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Two-beam coupling and response time analysis of phase conjugate wave

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Two-beam coupling and response time analysis of phase conjugate wave using a self-pumped configuration with barium titanate
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Kobesky, Jeffrey L
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87 leaves : illustrations ; 29 cm

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Optical phase conjugation ( lcsh )
Nonlinear optics ( lcsh )
Nonlinear optics ( fast )
Optical phase conjugation ( fast )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Includes bibliographical references (leaves 81-82).
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Submitted in partial fulfillment of the requirements for the degree, Master of Science, Department of Electrical Engineering, Department of Computer Science and Engineering.
Statement of Responsibility:
by Jeffrey L. Kobesky.

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University of Colorado Denver
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Full Text
TWO-BEAM COUPLING AND RESPONSE TIME ANALYSIS OF
PHASE CONJUGATE WAVE USING A SELF-PUMPED
CONFIGURATION WITH BARIUM TITANATE
by
JEFFREY L. KOBESKY
B.S., State University of New York, 1985
A thesis submitted to the
Faculty of the Graduate School of the
University of Colorado in partial fulfillment
of the requirements for the degree of
Master of Science
Department of Electrical Engineering and Computer
Science
1989


This thesis for the Master of Science degree by
Jeffrey L. Kobesky
has been approved for the
Department of
Electrical Engineering and Computer Science
by
Arun K. Majumdar
Edward Wall
Date 4--; 4 -


ACKNOWLEDGEMENT
I would like to thank Professor Arun K. Majumdar
for his enthusiasm in this work and resourcefulness in
the equipment supply business.


iv
Kobesky, Jeffrey Lawrence (M. S., Electrical Engineering)
Two-Beam Coupling and Response Time Analysis of Phase
Conjugate Wave using a Self-Pumped Configuration
with Barium Titanate
Thesis directed by Professor Arun K. Majumdar
Two-beam coupling and optical phase conjugation
using a self-pumped configuration in barium titanate
(BaTiOj) is demonstrated experimentally. The 514.5 nm
line of an argon ion laser is used as the source.
Two-beam coupling strength is analyzed as a function of
input angle and power. Build-up time and rise time slope
of the phase conjugate wave are also analyzed as
functions of input angle and power. Miscellaneous
observations during testing are given. A physical model
for two-beam coupling and phase conjugation in a
photorefractive material, such as BaTi03, is briefly
presented. The self-pumping method for producing a phase
conjugate wave is described.
The form and content of this abstract are approved. I
recommend its publication.
Arun K. Majumdar


CONTENTS
CHAPTER
1. INTRODUCTION........................................ 1
2. PHYSICAL MODEL DESCRIBING TWO-BEAM COUPLING
AND PHASE CONJUGATION IN PHOTOREFRACTIVE
MATERIALS......................................... 5
2.1 The Photorefractive Effect..................... 5
2.2 Two-Beam Coupling in
Photorefractive Materials.................... 9
2.3 Phase Conjugation in
Photorefractive Materials................... 12
2.4 Phase Conjugation in BaTi03 using
the Self-Pumped Configuration............... 12
3. EXPERIMENTAL PROCEDURES AND RESULTS................ 16
3.1 Two-beam Coupling in BaTiOg................... 16
3.1.1 Two-Beam Coupling vs. Input
Angles............................... 16
3.1.2 Two-Beam Coupling vs. Relative
Input Power of A^ and A2............. 22
3.2 Response Time of Phase Conjugate
Wave in BaTi03 usin9 the
Self-Pumped Configuration................... 24
4. ANALYSIS OF EXPERIMENTAL DATA...................... 63
4.1 Polynomial Fits to Rise Time Slope Data... 63
4.2 Graphical Representation of Build-Up
Time Data
71


vi
5. CONCLUSIONS.................................... 7 9
BIBLIOGRAPHY.......................................... 81
APPENDIX
A. LIST. OF EQUIPMENT............................. 83
B. INTERFACE TO DATA ACQUISITION SYSTEM........... 84
C. LASER STABILAZATION CONFIRMATION EXPERIMENT.... 8 6


vii
TABLES
Table
3.1 Results of two-beam coupling vs. input
angle experimentation......................... 20
3.2 Results of two-beam coupling vs. input
power experimentation.............................25
3.3 Build-up time of phase conjugate wave as
a function of input power and input angle.........34
3.4 Rise time slope (dP/dt) of phase conjugate
wave as a function of input angle and
input power..................................... 35
4.1 Coefficients of polynomial fits of rise time
slope data for various input angles...............70


FIGURES
Figure
1.1 Phase conjugator used for correcting distortions...2
2.1 Formation of a photorefractive phase grating.......7
2.2 Two-beam coupling in a photorefractive crystal....10
2.3 Four-wave mixing geometry.........................13
2.4 Self-pumped phase conjugation configuration.......14
3.1 Experimental configuration used for testing
two-beam coupling for various input angles........17
3.2 Close-up view of crystal/beam interaction.........19
3.3 Effect of table vibration on beam coupling........21
3.4 Experimental configuration used for determining
two-beam coupling as a function of relative
input intensity...................................23
3.5 Experimental configuration used to test phase
conjugate response time as a function of
input angle.......................................26
3.6 Close-up view of beam/crystal interaction for
testing phase conjugate response time.............28
3.7 Example of oscillatory behavior of phase
conjugate wave ...................................29
3.8 Definition of build-up time and rise time slope...32
3.9 Example of why rise time slope could not be
determined for input powers >10 mW................33


ix
3.10 Phase conjugate build-up time as a function
of input power for various input angles...........36
3.11 Phase conjugate build-up time as a function
of input power for various input angles...........37
3.12 Slope (dP/dt) of phase conjugate wave as a
function of input power for various
input angles......................................38
3.13 Slope (dP/dt) of phase conjugate wave as a function
of input power for various
input angles......................................39
3.14 Response time of phase conjugate wave for various
input angles with 1 mW incident on crystal........40
3.15 Response time of phase conjugate wave for various
input angles with 5 mW incident on crystal........41
3.16 Response time of phase conjugate wave for various
input angles with 10 mW incident on crystal.......42
3.17 Response time of phase conjugate wave for various
input angles with 50 mW incident on crystal.......43
3.18 Response time of phase conjugate wave for various
input angles with 100 mW incident on crystal......44
3.19 through 3.35 Response time of phase conjugate wave
for varying input powers and input angles......45-61
4.1 Polynomial fit for slope of phase conjugate
rise time vs. input power for 0= 50..............64
4.2 Polynomial fit for slope of phase conjugate
rise time vs. input power for 0= 55..............65
4.3 Polynomial fit for slope of phase conjugate
rise time vs. input power for 0= 60
66


X
4.4 Polynomial fit for slope of phase conjugate
rise time vs. input power for 0= 65..............67
4.5 Polynomial fit for slope of phase conjugate
rise time vs. input power for 0= 70..............68
4.6 Polynomial fit for slope of phase conjugate
rise time vs. input power for 0= 75..............69
4.7 Phase conjugate build-up time vs. input power
for 0 = 50.......................................72
4.8 Phase conjugate build-up time vs. input power
for 0 = 55.......................................73
4.9 Phase conjugate build-up time vs. input power
for 0 = 60.......................................74
4.10 Phase conjugate build-up time vs. input power
for 0 = 65.......................................75
4.11 Phase conjugate build-up time vs. input power
for 0 = 70.......................................76
4.12 Phase conjugate build-up time vs. input power
for 0 = 75.......................................77
4.13 Phase conjugate build-up time vs. input power
for 0 = 80.......................................78
B1 Computer interface for phase conjugation
experiments.......................................84
B-2 Low-pass filter used at input to data
acquisition system................................85
B-3 Amplifier used at input to data
acquisition system
85


xi
C-l Experimental configuration used to test
laser stability.............................
87


CHAPTER 1
INTRODUCTION
There exists certain crystals (barium titanate,
potassium tantalate niobate, bismuth silicate and bismuth
germanate, strontium barium niobate, lead lanthanum
zirconate titanate, lithium niobate, and various III-V
semiconductors) that are capable of producing a
phenomenon known as the Photorefractive Effect. This
Effect is used to describe other phenomena, such as
two-beam coupling and optical phase conjugation, that can
be observed in such crystals under the right conditions.
The phase conjugate (pc) wave produced by a
photorefractive crystal is capable of undoing the
distortion that laser beams suffer upon propagation
through as aberrating medium, such as a turbulent
atmosphere or an imaging system. Elimination of such
distortion will aid in, among other things, reducing
error in optical communication links.
Other applications of the pc wave include optical
image processing, holographic storage, automatic tracking
for optical communication links, resonator loss and


2
distortion compensation, and many others.
A major area of concern in the above applications
is response time of the pc wave. Consider Figure 1.1,
FIGURE 1.1 Phase conjugator used for correcting
distortions caused by turbulence.
where an optical beam is to be phase conjugated after
propagation through a turbulent atmosphere. If the
turbulence causes fluctuations that are faster than the
response time of the pc mirror, a pc wave will not be
produced. We must therefore know the response time of the
pc mirror and the maximum frequency components of the
dynamic distorting medium in order to say if a phase
conjugate wave can be produced or not.
Rigorous mathematical treatments can be found
that analytically describe two-beam coupling1, pc mirror


3
reflectivity and pc beam deflection^, as well as other
aspects of the photorefractive effect. The mathematics
involved is complicated and results tend to be inacurate
do to the nonuniformities (crystal abnormalities, optical
spectrum differences, etc.) encountered in actual
experimentation. Furthermore, equations describing
response time for pc waves in photorefractive materials
do not -exist in the literature to our knowledge.
With these facts in mind, the main goal of this
paper is to analyze experimentally obtained response
times of the pc wave for barium titanate (BaTi03) in the
self-pumped^ configuration with the 514.5 nm line of an
argon ion laser as the source. Response time is
analyzed as a function of both input angle and input
power.
It is hoped that these results will be useful to
those who desire an order of magnitude approximation for
the response time of this particular configuration.
It must be kept in mind that the results
presented pertain only to the BaTi03/514.5 nm/self-pumped
configuration. This is, however, a very popular
configuration due to the large pc reflectivity obtained.
Other configurations offer faster response time at the
cost of pc reflectivity. In actual practice, these


4
trade-offs must be made for each specific application to
obtain an optimum phase conjugator.
Additionally, two-beam coupling data is presented
as a function of input angle and input power.
A brief explanation of the photorefractive effect
and how the effect leads to two-beam coupling and phase
conjugation is given. A detailed explanation of these
phenonema is well beyond the scope of this thesis -
therefore many references are given to supplement the
omitted material.


CHAPTER 2
PHYSICAL MODEL DESCRIBING
TWO-BEAM COUPLING AND PHASE CONJUGATION
IN PHOTOREFRACTIVE MATERIALS
This chapter presents a brief explanation of the
photorefractive effect, two-beam coupling, and phase
conjugation in photorefractive crystals. Namely, we will
find an expression that relates two-beam coupling to
polarization, relative beam intensity, wavelength,
refractive index, angle of incidence, optical dielectric
tensor, electro-optic tensor and propagation vector.
Also, phase conjugation will be chatacterized by grating
reflectivity and mirror reflectivity, which are functions
of the same variables that describe two-beam coupling.
Many references are given for further study.
2.1 The photorefractive effect
When two linearly polarized coherent light beams
intersect, a spacial intensity interference pattern is
generated^ given by
I (r) =++Eq^ *Eq2COS (k-L ^-^2 (2.1)
where


6
and
Ejl (r, t) =Eq1cos (k]_ r-tot+e1)
E2 (r, t) =Eq2cos (k2 .r-tot+e1)
(2.2a)
(2.2b)
If the beam intersection occurs in a crystal
which has mobile charge carriers available^, the
interference pattern described by (2.1) will cause these
charge carriers to migrate either into or out of the
bright regions of the pattern (the direction of migration
depends on the sign of the charge carriers). The
resulting charge distribution, which varies sinusoidally
with (2.1), will produce an electric field (given by
Poisson's equation) that will also vary sinusoidally with
(2.1), but shifted in phase by tc/2 radians.
If the crystal containing the charge distribution
does not possess inversion symmetry^, the induced
electric field will produce a refractive index change via
the linear electro-optic effect. The entire process is
illustrated in Figure 2.1.
The process shown in Figure 2.1 is known as the
photorefractive effect and crystals capable of producing
the effect are called photorefractive crystals. Most of
the theory is agreed upon amoung scientists, but there
are still areas of controversy such as the origin of
the mobile charge carriers.


7
FIGURE 2.1 Formation of a photorefractive index grating.
From top to bottom: Light with spatially periodic
intensity I(x) rearranges the charge density p (x) in
the material. The mobile charges, here with positive
charge, tend to accumulate in the dark regions of the
intensity pattern. The resulting periodic charge
distribution p(x) causes a periodic electrostatic field
E(x) by Poisson's equation. This electric field then
causes a change in the refractive index An of the
crystal by the linear electro-optic (Pockels*) effect.
(From [7].)


