Table Of ContentPhotoelastic and
Electro-Optic
Properties of
Crystals
Photoelastic and
Electro-Optic
Properties of
Crystals
s.
T. Narasimhamurty
Osmania University
Hyderabad, India
PLENUM PRESS • NEW YORK AND LONDON
Library of Congress Cataloging in Publication Data
Narasimhamurty, T. S.
Photoelastic and electro'optic properties of crystals.
Bibliography: p.
Includes index.
1. Crystal optics. 2. Photoelasticity. I. Title.
QD941.N37 548'.9 79-409
ISBN 978-1-4757-0027-5 ISBN 978-1-4757-0025-1 (eBook)
DOI 10.1007/978-1-4757-0025-1
© 1981 Plenum Press, New York
Softcover reprint of the hardcover 1st edition 1981
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Acknowledgments
The author hereby expresses his appreciation and thanks to the authors of papers and to
the editors and publishers who so readily granted him their permission to include in this
book the following material:
Figures
4.9 W. G. Mayer and Michigan State University. From Ref. [1534].
4. lOA S. Hirzel Verlag, Stuttgart. From L. Bergmann [110].
4.10B M. A. Breazeale and E. A. Hiedemann, and American Institute of Physics.
From Ref. [190].
4.IOC W. G. Mayer and E. A. Hiedemann, and Acta Crysta/logr. (Denmark).
From Ref. [790].
4.12 V. Chandrasekharan and Proc. Indian Acad. Sci. From Ref. [240].
5.6 H. E. Pettersen and Michigan State University. From Ref. [922].
5.8 K. Vedam, E. D. D. Schmidt, and W. C. Schneider, and Plenum Publishing
Corp. From Ref. [1301].
5.9- Proc. Indian Acad. Sci. From Ref. [842].
5.11
5.12- M. Ziauddin and American Institute of Physics. From Ref. [844].
5.14
5.15 K. Veerabhadra Rao and American Institute of Physics. From Ref. [1303].
5.16 E. S. Jog and J. Indian Inst. of Science. From Ref. [586].
5.17 G. Jeelani and Osmania University. From Ref. [847].
5.21 G. Robertson and Institute of Physics, Bristol and London (U.K.). From
Ref. [1057].
5.22 G. N. Ramachandran and V. Chandrasekharan, and Proc. Indian Acad. Sci.
From Ref. [998].
5.23 H. F. Gates and E. A. Hiedemann, and American Institute of Physics. From
Ref. [413].
5.24(a). Myron P. Hagelberg and Michigan State University. From Ref. [464].
(b)
5.24(c) Osmania University. From Ref. [843].
5.25 K. Veerabhadra Rao and Osmania University. From Ref. [1306].
5.26 H. E. Pettersen and American Institute of Physics. From Ref. [924].
5.27 G. Alphonse and R.e.A. Review. From Ref. [32].
5.28 T. M. Smith and A. Korpel, and Institute of Electrical and Electronics
Engineers Inc., New York. From Ref. [1152].
5.29, R. W. Dixon and M.e. Cohen, and American Institute of Physics. From
5.30 Ref. [294].
5.31 N. F. Borrelli and R. A. Miller, and American Institute of Physics. From
Ref. [176].
5.32, R. Adler and the Institute of Electrical and Electronics Engineers Inc.,
5.33 New York. From Ref. [13].
6.1 R. Srinivasan and Zeitschrift Jur Physik (West Germany). From Ref. [1175].
6.2, A. Rahman and Osmania University. From Ref. [986].
6.3
,
,i Acknowledgments
6.4 V. G. Krishna Murty and Osmania University. From Ref. [681].
6.6
6.7 R. Ethirajan and Osmania University. From Ref. [330].
6.8 A. Rahman and K. S. Iyengar, and Acta Crystallogr. (Denmark). From Ref.
[988].
6.9 A. Rahman and Osmania University. From Ref. [986].
8.13 American Institute of Physics. From Ref. [1419].
8.14 R. Adhav and American Institute of Physics. From Ref. [10].
8.15 American Institute of Physics. From Ref. [1417].
8.16. S. Namba and American Institute of Physics. From Ref. [838].
8.17 American Institute of Physics. From Ref. [1417].
Tables
5.8 H. E. Pettersen and American Institute of Physics. From Ref. [925].
5.10 V. Chandrasekharan and J. Indian Inst. Science. From Ref. [241].
6.1 H. E. Pettersen and Michigan State University. From Ref. [922].
6.3- V. G. Krishna Murty and Osmania University. From Ref. [681].
6.5
6.6- A. Rahman and Osmania University. From Ref. [986].
