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Photorefractive Materials For Optical
Computing And Image Processing
George A Rakuljic, Amnon Yariv
George A Rakuljic, Amnon Yariv, "Photorefractive Materials For Optical
Computing And Image Processing," Proc. SPIE 0881, Optical Computing and
Nonlinear Materials, (3 May 1988); doi: 10.1117/12.944074
Event: 1988 Los Angeles Symposium: O-E/LASE '88, 1988, Los Angeles, CA,
United States
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Invited Paper
Photorefractive materials for optical computing and image processing
George A. Rakuljic and Amnon Yariv
California Institute of Technology, Department of Applied Physics
Pasadena, California 91125
ABSTRACT
Photorefractive materials have been used as the nonlinear optical media in various optical computing and
image processing applications. Devices such as passive phase conjugate mirrors, image subtractors, optical
limiters and thresholders can be constructed with materials whose index of refraction is a function of light
intensity.
It is the purpose of this paper, then to describe some of these materials on the basis of their
nonlinear optical response.
1. INTRODUCTION
Photorefractive crystals are promising materials for optical data processing applications. A large number
of parallel operations can be processed in a single crystal.
Photorefractive materials can store optical
holograms for time durations of hours to years, depending on their dark conductivity. Optical amplifiers
with gain factors of 4000 have been constructedl, and phase conjugate reflectivities greater than 20 have
been observed in BaTiOg with four -wave mixing2.
Operation on nanosecond time scales has been demonstra-
ted3 -5 with Q- switched pulses from doubled Nd:YAG lasers.
Finally, the requirements on write and erase
energy density in photorefractive crystals such as BS06 are comparable to the best photographic plates.
There are two major factors that limit widespread application of photorefractive materials at present.
First, some of the promising crystals such as BaTiO3, SBN, and KNb03 are not widely available in large
samples with high optical quality. Second, the crystals that are available are not optimal in all respects.
For instance, in order to demonstrate high speed, low write energy, long memory, or large gain, it is neces-
sary to use several different types of materials. The purpose of this paper is, therefore, to compare
photorefractive materials including BaTiO3, SBN, and BSKNN on the basis of several figures of merit which
are introduced in the next section.
Both ferroelectric and non -ferroelectric materials will be considered
in the comparison.
2. FIGURES OF MERIT
2.1 Steady -state index change
The steady -state change in the refractive index is defined as the index change after illumination for a
time that is long compared to the photorefractive response time T.
The index change is related directly to
the space charge field through
Anss = 1/2 nbreffEsc,
(1)
where nb is the background refractive index, reff is the effective electrooptic coefficient, and Esc is the
internally generated space charge electric field.
Esc is given by
E0 + iEd
Esc = -iEq
Eo + i(Ed + Eq)
where E0 = externally applied electric field
Eq = eNA /(EK) = limiting space charge field
Ed = kBTK /e = diffusion field.
The steady -state index change is also related to the two beam coupling coefficient r by
An
= Pc/to
ss
(2)
(3)
= Xr /2Tr,
where A is the wavelength of light.
In order to determine the materials dependence of Anss, the space charge field Esc needs to be considered.
Three limits for Esc exist:
146 / SPIE Vol. 881 Optical Computing and Nonlinear Materials (1988)
Invited
Paper
Photorefractive
materials
for
optical
computing
and
image
processing
George
A.
Rakuljic
and
Amnon
Yariv
California
Institute
of
Technology,
Department
of
Applied
Physics
Pasadena,
California
91125
ABSTRACT
Photorefractive
materials
have
been
used
as
the
nonlinear
optical
media
in
various
optical
computing
and
image
processing
applications.
Devices
such
as
passive
phase
conjugate
mirrors,
image
subtracters, optical
limiters
and
thresholders
can
be
constructed
with
materials
whose
index
of
refraction
is
a
function
of
light
intensity.
It is
the
purpose
of
this
paper,
then
to
describe
some
of
these
materials
on
the
basis
of
their
nonlinear
optical
response.
1
.
INTRODUCTION
Photorefractive
crystals
are
promising materials
for
optical
data
processing
applications.
A
large
number
of
parallel
operations
can be
processed
in
a
single
crystal.