8
The derivation of an analytical expression for
E(r) is somewhat complex; there is no need for
derivation here many articles do this quite elegantly"^.
Here, we just state that, in the absence of an externally
applied field,
E(r)=- (kBT/q)m[k/l+(k/kg)2]sin(k*r) (2.3)
where kBT is the thermal energy of the crystal lattice, q
is the charge of the mobile charge carriers, m is a
dimensionless modulation index given by
m-2E1*2E2*/(I1+I2)# (2-4)
k is a grating wave vector given by
k=k1-k2, (2.5)
k is the absolute value of k, and kg is a constant of the
material that depends on the number density N of charge
carriers available for charge migration according to
k0=(Nq2/££0kBT)1/2. (2.6)
Note that upon comparison of (2.3) with (2.1), we see
I(r) is 90 out of phase with E(r), as shown in Figure
2.1.


9
2.2 Two-beam coupling in photorefractive materials
When two beams of the same optical frequency
intersect in a photorefractive crystal, intensity can be
transferee! from one beam to the other. The amount of
two-beam coupling depends on several parameters (to be
discussed shortly) and can be quite large. In BaTiOg, for
example, one beam can transfer essentially all its power
to the other beam over an interaction distance of only a
few millimeters9. The direction of the crystal's c axis
determines the direction of power transfer as shown in
Figure 2.2.
The derivation of equations describing two-beam
coupling is complicated and only the results are shown
here (see [7] for details). The amplitude % of the change
in the optical susceptability RE [j£exp (ik* r) ] caused by
E(r) is
X=eco- (tt-Ek) -Eq, (2.7)
where 6^ is the optical dielectric tensor at (0 and 9t is
the third-rank electro-optic tensor. Also, defining
Ks[ico/2nccos (0) ] [%/m]
(2.8)


10

FIGURE 2.2 Two-beam coupling in a photorefractive
crystal. The direction of the positive c axis is shown.
In (a) two'incident beams of equal intensity emerge
with unequal intensity. In (b) the beams are misaligned
and do not intersect in the crystal, therefore no
coupling occurs. In (c) the crystal is rotated 180 and
the direction of intensity transfer is opposite to (a).
(From [9] ) .


11
where 0 is the small angle that the incident beam makes
with a normal to the front crystal face. We can write the
coupled-wave equations for the intensities as
O/az)I1=2RE[K1^2]I1I2/I0 (2.9a)
(3/3z)l2=-2RE[K1^2]I1I2/Io (2.9b)
where
k1,2=tei*K*£2) (£l£2*) (2.10)
and
I0=Ii+I2- (2.11)
Equations (2.9a) and (2.9b) are the main results
of this section. Together they describe how the intensity
changes as the beams propagate in the z direction.
An important point to be made here is that
two-beam coupling provides a way to measure both the sign
and the density of the mobile charge carriers. The sign
of the mobile charges is determined by the direction of
two-beam coupling with respect to the crystal's c axis.
The density of mobile charge carriers is found by the
variations of two-beam coupling strength with the
crossing angles of the two beams, because coupling is at


12
a maximum when k=kg (i.e. since we know the value of k,
we can plug it in (2.6) and solve for N). These facts are
valuable in understanding the physics involved in the
photorefractive process.
2.3 Phase conjugation in photoretractive materials
Phase conjugation in photorefractive materials is
a difficult topic to describe briefly, therefore its
complete description will not be given. There are many
good references, such as (2], available for the reader
who desires all the details.
We will, however, show the beam/crystal
interaction used to obtain a phase conjugate wave in a
photorefractive material. This interaction, known as four
-wave mixing, is shown in Figure 2.3.
Ai and A2 are known as pump beams. Their job is
to "prepare" the material so that a phase conjugate wave
can be produced. A2 is called the probe beam. The phase
conjugate beam, A4, is derived from A2 after the medium
is properly prepared by A^ and A3.
2.4 Phase conjugation in BaTiO^ using the self-pumped
configuration
The geometry used to produce a phase conjugate
wave in BaTi03 using the self-pumped configuration is


PHOTOREFRACTIVE
CRYSTAL
A
3
FIGURE 2.3 Four wave mixing geometry used to produce a
phase conjugate wave. A^ and A3 are the pump beams, A
is the probe beam, and A4 is the phase conjugate of
A2.(From [7].)


14
BaTiO
3
INCIDENT
BEAM
FANNING
FIGURE 2.4 Geometry used for obtaining a phase conjugate
wave in the self-pumped configuration. Four wave mixing
is achieved by using only one input beam and relying on
properties of the photorefractive crystal (such as beam
fanning) to generate the needed pump beams.


15
shown in Figure 2.4. Note that only a single input beam
is required (hence the term "self-pumped"). The two pump
beams required for four-wave mixing are derived from the
incident probe beam. Beam fanning!^ in the crystal is
responsible for the ray directions shown in Figure 2.4.
The pump beams are generated through internal reflections
near the edge of the crystal.
The edge of the crystal acts as a retroreflector
for the pump beams therefore the beam interaction is
self-aligned. This property makes the self-pumped
configuration relatively simple to use and also allows
phase conjugation to be achieved at a large variety of
input angles. These desirable properties come at the cost
of lower mirror reflectivity and slower response time
compared to the configuration of Figure 2.3. However, due
to its relative ease of implimentation and practical
importance!!' !^/ 13^ the self-pumped configuration will be
the only one used in this thesis.


CHAPTER 3
EXPERIMENTAL PROCEDURES AND RESULTS
This Chapter describes experimental procedures
and results obtained pertaining to two-beam coupling and
phase conjugation testing.
Experimentation was done in the Electro-Optics
Laboratory at the University of Colorado at Denver.
A list of test equipment used appears in Appendix
A. A description of the data acquisition interface
appears in Appendix B.
All data was taken using an argon ion laser at
X = 514.5 nm.
3.1 Two-beam Coupling in BaTiQ^
In this section we present experimental
procedures and results obtained in two-beam coupling
experiments. In particular, we investigate two-beam
coupling as a function of input angle (section 3.1.1) as
well as input power (section 3.1.2).
3.1.1 Two-beam Coupling vs. Input Angles
The experimental set-up for this test is shown in
Figure 3.1 and a close-up of the crystal/beam interaction


17
VARIABLE
NEUTRAL
DENSITY
FIGURE 3.1 Experimental configuration used for testing
two-beam coupling for various input angles. The input
angles were constrained to H1 H2 0H*


18
is shown in Figure 3.2.
Test objective. We wish to determine how beam
coupling varies as a function of input angles.
Procedure. Keep the power in beams A-j_ and A2
constant at 10 mW for all data the variable neutral
density filter is used to accomplish this.
Vary input angles (with constraint 0{jl=H2 =
from -12 to ~29 and record the powers and PA2
(i.e. observe beam coupling at various input angles).
Angles are varied by adjusting M-j_, M2, and crystal
position.
The experiment will be repeated three times, on
three different days, to see how repeatable the data
is.
Results. See Table 3.1.
Miscellaneous observations.
1. Assume we have = PA2 =10 mW incident on
the crystal. In the steady state we have coupling from A-^
to A2 for example, let PAii= 3.4 mW and PA2,=5*7 mW- If


19
FIGURE 3.2 Close-up view of crystal/beam interaction. A]_
and A2 are incident at the same angle from the normal to
the crystal face. The polarization vector of both beams
is parallel to the crystal's c axis.


20
TABLE 3.1
Results of two-beam coupling vs. input angle
experimentation. PA1i and P^1 refer to measurements
taken at the output of the crystal (see Figure 3.1).
H
Al'
RUN #1
A2'
A2'
Al'
Al1
RUN #2
A2
A2'
Al'
Al'
RUN #3
A2 1
A2 '
Al'
12.0
3.30
6.40
1.94
3.20
6.30
1.97
3.35
6.15
1.84
14.5
3.15
6.45
2.05
3.15
6.45
2.05
3.05
6.40
2.10
17.0
3.10
6.20
2.00
2.95
6.30
2.14
3.15
6.10
1.94
20.0
2.95
6.15
2.08
2.90
6.05
2.09
2.95
6.10
2.07
22.5
2.80
5.55
1.98
2.80
5.60
2.00
2.85
5.85
2.05
26.0
2.80
4.80
1.71
2.80
5.15
1.84
2.80
5.30
1.89
29.0
2.80
4.00
1.43
2.75
4.25
1.55
2.85
3.95
1.39


21
we block Alf it takes ~80 sec for PA2 to settle into
steady state. If instead we block A2, ?A1' settles into
steady state almost instantaneously.
Also, if we restore beam Alf PA21 goes back to
5.7 mW in ~10 sec (note much faster than decrease this
is probably due to the phase grating already being set up
when A^ is restored).
2. Table vibrations change PA1 and
drastically, whereas PA1 and PA2 are unaffected by
vibration. However, this effect is seen only when both
beams are in the crystal. Pictorially,
FIGURE 3. Effect of table vibration on beam coupling.


22
3. Suppose we:
Move the crystal with beams incident upon it (i.e.
erase the crystal).
Block both beams with the crystal still erased.
Allow A2 to enter the crystal; beam fan appears in ~2
sec with PA2 = 10 mW.
Block A2/ then let A2 be incident again; this time
the beam fan appears instantaneously because the phase
grating is already established.
4. Beam coupling was unstable (oscillatory) for
the two largest angles of 26 and 29.
3.1.2 Two-beam Coupling vs. Relative Input Power of A^
and A2
The experimental set-up for this test is shown in
Figure 3.4.
Test objective. We wish to determine how beam
coupling varies as a function of relative input power.
Procedure. The input angles, 0H1 = 0H2 = 0H, will
be kept constant at 14.4 throughout the test. PA2 will
be kept constant at 10 mW throughout the test. PAi will


23
VARIABLE
NEUTRAL
DENSITY
FIGURE 3.4 Experimental configuration used for
determining two-beam coupling as a function of relative
input intensity. 0H is kept constant at 14.4. PA2 is
constant at 10 mW. PA^ varies from 10 mw to 0 mW in
increments of 0.5 mW. The beam/crystal interaction is
the same as in Figure 3.2.


24
be varied from 10 mW to 0 mW in increments of 0.5 mW and
beam coupling will be observed at each increment (i.e.
PA1' an<* PA2' be measured) .
The power in is varied by adjusting the
variable neutral density filter.
The crystal is erased after each data point by
moving the crystal while the incident beams are present.
The experiment was done twice for repeatability
purposes.
Results. See Table 3.2.
Miscellaneous observation. For the lower powers
of (<4.00 mW), like the higher 0H, the beam coupling
is oscillatory that is PA2' Is oscillatory and P^i' is
relatively stable.
3.2 Response time of phase conjugate wave in BaTiO^
using the self-pumped configuration.
This section describes experimental set-ups,
procedures, and results pertaining to the response time
of the phase conjugate wave in a self-pumped crystal of
BaTi03. The response time is determined as a function of
input angle and input power. The experimental set-up is
shown in Figure 3.5 and a close up view of the


25
TABLE 3.2
Results of two-beam coupling vs. relative input power
experiment. See Figure 3.4 for meaning of P sub's.
RUN #1 P h]/' RUN #2 P A2//>
p P p P A P p At
A1 A2 Al' A2' Al' Al' A2' Al'
10.0 10. 0 3.30 6.20 1.88 3.15 6.25 1.98
9.5 3.15 6.10 1.94 3.05 . 6.15 2.02
9.0 2.95 6.05 2.05 2.95 6.00 2.03
8.5 2.90 5.95 2.05 2.80 5.95 2.13
8.0 2.70 5.90 2.19 2.70 5.90 2.19
7.5 2.60 5.75 2.21 2.60 5.75 2.21
7.0 2.45 5.55 2.27 2.45 5.60 2.29
6.5 2.30 5.50 2.39 2.25 5.50 2.44
6.0 2.10 5.40 7.57 7.10 5.35 2.55
5.5 1.95 5.30 2.72 1.95 5.25 2.69
5.0 1.80 5.25 2.92 1.80 5.15 2.86
4.5 1.60 5.05 3.16 1.65 5.05 3.06
4.0 1.45 4.85 3.34 1.45 4.90 3.38
3.5 1.30 4.85 3.75 1.25 4.75 3.80
3.0 1.10 4.75 4.32 1.10 4.15 3.77
2.5 0.90 4.60 5.11 0.95 3.90 4.10
2.0 0.75 3.90 5.70 0.75 3.65 4.87
1.5 0.60 3.60 6.00 0.60 3.45 5.75
1.0 r 0.40 3.35 8.38 0.40 3.30 8.25
0.5 0.20 3.20 16.00 0.20 2.90 14.50
0.0 10. 0 0.026 2.65 101.92 0.04 2.50 62.50


26
vertical
polarization
+
argon
X =514.5 run
apature setting is 5
spot size is 1.25 nun in diameter
-2
polarization
rotator
horizontal
polarization
I
detector
-o
data
acquisition
system
FIGURE 3.5 Experimental set-up used to test phase
conjugate response time as a function of input angle


27
beam/crystal interaction is shown in Figure 3.6. All the
important parameters can be found in these two figures.
Test objective. We wish to determine the response
time of the phase conjugate wave build-up for various
input angles and input powers.
Procedure. First, make sure the crystal is erased
for each data point. Then allow the beam to be incident
upon the crystal at the same instant the data acquisition
system starts to acquire data from the detector. We then
monitor the output of the detector as a function of time.
This essentially monitors the build-up of the phase
conjugate wave as a function of time.
This process is repeated over a number of
different input angles and input powers. In particular,
we vary the input angle 0 from 50 to 80 in increments
of 5. Also, we vary input power from 1 mW to 100 mW in
logarithmic intervals i.e.(1,2,...,9,10,20,...100).
Comments. During the experiment it was
discovered that the phase conjugate beam becomes
oscillatory for input powers greater than ~3 mW. This
oscillation did not start until the phase conjugate wave
reached a certain peak value. An example of this
phenomenon is shown in Figure 3.7, where we show the


28
FIGURE 3.6 Close-up view of beam/crystal interaction
used for testing phase conjugate response time. Note
that the input beam is polarized parallel to the
crystal's c axis this condition yields maximum pc
reflectivity. Also, the beam travels in the
direction of the positive c axis (in the direction of
the arrow) which is necessary for phase conjugation
to occur in the self-pumped configuration.