6.8
8.4, American Institute of Physics. From Ref. [1042].
8.5
Text
pp. 212- J. A. Mandarino and University of Michigan. From Ref. [765].
213
Foreword
This comprehensive treatise reviews, for the first time, all the essential
work over the past 160 years on the photoelastic and the closely related
linear and quadratic electro-optic effects in isotropic and crystalline mate
rials. Emphasis is placed on the phenomenal growth of the subject during
the past decade and a half with the advent of the laser, with the use of
high-frequency acousto-optic and electro-optic techniques, and with the
discovery of new piezoelectric materials, all of which have offered a feedback
to the wide interest in these two areas of solid-state physics.
The first of these subjects, the photoelastic effect, was discovered by
Sir David Brewster in 1815. He first found the effect in gels and subsequently
found it in glasses and crystals. While the effect remained of academic
interest for nearly a hundred years, it became of practical value when Coker
and Filon applied it to measuring stresses in machine parts. With one
photograph and subsequent analysis, the stress in any planar model can
be determined. By taking sections of a three-dimensional model, complete
three-dimensional stresses can be found. Hence this effect is widely applied
in industry.
The photoelastic effect was analyzed for crystals by Pockels, who also
discovered the electro-optic effect, i.e., the production of birefringence of
light on the application of an electric field. Pockels produced a phenom
enological theory for both of these effects for all the crystal classes. The
electro-optic effect remained of purely theoretical interest for a number of
years until it became desirable to produce very short light pulses. The Kerr
effect in liquids had been used for this purpose for many years. This is a
quadratic effect which produces a birefringence proportional to the square
of the voltage. Pockels' linear electro-optic effect requires less voltage and
can give a shorter light pulse than can the Kerr effect and is being considered
as a modulator for obtaining very short light pulses. Hence both the photo
elastic and electro-optic effects have graduated from the academic stage
to the broad-application stage as acousto-optic and electro-optic modulators
and deflectors of light.
The present book has the most complete description of these two
vii
v;;; Foreword
effects known to the writer. It covers all the significant contributions made
by the several scientists from the day of discovery up to 1976. Considerable
material in the text has been collected from a score of recent Ph.D. theses
that are not available to the general reader. A number of papers are by the
author, T. S. Narasimhamurty.
The book also includes descriptions of ultrasonic methods for the
study of the photoelastic behavior of glasses and crystals. These methods
in the hands of Mueller have fully brought out the potentialities for the
elasto-optic studies of amorphous and crystalline solids. The book contains
a chapter on the piezoelectric effect in crystals since a knowledge of this
effect is an essential prerequisite to understanding Pockels' linear electro
optic effect. A chapter is also given on the atomistic theory of photo
elasticity of cubic crystals that is based mostly on Mueller's work.
Hence the book can be recommended as the most complete discussion
of the two effects and related subjects known to the writer.
Columbia University Warren P. Mason
Preface
This book presents an attempt to collect between the covers of one volume
some of the material, widely scattered in the literature for over 160 years,
on the photoelastic and electro-optic effects in crystals. The stimulus to
write this book resulted from the personal contacts that the author has
had with solid-state physicists, industrial physicists, mineralogists, en
gineers, and graduate students. The book is intended for all such persons
with varying backgrounds. Because of this broad spectrum of readers with
naturally widely differing goals, some of the more elementary but funda
mental ideas have been dealt with in a little more detail. The specialist, of
course, can skip such topics without losing the general trend of the contents;
for his benefit, the references to the existing literature on the topics are
given as exhaustively as possible.
The subject of photoelasticity of crystals deals with the artificial bi
refringence in crystals produced by mechanical stress, and it forms an
important aspect of solid-state physics. The photoelastic behavior of
crystals is a fourth-rank tensor property, relating the stress tensor or strain
tensor to the change in the optical-index ellipsoid.
The fundamental discovery of photoelastic birefringence in glasses and
crystals was made by Sir David Brewster in 1815. This phenomenon was
later observed in other solids, both amorphous and crystalline, by various
investigators, notably Neumann, Mach, Wertheim, and Kerr. But it was
not until 1889 that the fundamental difference in the photoelastic behavior
of amorphous and crystalline solids was observed by Pockels, who evolved
the phenomenological theory of photoelasticity in crystals. By developing
suitable techniques, he studied the photoelastic behavior of some crystals,
both cubic and noncubic, in support of his phenomenological theory. The
discovery of photoelasticity made in 1815 remained just a topic of academic
interest for nearly a century until it was successfully applied to structural
engineering early in this century (1902) by Coker. Subsequently the interest
in this subject has shifted to technical problems, and today it is the most
powerful and indispensable tool in solving intricate problems in structural
engineering.
ix
x Pre/ace
After the systematic investigations by Pockels (1880-J906) there seem
to have been very few contributions to this branch of crystal physics until the
1930s, when Bergmann and Fues and also Hiedemann and Hoesch success
fully applied ultrasonic methods for studies on the elasto-optic behavior of
glasses. Mueller's theoretical paper (1938), based on the results of Pockels
(1880-1906), Bergmann and Fues (1936), and Hiedemann and Hoesch (1936)
and dealing with the elasto-optic behavior of glasses and cubic crystals, has
fully brought out the potentialities of ultrasonic methods for these studies.