Photorefractive
materials
can
store
optical
holograms
for
time
durations
of
hours
to
years,
depending
on
their
dark
conductivity.
Optical
amplifiers
with
gain
factors
of
4000
have
been
constructed
1
,
and
phase
conjugate
reflectivities
greater
than
20
have
been
observed
in
BaTiOs
with
four-wave
mixing
2
.
Operation
on
nanosecond
time
scales
has
been
demonstra-
ted
3
"
5
with
Q-switched
pulses
from
doubled
NdrYAG
lasers.
Finally,
the
requirements
on
write
and
erase
energy
density
in
photorefractive
crystals
such
as
BSO
6
are
comparable
to
the
best
photographic
plates.
There
are
two
major
factors
that
limit
widespread
application
of
photorefractive
materials
at
present.
First,
some
of
the
promising
crystals
such
as
BaTi03
,
SBN,
and
KNbOs
are
not
widely
available
in
large
samples
with
high
optical
quality.
Second,
the
crystals
that
are
available
are
not
optimal
in
all
respects.
For
instance,
in
order
to
demonstrate
high
speed,
low
write
energy,
long
memory,
or
large
gain,
it
is
neces-
sary
to
use
several
different
types
of
materials.
The
purpose
of
this
paper
is,
therefore,
to
compare
photorefractive materials
including
BaTiOs
,
SBN,
and
BSKNN
on
the
basis
of
several
figures
of
merit which
are
introduced
in
the
next
section.
Both
ferroelectric
and
non-ferroelectric
materials
will
be
considered
in
the
comparison.
2.
FIGURES
OF
MERIT
2.1
Steady-state
index
change
The
steady-state
change
in the
refractive
index
is
defined
as
the
index
change
after
illumination
for
a
time
that
is
long
compared
to
the
photorefractive
response
time
T.
The
index
change
is
related
directly
to
the
space
charge
field
through
Anss =
1/2
nbr
eff
Esc
,
(1)
where
n^
is
the
background
refractive
index,
r
e
ff is
the
effective
electrooptic
coefficient,
and
E
gc
is
the
internally
generated
space
charge
electric
field.
E
sc is
given
by
E
0
+
iE
d
SC
-
-q
E,
+
i(E
d
+
E
q
)
where
E
o
=
externally
applied electric
field
Eq
=
eN^/(eK)
=
limiting
space
charge
field
Ed
-
k
B
TK/e
-
diffusion
field.
The
steady-state
index
change
is
also
related
to
the
two
beam
coupling coefficient
T
by
An
ss
(3)
-
xr/27r,
where
X
is
the
wavelength
of
light.
In
order
to
determine
the
materials
dependence
of
An
ss
,
the
space
charge
field
E
sc
needs
to
be
considered.
Three limits
for
E
sc
exist:
146
/
SPIE
Vol.
881
Optical
Computing
and Nonlinear
Materials
(1988)
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(1): Esc = Ed.
From Eq.
(2), this occurs when Eo <Ed <Eq which is a common condition when no electric
field is applied and the grating period is large.
In this case
3
4nss a nbreffEd
(4)
a n-greff,
since Ed does not depend on material parameters.
(2)
Esc
Eq.
This occurs when Eq <Ed or E0; that is, when a large electric field is applied or when the
grating period is small. In this case
3
Anss a nbreffEq
(5)
a nbreff/e
where e is the dielectric constant of the material.
(3) Esc _ Eo. This occurs when Ed <Eo<Eq which holds in cases where moderately large electric fields are
applied to the crystal.
Hence,
3
Anss a nbreffEo
3
a nbreff'
(6)
Therefore, photorefractive crystals with large values of nbreff and nbreff /e are desirable for applications
such as passive phase conjugation that require large steady -state index changes.
2.2
Response time
The photorefractive response time T is a useful figure of merit for applications in which available
energy limits the illumination time, or in which the grating must be written or erased in a set time scale.
The response time scales with intensity until times as short as either the time for a charge carrier to
move one grating period or the time necessary for the electrooptic effect to respond to the Coulomb field of
the displaced charge. The longer of these times is the fundamental limit.
Diffusion times in semiconductors
such as GaAs are known to be <10 psec7.