PHASE CONJUGATE POWER (uW)
55 DEG 3mW
FIGURE 3.7 Example of oscillatory-nature of phase conjugate wave.
N>
vO


30
build-up of the phase conjugate wave throughout time.
After discovery of this phenomenon, a reference1^
was found where past experimenters experienced the same
effect. Reference [14] states the oscillation phenomenon
is most likely induced by four-wave mixing of the pump
beam with a self-induced reference beam produced by
scattered light amplified by two-beam coupling, and its
retroreflected beam from the face perpendicular to the
entrance face.
Whatever the explanation, we found it necessary
to varify that the oscillation was not produced by the
instability of our laser source due to the phase
conjugate wave being fed back into the cavity. An
experiment was conducted, which is described in Appendix
C, that semi-satisfied us that the oscillations are not
caused by an unstable source.
We also found it necessary, because of the
oscillations, to characterize the response time by using
two seperate parameters. These parameters and their
discription are as follows:
1.Build-up time. This is a measure of time from
the instant the input beam is incident on the crystal to
the instant a phase conjugate wave appears.
2.Rise time slope. This is a measure of the


31
slope, dP/dt, of the initial rise of the phase conjugate
wave.
These two quantities are pictured in Figure 3.8.
Build-up time was calculated for all data points. Rise
time slope, however, was only calculated for input powers
from 1 mW to 10 mW; this is because of the slope being
impossible to determine at higher powers due to the
intense oscillations (see Figure 3.9).
Rise time slope and build-up time will be
collectively refered to as response time.
Results. Build-up time is tabulated in Table 3.3.
Rise time slope is found in Table 3.4. Both of these
tables are plotted in Figures 3.10 through 3.13 for
graphical comparison purposes.
Plots of the actual data taken by the data
acquisition system can be found in Figures 3.14 through
3.35. These plots are constructed to yield a comparison
between response time for varying input angles (Figures
3.14 through 3.18) and response time for varying input
powers (Figures 3.19 through 3.35).
It would be impossible at this time to completely
analyze the data and give physical and mathematical
meaning to it (that is, in addition to the information
presently found in the literature). It is


160
140
120
100
eo
60
40
20
0
-20
I
GUR]
60 DEG 6mW
50 100 150 200 250
TIME (sec)
3.8 Definitions of build-up time and rise time slope.
U)
ro


PHASE CONJUGATE POWER (uW)
65 OEG 90mW
FIGURE 3.9 Example of difficulties encountered in defining rise time slope for
input powers greater than 10 irfrJ. Here, the input pcwer is 90 irf'7.


34
TABLE 3.3
Build-up time of phase conjugate wave as a function of
input power and input angle. All entries are build-up
time in seconds.
\ 0 N. (deg) P \ (mW) X 50 55 60 65 70 75 80
1 120 163 121 99 573 >600 >600
2 76 78 61 52 62 >600 >600
3 38 70 24 13 48 >600 >600
4 35 58 45 37 16 134 >600
5 28 27 29 22 30 65 >600
6 18 33 28 28 26 43 >600
7 16 17 24 21 22 36 >600
8 17 26 18 18 18 31 >600
9 16 23 14 20 18 28 *
10 13 20 13 15 14 25 74
20 5 9 7 14 15 21 23
30 3 5 4 7 8 15 13
40 2 3 4 4 5 10 10
50 1 2 2 4 4 7 7
60 1 2 2 3 3 5 8
70 1 2 2 2 2 4 7
80 1 1 2 3 2 4 6
90 1 1 2 2 2 3 4
100 1 1 2 2 2 3 3
* Start of pc wave is hard to determine for this point.


35
TABLE 3.4
Rise time slope (dP/dt) of phase conjugate wave as a
function of input angle and input power.
\ (deg) p \ (mW) 50 55 60 65 70 75 80
1 0.20 0.13 0.07 0.04 0.00 0.00 0.00
2 0.53 0.48 0.26 0.18 0.05 0.00 0.00
3 0.83 1.20 0.43 0.37 0.16 0.00 0.00
4 2.33 2.28 0.67 0.42 0.28 0.10 0.00
5 3.09 4.00 0.81 0.79 0.32 0.15 0.00
6 4.50 4.50 2.00 1.25 0.58 0.26 0.00
7 7.00 8.00 1.69 1.49 0.55 0.35 0.00
8 8.00 11.7 3.65 3.06 1.10 0.40 0.00
9 8.67 11.5 5.07 3.63 1.43 0.75 *
10 9.20 20.0 5.73 4.60 3.23 0.78 0.08


POWER (mW)
FIGURE .3.10 Phase conjugate build-up time as a function of input power
for various input angles. Data was taken using the experimental
set-up of Figure 3.5.
U>
ON


POWER (mW)
FIGURE 3.11 Phase conjugate build-up time as a function of input power
for various input angles. Data was taken using the experimental set-up
of Figure 3.5.
LO


5
4
dP/dt.
of P.C.
WAVE
1
o
1 23456789 10
POWER INCIDENT ON CRYSTAL (mW)
FIGURE 3.12 Slope (dP/dt) of phase conjugate wave as a function of input
power for various input angles. Data was taken using the experimental
set-up of Figure 3.5.
+ O = 65
= 70<
A = 75(
= 80(
O
O
O
II
O
o
o
a t 8 t i I t .


25
20--
dP/dt
of P.C.
WAVE 10-
O = 50
= 55
A 60
= 65
Oft---------f-
8
4
8
o
o
£
4-
A
A *

h----h---h
12345 6 789
()
10
POWER INCIDENT ON CRYSTAL (mW)
FIGURE 3.13 Slope (dP/dt) of phase conjugate wave as a function of input
power for various input angles. Data was.taken using the experimental
set-up of Figure 3.5.


30
25
20
15
10
5
0
-5
I
IRE
itfi'J
100
200
300
TIME (sec)
400
500
60
1.14 Response time of phase conjugate wave for various input angles wit
ncident on crystal.


PHASE CONJUGATE POWER (uW)
FIGURE 3.15 Response time of phase conjugate wave for various input angles with
5 mW incident on crystal.


250
200
150
100
50
0
-50
0
GURE
10 irf
0=65
6=75
-i---------1---------1----------1---------1---------1---------1___,_____i_________i_
10 20 30 40 50 60 70 60 90
TIME (sec)
3.16 Response time of phase conjugate wave for various input angles wi
f incident on crystal.


1400
1200
1000
BOO
600
400
200
0
-200
(
:gure
50 ill
30
TIME (aec)
1.17 Response time of phase conjugate wave for various input angles with
incident on crystal.
>
U>


3500
3000
2500
2000
1500
1000
500
0
-500
I
GURE
100 l
9=00
10
15
--------1------
20
TIME (sec)
25
30
1_
35
40
3.18 Response time of phase conjugate wave for various input angles with
incident on crystal.
-O'
4>


PHASE CONJUGATE POWER (uW)
100
1
FIGURE 3.19 Response time of phase conjugate wave for varying input powers
with the input'angle equal to 50 'degrees.


140
120
100
80
60
40
20
0
-20
I
[GUI
20 40 60 80 100 120 140 160
TIME (sec)
3.20 Response time of phase conjugate wave for varying input powers
input angle equal to 50 degrees.


1600
1400
1200
1000
800
600
400
200
0
-200
I
TGUF
3.21 Response time of phase conjugate wave for varying input powers
the input angle equal to 50 degrees.


3500
3000
2500
2000
1500
1000
500
0
-500
I
IGOR
i------------1-----------1-----------1-----------1-----------r
------1-------1------1________i______i--------1______i________i______i________
0.5 1 1.5 2 2.5 3 3.5 4 4.5 5
TIME (sec)
3.22 Response time of phase conjugate wave for varying input powers
the input angle equal to 50 degrees.


PHASE CONJUGATE POWER (uW)
FIGURE 3.23 Response time of phase conjugate wave for varying input powers
with the input angle equal to 60 degrees.
p>
VO


PHASE CONJUGATE POWER (uW)
FIGURE 3.24 Response time of phase conjugate wave for varying input powers
with the input angle equal to 60 degrees.
Ul
o


PHASE CONJUGATE POWER (uW)
FIGURE 3.25 Response time of phase conjugate wave for varying input pcw&rs
with the input angle equal to 60 degrees.
Ln


PHASE CONJUGATE POWER (uW)
1800
1600
1400
1200
1000
800
600
400
200
0
-200
0 10 20 30 40 50 60
TIME (sec)
FIGURE 3.26 Response time of phase conjugate wave for varying input powers
with the input angle equal to 60 degrees.


PHASE CONJUGATE POWER (uW)
FIGURE 3.27 First five seconds of Figure 3.26.
Ln
LO


PHASE CONJUGATE POWER (uW)
FICURE 3.28 Response time of phase conjugate wave for various input powers
with the input angle equal to 70 degrees.
Ln
4N


PHASE CONJUGATE POWER (uW)
140
FIGURE 3.29 Response time of phase conjugate wave for various input pcwers
with the input angle equal to 70 degrees.


PHASE CONJUGATE POWER (uW)
FIGURE 3.30 Response time of phase conjugate wave for various input powers
with the input angle equal to 70 degrees.
Ui
ON


80
60
40
20
0
20
t------------1------------1-------------1------------1------------1------------1------------1------------r

60 niW
30 itW
MMrw~v
20 mW
_l-1_I_I_I_:_I_I_I_
23456789 10
TIME (sec)
3.31 First ten seconds of Figure 3.30.
Ln


BOO
700
600
500
400
300
200
100
0
100
I
[GUT
_j----------------1__________________i_________________i_________________i_________________
5 10 15 20 25 30
TIME (sec).
3.32 Response time of phase conjugate wave for varying input powers
the input angle equal to 70 degrees.
Ln
00


PHASE CONJUGATE POWER (uW)
0 100 200 300 400 500 600
TIME (sec)
FIGURE 3.33 Response time of phase conjugate wave for varying input pcwers
with the input angle equal to 80 degrees.
Ui
v


350
300
250
200
150
100
50
0
-50
I
IGU1
ii---------1---------1---------1---------r
_i_________i_________i_
10 20 30
_l________I---------1________I---------1________L_
40 50 60 70 80 90
TIME (sec)
3.34 Response time of phase conjugate wave for varying input powers
the input angle equal to 80 degrees.


PHASE CONJUGATE POWER (uW)
FIGURE 3.35 Response time of phase conjugate wave for varying input powers
with the input angle equal to 80 degrees.


62
hoped, however, that the data taken will someday lead to
or explain new theories and observations of the
photorefractive effect. It is also hoped that the data
will be of value to those who are considering the use of
these devices for a particular application.
Although it is beyond the scope of this thesis to
do a complete analysis of the data and possibly arrive at
new physical concepts, we do, in Chapter 4, give
polynomial fits of the data for slope of the phase
conjugate rise time vs. input power for the various input
angles. To the best of our knowledge, this analysis does
not appear in any of the literature. It is our opinion
that this is a very practical analysis.


CHAPTER 4
POLYNOMIAL FITS FOR RISE
TIME SLOPE DATA
This Chapter gives polynomial fits to rise time
slope data (section 4.1) and graphical representations of
build-up time data (section 4.2).
4.1 Polynomial fits for rise time slope data
This section gives polynomial fits for the data
in Table 3.4, which gives rise time slope of the phase
conjugate wave as a function of input angle and input
power. The fits are done in a least squares sense.
Figures 4.1 through 4.6 contain the data points
(circles), polynomial fits (solid lines), and the
coefficients of the polynomials (Cg, C2, C3) Each
figure corresponds to a different input angle.
All figures are fit with a third degree
polynomial of the form
Slope = dP/dt = C0+C1P+C2P2+C3P3 (4.1)
where P is input power to the crystal and the C's are
coefficients. These coefficients are tabulated in Table
4.1.


