An Introduction to Electrooptic Devices. Selected Reprints and Introductory Text By

411 Pages·1974·18.576 MB·English

by  Ivan P. Kaminow (Auth.)

AN
INTRODUCTION
TO ELECTROOPTIC
DEVICES
SELECTED REPRINTS AND INTRODUCTORY TEXT BY
IVAN P. KAMINOW
Bell Telephone Laboratories, Inc.
Crawford Hill Laboratory
Holmdel, New Jersey
®
ACADEMIC PRESS New York and London 1974
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COPYRIGHT © 1974, BY BELL TELEPHONE LABORATORIES, INC.
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Library of Congress Cataloging in Publication Data
Kaminow, Ivan P Date comp.
An introduction to electrooptic devices.
Includes bibliographical references.
1. Electrooptical devices. 2. Crystal optics.
3. Dielectrics. I. Title.
TA1770.K35 621.38Ό414 73-793
ISBN 0-12-395050-3
PRINTED IN THE UNITED STATES OF AMERICA
For Florence
PREFACE
The term electrooptic effect as it is employed here refers to a change in
the refractive index of a transparent substance induced by an applied electric
field, usually at a frequency below the optic vibrational resonance of the
lattice or molecule involved. The linear and quadratic electrooptic effects are
known as the Pockels and Kerr effects, respectively. Devices based on these
phenomena have been used for the control of light for nearly a century, but
it was the discovery of the laser in 1960 that stimulated most of the recent
study and application of these effects. It is the purpose of this monograph
to present an introduction to the electrooptic effect and to summarize recent
work on devices employing the electrooptic effect.
Chapter I provides the necessary background in classical crystal optics.
The topics covered include crystal symmetry, the tensor description of linear
dielectric properties, propagation in anisotropic media, and passive crystal
optic devices. Chapter II introduces the phenomenological description of
tensor nonlinear dielectric properties of crystals. Although the emphasis is
on the electrooptic effect, an effort is made to show its relationship to more
general nonlinear optical phenomena.
The remainder of the book consists of selected reprints that treat various
aspects of the materials and device problem in detail. Two review papers
give a survey of device design and application. A third contains a thorough
listing of linear electrooptic coefficients for various substances. A table of
quadratic coefficients can be found elsewhere.*
*S. H. Wemple and M. DiDomenico, Jr., Appl. Solid State Sei. 3 ( 1972).
xiii
Techniques for measuring and characterizing the electrooptic properties
of crystals are covered by several recent reprints. Also included is a trans-
lation by Mrs. A. Werner of Bell Laboratories of the chapter on electrooptic
effects in the 1906 edition of "Lehrbuch der Kristalloptic" by F. Pockels.
He introduces the mathematical description of the electrooptic effect used
today. He also describes his experiments to prove to the skeptics of the day
that a "true" linear electrooptic effect, independent of strain, does in fact
exist.
Device configurations that have been employed to modulate and deflect
laser beams are covered by other groups of reprints. Some very recent work
on producing these devices in thin film or integrated optics configurations is
also included.
Experimental work exploring the physics of the electrooptic effect is
treated briefly. However, theoretical studies of the physical origin of the
electrooptic effect is not included as it is still imperfectly understood. The
present theoretical situation has been reviewed thoroughly by Wemple and
DiDomenico.*
Several experiments have demonstrated picture display devices employing
electrooptic crystalst or ceramic materials.* Unfortunately, space limitations
do not permit their inclusion.
Internal modulation of lasers for ß-switching, mode-locking, and coup-
ling modulation is chiefly a laser problem and is not covered here.
The first two chapters are taken from notes prepared for courses on non-
linear optics given at Princeton University in 1968, at UCLA in the summer
of 1970, and at Bell Laboratories in 1972. I am grateful to Professor M. E.
Van Valkenburg, Dr. Harold Lyons, Dr. L. K. Anderson, and the students
at the respective institutions for providing the opportunity to organize this
material.
I am also grateful to the authors and publishers who have generously
allowed their work to be reproduced here.
*See footnote on page xiii.
fSee for example: C. J. Salvo, IEEE Trans. Electron. Devices ED-18, 748 (1971);
M. Grenot, J. Pergale, J. Donjon, and G. Marie, Appl. Phys. Lett. 21, 83 (1972).
ÎSee for example: J. R. Maldanado and A. H. Meitzler, Proc. IEEE 59, 368 ( 1971 ).