The electrooptic response time is of the order of attoseconds fbr
the electronic component of the electrooptic coefficient, reff, and picoseconds for the ionic part. The mix
of these two components varies, but the ultimate response time of a photorefractive crystal is in the pico-
second range.
2.3
Photorefractive sensitivity
The photorefractive sensitivity S is defined as the index change per absorbed energy per unit volume$ -11.
That is
S -
An .
aI t
0
(7)
The photorefractive sensitivity is a useful figure of merit because it tells us how well a material uses a
given amount of optical energy.
Alternatively, it allows comparison of crystals with different absorption
coefficients on an equal basis.
The refractive index change An can be given by
An = Anss(1 - e
-t/T
(1
where a stationary index grating is assumed.
For t« T,
An = Ansst/T.
Since T is inversely proportional to aIo, then
(8)
(9)
SPIE Vol. 881 Optical Computing and Non linear Materials (1988) / 147
(1):
E
SC
-
E^.
From
Eq.
(2),
this
occurs
when
E
Q
<E
(
j<Eq
which
is
a
common
condition
when
no
electric
field
is
applied
and
the
grating
period
is
large.
In
this
case
An
ss
a
n
b
r
eff
E
d
(4)
a
n|r
eff
,
since
E^
does
not
depend
on
material
parameters.
(2)
Esc
-
Eq.
This
occurs
when
Eq<E
cj
or
E
o
;
that
is,
when
a
large
electric
field
is
applied
or
when
the
grating
period
is
small.
In
this
case
An
cc
a
-
3
(5)
a
Veff
/e
where
e
is
the
dielectric
constant
of
the
material.
(3)
E
SC
-
E
0
.
This
occurs
when
E
c
j<E
0
<Eq
which
holds
in
cases
where
moderately
large
electric
fields
are
applied
to
the
crystal.
Hence,
An
a
n._r
,.,-E
(6)
ss
b
eff
o
Therefore,
photorefractive
crystals
with
large
values
of
%r
e
ff
and
n^rgff/e
are
desirable
for
applications
such
as
passive
phase
conjugation
that
require
large
steady-state
index
changes.
2.2
Response
time
The
photorefractive
response
time
T
is
a
useful
figure
of
merit
for
applications
in
which
available
energy
limits
the
illumination
time,
or
in
which
the
grating
must
be
written
or
erased
in
a
set
time
scale.
The
response
time
scales
with
intensity
until
times
as
short
as
either
the
time
for
a
charge
carrier
to
move
one
grating
period
or
the
time
necessary
for
the
electrooptic
effect
to
respond
to
the
Coulomb
field
of
the
displaced
charge.
The
longer
of
these
times
is
the
fundamental
limit.
Diffusion
times
in
semiconductors
such
as
GaAs
are
known
to
be
<10
psec
7
.
The
electrooptic
response
time
is
of
the
order
of
attoseconds
fbr
the
electronic
component
of
the
electrooptic
coefficient,
*
e
ff
»
and
picoseconds
for
the
ionic
part.
The
mix
of
these
two
components
varies,
but
the
ultimate
response
time
of
a
photorefractive
crystal
is
in
the
pico-
second
range.
2.3
Photorefractive
sensitivity
The
photorefractive sensitivity
S
is
defined
as
the
index
change
per
absorbed
energy
per
unit
volume
8
"
11
.
That
is
S
-
l
t
o
The
photorefractive
sensitivity
is
a
useful
figure
of
merit
because
it
tells
us
how
well
a
material
uses
a
given
amount
of
optical
energy.
Alternatively,
it
allows
comparison
of
crystals
with
different absorption
coefficients
on an
equal
basis.
The
refractive
index
change
An
can
be
given
by
An
=
An
(1
-
e~
t/T
),
(8)
s s
where
a
stationary
index
grating
is
assumed.
For
t«T,
An
=
An
gs
t/T.
(9)
Since
T
is
inversely
proportional
to
al
o
,
then
SPIE
Vol.
881
Optical
Computing
and
Nonlinear
Materials
(1988)
/
147
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Eo + i(Ed + Eq)
S a Anss
Eo + (Ed + Ep)
where E = yNA /(pK) = drift field.
(10)
Clearly a large steady -state index change is preferred.