10
9
e
7
6
5
4
3
2
1
0
4.1
Polynomial fit (solid line) of data (circles) for slope of phase
rise time vs. input paver at 50Q input angle.
ON


SLOPE OF PC RISE TIME (dP/dt)
FIGURE 4.2 Polynomial fit (solid line) of data (circles) for slope of phase
conjugate rise time vs. input pcwer at 55 input angle.
Ln


SLOPE OF PC RISE TIME (dP/dt)
FIGURE 4.3 Polynomial fit (solid line) of data (circles) for slope of phase
conjugate rise time vs. input power at 60 input angle.
ON


SLOPE OF PC RISE TIME (dP/dt)
FIGURE 4.4 Polynomial fit (solid line) of data (circles) for slope of phase
conjugate rise time vs. input power at 65 input angle.
CT\


SLOPE OF PC RISE TIME. (dP/dt)
FIGURE 4.5 Polynomial fit (solid line) of data (circles) for slope of phase
conjugate rise time vs. input power at 70 input angle.
ON
00


SLOPE OF PC RISE TIME (dP/dt)
FIGURE 4.6 Polynomial fit (solid line) of data (circles) for slope of phase
conjugate rise time vs. input power at 75 input angle.
ON
VO


70
To our knowledge this type of analysis does not
exist in the available literature. It is hoped that the
polynomial fits will be of practical value to anyone who
is considering using BaTiC>3 for a particular phase
TABLE 4.1
Coefficients of polynomial fits of rise time slope data
for various input angles. The data was fit in a least
squares sense.
0 (deg) C C C C
0 1 2 3
50 1.2383 -1.3672 0.5051 -0.0289
55 -1.0753 1.1025 -0.1617 0.0252
60 0.2639 -0.1520 0.0500 0.0023
65 0.1800 -0.1057 0.0360 0.0020
70 -0.6609 0.7058 -0.1730 0.0139
75 0.0227 -0.0387 0.0137 -0.0002
conjugation application. It must be remembered that this
analysis is useful only for the 514.5/BaTi03/self-pumped
configuration. This is, however, a popular configuration
due to the high phase conjugate reflectivity and relative
ease of use.


71
4.2 Graphical representation of build-up time data
Figures 4.7 through 4.13 are plots of the data
presented in Table 3.3 concerning .the build-up time of
the phase conjugate wave as a function of input power at
the various input angles; they are shown here as a matter
of practical importance. The negative exponential nature
of these plots is evident and becomes more pronounced
when a linear scale is used as the ordinate.


5
5
A
5
3
5
2
5
1
5
0
50 DEGREES
O
0
0
0
0
-------1------1_______i_______i_______I_______i_______i i_______i___
10 20 30 40 50 60 70 60 90
POWER INCIDENT ON CRYSTAL (mW)
4.7 Build-up time of phase conjugate wave vs. input paver for 50
100
input
ts>


NATURAL LOG OF BUILD-UP TIME
6
55 DEGREES
o
5 -
a
o
4 0
a
a
3 -
2 -
1 -
0 ----
0
FIGURE 4.
angle.
i-------1--------1--------1--------1--------1--------1--------r
o
o
o
0
0
o
o
_i-------1--------1-------1--------1-------1--------1-------i 4 ----i
10 20 30 AO 50 60 70 BO 90 100
POWER INCIDENT ON CRYSTAL (mW)
8
Build-up time of phase conjugate wave vs.
input power for 55
input
uj


5
5
4
5
3
5
2
5
1
5
60 DEGREES
--------1--------1--------T--------1------:-1-----
0
T
O
O
0
0
0
o o
o o o o o
_______I______I_______I_______I-------1_______I_______I-------1-------1___
10 20 30 40 50 60 70 80 90
POWER INCIDENT ON CRYSTAL (mW)
4.9 Build-up time of phase conjugate wave vs. input power for 60
100
input i.
45-


5
5
4
5
3
5
2
5
1
5
I
RE
ci]
65DEGREES
t-------1--------1-------1-------1-------1-------1--------1-------r
o
o
o
o
0
0 0
o
0
0 0
_______i_______i________i_______i_______i____:___i_______i________i_______i____
10 20 30 40 50 60 70 60 90
POWER INCIDENT ON CRYSTAL (mW)
4.10 .Build-up time of phase conjugate wave vs. input power for 65
100
input
^1
Ui


NATURAL LOG OF BUILD-UP TIME
7
70 DEGREES
6 -
5 -
o
4 -
l
3 -
2 -
1 -
0
0
FIGURE 4
angle.
t--------------1--------------1--------------1--------------1--------------1--------------1--------------1--------------r
o
0
0
00
0
0
0
0
0
0
o
I________I_______I________I________L_______I________I_______I________I_______
10 20 30 40 50 60 70 60 90 100
POWER INCIDENT ON CRYSTAL (mW)
.11 Build-up time of phase conjugate wave vs. input power for 70 input
ON


NATURAL LOG OF BUILD-UP TIME
5 ---
4.5 -
4 -
3.5 -
3 -
2.5 -
2 -
1.5 -
1 ---
0
FIGUPE 4
angle.
75 DEGREES
i i--------1--------1--------1-------1--------1--------1-------r
o
o
0
D
_____I_______I_______I_______I_______I_______I_______I_______I_______I______I
10 20 30 40 50 60 70 00 90 100
POWER INCIDENT ON CRYSTAL (mW)
.12 Build-up time of phase conjugate wave vs. input power for 75 input


NATURAL LOG OF BUILD-UP TIME
4.5
BO DEGREES
4 -
3.5 -
3 -
2.5 -
2 -
1.5 -
1
10
FIGURE 4
angle.
T
0
0
0
0
O
0
______I________I________I________I_______I________I________I________I________I
20 30 40 50 60 70 BO 90 100
POWER INCIDENT ON CRYSTAL (mW)
.12 Build-up time of phase conjugate wave vs. input power for 80 input
00


CHAPTER 5
CONCLUSIONS
Due to the limited amount of time available,
conclusions are drawn only on the most elementary
analyses of the experimental data. Many other worthwhile
endeavors are possible, such as verification of the
theory by data analysis.
With this in mind, the following conclusions are
made from the experimental data contained in this paper:
1. Two-beam coupling power transfer is largest
for 14.5 < 6< 20.0.
2. All crystal interactions are sensitive to
vibration.
3. Once a phase grating is set-up in a crystal it
stays there until it is erased (at least for a day or
so) .
4. Beam coupling is oscillatory for input angles
equal to or greater than 26.
5. Beam coupling is oscillatory for input powers
(of A^) less than 4 mW.
6. The phase conjugate beam becomes oscillatory
for input powers greater than ~3 mW.


80
increased.
8. Build-up time decreased slightly as input
angle 0 decreased with constraint 50 ^ 0 < 80.
9. Rise time slope (dP/dt) of the phase conjugate
wave is greatest for 0 =55.
10. Rise time slope (dP/dt) of the phase
conjugate wave increased with increasing input power.


BIBLIOGRAPHY
[1] M.B.Klein,G.C.Valley, "Beam coupling in BaTi03 at
442 nm,"J.Appl.Phys.,57(11),pp.4901-4905,1985.
[2] M.Cronin-Golomb,B.Fischer,J.O.White,A.Yariv,
"Theory and applications of four-wave mixing in
photorefractive media,"IEEE J.of Q.E.,vol.QE-20,
pp.12-30,1984.
[3] K.R.MacDonald,J.Feinberg,"Theory of a self-pumped
phase conjugator with two coupled interaction
regions,"J.Opt.Soc.Am.,vol.73,no.5,pp.548-553,1983.
[4] E.Hecht,OPTICS,Addison-Wesley,pp.334-336,1987.
[5] M.B.Klein,R.N.Schwartz,"Photorefractive effect in
BaTi03microscopic origins," J.Opt.Soc.Am.B,vol.3,
no.2,pp.293-305,1986.
[6] A.Yariv,OPTICAL ELECTRONICS,HRW,ch.9,1985.
[7] R.A.Fisher,Editor,OPTICAL PHASE CONJUGATION,Academic
Press,ch.11,1983.
[8] D.L.Staebler,J.J.Amodei,"Coupled wave analysis of
holographic storage in LiNb03,"J.Appl.Phys.,vol.43,
no.3, pp.1042-1049,.1972.
[9] J.Feinberg,D.Heiman,A.R.Tangruay Jr.,R.W.Hellwarth,
"Photorefractive effects and light induced charge
migration in barium titanate,"J.Appl.Phys.,51, pp.
1297-1305,1980.
[10] J.Feinberg,"Asymetric self-defocusing of an optical
beam from the photorefractive effect,"J.Opt.Soc.Am.,
vol.72,no.l,pp 46-51,1982.


82
[11] R.K.Jain,K.Stenersen,"Small-Stokes-shift frequency
conversion in single mode birefringent fibers,
Opt.Comm.,vol.51,no.2,pp.121-126,1984.
[12] R.A.McFarlane,D.G.Steel,"Laser oscillation using
resonator with self-pumped phase conjugate mirror,"
Opt.Lett.,8,pp.208-210,1983.
[13] J.Feinberg,"Continuous-wave self-pumped phase
conjugator with wide field of view,"Opt.Lett.,8,
pp.480-482,1983.
[14] P.Gunter,E.Voit,M.Z.Zha,"Self-pulsation and optical
chaos in self-pumped photorefractive BaTiOg,"
Opt.Comm.,vol.55,no.3,pp.210-214,1985.


APPENDIX A
LIST OF EQUIPMENT
The following is a list of equipment that was
used in the experiments described within this thesis.
LASER: Spectra-Physics Series 2000 argon ion
CRYSTAL: melt grown, single domain BaTiOj
LASER POWER METER: Newport Research Corporation model 820
DATA ACQUISITION SYSTEM: -Data Translation's DT2814
A/D converter board
-Zenith AT compatible
-op-amp circuit with TL081
-low-pass filter
VARIABLE NEUTRAL DENSITY FILTER: by Oriel
POLARIZATION ROTATOR: Consists of two plain mirrors
oriented at 45 with respect to
each other


APPENDIX B
INTERFACE TO DATA ACQUISITION SYSTEM
This Appendix describes the interface between the
optical power meter and computer that was used in the
experiments contained within this thesis.
The entire interface is shown in Figure B-l. The
low-pass filter and the amplifier are shown in Figures
B-2 and B-3, respectively. The twelve bit analog to
digital converter is the DT2814 supplied by Data
Translation, Inc. The digital computer is a Zenith Z-200
AT compatible.
detector
head
optical
power
meter
ADC
low-pass interface digital
filter amplifier board computer
FIGURE B-l Computer interface for phase conjugation
experiments.


85
2.67 k
0
V. ___ 40 LIF
m
0-------------------
0
V
out
0
1 = 125 msec
3 dB point is 1.5 Hz
FIGURE B-2 Low-pass filter used to get rid of 60 Hz ac
noise at input of amplifier.
+V.
in
FIGURE B-3 Amplifier used to increase 0 100 mV signal
to 0 4 V signal for increased resolution of A/D
converter.


APPENDIX C
LASER STABILIZATION CONFIRMATION EXPERIMENT
This Appendix describes an experiment that was
conducted to verify laser stability in the presence of
phase conjugate feedback into the cavity.
The experimental set-up is shown in Figure C-l.
It was found that power meter 1, which essentially
monitors the laser cavity, did not oscillate even when
intense oscillation was seen in power meter 2, which
monitors the phase conjugate wave. We therefore concluded
that the oscillation of the phase conjugate wave is not
due to an unstable laser source. It is possible, however,
that an oscillation could be seen in the laser cavity
with more sophisticated equipment that was not available
to us.
Finally, it should be noted that an optical
isolator could be used if there is any doubt as to laser
instability due to optical feedback into the cavity.
Unfortunately, such a device was not available to us
during the testing reported on in this paper.


87
FIGURE C-l Experimental configuration used to test laser
stability. Detector 1 monitors the laser cavity output
while detector 2 monitors the oscillating phase
conjugate wave.


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TWO-BEAM COUPLING AND RESPONSE TIME ANALYSIS OF PHASE CONJUGATE WAVE USING A SELF-PUMPED CONFIGURATION WITH BARIUM TITANATE by JEFFREY L. KOBESKY B.S., State University of New York, 1985 A thesis submitted to the Faculty of the Graduate School of the University of Colorado in partial fulfillment of the requirements for the degree of Master of Science Department of Electrical Engineering and Computer Science 1989

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This thesis for the Master of Science degree by Jeffrey L. Kobesky has been approved for the Department of Electrical Engineering and Computer Science by John R. Clark Date

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ACKNOWLEDGEMENT I would like to thank Professor Arun K. Majumdar for his enthusiasm in this work and resourcefulness in the equipment supply business.