This may be considered yet another landmark in experimental techniques
to study the photoelastic behavior of crystalline and amorphous solids.
Pockels' scheme for the photoelastic constants of the 32 point groups
has been revised by Bhagavantam (1942), who observed from group
theoretical considerations certain discrepancies in Pockels' scheme of
describing the photoelastic behavior of the various classes of crystals. Some
of his findings have already been confirmed experimentally, and others are
awaiting such confirmation.
Almost all the experimental work done until about 1950 was confined
to glasses and cubic crystals, and that too mostly for one wavelength oflight
radiation. The then existing methods of studying stress birefringence could
not be employed for a sufficiently accurate measurement of the photo
elastic dispersion in cubic and noncubic crystals and its temperature depen
dence; new techniques were developed to this end in subsequent years.
The photoelastic behavior of crystals plays a significant role in the
Brillouin scattering of light, and the development of the laser has served as
a feedback to the wide interest evinced in this area during the last 15 years.
Other interesting and closely related properties include the linear
electro-optic effect (Pockels effect) and the quadratic electro-optic effect
(Kerr effect) in crystals. The Pockels effect is a third-rank tensor property
that can be exhibited only by noncentrosymmetric crystals, whereas the
Kerr effect is a fourth-rank tensor property and is a universal effect in the
sense that it can be exhibited by all crystals, both centro symmetric and
noncentrosymmetric.
Although the phenomenon of photoelasticity in plastics has rightly
received its due attention in the hands of structural engineers, the photo
elastic behavior of crystals, which was put on a sound phenomenological
basis by Pockels as early as the 1880s, does not seem to have attained, until
recently, the importance that it richly deserves. The fate of Pockels' linear
electro-optic effect was similar, notwithstanding the fact that it was well
established by Pockels as early as 1895. Billing's contribution in 1947
demonstrating the potentialities of ADP and KDP crystals for light modula-
Preface xi
tion and as optical shutters has opened up a new field in technology, and
this has spurred some more extensive investigations of the linear electro
optic effect in crystals. However, it is only with the advent of the laser in
the early 1960s that there has been a phenomenal growth of activity in
these two areas of crystal physics, namely photoelastic and electro-optic
effects, as a result of their applications in industry. For example, the develop
ment of the laser and high-frequency acoustic techniques, along with the
discovery of new piezoelectric materials with high coupling factors, has
made it possible to apply the acousto-optic phenomenon to devices such
as light deflectors, light modulators, and signal processors. This, in turn,
has demanded a relentless search for acousto-optic materials suitable for
practical use. Similarly, the Pockels effect has now almost completely
replaced the hitherto indispensable quadratic electro-optic effect in polar
liquids, and has found many interesting and useful applications in science
and technology, such as high-voltage measurements, optical range finders,
sound recording on cine films, color television, lasers, and optical elements
of computer systems. Today we find that several research laboratories
attached to various industries are deeply involved in the problems of light
modulators and light deflectors based on acousto-optic and electro-optic
effects in crystals.
Coker and Filon (1931) pointed out in the preface to their Treatise
on Photoelasticity that: "Photoelasticity has also its value for the pure
physicist, and it provides an additional means of exploring the interaction
of molecules and atoms with radiation, a means to which little attention
has hitherto been paid, and which should not be neglected, as it may
throw much light upon conditions of matter in the solid state." It is only
in the recent past that these macrosCDpic properties of crystals have been
receiving the attention of solid-state physicists.
A large number of papers have been published on the several aspects
of photoelasticity and electro-optics of crystals during the past 160 years,
and yet there has been no attempt to present in one volume all the essential
information contained therein.
The above circumstances have prompted the author to write the present
book on the photoelastic and the closely related linear and quadratic
electro-optic effects in crystals. Much of the information in Chapters 1,
3, and 4 forms a necessary background for both photoelastic and electro
optic eff~cts in crystals.
Two parallel notations, namely Schonflies and International, are used
throughout the book; this is necessary as long as books and journals
employing the older Schonflies notation remain in use.