XIV PREFACE
CHAPTER I
CRYSTAL OPTICS
For the most part, electrooptic materials are employed in the form of
single crystals. In order to characterize these materials it will be necessary
to introduce some of the nomenclature of crystallography. The physical
properties of anisotropic media are described by tensors and these tensors
can be greatly simplified by taking account of crystal symmetry.
Methods have been developed to describe the propagation of electromag-
netic waves in crystals and are discussed briefly in this chapter.
A more thorough discussion of crystal optics is given in books by Nye,1
Landau and Lifshitz,2 and Born and Wolf.3 A concise discussion of
elementary crystallography is given by Kittel.4
1. Crystallography
1.1 Bravais Lattice
A crystal is a periodic array of atoms in three dimensions. The periodic
building block is the unit cell. Typical unit cell dimensions in inorganic
materials are ~10 A = 10~9m. Hence, any crystal of macroscopic size
(~1 cm) may be regarded as infinite in extent on the scale of unit cell
dimensions. There are only seven shapes that a unit cell may have and still
1
fill all space. These shapes define a set of crystallographic systems, which are
listed in Table 1.1. The shapes of the three-dimensional cells belonging to
each system are shown in Fig. 1.1. The simplest cell in each system is the
primitive cell P and it contains one atom. There are 8 atoms at the corners
of the cell but each atom is shared by 8 other cells. One can also form body
centered cells / which contain 2 atoms; face centered cells F with 4 atoms;
and partially face centered cells C with 2 atoms. There is also a rhombohedral
cell R which is obtained from a cubic cell by stretching along a body
diagonal.
The edges of the cells define a three-dimensional coordinate system with
base vectors a, b, c which need not be orthogonal. The angles between a and
b, b and c, c and a are γ, α, and /?, respectively. When unit cells of one kind
are stacked to fill all space, the atomic positions form an array of lattice
points, or simply a lattice. The space lattices formed from the 14 elementary
cells in Fig. 1.1 are called Bravais lattices. Certain elemental crystals are
formed by placing identical atoms at the lattice points. For example,
TABLE 1.1
The Fourteen Lattice Types in Three Dimensions8
Number
of Restrictions on
lattices conventional
in Lattice unit-cell
System system symbols axes and angles
Triclinic 1 P a Φ b Φ c
a Φ β Φ y
Monoclinic 2 P,C a Φ b Φ c
a = y = 90° Φ β
Orthorhombic 4 P, C, /, F a φ b φ c
a = β = γ = 90°
Tetragonal 2 Ρ,Ι a = b Φ c
a = β = y = 90°
Cubic 3 P or se a = b = c
/ or bec a = β = γ = 90°
F or fee
Trigonal 1 R a = b = c
a = β = y < 120°,
Φ 90°
Hexagonal 1 P a = b Φ c
= β = 90°
a
γ = 120°
a After C. Kittel "Introduction to Solid State Physics," 4th ed. Wiley, New
York, 1971. Copyright © 1971 by John Wiley and Sons, Inc. Used with
permission of the publisher.
2 I. CRYSTAL OPTICS
^=^t
CUBIC P CUBIC I CUBIC F
^=Pi
TETRAGONAL P TETRAGONAL I
ff=PT î i TÎ
II * H ■* H
ORTHORHOMBIC P ORTHORHOMBIC C ORTHORHOMBICI ORTHORHOMBIC F
4=7
k=y Ι£ΞΡ
MONOCLINIC P MONOCLINIC C TRICLINIC
TRIGONAL R TRIGONAL AND HEXAGONAL R
FIg. 1.1 Unit cells of the fourteen Bravais lattices (After C. Kittel, "Introduction to Solid
State Physics," 4th ed., Wiley, New York, 1971. Copyright © 1971 by John Wiley and Sons,
Inc. Used with permission of the publisher.)
aluminum is face centered cubic (fee); and iron is body centered cubic
(bcc).
Distances in the lattice can be measured in terms of the lattice constants
a, b, c. If the origin is taken at a lattice point, the radius vector to any other
lattice point is
r = /za + kb + /c (1)
where h, k, I are integers. A particular direction can be specified by the set
of integers [hkl] defining r. Thus, [1 0 0], [0 1 0], and [0 0 1] point along the
coordinate axes a, b, and c, respectively; and [Ï 0 0], [0 T 0], [0 0 Ï] point in
the opposite directions. It is conventional to use square brackets for this set.