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iv Kobesky, Jeffrey Lawrence (M. S., Electrical Engineering) Two-Beam Coupling and Response Time Analysis of Phase Conjugate Wave using a Self-Pumped Configuration with Barium Titanate Thesis directed by Professor Arun K. Majumdar Two-beam coupling and optical phase conjugation using a self-pumped configuration in barium titanate (BaTi03 ) is demonstrated experimentaliy. The 514.5 nm line of an argon ion laser is used as the source. Two-beam coupling strength is analyzed as a function of .input angle and power. Build-up time and rise time slope of the phase conjugate wave are also analyzed as functions of input angle and power. Miscellaneous observations during testing are given. A physical model for two-beam coupling and phase conjugation in a photorefractive material, such as BaTio3 is briefly presented. The self-pumping method for producing a phase conjugate wave is described. The form and content of this abstract are approved. I recommend its publication. Arun K. Majumdar

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CONTENTS CHAPTER 1. IN':I?RODUCTION. . . . . . . . . . . . . . 1 2. PHYSICAL MODEL DESCRIBING TWO-BEAM COUPLING AND PHASE CONJUGATION IN PHOTOREFRACTIVE MATERIALS. . . . . . . . . . . . . . . 5 2.1 The Photorefractive Effect................ 5 2.2 Two-Beam Coupling in Photorefractive Materials............... 9 2.3 Phase Conjugation in Photorefractive Materials............... 12 2.4 Phase Conjugation in BaTi03 using the Self-Pumped Configuration........... 12 3. EXPERIMENTAL PROCEDURES AND RESULTS............ 16 3.1 Two-beam Coupling in BaTi63.............. 16 3.1.1 Two-Beam Coupling vs. Input 16 3.1.2 Two-Beam Coupling vs. Relative Input Power of A 1 and A 2........ 22 3.2 Response Time of Phase Conjugate Wave in BaTi03 using the Self-Pumped Configuration............... 24 4. ANALYSIS OF EXPERIMENTAL DATA.................. 63 4.1 Polynomial Fits to Rise Time Slope Data... 63 4.2 Graphical Representation of Build-Up Time Data............................... 71

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vi 5. CONCLUSIONS. . . . . . . . . . . . . . . . . . 7 9 BIBLIOGRAPHY ..................... . . . . . . . . . . 81 APPENDIX A. LIST. OF . . . . . . . . . . . . . . . 83 B. INTERFACE TO DATA ACQUISITION SYSTEM............ 84 C. LASER STABILAZATION CONFIRMATION 86

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vii TABLES Table 3.1 Results of two-beam coupling vs. input angle experimentation ...................... 20 3.2 Results of two-beam coupling vs. input power experimentation .......................... 25 3.3 Build-up time of phase conjugate wave as a function of input power and input angle ..... 34 3.4 Rise time slope (dP/dt) of phase conjugate wave as a function of input angle and input power ....................................... 35 4.1 Coefficients of polynomial fits of rise time slope data for various input angles ............... 70

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FIGURES Figure 1.1 Phase conjugator used for correcting distortions ... 2 2.1 Formation of a photorefractive phase grating ....... ? 2.2 Two-beam coupling in a photorefractive crystal .... 10 2.3 Four-wave mixing geometry ....................... 13 2.4 Self-pumped phase conjugation configuration ..... 14 3.1 Experimental configuration used for testing two-beam coupling for various input angles ........ 17 3.2 Close-up view of crystal/beam interaction ......... 19 3.3 Effect of table vibration on beam coupling ........ 21 3.4 Experimental configuration used for determining two-beam coupling as a function of relative input intensity ................................... 23 3.5 Experimental configuration used to test phase conjugate response time as a function of input angle ....................................... 2 6 3.6 Close-up view of beam/crystal interaction for testing phase conjugate response time ........ 28 3.7 Example of oscillatory behavior of phase . conJugate wave ................................ 2 9 3.8 Definition of build-up time and rise time slope ... 32 3.9 Example of why rise time slope could not be determined for input powers >10 mw ............... 33

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ix 3.10 Phase conjugate build-up time as a function of input power for various input angles ...... 36 3.11 Phase conjugate build-up time as a function of input power for various input angles ... 37 3.12 Slope (dP/dt) of phase conjugate wave as a function of input power for various input angles ..................................... 3 8 3.13 Slope (dP/dt) of phase conjugate wave as a function of input power for various input angles ......................... ............ 3 9 3.14 Response time of phase conjugate wave for various input angles with 1 mW incident on crystal ...... 40 3.15 Response time of phase conjugate wave for various input angles with 5 mW incident on crystal ...... 41 3.16 Response time of phase conjugate wave for various input angles with 10 mW incident on crystal ...... 42 3.17 Response time of phase conjugate wave for various input angles with 50 mW incident on crystal ... 43 3.18 Response time of phase conjugate wave for various input angles with 100 mW incident on crystal . 44 3.19 through 3.35 Response time of phase conjugate wave for varying input powers and input angles ... 45-61 4.1 Polynomial fit for slope of phase conjugate rise time vs. input power for 9= 50 ............ 64 4.2 Polynomial fit for slope of phase conjugate rise time vs. input power for 9= 55 ............ 65 4.3 Polynomial fit for slope of phase conjugate rise time vs. input power for e = 60 ........ .... 66

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X 4.4 Polynomial fit for slope of phase conjugate rise time vs. input power for a= 65 ............ 67 4.5 Polynomial fit for slope of conjugate rise time vs. input power for a= 70 ............ 68 4.6 Polynomial fit for slope of phase conjugate rise time vs. input power for 75 ............ 69 4.7 Phase conjugate build-up time vs. input power for a = 50 ...................................... 72 4.8 Phase conjugate build-up time vs. input power for a= 550 73 4.9 Phase conjugate build-up time vs. input power for 9 = 60 ...................................... 7 4 4.10 Phase conjugate build-up time vs. input power for a = 65 ...................................... 75 4.11 Phase conjugate build-up time vs. input power for a = 70 ...................................... 76 4.12 Phase conjugate build-up time vs. input power for a = 1 s0 ...................................... 7 1 4.13 Phase conjugate build-up time vs. input power for a = 80 ...................................... 78 B-1 Computer interface for phase conjugation experiments ...................................... 84 B-2 Low-pass filter used at input to data acquisition system ............................... 85 B-3 Amplifier used at input to data acquisition system ............................... 85

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xi C-1 Experimental configuration used to test laser stability ................................... 87

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CHAPTER 1 INTRODUCTION There exists certain crystals (barium titanate, potassium tantalate niobate, bismuth silicate and bismuth germanate, strontium barium niobate, lead lanthanum zirconate titanate, lithium niobate, and various III-V semiconductors) that are capable of producing a phenomenon known as the Photorefractive Effect. This Effect is used to describe other phenomena, such as two-beam coupling and optical phase conjugation, that can be observed in such crystals under the right conditions. The phase conjugate (pc) wave produced by a photorefractive crystal is capable of undoing the distortion that laser beams suffer upon propagation through as aberrating medium, such as a turbulent atmosphere or an imaging system. Elimination of such distortion will aid in, among other things, reducing error in optical communication links. Other applications of the pc wave include optical image processing, holographic storage, automatic tracking for optical communication links, resonator loss and

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2 distortion compensation, and many others. A major area of concern in the above applications is response time of the pc wave. Figure 1.1, INPUT BEAM OUTPUT BEAM TURBULENT LAYER FIGURE 1.1 Phase conjugator used for correcting distortions caused by turbulence. PC MIRROR where an optical beam is to be phase conjugated after propagation through a turbulent atmosphere. If the turbulence causes fluctuations that are faster than the response time of the pc mirror, a pc wave will not be produced. We must therefore know the response time of the pc mirror and the maximum frequency components of the dynamic distorting medium in order to say if a phase conjugate wave can be produced or not. Rigorous mathematical treatments can be found that analytically describe two-beam coupling1 pc mirror

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3 reflectivity and pc beam deflection2 as well as other aspects of the photorefractive effect. The mathematics involved is complicated and results tend to be inacurate do to the nonuniformities (crystal abnormalities, optical spectrum differences, etc.) encountered in actual experimentation. Furthermore, equations describing response time for pc waves in photorefractive materials do not-exist in the literature to our knowledge. With these facts in mind, the main goal of this paper is to analyze experimentally obtained response times of the pc wave for barium titanate (BaTi03 ) in the self-pumped3 configuration with the 514.5 nm line of an argon ion laser as the source. Response time is analyzed as a function of both input angle and input power. It is hoped that these results will be useful to those who desire an order of magnitude approximation for the response time of this particular configuration. It must be kept in mind that the results presented pertain only to the BaTi03/514.5 nm/self-pumped configuration. This is, however, a very popular configuration due to the large pc reflectivity obtained. Other configurations offer faster response time at the cost of pc reflectivity. In actual practice, these

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. 4 trade-offs must be made for each specific application to obtain an optimum phase conjugator. Additionally, two-beam coupling data is presented as a function of input angle and input power. A brief explanation of the photorefractive effect and how the effect leads to two-beam coupling and phase conjugation is given. A detailed explanation of these phenonema is well beyond the scope of this thesis -therefore many references are given to supplement the omitted material.

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CHAPTER 2 PHYSICAL MODEL DESCRIBING TWO-BEAM COUPLING AND PHASE CONJUGATION IN PHOTOREFRACTIVE MATERIALS This chapter presents a brief explanation of the photorefractive effect, two-beam coupling, and phase conjugation in photorefractive crystals. Namely, we will find an expression that relates two-beam coupling to polarization, relative beam intensity, wavelength, refractive index, angle of incidence, optical dielectric tensor, electro-optic tensor and propagation Also, phase conjugation will be chatacterized by grating reflectivity and mirror reflectivity, which are functions of the same variables that describe two-beam coupling. Many references are given for further study. 2.1 The photorefractiye effect When two linearly polarized coherent light beams intersect, a spacial intensity interference pattern is generateds given by (2.1) where

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6 (2.2a) (2.2b) If the beam intersection occurs in a crystal which has mobile charge carriers available5 the interference pattern described by (2.1) will cause these charge carriers to migrate either into or out of the bright regions of the pattern (the direction of migration depends on the sign of the charge carriers) The resulting charge distribution, which varies sinusoidally with (2.1), will produce an electric field (given by Poisson's equation) that will also vary sinusoidally with (2.1), but shifted in phase by radians. If the crystal containing the charge distribution does not possess inversion symmetry6, the induced electric field will produce a refractive index change via the linear electro-optic effect. The entire process is illustrated in Figure 2.1. The process shown in Figure 2.1 is known as the photorefractive effect and crystals capable of producing the effect are called photorefractive crystals. Most of the theory is agreed upon amoung scientists, but there are still areas of controversy -such as the origin of the mobile charge carriers.

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7 I(x) p(x) E(x) An(x) FIGURE 2.1 Formation of a photorefractive index grating. From top to bottom: Light with spatially periodic intensity I(x) rearranges the charge density p(x) in the material. The mobile charges, here with positive charge, tend to accumulate in the dark regions of the intensity pattern. The resulting periodic charge distribution p(x) causes a periodic electrostatic field E(x) by Poisson's equation. This electric field then causes a change in the refractive index An of the crystal by the linear electro-optic (Pockels') effect. (From [7] .)

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8 The derivation of an analytical expression for E(r) is somewhat complex; there is no need for derivation here-many articles do this quite elegantly7 Here, we just that, in the absence of an externally applied field, E(r)=-(kBT/q)m[k/l+(k/ko)2]sin(kr) (2. 3) where kBT is the thermal energy of the crystal lattice, q is the charge of the mobile charge carriers, m is a dimensionless modulation index given by (2. 4) k is a grating wave vector given by (2. 5) k is the absolute value of k, and ko is a constant of the material that depends on the number density N of charge carriers available for charge migration according to (2. 6) Note that upon comparison of (2.3) with (2.1), we see I(r) is 90 out of phase with E(r), as shown in Figure 2 .1.

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2.2 Two-beam coupling in photorefractive materials When two beams of the same optical frequency intersect in a ph9torefractive crystal, intensity can be transfered from one beam to the otherB. The amount of two-beam coupling depends on several parameters (to be 9 discussed shortly) and can be quite large. In BaTio3 for example, one beam can transfer essentially all its power to the other beam over an interaction distance of only a few millimeters9. The direction of the crystal's c axis determines the direction of power transfer as shown in Figure 2.2. The derivation of equations describing two-beam coupling is complicated and only the results are shown here (see [7] for details). The amplitude X of the change in the optical susceptability RE[Xexp(ikr)] caused by E(r) is 'V=f (9t Ek) E "' (J) 0) (2. 7) where e00 is the optical dielectric tensor at ro and 9t is the third-rank electro-optic tensor. Also, defining 1C = [ iro/2nccos (9) ] [X/m] (2.8)

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I 1 I 2 I 1 I 10 2 FIGURE 2.2 Two-beam coupling in a photorefractive crystal. The direction of the positive c axis is shown. In (a) two'incident beams of equal intensity emerge with unequal intensity. In (b) the beams are misaligned and do not intersect in the crystal, therefore no coupling occurs. In (c) the crystal is rotated 180 and the direction of intensity transfer is opposite to (a) (From [ 9])

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11 where 9 is the small angle that the incident beam makes with a normal to the front crystal face. We can write the coupled-wave equations for the intensities as (2. 9a) (2. 9b) where (2.10) and (2 .11) Equations (2.9a) and (2.9b) are the main results of this section. Together they describe how the intensity changes as the beams propagate in the z direction. An important point to be made here is that two-beam coupling provides a way to measure both the sign and the density of the mobile charge carriers. The sign of the mobile charges is determined by the direction of two-beam coupling with respect to the crystal's c axis. The density of mobile charge carriers is found by the variations of two-beam coupling strength with the crossing angles of the.two beams, because coupling is at

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12 a maximum when k=ko (i.e. since we know the value of k, we can plug it in (2.6) and solve for N). These facts are valuable in understanding the physics involved in the photorefractive process. 2.3 Phase conjugation in photorefractiye materials Phase conjugation in photorefractive materials is a difficult topic to describe briefly, therefore its complete description will not be given. There are many good references, such as [2], available for the reader who desires all the details. We will, however, show the beam/crystal interaction used to obtain a phase conjugate wave in a photorefractive material. This interaction, known as four -wave mixing, is shown in Figure 2.3. A 1 and A 2 are known as pump beams. Their job is to "prepare" the material so that a phase conjugate wave can be produced. A 2 is called the probe beam. The phase conjugate beam, A 4 is derived from A2 after the medium is properly prepared by A1 and A3. 2.4 Phase conjugation in using the self-pumped configuration The geometry used to produce a phase conjugate wave in BaTi03 using the self-pumped configuration is

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A 3 PHOTOREFRACTIVE CRYSTAL CRYSTAL .AXIS A 1 13 FIGURE 2.3 Four wave mixing geometry used to produce a phase conjugate wave. A 1 and A 3 are the pump beams, A2 is the probe beam, and A 4 is the phase conjugate of A 2 (From [ 7] )

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INCIDENT BEAM BaTiO 3 14 BEAM FANNING FIGURE 2.4 Geometry used for obtaining a phase conjugate wave in the self-pumped configuration. Four wave mixing is achieved by using only one input beam and relying on properties of the photorefractive crystal (such as beam fanning) to generate the needed pump beams.