Moreover, large mobilities and long recombination
rates are generally desirable because these properties allow the carriers to diffuse or drift longer dis-
tances before they recombine, thereby reducing the drift field Ep.
In either case the photorefractive
sensitivity is increased.
3.
SUMMARY OF MATERIAL PARAMETERS AND FIGURES OF MERIT FOR PHOTOREFRACTIVE CRYSTALS
Table 1 summarizes the material parameters of interest for BaTiO3, SBN, and BSKNN along with other photo -
refractive crystals, while in Table 2 the corresponding figures of merit are given.
Included is the wave-
length range in which the crystals are known to be photorefractive.
As expected, the ferroelectric crystals BaTiO3, SBN:60, SBN:75, BSKNN, LiNb03, and Knb01 exhibit the
largest photorefractive effect due to their large nbreff values.
Although n -greff /e is approximately equal
in all the materials, the former term apparently is more important for determining the steady state refrac-
tive index change. However, the non -ferroelectric crystals BSO, GaAs, and InP:Fe are significantly faster
than the ferroelectrics.
Owing primarily to their larger mobilities and their generally favorable transport
properties, these materials have photorefractive response times 2 to 3 orders of magnitude smaller than
those of the ferroelectric crystals.
Table 1.
Material Parameters of Select Photorefractive Crystals
Crystal
ni3ri,j(Pm/V)
ni3ri/E(Pm/V)
p(cm2/Vsec
yR(cm3/sec)
BaTiO3
11300 4.9
0.5
5 x 10-8
SBN:60
5100
5.8
0.5
5 x 10-8
SBN:75
17000 5.0
0.5
5 x 10-8
BSKNN
4600 13.2 ---
LiNb03(10,12-15)
320 11.0
0.8
KNb03(16-18) 690
14.0
0.5 ---
BS0(20t21)
82 1.8
0.03
2 x 10-11
GaAs(22'23)
43 3.3
5800.0
---
InP(24)
52
4.1 >5000.0
Table 2.
Figures of Merit of Select Photorefractive Crystals
(Eo = 0 V /cm)
Crystal
Wavelength
Range (pm)
On
ss
t for 1W /cm2,X
S(cm3/J)
BaTiO3
0.4-1.1
4.8 x 10-5
50msec, 0.5pm
2.4 x 10-4
SBN:60
0.4-0.85 3.2 x 10-5
120msec,
0.5pm
5.3 x 10-3
Ce-doped
SBN:60
0.04-0.85
9.6 x 10-5
80 msec, 0.5pm
6.0 x 10-4
Ce-doped
SBN:75
0.4-0.85
4.0 x 10-5
150msec, 0.5pm
3.0 x 104
Ce-doped
BSKNN
0.4-0.85
4.0 x 10-5
200msec,
0.5pm
2.0 x 10-4
LiNb03(10,12-15)
0.4-0.7
10-5 - 10-3
> lsec
5x10-6-5x10-5
KNb03(16-19)
0.4-0.7
5.0 x 10-5
<100msec,
0.05pm 1.7 x 10-4
BS0(25-27)
0.4-0.7
5.0 x 10-6
<
lmsec, 0.05pm
3 x 10-3
GaAs(22'23)
0.8-1.8
6.4 x 10-6
80psec,
1.06pm
5.0 x 10-2
InP:Fe(24)
0.85-1.3
0.2 x 10-6
<100psec,
1.06pm >2 x 10-3
Since the photorefractive sensitivity is proportional to
nss /T, these differences in the values of 4nss
and t between the nonferroelectrics and the ferroelectrics essentially cancel, and large values of S are,
therefore, possible with either type of crystal.
It is interesting to note that the photorefractive sensi-
tivity of SBN:60 is reduced by the addition of cerium, although such a doped crystal exhibits improved
148 / SPIE Vol. 881 Optical Computing and Nonlinear Materials (1988)
S
a
An
E
+
i(E.
+
E
)
o___
a___q
ss
E
+
(E,
+
E
)
o
d
y
(10)
where
E
y
=
yNA
/(yK)
=
drift
field.
Clearly
a
large
steady-state
index
change
is
preferred.
Moreover,
large
mobilities
and
long
recombination
rates
are
generally
desirable
because
these
properties
allow
the
carriers
to
diffuse
or
drift
longer
dis-
tances
before
they
recombine,
thereby
reducing
the
drift
field
Ey.
