The relationship between mechanical stresses and optical anomalies in germanium
and paratellurite
I.A. Kaplunov,A. I. Kolesnikov, K. P. Skokov, R. M. Grechishkin, L. V. Sedova,
and S. A. Tret’yakov
Tver State University, Tver
Submitted December 30, 2004
Opticheski Zhurnal 72, 85–89 July 2005
Optical interference and x-ray analysis methods are used to determine the mechanical stresses in
single crystals of germanium and paratellurite, which cause local distortions of the
wavefronts due to the photoelastic effect. The dislocation structure of the crystals close to optical
anomalies is studied. The effect of high-temperature annealing on stress relaxation in
germanium and paratellurite is investigated. © 2005 Optical Society of America
INTRODUCTION
Three-dimensional defects of the crystal lattice that arise
during the growth of crystals—bubbles, pores, inclusions of
foreign phases—are also optical defects, because they are
commensurable with the wavelengths of light. Combinations
of small defects—impurity atoms, vacancies, dislocations,
small-angle boundaries, boundaries of blocks—produce local
inhomogeneities of the permittivity and are also sources of
various optical anomalies.
1–4
Various methods and apparatus have been developed and
used for crystals of many substances to estimate the optical
quality of the materials. The parameters and properties to be
determined are optical transmittance, attenuation and scatter-
ing indices, refractive-index inhomogeneity n / n , wave-
front distortions /, and striations narrow local regions
with altered refractive indices.
Single crystals of germanium and paratellurite are
among the most important types of optical materials. Germa-
nium is used as lenses and entrance windows of the objec-
tives of IR optics thermal viewers. Paratellurite is the most
efficient acoustooptic material for creating modulators, de-
flectors, and tunable radiation filters in the 0.35–5-m wave-
length region. For both materials, the problem of obtaining
stable crystals with high optical homogeneity is far from
soilved.
1–5
Despite the substantial differences in the physical prop-
erties and growth technologies of germanium and paratellu-
rite using the Czochralski method, many regularities in the
determination of the structural defects responsible for the
appearance of optical anomalies are extremely similar.
Therefore, the main goal of this paper was to establish a
relationship between the dislocation structure of germanium
and paratellurite, the post-growth mechanical stresses in
these crystals, and the optical anomalies that characterize
them. The common technique used for these studies can be
useful when solving problems of increasing the optical qual-
ity of other crystals grown by the Czochralski method.
ANISOTROPY OF THE ELASTIC PROPERTIES
For the symmetry point groups m 3 m , to which germa-
nium crystals belong, and 422, to which paratellurite crystals
belong, the matrices S
ij
of the resilience constants have, re-
spectively, the forms
6
Ge:
s
11
s
12
s
12
0 0 0
s
12
s
11
s
12
0 0 0
s
12
s
12
s
11
0 0 0
0 0 0 s
44
0 0
0 0 0 0 s
44
0
0 0 0 0 0 s
44
, 1
TeO
2
:
s
11
s
12
s
13
0 0 0
s
12
s
11
s
13
0 0 0
s
13
s
13
s
33
0 0 0
0 0 0 s
44
0 0
0 0 0 0 s
44
0
0 0 0 0 0 s
66
. 2
The expressions for Young’s moduli in the directions
determined by the direction cosines l
1
, l
2
, and l
3
for germa-
nium and paratellurite, respectively, are written in the form
E
l
1
l
2
l
3
-1
=s
11
+2
s
11
-s
12
-
1
2
s
44
l
1
2
l
2
2
+l
2
2
l
3
2
+l
3
2
l
1
2
, 3
E
l
1
l
2
l
3
-1
= l
1
4
+l
2
4
s
11
+l
3
4
s
33
+l
1
2
l
2
2
2 s
12
+s
66
+l
3
2
1 -l
3
2
2 s
13
+s
44
. 4
According to Eqs. 3 and 4, using numerical values of
S
ij
taken from Ref. 7, the characteristic surfaces of Young’s
moduli of germanium and paratellurite Fig. 1 are con-
structed in this paper.
An analysis of the dependences presented here shows
that germanium, because of its cubic structure, displays sig-
nificantly less anisotropy of the elastic properties than does
paratellurite.Actually, the maximum value of Young’s modu-
lus for germanium differs from the minimum by a factor of
only one and a half, whereas this ratio for paratellurite is
572 572 J. Opt. Technol. 72 (7), July 2005 1070-9762/2005/070572-05$15.00 © 2005 The Optical Society of America