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15 shown in Figure 2. 4. Note that only a single input beam is required (hence the term 11Self-pumped11). The two pump beams required for four-wave mixing are derived from the incident probe beam. Beam fanninglO in the crystal is responsible for the ray directions shown in Figure 2.4. The pump beams are generated through internal reflections near the edge of the crystal. The edge of the crystal acts as a retroreflector for the pump beams -therefore the beam interaction is self-aligned. This property makes the self-pumped configuration relatively simple to use and also allows phase conjugation to be achieved at a large variety of input angles. These desirable properties come at the cost of lower mirror reflectivity and slower response time compared to the configuration of Figure 2.3. However, due to its relative ease of implimentation and practical importance11,12,13, the self-pumped configuration will be the only one used in this thesis.

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CHAPTER 3 EXPERIMENTAL PROCEDURES AND RESULTS This Chapter describes experimental procedures and results obtained pertaining to two-beam coupling and phase conjugation, testing. Experimentation was done in the Electro-Optics Laboratory at the University of Colorado at Denver. A list of test equipment used appears in Appendix A. A description of the data acquisition interface appears in Appendix B. All data was taken using an argon ion laser at A.= 514.5 nm. 3.1 Two-beam Coupling in BaTi03 In this section we present experimental procedures and results obtained in two-beam coupling experiments. In particular, we investigate two-beam coupling as a function of input angle (section 3.1.1) as well as input power (section 3.1.2). 3.1.1 Two-beam Coupling vs. Input Angles The experimental set-up for this test is shown in Figure 3.1 and a close-up of the crystal/beam interaction

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POLARIZED POLARIZED VARIABLE NEUTRAL DETECTOR HEAD 17 DETECTOR HEAD POWER METER FIGURE 3.1 Experimental configuration used for testing two-beam coupling for various input angles. The input angles were constrained to 9H1 = 9H2 = 9H.

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is shown in Figure 3.2. Test objective, We wish to determine how beam coupling varies as a function of input angles. Procedure, Keep the power in beams A 1 and A2 constant at 10 mW for all data -the variable neutral density filter is used to accomplish this. 18 Vary input angles (with constraint 9Hl =9H2 = 9H) from -120 to -29 and record the powers PAl' and PA2 (i.e. observe beam coupling at various input angles). Angles are varied by adjusting M 1 M 2 and crystal position. The experiment will be repeated three times, on three different days, to see how repeatable the data is. Results. See Table 3.1. Miscellaneous observations, 1. Assume we have PAl = PA2 = 10 mW incident on the crystal. In the steady state we have coupling from A 1 to A 2 -for example, let PAl'= 3.4 mw and PA2,=S.7 mw. If

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29 H 19 FIGURE 3.2 Close-up view of crystal/beam interaction. A 1 and A2 are incident at the same angle from the normal to the crystal face. The polarization vector of both beams is parallel to the crystal's c axis.

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20 TABLE 3.1 Results of two-beam coupling vs. input angle experimentation. PAl' and PA2' refer to measurements taken at the output of the crystal (see Figure 3.1). RUN #1 RUN #2 RUN #3 p p p A2' A2' A2' p p -p p -p p -9 A1' A2' p A1' A2' p A1' A2' p H A1' A1' A1' 12.0 3.30 6.40 1. 94 3.20 6.30 1.97 3.35 6.15 1.84 14.5 3.15 6.45 2.05 3.15 6,;45 2.05 3.05 2.10 17.0 3.10 6.20 2.00 2.95 6.30 2.14 3.15 6.10 1.94 20.0 2.95 6.15 2.08 2.90 6.05 2.09 2.95 6.10 2.07 22.5 2.80 5.55 1. 98 2.80 5.60 2.00 2.85 5.85 2.05 26.0 2.80 4.80 1.71 2.80 5.15 1.84 2.80 5.30 1.89 29.0 2.80 4.00 1.43 2.75 4.25 1.55 2.85 3.95 1.39

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we block A 1 it takes -80 sec for PA2 to settle into steady state. If instead we block A 2 PAl' settles into steady state almost instantaneously. 21 Also, if we restore beam A 1 PA2' goes back to 5.7 mW in -10 sec (note much faster than decrease-this is probably due to the phase grating already being set up when.A1 is restored). 2. Table vibrations change PAl' and PA2' drastically, whereas PAl and PA2 are unaffected by vibration. However, this effect is seen only when both beams are in the crystal. Pictorially, POWER POWER + - Al' A2' Al' A2' FIGURE 3. Effect of table vibration on beam coupling.

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3. we: Move the crystal with beams incident upon it (i.e. erase the crystal) Block both beams with the crystal still erased. Allow A 2 to enter the crystal; beam fan appears in -2 sec with PA2 = 10 mw. Block A 2 then let A 2 be incident again; this time 22 the beam fan appears instantaneously -because the phase grating is already established. 4. Beam coupling was unstable (oscillatory) for the two largest angles of 26 and 29. 3.1.2 Two-beam Coupling vs. Relative Input Power of A1 and A 2 The experimental set-up for this test is shown in Figure 3.4. Test objectiye. We wish to determine how beam coupling varies as a function of relative input power. Procedure, The input angles, 9Hl = 9H2 = 9H, will be kept constant at 14.4 throughout the test. PA2 will be kept constant at 10 mW throughout the test. PAl will

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POLARIZED POLARIZED VARIABLE NEUTRAL DENSITY DETECTOR HEAD 23 DETECTOR HEAD POWER METER FIGURE 3.4 Experimental configuration used for determining two-beam coupling as a function of relative input intensity. 9H is kep-t constant at 14.4. PA2 is constant at 10 mW. PAl varies from 10 mw to 0 mW in increments of 0.5 mw. The beam/crystal interaction is the same as in Figure 3.2.

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24 be varied from 10 row to 0 mW in increments of 0.5 roW and beamcoupling will be observed at each increment (i.e. PAl' and PA2' will be measured). The power in A 1 is varied by adjusting the variable neutral density filter. The crystal is erased after each data point by moving the crystal while the incident beams are present. The was done twice for repeatability purposes. Results. See Table 3.2. Miscellaneous observation. For the lower powers of PAl (<4.00 mW), like the higher 9H, the beam coupling is oscillatory -that is PA2' is oscillatory and PAl' is relatively stable. 3.2 Response time of phase conjugate waye in BaTiO:l using the self-pumped configuration. This section describes experimental set-ups, procedures, and results pertaining to the response time of the phase conjugate wave in a self-pumped crystal of BaTio3 The response time is determined as a function of input angle and input power. The experimental set-up is shown in Figure 3.5 and a close up view of the

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TABLE 3.2 Results of two-beam coupling vs. relative input power experiment. See Figure 3.4 for meaning of P sub's. RUN 1 RUN #2 p p p p )( p p j( A1 A2 A1' A2' A1' A1' A2' A1' 10.0 10.0 3.30 6.20 1.88 3.15 6.25 1. 98 9.5 3.15 6.10 1. 94 3.05. 6.15 2.02 9.0 2.95 6.05 2.05 2.95 6.00 2.03 8.5 2.90 5.95 2.05 2.80 5.95 2.13 8.0 2.70 5.90 2.19 2.70 5.90 2.19 7.5 2.60 5.75 2.21 2.60 5.75 2.21 7.0 2.45 5.55 2.27 2.45 5.60 2.29 6.5 2.30 5.50 2.39 2.25 5.50 2.44 6.0 2_ 1_0 5. 40 57 2 10 5.15 55 5.5 1. 95 5.30 2. 72 1. 95 5.25 2.69 5.d 1 80 5.25 2.92 1.80 5.15 2.86 4.5 1.60 5.05 3.16 1.65 5.05 3.06 4.0 1.45 4.85 3.34 1.45 4.90 3.38 3.5 1 30 4.85 3 75 1 25 4 75 3 80 3.0 1.10 4.75 4.32 1.10 4.15 3. 77 2.5 0.90 4. 60 5.11 0.95 3.90 4.10 2.0 n 7'i 3 90 5 .20 0 75 3 65 4. 87 1.5 0.60 3.60 6.00 0.60 3.45 5.75 1.0 0.40 3.35 8.38 0.40 3.30 8.25 0.5 0.20 3.20 16.00 0.20 2.90 14.50 0.0 10.0 0.026 2.65 101.92 0.04 2.50 62.50 25

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vertical polarization + argon ). =514 .5 run apature setting is 5 spot size is 1.25 mm in diameter -2 at the e intensity points 50% of phase conjugate beam 9 polarization rotator horizontal polarization variable neutral density filter bs (50%) 50% of phase conjugate beam 26 detector data acquisition system FIGURE 3.5 Experimental set-up used to test phase conjugate response time as a function of input angle.

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27 beam/crystal interaction is shown in Figure 3.6. All the important parameters can be found in these two figures. Test objectiye. We wish to determine .the response time of the phase conjugate wave build-up for various input angles and input powers. Procedure, First, make sure the crystal is erased for each data point. Then allow the beam to be incident upon the crystal at the same instant the data acquisition system starts to acquire data from the detector. We then monitor the output of the detector as a function of time. This essentially monitors the build-up of the phase conjugate wave as a function of time. This process is repeated over anumber of different input angles and input powers. In particular, we vary the input angle e from S0 to 80 in increments of S0 Also, we vary input pO\
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incident beam FIGURE 3.6 Close-up view of beam/crystal interaction used for testing phase conjugate response time. Note that the input beam is polarized parallel to the crystal's c axis -this condition yields maximum pc reflectivity. Also, the beam travels in the 28 direction of the positive c axis (in the direction of the arrow) -which is necessary for phase conjugation to occur in the self-pumped configuration.

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90 55 DEG 3mW 60 .a a: w 3: 0 Q. w 1-
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30 build-up of the phase conjugate wave throughout time. After discovery of this phenomenon, a reference1 4 was found where past experimenters experienced the same effect. Reference [14] states the oscillation phenomenon is most likely induced by four-wave mixing of the pump beam with a self-induced reference beam produced by scattered light amplified by two-beam coupling, and its retroreflected beam from the face perpendicular to the entrance face. Whatever the explanation, we found it necessary to varify that the oscillation was not produced by the instability of our laser source due to the phase conjugate wave being fed back into the cavity. An experiment was conducted, which is described in Appendix C, that semi-satisfied us that the oscillations are not caused by an unstable source. We also found it necessary, because of the oscillations, to characterize the response time by using two seperate parameters. These parameters and their discription are as follows: l.Build-up time. This is a measure of time from the instant the input beam is incident on the crystal to the instant a phase conjugate wave appears. 2.Rise time slope. This is a measure of the

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31 slope, dP/dt, of the initial rise of the phase conjugate wave. These two quantities are pictured in Figure 3.8. Build-up time was calculated for all data points. Rise time slope, however, was only calculated for input powers from 1 mW to 10 mW; this is because of the slope being impossible to determine at higher powers due to the intense (see Figure 3.9). Rise time slope and build-up time will be collectively refered to as response time. Results. Build-up time is tabulated in Table 3.3. Rise time slope is found in Table 3;4. Both of these tables are plotted in Figures 3.10 through 3.13 for graphical comparison purposes. Plots of the actual data taken by the data acquisition system can be found in Figures 3.14 3.35. These plots are constructed to yield a comparison between response time for varying input angles (Figures 3.14 through 3.18) and response time for varying input powers (Figures 3.19 through 3.35). It would be impossible at this time to completely analyze the data and give physical and mathematical meaning to it (that is, in addition to the information presently found in the literature) It is

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60 DEG 6mW --.--I I 140 .a 100 a: l&J 31: 0 80 0. UJ t-"" m 60 :::l "") z 0 u UJ 40 UJ RISE TIME SIDPE "" X 0. 20 0 -20 0 50 100 150 200 250 TIME (sec) FIGURE 3.8 Definitions of build-up time and rise time slope. w N

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65 DEG 90inW 1200 1000 a: IIJ X 0 Q. IIJ t-(!) ""] z 0 u UJ CIJ :I: Q. BOO 600 400 200 0 _, 0 5 10 15 TIME (sec) 20 25 30 FIGURE 3.9 Example of difficulties encountered in defining rise time slope for input pc:Mers greater than 10 m-. Here, the input pc:Mer is 90 mi. UJ UJ

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34 TABLE 3.3 Build-up time of phase conjugate wave as a function of input power and input angle. All entries are build-up time in seconds. (deg) p (mW) 50 55 60 65 70 75 80 1 120 163 121 99 573 >600 >600 2 76 78 61 52 62 >600 >600 3 38 70 24 13 48 >600 >600 4 35 58 45 37 16 134 >600 5 28 27 29 22 30 65 >600 6 18 33 28 28 26 43 >600 7 16 17 24 21 22 36 >600 8 17 26 18 18 18 31 >600 9 16 23 14 20 18 28 10 13 20 13 15 14 25 74 20 5 9 7 14 15 21 23 30 3 5 4 7 8 15 13 40 2 3 4 4 5 10 10 so 1 2 2 4 4 7 7 60 1 2 2 3 3 5 8 70 1 2 2 2 2 4 7 80 1 1 2 3 2. 4 6 90 1 1 2 2 2 3 4 100 1 1 2 2 2 3 3 Start of pc wave is hard to determine for this point.

