Ml 48824
Shahab Etemad (433), Bell Communications Research, Red Bank, NJ 07701
Ryoichi Ito (201), Department of Applied Physics, Faculty of Engineering, The
University of Tokyo, Bunkyo-ku, Tokyo 113 Japan
Takayoshi Kobayashi (47), Department of Physics, University pf Tokyo,
Hongo, Bunkyo, Tokyo 113, Japan
Takashi Kondo (201), Department of Applied Physics, Faculty of Engineering,
The University of Tokyo, Bunkyo-ku, Tokyo 113, Japan
Mark G. Kuzyk (299), Department of Physics, Washington State University,
Pullman, WA 99164-2814
Hilary S. Lackritz (339) (formerly Hilary L. Hampsch), Department of
Chemical Engineering, Purdue University, West Lafayette, IN 47907
Pierre Le Barny (379), Thomson-CSF, Laboratoire Central de Recherches,
Domaine de Corbeville, 91404, Orsay Cedex, France
Isabelle Ledoux (129), Centre National d'Etudes des Télécommunications,
Molecular Quantum Electronics Department, 196 avenue Henri Ravera, 92220,
BP-107, Bagneux, France
IX
X Contributors
Vincent Lemoine (379), Thomson-CSF, Laboratoire Central de Recherches,
Domaine de Corbeville, 91404, Orsay Cedex, France
Shaul Mukamel (1), Department of Chemistry, University of Rochester,
Rochester, NY 14627
Jean-François Nicoud (129), Groupe des Matériaux Organiques, Institut de
Physique et Chimie des Matériaux de Strasbourg (ICPMS), 6, rue Boussin-
gault, 67083, Strasbourg Cedex, France
Jean Paul Pocholle (379), Thomson-CSF, Laboratoire Central de Recherches,
Domaine de Corbeville, 91404, Orsay Cedex, France
Constantina Poga (299), Department of Physics, Washington State University,
Pullman, WA 99164-2814
Philippe Robin (379), Thomson-CSF, Laboratoire Central de Recherches,
Domaine de Corbeville, 91404, Orsay Cedex, France
Y. R. Shen (101), Department of Physics, University of California and
Materials Science Division, Lawrence Berkeley Laboratory, Berkeley, CA
94720
Kenneth D. Singer (245), Case Western Reserve University, Department of
Physics, Cleveland, OH 44106-7079
Zoltan G. Soos (433), Department of Chemistry, Princeton University, Prince
ton, NJ 08544
John M. Torkelson (339), Department of Chemical Engineering, Department
of Materials Science and Engineering, Northwestern University, Evanston,
IL 60208
Joseph Zyss (129), Centre National d'Etudes des Télécommunications, Molec
ular Quantum Electronics Department, 196 avenue Henri Ravera, 92225,
BP107-Bagneux, France
Preface
Seven years after the publication, in that same series, of two volumes
dedicated to the quadratic and cubic nonlinear properties of organic
materials, time has come for an update to help the reader keep up with an
active level of worldwide research effort in both fundamental and applied
directions. While some of the scientific foundations of the field, as outlined
in the two previous volumes, had already been firmly established at the time
and have remained relatively untouched, many important pending issues
were recognized at this early stage but left unsettled. Among them were the
relative perspectives opened up by χ{2) and χ(3) related phenomena toward
application endgoals; the comparative assets of crystalline versus polymeric
materials; and the technological potential of organics, be they crystalline,
polymeric, or others for integration in waveguiding passive and active
optoelectronic devices, such as modulators and switches. As a result of
intensive work combining the contributions of physicists, chemists, and
device engineers, these basic questions have now been clarified to a significant
extent with some important technological bottlenecks identified and addressed
in the realm of both crystalline and polymeric materials. Owing to recent
remarkable developments that encompass microlithographic patterning and
organic molecular beam epitaxy, current attitudes towards the viability of
an "organic technology" is much less biased by prejudice than a decade ago.