In
either
case
the
photorefractive
sensitivity
is
increased.
3.
SUMMARY
OF
MATERIAL
PARAMETERS
AND
FIGURES
OF
MERIT
FOR
PHOTOREFRACTIVE
CRYSTALS
Table
1
summarizes
the
material
parameters
of
interest
for
BaTi0
3
,
SEN,
and
BSKNN
along
with
other
photo-
refractive
crystals,
while
in
Table
2
the
corresponding
figures
of
merit
are
given.
Included
is
the
wave-
length
range
in
which
the
crystals
are
known
to
be
photorefractive.
As
expected,
the
ferroelectric
crystals
BaTi0
3
,
SBN:60, SBN:75,
BSKNN,
LiNh0
3
,
and
KnbO^,
exhibit
the
largest
photorefractive
effect
due
to
their
large
nt,r
e
ff
values.
Although
n|r
e
ff/e
is
approximately
equal
in
all
the
materials,
the
former
term
apparently
is
more
important
for
determining
the
steady
state
refrac-
tive
index
change.
However,
the
non-ferroelectric
crystals
BSD,
GaAs,
and
InP:Fe
are
significantly
faster
than
the
ferroelectrics.
Owing
primarily
to
their
larger
mobilities
and their
generally
favorable transport
properties,
these
materials
have
photorefractive
response
times
2
to
3
orders
of
magnitude
smaller
than
those
of
the
ferroelectric
crystals.
Table
1.
Material
Parameters
of
Select
Photorefractive
Crystals
Crystal
BaTi0
3
SBN:60
SBN:75
BSKNN
KNb0
3
(l6
~
19)
BSO
(20,2l)
GaAs
(22
'
23)
InP
(24)
Crystal
BaTi0
3
SBN:60
Ce-doped
SBN:60
Ce-doped
SBN:75
Ce-doped
BSKNN
LiNb0
3
(l
°'
12
- l5)
KNb0
3
(l6
~
19)
BSO
(25-27)
GaAs
(22
>
23)
InP:Fe
(24)
i
ij
11300
5100
17000
4600
320
690
82
43
52
Table
2.
Figures
Wavelength
Range
(ym)
0.4-1.1
0.4-0.85
0.04-0.85
0.4-0.85
0.4-0.85
0.4-0.7
0.4-0.7
0.4-0.7
0.8-1.8
0.85-1.3
n
i
3r
i
of
Merit
of
(En
-
0
An
ss
4.8
x
10~
5
3.2
x
10~
5
9.6
x
10"
5
4.0
x
10"
5
4.0
x
10~
5
10-5
.
10
-3
5.0
x
10~
5
5.0
x
10"
6
6.4
x
10~
6
0.2
x
10~
6
./e.(pm/V)
4.9
5.8
5.0
13.2
11.0
14.0
1.8
3.3
4.1
Select
V/cm)
y(cm
/Vsec
0.5
0.5
0.5
0.8
0.5
0.03
5800.0
>5000.0
Y
R
(cm
5
x
5
x
5
x
2
x
3
/sec)
10"
8
io-
8
io-
8
-
;>-..
-
Photorefractive
Crystals
T
for
!W/cm
2
,X
50msec,
120msec,
80
msec
150msec,
200msec,
>
Isec
<
100msec
<
1msec
80ysec
<100ysec
0.5ym
0.5ym
,
0.5ym
0.5ym
0.5ym
,
0.05ym
,
0.05ym
,
1.06ym
,
1.06ym
S(cm
3
/J)
2.4
x
10"
1
*
5.3
x
10~
3
6.0
x
10"
4
3.0 x
10"
4
2.0
x
Kf
1
*
5
x
10~
6
-
5
x
1.7
x
10~
4
3
x
10~
3
5.0
x
10-
2
>2
x
10"
3
ID'
5
Since
the
photorefractive
sensitivity
is
proportional
to
An
ss
/T,
these
differences
in the
values
of
and
T
between
the
nonferroelectrics
and
the
ferroelectrics
essentially
cancel,
and
large
values
of
S
are,
therefore,
possible
with
either
type
of
crystal.