In the cubic system all three directions a, b, c are equivalent and one speaks
of "the set of <100) directions." Specific directions are given in square
brackets and a set of equivalent directions in angular brackets.
A primitive cell containing only one lattice point may be defined for any
Bravais lattice. However, the primitive cells may not exhibit the symmetry
1. CRYSTALLOGRAPHY 3
c
Fig. 1.2 The (623) plane.
of the appropriate system as well as the unit cells in Fig. 1.1. For example,
in the fee lattice with unit cell base vectors a, b, c of equal length a, the
primitive cell base vectors are
a' = Ka + b), b' = Kb + c), c' = |(a + c) (2)
and the primitive cell volume V
V = (a' X b') · c' = W = \V. (3)
Thus, the primitive cell has a curious shape containing one-fourth the
volume of the cubic unit cell. (See Fig. 1.6.)
Planes of lattice points can be specified by a set of Miller indices as
follows: (a) Write the set of numbers giving the intercepts of the plane on
a, b, c in units of lattice constants a, b, c. In Fig. 1.2 the intercepts are 1, 3,
2. (b) Take the reciprocals, 1/1, 1/3, 1/2. (c) Multiply by the smallest
number that will make each reciprocal an integer, i.e., 6(1/1,1/3,1/2)
= (6,2,3). The integers are enclosed in parentheses and the plane is called
the (623) plane. Other planes in the cubic system are shown in Fig. 1.3. The
bar over ä number, e.g., (TOO), means a negative intercept. The planes need
not pass through lattice points, e.g., (200) is midway between lattice point
planes. Equivalent sets of planes are enclosed in braces; e.g., in the cubic
system (100), (010), and (001) are {100} planes.
In the cubic system the plane (hkl) is perpendicular to the direction
[hkl]. In the tetragonal system only (hkO) planes are perpendicular to [M0]
directions; in the orthorhombic system only (hOO) planes and [hOO] direc-
tions are perpendicular.
1.2 Symmetry Operations of Point Groups
In order to reduce tensor quantities that describe the physical properties
of a Bravais lattice, it will be necessary to know what symmetry operations
4 I. CRYSTAL OPTICS
leave the lattice invariant. These same operations must also leave any
mathematical description of a physical property of the lattice invariant.
Of course, any translation
t = Aa + kb + /c,
with A, k, I integers, is a symmetry operation. However, this operation will
not simplify a tensor that describes a macroscopic property—i.e., one that
treats many cells identically. Typical optical wavelengths of 10,000 A
extend over ~1000 cells, and radio frequency wavelengths are at least 103
greater. Hence, displacements of an infinite lattice by a few lattice constants
does not change the physical or mathematical situation significantly. Only
if wavelengths comparable to lattice spacing (e.g. X rays) are used must the
translational variation of the field be considered. For our purposes, we may
ignore translations much shorter than an optical wavelength and, in
particular, translations on the order of a, b, or c. We may, therefore, refer
all symmetry operations to a convenient point in a cell through which all
symmetry elements pass. We then speak of the point symmetry properties of
the lattice.
The allowed symmetry elements for a Bravais lattice are limited as
follows. The identity operation E corresponds to a rotation of 0 or 2π
about any axis and is an element of every lattice. An n-fold rotation C
n
corresponds to a rotation of ρ(2π/η) about an axis, where p and n are
integers. Only two-, three-, four-, and sixfold axes are consistent with an
infinite lattice. In a cubic lattice, 2C rotations of 2ττ/3 and 477/3 about the
3
[111] axis are symmetry operations, as are similar rotations about [111],
[lTl], and [111]—there are 8C operations. Rotations of m about [110] and
3
the five other equivalent directions make up 6C operations. Rotations of π
2
(100) l J (110) (III)
I
(200) (TOO)
Fig. 1.3 Principal planes in the cubic system (After C. Kittel, "Introduction to Solid State
Physics," 4th ed., Wiley, New York, 1971. Copyright © 1971 by John Wiley and Sons, Inc.
Used with permission of the publisher.)
1. CRYSTALLOGRAPHY 5