Electro-optic poled polymers, as reported mainly in Part III, have matured
into patternable thin-film materials compatible with sophisticated multilayer
XI
XU Preface
architectures for integrated optics. Furthermore, their compatibility with
semiconductor technology should ensure a smooth transition from present
purely semiconductor-based systems to hybrid solutions whereby polymers
and semiconductors are adequately combined in view of their respective
advantages. Such developments have been based, and will further depend,
on a deeper understanding of the physical properties of polymers, in
particular as they relate to the quality of interfaces and the thermal relaxation
dynamics of the induced polar order in view of its subsequent stabilization.
Fundamental as well as application-related aspects have thus been closely
associated in this book, with successive sections, such as 3-1, 3-3 and 3-4,
jointly addressing closely related physical and technological issues from
different perspectives.
As far as single crystals are concerned, various demonstrations in bulk
formats have confirmed their potential for frequency doubling and optical
parametric oscillation based on the availability of an increasing variety of
molecular and lattice structures. Furthermore, the possibility of shaping
crystalline structures in waveguides, as reported in Chapter 2-3, will further
enhance the prospects for single crystals in quadratic nonlinear optics with
near infrared laser frequency doubling to the blue as one of the main strategic
goals.
Development and refinement of a molecular engineering approach toward
quadratic nonlinear effects has helped point out new families of molecules
more precisely targeted to satisfy precise transparency-efficiency require
ments. While paranitroaniline has been serving as a dominant paradigm in
the field since the mid-seventies, related dipolar intramolecular charge
transfer systems may now be viewed as special cases of more general
multipolar nonlinear systems. Organometallic and organomineral systems,
self-assembling methods, and mesogenic nonlinear systems also appear as
new and promising avenues with perspectives discussed in Chapter 2-2.
Besides their intrinsic nonlinear behavior, molecules are very sensitive to
environmental conditions that become dominant at interfaces; Chapter 2-1
reviews this increasingly important domain of surface science in the case of
air-water interfaces.
Cubic nonlinear properties are more elusive than quadratic ones, and
fundamental work, of both theoretical and experimental nature, is still
needed to deepen our understanding of the underlying mechanisms so as to
point out relevant structural and electronic features. This important issue is
dealt with in Part I (Chapters 1-1 and 1-2) and again in Chapters 3-2 and
3-5. In this context, the magnitudes of cubic nonlinear susceptibilities do not
suffice to account for subtle transient processes; the position and absorption
xiii
Preface
cross-section of two-photon peaks as well as the dynamical features of
induced absorption from photoexcited states play a dominant role. Advances
in theoretical approaches (Chapter 1-1) and femtosecond probing techniques
(Chapter 1-2) have significantly contributed to these issues.
While amorphous side-chain polymers qualify for quadratic nonlinear
optics and conjugated ones for cubic effects, it would nevertheless seem
erroneous to confine crystals to quadratic applications; results that have
appeared in course of publishing this book tend to blur this barrier as they
point out the relevance for χ(3), by way of cascading mechanisms, of
molecular crystals initially conceived for χ(2).
While it may still be premature to predict the nature and extent of
application breakthroughs in this field, the last decade has undoubtedly seen
molecular nonlinear optics acquire full-fledged scientific status with recog
nition from both physicists and chemists. Few other fields have benefitted
to such extent from a fruitful and convergent cooperation between the two
communities, although motivations may be somewhat different: Nonlinear
susceptibilities at both microscopic and macroscopic levels have now come
to be widely adopted by chemists in view of their enhanced sensitivity to
such features as conjugation, charge transfer, protonation, environment and
local field effects, and crystalline or polymeric organization. As a consequence
β and y susceptibilities are now increasingly finding their way in chemical
data bases, alongside absorption, dipole moment, dielectric constant, and
other more traditional physico-chemical data. Conversely, physicists are
attracted by the virtually unlimited possibilities to implement and manipulate
properties at the ultimate molecular level. Advanced "guided" organic
synthesis and molecular assembling techniques, combined with newly de
veloped experimental tools, capable of probing and manipulating molecules
at ultimate spatial, spectral, and time resolutions, are bound to open up a
new frontier in molecular optical sciences.