It
is
interesting
to
note
that
the
photorefractive
sensi
tivity
of
SBN:60
is
reduced
by
the
addition
of
cerium,
although
such
a
doped
crystal
exhibits improved
148
/
SPIE
Vol.
881
Optical
Computing
and
Nonlinear
Materials
(1988)
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values of Anss and T. This implies that not all of the optical absorption in the cerium -doped SBN:60 crystal
contributes to the photorefractive effect.
Finally, the wavelength ranges given in Table 2 indicate that the photorefractive effect in the oxides is
observed only with visible or very near infrared radiation. At longer wavelengths only the semiconductors
such as GaAs and InP are known to be photorefractive.
4.
ACKNOWLEDGMENTS
The research
the U.S.
1.
F.
2. J.
3.
C.
4. J.
5.
L.
6.
J.
7. G.
8.
P.
9.
D.
10.
A.
11. E.
12.
A.
13. H.
14. H.
1977.
15.
R.
16.
P.
17.
P.
18.
P.
19. A.
reported in this paper was supported by grants from the Rockwell International Corporation,
Air Force Office of Scientific Research and the U.S. Army Research Office.
5.
REFERENCES
1986.
Phys 12 (355)
Laeri, T. Tschudi, and J. Llbers, Opt. Commun.47(387) 1983.
Feinberg and R. W. Hellwarth, Opt. Lett. 5 (519) 1980.
T. Chen, D. M. Kim, and D. Von der Linde, IEEE J. Quantum Electron. QE -16 (126) 1980.
P. Hermann, J. P. Herriau, and J. P. Huignard, Appl. Opt. 20 (2173) 1981.
K. Lam, T. Y. Chang, J. Feinberg, and R. W. Hellwarth, Opt. Lett. 6 (475) 1981.
P. Huignard and J. P. Herriau, Appl. Opt. 17 (2671) 1978.
C. Valley, A. L. Smirl, M. B. Klein, K. Bohnert and T. F. Boggess, Opt. Lett. 11 (647)
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Gunter and A. Krumins, Appl. Phys. 23 (199) 1980.
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E. Krumins and P. Gunter, Phys. Stat. Sol.
(a) 55 (K185) 1979.
SPIE Vol. 881 Optical Computing and Nonlinear Materials (1988) / 149
values
of
An
ss
and
T.
This
implies
that
not
all
of
the
optical
absorption
in the
cerium-doped
SEN:60
crystal
contributes
to
the
photorefractive
effect.
Finally,
the
wavelength
ranges
given
in
Table
2
indicate
that the
photorefractive
effect
in
the
oxides
is
observed
only
with
visible
or
very
near
infrared
radiation.
At
longer
wavelengths
only
the
semiconductors
such
as
GaAs
and
InP
are
known
to
be
photorefractive.
4.
ACKNOWLEDGMENTS
The
research
reported
in this
paper
was
supported
by
grants
from
the
Rockwell
International
Corporation,
the
U.S.
Air
Force
Office
of
Scientific Research
and
the
U.S.
Army
Research
Office.
5.
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1.
F.
Laeri,
T.
Tschudi,
and
J.
Libers,
Opt.
Commun.47(387)
1983.
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J.
Feinberg
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R.
W.
Hellwarth,
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5
(519)
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C.
T.
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D.
M.
Kirn,
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D.
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der
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T.
Y.
Chang,
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R.
W.
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6
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1981.
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J.
P.
Huignard
and
J. P.
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17
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G. C.
Valley,
A.
L.
Smirl,
M.
B.
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K.
Bohnert
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11
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D.
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der
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M.
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A.
M.
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Kratzig
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15
(133)
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A.
M.
Glass,
J.
Electron.
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4
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H.
Kurz,
Philips
Tech.
Rev.
37
(109)
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H.
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E.
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W.
Keune,
H.
Engelmann,
U.
Gonser,
B.
Dischler
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A.
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(355)
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R.
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20
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P.
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23
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P.
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F.
Micheron,
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18
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P.
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22 (671)
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A.
E.
Krumins
and
P.
Gunter,
Phys.
Stat.
Sol.
(a)
55
(JC185)
1979.
SPIE
Vol.
881
Optical
Computing
and
Nonlinear
Materials
(1988)
/
149
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