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TABLE 3.4 Rise time slope (dP/dt) of phase conjugate wave as a function of input angle and input power. 9 (deg) p (mW) 50 55 60 65 70 75 80 1 0.20 0.13 0.07 0.04 0.00 0.00 0.00 2 0.53 0.48 0.26 0.18 0.05 0.00 0.00 3 0.83 1.20 0.43 0.37 0.16 0.00 0.00 4 2.33 2.28 0.67 0.42 0.28 0.10 0.00 5 3.09 4.00 0.81 0.79 0.32 0.15 0.00 6 4.50 4.50 2.00 1.25 0.58 .26 0.00 7 7.00 8.00 1. 69 1.49 0.55 0.35 0.00 8 8.00 11.7 3.65 3.06 1.10 0.40 0.00 9 8.67 11.5 5.07 3.63 1.43 0.75 10 9.20 20.0 5.73 4.60 3.23 0.78 0.08 35

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100 0 0 oe 6. P.C. BUILD- UP 10 TIME (sec) 0 = soo 0 = 65 0 0 6. = 80 0ooo 1 1 10 100 POWER (mW) .':3.10 Phase conjugate build-up time as a function of input pc:Mer for various input angles. Data was taken using the experirrental set-up of Figure 3.5. w 0'\

PAGE 48

FIGURE 3.11 Phase conjugate build-up time as a function of input power for various input angles. Data was taken using the set-up of Figure 3. 5. w -...J

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4+ 0 65 = 70 0 dP/dt. 3r 6. = 75 0 A= 80 of P.C. WAVE 2 I 0 0 1+ 0 -6. 6. .1. 0 -.. "77r D. 0 ---1 2 .3 4 5 6 7 8 9 10 POWER INCIDENT ON CRYSTAL (mW) FIGURE 3.12 Slope (dP/dt} of phase oonjugate wave as a function of input pJWer for various input angles. Data was taken using tlie experirrental set-up of Figure 3.5. w 00

PAGE 50

dP/dt of P.C. WAVE 20 15 10 5 0. 50 = 55 6....:... 60 ... = 65 0 o .Ill 'T I I I 1 2 3 4 5 6 7 8 POWER INCIDENT ON CRYSTAL (mW) 0 ... 9 10 FIGJRE 3.13 Slope (dP,0dt) of phase conjugate wave as a ftmction of input power for various input angles. Data was. taken using the experimental set-up of Figure 3.5. w \0

PAGE 51

..... 3: ::::J .... a: UJ ll:' 0 D. I1J 1-"' C9 ::::. "") .z 0 u UJ m D. 25 20 15 10 5 0 0 100 200 300 TIME (sec) 400 500 600 FIGURE 3.14 Response time of pl"lclse conjugate wave for various input angles with 1 mN incident on crystal. .p. 0

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100 80 :I a: UJ 31: 60 0 Q. UJ ....
PAGE 53

__, 9=65 I 1:1=..,.., J 200 .a 150 II: UJ 31: 0 a. UJ 100 ... "( (!) :l z .... 0 I 1/Y / v 0 u .r9=75 UJ 50 (I) "( X D. ol ...C::: .... 9=30 -5oL-----J____ _L ____ _J ______ L_ ____ J_ ____ _L ____ _J ______ L_ ____ J_ ____ 0 10 20 30 40 50 60 70 80 90 100 TIME (sec) FIGURE 3.16 Resp:>nse time of phase ronjugate wave for various input with 10 m\1 incident on crystal. N

PAGE 54

1400 r= I I I I I l 1200 3 a: UJ JC 0 Q. UJ t!) ::J .., z 0 .U UJ (I) Q. 1000 BOO \ 9=50 600 400 200 9=300 -200 l I I 1 0 ' 20 30 TIME (sec) 40 50 60 10 FIGURE 3.17 Response time of phase conjugate wave for various input angles with 50 !W1 incident on crystal. p w

PAGE 55

3500 r-----r---------1 ------r ------..----------,----------,----_---.. l x .a 3000 2500 a: 2000 .. 0 a. 1500 0 u ILl m f 1000 500 7-0 9= 0 I Jle;t'J rCt A ec.AcV: n -500 _...__ J--------'---0 5 10 15 20 25 30 35 TIME (aec) FIGURE 3.18 Res:p:>nse tine of phase CDnjugate wave for various input angles with 100 rrN incident on crystal.

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100 ---r--r--------r----T------,----, I /\ I \ t--4 rn-7 80 . . 3mW .a 60 a: l&J I _/\ J :/ lJ"' 3: 0 Q. 40 ..: (!J ::J "'). z 0 u l&J UJ ..: :1: Q. 20 0 -20 0 _.J ____ I I _____ ___ __., ___ ___. 50 100 150 200 250 300 350 TIME (sec) FIGURE 3.19 Response time of phase conjugate wave for varying input powers with the input 'angle equal to.so 'degrees. 400 "" 1.11

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z :I -ffi :z 0 a. I!! 4( C!t ;:::) ""') z 0 u LLI en 4( l: a. 140r----y------, 120r II \\ 10 mi 100 I 111"1 \ 9 nl'l. 40 20 I Ill/ I B m!J Ol '%'"''6 rm'J -20 .J. 0 20 40 60 BO 100 120 140 160 TIME (sec) FIGURE 3.20 Response time of phase conjugate wave for varying input powers with input angle equal to 50 degrees. 180 "'

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a a: lU 31: 0 0. lU 1-4( C!t ::I '"1 z 0 0 lU en 4( ::t: 0. 1600 .---I 1-400 1200 1000 BOO 600 -400 200 0 -200 0 2 o4 I I I I I 6 8 10 TIME (sec) 12 1-4 16 18 FIGURE 3.21 Response time of :phase conjugate wave for varying input powers with the input angle equal to 50 degrees. 20 .....

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3500 y------, --------. ._______ 3000 2500 :i .a ffi 2000 31: 0 Q. 15oo I I I / m ::l .., z 8 1000 UJ UJ :::c Q. 500 ol ----500 L.. __ _, 0 0.5 1 1.5 2 2.5 3 3.5 ... -4.5 TIME (aec) FIGURE 3.22 Response time. of phase conjugate wave for varying input powers with the input angle equal to 50 degrees. 5 00

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:I .... a: UJ 3: 0 a. UJ ..... '"' (!) z 0 u UJ UJ '"' J: a. 120.-r--80 s.l I / L:-3rrW 40 20 oJ-u(( J J --0 50 100 150 TIMI: (sec) 200 250 300 FIGURE 3.23 Response time of phase conjugate wave for varying input powers with the input angle equal to 60 degrees. +:-\0

PAGE 61

.3 a: IIJ 3: 0 Q. IIJ t-4( (!) ::J "") z 0 u l1J en 4( :I: Q. 200 150 100 50 0 -50 --L---0 20 40 60 eo 100 120 140 160 TIME (sec) FIGURE 3.24 Response time of phase conjugate wave for varying input powers with the input angle equal to 60 degrees. -180 1.11 0

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'% .a a: UJ 3C 0 (1. 4( (!) :::: "') z 0 u UJ UJ 4( X: (1. 1200 --1000 BOO 600 -400 200 0 --30 nW -200 L-------.....&..... I I 0 10 20 30 -40 50 TIME (sec) FlamE 3. 25 P.esponse tirre of phase conjugate wave for varying input p:::wers with the input angle equal to 60 degrees. 60 V1 ......

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1800 r---.-1600 1400 1200 a: 1000 0 a.. 1&1 BOO 1-..c C!) :;:) -, z 600 0 u 1&1 U) 400 ..c :a: a.. 200 0 From left to right, 100 m\1, 90 111'1, 80 nN, 70 ni"l -200 0 10 20 30 40 50 TIME (sec) FIGURE 3.26 Res};X)nse time of phase oonjugate wave for varying input powers with the input angle equal to 60 degrees. 60 VI N

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500 .,-----,-----y----y------,r.a a: UJ 31: 0 a. UJ .... "" m z 0 u UJ CIJ "" ::a: a. 400 I I 300 200 100 I / // I __./ __,.-0 -100 .l-----L--0 0.5 1 1.5 2 2.5 TIME (sec) FIGURE 3.27 First five seconds of Figure 3.26. 100 nW / "'-70 m 3 3.5 4 4.5 5 V1 w

PAGE 65

.a ffi :z: 0 a.. UJ ..... "' (!) ::l .., z 0 u UJ (I) "' :J: a.. 601' -----,-40 30 20 10 2.nt'J .. .. .. ..... lnW w.r---1 0 50 100 150 200 250 300 TIME (sec) FICIJRE 3.28 Response tirre of phase conjugate wave for various input pavers with the inp.tt angle equal to 70 degrees. VI

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3 .a a: 1.&1 ll: 0 Q. 1.&1 t-(!J .., z 0 u 1.&1 UJ ::t: Q. I I 140 1--, -r ---r I __,.-10 rrW 9 rrW = ::1 1201/ / I // 8 ni'l 60 40 20 0 tVL.J.......0 20 40 60 80 100 120 1-40 160 TIME (sec) FIGURE 3.29 Response time of phase oonjugate wave for various input powers with the input angle equal to 70 degrees. 180 lJ1 lJ1

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z .a 0 Q. ILl '"' C!) :1 z 0 u I&J CIJ '"' ::t: 11. r--------- 500 4oor 60 n1i'7 300 200 100 I 40 nli 0 -100 o ro 50 TIME (sec) FIGURE 3.30 Response time of phase conjugate wave for various input powers with the input angle equal to 70 degrees. 60 l.n 0'

PAGE 68

X' ::2 .... a: Ul 31: 0 D. Ul 1-o( (!) ;::::) .., z 0 u UJ CIJ a. 100 r----,---60 40 20 0 ..... H& 20 mt-7 -20 L----L. I I 0 1 2 3 4 5 6 7 8 9 10 TIME (sec) FIGURE 3. 31 First ten seconds of Figure 3. 30. V1 '-I

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.a a: 111 :E 0 a. 111 .... "" (!) z 0 u 111 U1 "" :I: a. BOO 700 100 m'7 1 600 500 -400 300 200 70 mN 100 0 -100 I I I I 0 5 10 15 20 25 TIME (sec). FIGURE 3.32 Response time of conjugate wave for varying input powers with the input angle equal to 70 degrees. 30 lJl CX>

PAGE 70

x .3 a: UJ 3: 0 Q. UJ 1-(!) ::l "") z 0 u UJ UJ J: Q. 10 -----r----------r---8 6 4 2 0 -2 L--...---L------'--0 100 200 300 TIME (sec) 400 500 FIGURE 3. 33 Response tine of phase conjugate wave for varying input pcMers with the input angle equal to 80 degrees. 600 V1 \.0

PAGE 71

z .3 a: UJ 0 a. UJ .... (D :::. "') z 0 0 UJ Cl) :I: a. 350 ----.------..--------.-----.,.----. r 300 250 200 150 100 50 I ,. /-'-20ni.-J l 0 -50 L------L--. ...!___ 0 10 20 30 40 50 60 70 80 90 100 TIME (aec) FIGURE 3.34 Response time of phase conjugate wave for varying input powers with the input angle equal to 80 degrees. 0\ 0

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300 --,-------T ------,---- ----l 3 .a a: l1J 3: 0 a. l1J .... (!) :::l z 0 u l1J UJ :.:: a. 250 200 150 100 50 0 t.n.W"fr-JW -50 0 10 70 rrN 20 30 TIME (sec) 40 50 FIGURE 3.35 Response time of phase conjugate wave for varying input powers with the input angle equal to 80 degrees. 60 (J\ ........

PAGE 73

62 hoped, however, that the data taken will someday lead to or explain new theories and observations of the photorefractive effect. It is also hoped that the data will be of value to those who are considering the use of these devices for a particular application. Although it is beyond the scope of this thesis to do a complete analysis of the data and possibly arrive at new physical concepts, we do, in Chapter 4, give polynomial fits of the data for slope of the phase conjugate rise time vs. input power for the various input angles. to the best of our knowledge, this analysis does not appear in any of the literature. It is our opinion that this is a very practical analysis.

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CHAPTER 4 POLYNOMIAL FITS FOR RISE TIME SLOPE DATA This Chapter gives polynomial fits to rise time slope data (section 4.1) and graphical representations of build-up time data (section 4.2). 4.1 Polynomial fits for rise time slope data This section gives polynomial fits for the data in Table 3.4, which gives rise time slope of the phase conjugate wave as a function of input angle and input power. The fits are done in a least squares sense. Figures 4.1 through 4.6 contain the data points (circles), polynomial fits (solid lines), and the coefficients of the polynomials (C0 c1 C2, c3 ) Each figure corresponds to a different input angle. All figures are fit with a third degree polynomial of the form (4.1) where P is input power to the crystal and the C's are coefficients. These coefficients are tabulated in Table 4.1.