This book will have fulfilled its dual goal when supplying state-of-the-art
information to the benefit of currently committed scientists while helping
renew the field by attracting needed future contributors.
JOSEPH ZYSS
Chapter 1
MANY-BODY EFFECTS IN
NONLINEAR SUSCEPTIBILITIES;
BEYOND THE LOCAL-FIELD
APPROXIMATION
Shaul Mukamel
Department of Chemistry, University of Rochester, Rochester, New York
1. INTRODUCTION 2
2. MODEL HAMILTONIAN FOR MOLECULAR MATERIALS;
FRENKEL-EXCITONS 5
3. EQUATIONS OF MOTION: THE ANHARMONIC-OSCILLATORS
PICTURE 7
4. THE SINGLE-PARTICLE LEVEL AND THE LOCAL-FIELD
APPROXIMATION 11
5. THE ROLE OF TWO-EXCITON VARIABLES: ENHANCED
NONLINEAR SUSCEPTIBILITIES IN MOLECULAR AGGREGATES 13
6. EXCITON-POPULATÏON VARIABLES AND EXCITON
TRANSPORT 20
6.1 Interaction-Induced Extra Resonances: Degenerate Four-Wave
Mixing 20
6.2 Exciton Transport in Real Space: The Wigner Representation . . .. 24
6.3 Transient Grating: The Time-Domain Analogue of Degenerate
Four-Wave Mixing 25
7. GREEN FUNCTION EXPRESSIONS FOR χ(3) IN MOLECULAR
NANOSTRUCTURES WITH ARBITRARY GEOMETRY 26
8. DISCUSSION 39
ACKNOWLEDGMENTS 42
REFERENCES 42
All rights of reproduction in any form reserved.
ISBN 0-12-784450-3
2 Shaul Mukamel
1. INTRODUCTION
The systematic calculation of nonlinear susceptibilities of optical materials,
and the precise relationship between individual molecular hyperpolarizablities
and the macroscopic optical response, constitute a complex challenge that
has drawn a considerable theoretical attention [1-5]. The design of new
optical materials with specified characteristics (fast switching, large suscepti
bilities) and the interpretation of nonlinear optical measurements in terms
of molecular properties and intermolecular forces require the development
of a suitable theoretical framework.
The response of a medium to optical fields is most conveniently formulated
in terms of wave vector and frequency-dependent optical susceptibilities,
which are the expansion coefficients of the macroscopic polarization field in
powers of the Maxwell electric field E [6-9]. The problem of incorporating
intermolecular forces in the linear optical response (i.e., the dielectric
function) has a long history [10-15]. The local-field approximation provides
a simple way to relate the polarizabilities of isolated molecules to the
macroscopic susceptibilities. In this approach, the effect of intermolecular
forces is included in an effective local electric field. The problem of calculating
the response of an interacting ensemble of molecules to the electromagnetic
field is then reduced to the response of isolated molecules interacting with the
local field E , through an interaction Hamiltonian — μ-Ε^ where μ denotes
L
the molecular dipole operator. The Lorentz relation between the local field
and the Maxwell field E (Eq. 1.4.2) can then be used to calculate the dielectric
function. This procedure, which reduces the complex many-body problem
to a single-body problem, was subsequently generalized and applied also to
the calculation of nonlinear susceptibilities [3,5,9,16-18]. The nonlinear
susceptibilities at a given order are then given in terms of sums of products
of molecular polarizabilities of that order and lower orders. This simple,
back-of-the-envelope calculation of macroscopic susceptibilities is, however,
not rigorous [5,19]. It fails to take properly into account the correlated
dynamics of the interacting many-body system, i.e. correlations among the
molecules, as well as correlations between the molecules and the radiation
field. Short-range (e.g., exchange) forces are totally neglected in this proce
dure. Moreover, even the dipole-dipole forces are not fully taken into
account. In addition, the resulting susceptibilities do not depend on the
wavevectors, apart from the local-field contribution, but just on the frequen
cies. This indicates that processes such as exciton migration and energy
transfer and transport (e.g., the Forster transfer) [20,21] are neglected. Such
processes are often added phenomenologically in order to interpret transient