PAGE 75

10 9 8 :;:; '0 7 D. 0 .:s UJ ::E 6 1-1 1UJ 5 (I) 1-1 a: u 4 D. lL 0 UJ 3 D. 0 _. (I) 0 2 1 0 0 I I 1 2 3 4 5 6 7 B 9 POWER INCIDENT ON CRYSTAL (mW) FIGURE 4.1 Polynorrdal fit (solid line) of data (circles) for slope of phase conjugate rise time vs. input power at soo input angle. 10 0\

PAGE 76

15 'C ....... 0. I w / 0 UJ 10 ::E H UJ tn H a: u 0. 5 lL 0 UJ 0. 0 J tn 0 1 2 3 4 5 6 7 8 9 10 POWER INCIDENT ON CRYSTAL (mW) FIGURE 4.2 POlynomdal fit (solid line) of data (circles) for slope of phase conjugate rise time vs. input power at 55 input angle. 0\ U1

PAGE 77

7 ----, 6 4-1 1J ..... 5 Q. !! w ::E H 4 1-w Ul H a: u 3 Q. LL 0 w Q. 2 0 __. Ul 1 D 0 1 2 3 4 5 6 7 8 9 POWER INCIDENT ON CRYSTAL (mW) FIGURE 4.3 fit (solid line) of data (circles) for slope of phase conjugate rise time vs. input power at 60 input angle. 10 "' "'

PAGE 78

5 4.5 4 ..... '0 3 5 D. ;g UJ 3 :1: H I-.UJ 2.5 rn H a: u D. 2 IL 0 UJ 1.5 D. 0 0 ..J rn 1 0.5 0 0 1 2 3 4 5 6 7 B 9 POWER INCIDENT ON CRYSTAL (mW) FIWRE 4.4 Polynanial fit (solid line). of data (circles) for slope of phase conjugate rise time vs. input pawer at 65 input angle. 10 0'\ .......

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4.1 '1:1 ...... Q. s 11.1 ::E H 1-11.1 U) H a: u Q. lL 0 11.1 Q. 0 ...J U) 3 2.5 2 1.5 1 0.5 I 0 0 I 0 1 2 3 .. 5 6 POWER INCIDENT ON CRYSTAL 7 (mW) B 9 10 FIGURE 4.5 Polynomial fit (solid line) of data (circles) for slope of phase cx:>njugate rise time vs. input power at 70 input angle. 0'\ ())

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0.9 0.8 0.7 -""' '0 ....... 0.6 D. ;g UJ 0.5 % .... 1-UJ 0.-4 UJ .... a: u 0.3 D. u.. 0 UJ 0.2 D. 0 ...J UJ 0.1 0 -0.1 1 2 3 4 5 6 7 8 9 POWER INCIDENT ON CRYSTAL (mW) FIQJRE 4. 6 Polynomial fit (solid line) of data (circles) for slope of phase conjugate rise time vs. input at 75 input angle. 10 0' \0

PAGE 81

70 To our knowledge this type of analysis does not exist in the available literature. It is hoped that the polynomial fits will be of practical value to anyone who is considering using BaTi03 for a particular phase TABLE 4.1 Coefficients of polynomial fits of rise time slope data for various input angles. The data was fit in a least squares sense. 9 (deg) c c c c 0 1 2 3 50 1.2383 -1.3672 0.5051 -0.0289 55 -1.0753 1.1025 -0.1617 0.0252 60 0.2639 -0.1520 0.0500 0.0023 65 0.1800 -0.1057 0.0360 0.0020 70 -0.6609 0.7058 -0.1730 0.0139 75 0.0227 -0.0387 0.0137 -0.0002 conjugation application. It must be remembered that this analysis is useful only for the 514.5/BaTi03/self-pumped configuration. This is, however, a popular configuration due to the high phase conjugate reflectivity and relative ease of use.

PAGE 82

71 4.2 Graphical representation of build-up time data Figures 4.7 through 4.13 are plots of the data presented in Table 3.3 concerning.the build-up time of the phase conjugate wave as a function of input power at the various input angles; they are shown here as a matter of practical importance. The negative exponential nature of these plots is evident -and becomes more pronounced when a linear scale is used as the ordinate.

PAGE 83

5 4 ILl ':1: 3.5 r DDQ H 1-n. :J ,. 0 3 _J I H :J ID LL 2.5 0 [!) 0 _J 2 _J "' a: :J 1.5 1-"' z 1 0.5 0 0 FIGURE 4.7 angle. Q D Q D Q 0 10 20 1---r D D 50 DEGREES -,-------r D D Q 30" 40 50 60 70 POWER INCIDENT ON CRYSTAL (mW) D 80 90 100 Build-up time of phase conjugate wave vs. input for 50 input ....... N

PAGE 84

w ::::E H 1-Q. ::J I 0 ..J H ::J m LL 0 (!) 0 ..J ..J "' a: ::J 1-"' z 55 DEGREES 6r---D 5 41 3 2 1 D D D D D D D D ;_ _, D -D -D D -D D D 0 FI
PAGE 85

5 D 4.5 D 4 UJ I D ::::E H 1Q. 3.5 I Dg I 0 D _J H 3 m I 11. 2.51 0 (!) 0 _J _J "' 21 a: 1-"' z 1.5 1 0.5 0 FIGURE 4.9 angle. D D 60 DEGREES -.-----,-----rD D D D D D D D D D 10 20 30 40 50 60 70 80 90 100 POWER INCIDENT ON CRYSTAL (mW) Build-up tine of phase conjugate wave vs. input p:J\'ler for 60 input 1. -....!

PAGE 86

65"DEGREES 5 a 4.5 41 a UJ H I 1a a. 3.5 :::> I I a c ..J ., ..... H :::> m 11. 0 a (.!) 2.5 a 0 ..J ..J "" 2J-a: a :::> 1-"" z 1.5la a a a 11 a a 0.5 0 10 20 30 40 50 60 70 eo 90 100 POWER INCIDENT ON CRYSTAL (mW) FIGJRE 4.10 .Build-up time of phase conjugate vs. input power for 65 input angle. ..... VI

PAGE 87

70 DEGREES 7 r-----...----,.-----.--UJ ::: .... 1-a. :::> I 0 _J .... :::> UJ 11. 0 (!) 0 _J _J c( a: :::> 1-c( z D 6 5 0 4 0 ] 0 0 0 0 0 FIQJRE 4.11 angle. 00 0 0 0 0 0 0 0 0 0 I I I I I I I I I 10 20 30 40 50 60 70 eo 90 100 POWER INCIDENT ON CRYSTAL (mW) Build-up time of phase conjugate wave vs .input p:JWer for 70 .input ....... 0\

PAGE 88

75 DEGREES 5.-----I I I I a 4] 0 UJ .... _I-0 a. 0 :J I a c ...J a .... a :J m a 11. 3 0 (!) I 0 0 ...J ...J 2.5 c( [[ I 0 :J 1-c( z 21--1 a 0 -a 0 a 1 0 10 20 30 40 50 60 70 80 90 100 POWER INCIDENT ON CRYSTAL (mW) FIGURE 4.12 Build-up time of phase conjugate wave vs. input power for 75 input angle. ....... .......

PAGE 89

80 DEGREES 4.5 4 UJ 3.5 1-1 t-0.. :::1 I I 0 _. 1-1 :::1 m lL 0 (!) I 0 _. _. I <( a: :::1 t2 <( z 1.5 1 10 FIGJRE 4.12 angle. 0 0 0 D D 0 D D 20 30 40 50 60 70 80 90 100 POWER INCIDENT ON CRYSTAL (mW) Build-up time of phase conjugate wave vs. input power for 80 input ....... CXl

PAGE 90

CHAPTER 5 CONCLUSIONS Due to the limited amount of time available, c?nclusions are drawn only on the most elementary analyses of the experimental data. Many other worthwhile endeavors are possible, such as verification of the theory by data analysis. With this in mind, the following conclusions are made from the experimental data contained in this paper: 1. Two-beam coupling power transfer is largest for 14.5 s es 20.0. 2. All crystal interactions are sensitive to vibration. 3. Once a phase grating is set-up in a crystal it stays there until it is erased (at least for a day or so) 4. Beam coupling is oscillatory for input angles equal to or greater than 26. 5. Beam coupling is oscillatory for input powers (of A 1 ) less than 4 mW. 6. The phase conjugate beam becomes oscillatory for input powers greater than -3 mW.

PAGE 91

increased. 8. Build-up time decreased slightly as input angle a decreased with constraint 50 sa s 80. 80 9. Rise time slope (dP/dt) of the phase conjugate wave is greatest for a =55. 10. Rise time slope (dP/dt) of the phase conjugate wave increased with increasing input power.

PAGE 92

BIBLIOGRAPHY [1] M.B.Klein,G.C.Valley,"Beam coupling in BaTi03 at 442 nm,"J.Appl.Phys.,57(11),pp.4901-4905,1985. [2] M.Cronin-Golornb,B.Fischer,J.O.White,A.Yariv, "Theory and applications of four-wave mixing in photorefractive media,"IEEE J.of Q.E.,vol.QE-20, pp.12-30,1984. [3] K.R.MacDonald,J.Feinberg,"Theory of a self-pumped phase conjugator with two coupled interaction regions,"J.Opt.Soc.Am.,vol.73,no.5,pp.548-553,1983. [4] E.Hecht,OPTICS,Addison-Wesley,pp.334-336,1987. [5] M.B.Klein,R.N.Schwartz,"Photorefractive effect in BaTi03:microscopic origins," J.Opt.Soc.Am.B,vol.3, no.2,pp.293-305,1986 .. [6] A.Yariv,OPTICAL ELECTRONICS,HRW,ch.9,1985. [7] R.A.Fisher,Editor,OPTICAL PHASE CONJUGATION,Academic Press,ch.11,1983. [8] D.L.Staebler,J.J.Amodei,"Coupled wave analysis of holographic storage in LiNbo 3,"J.Appl.Phys.,vol.43, no.3, pp.1042-1049,.1972. [9] J.Feinberg,D.Heiman,A.R.Tanguay Jr.,R.W.Hellwarth, "Photorefractive effects and light induced charge migration in barium titanate,"J.Appl.Phys.,51, pp. 1297-1305,1980. [10] J .Feinberg, "Asyme_tric self-defocusing of an optical beam from the photorefractive effect,"J.Opt.Soc.Am., vol.72,no.1,pp 46-51,1982.

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[11] R.K.Jain,K.Stenersen,"Small-Stokes-shift frequency conversion in single mode birefringent fibers," Opt.Comm.,vol.51,no.2,pp.l21-126,1984. 82 [12] R.A.McFarlane,D.G.Steel,"Laser oscillation using resonator with self-pumped phase conjugate mirror," Opt.Lett.,8,pp.208-210,1983. [13] J.Feinberg,"Continuous-wave self-pumped phase conjugator with wide field of view,"Opt.Lett.,B, pp.480-482,1983. [14] P.Gunter,E.Voit,M.Z.Zha,"Self-pulsation and optical _chaos in self-pumped photorefractive BaTio3," Opt.Cornm.,vol.55,no.3,pp.210-214,1985.

PAGE 94

APPENDIX A LIST OF EQUIPMENT The following is a list of equipment that was used in the experiments described within this thesis. LASER: Spectra-Physics Series 2000 argon ion CRYSTAL: melt grown, single domain BaTio3 LASER POWER METER: Newport Research Corporation model 820 DATA ACQUISITION SYSTEM: -Data Translation's DT2814 A/D converter board -Zenith AT compatible -op-amp circuit with TL081 -low-pass filter VARIABLE NEUTRAL PENSITY FILTER: by Oriel POLARIZATION ROTATOR: Consists of two plain mirrors oriented at 45 with respect to each other

PAGE 95

APPENDIX B INTERFACE TO DATA ACQUISITION SYSTEM This Appendix describes the interface between the optical power meter and computer that was used in the experiments contained within this thesis. The entire interface is shown in Figure B-1. The low-pass filter and the amplifier are shown in Figures B-2 and B-3, respectively. The twelve bit analog to digital converter is the DT2814 supplied by Data Translation, Inc. The digital computer is a Zenith Z-200 AT compatible. detector head optical power meter low-pass filter amplifier ADC interface board X 40 1-----f 0-4 v digital computer FIGORE B-1 Computer interface for phase conjugation experiments.

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2.67 k v in I 40 !LF v out 85 t = 125 msec 3 dB point is 1.5 Hz FIGURE B-2 Low-pass filter used to get rid of 60 Hz ac noise at input of amplifier. +V. 1n +V out v = 40 v out in FIGURE B-3 Amplifier used to increase 0 100 mV signal to 0 -4 V signal for increased resolution of A/D converter.

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APPENDIX C LASER STABILIZATION CONFIRMATION EXPERIMENT This Appendix describes an experiment that was conducted to verify laser stability in the presence of phase conjugate feedback into the cavity. The experimental set-up is shown in Figure C-1. It was found that power meter 1, which essentially monitors the laser cavity, did not oscillate even when intense oscillation was seen in power meter 2, which monitors the phase conjugate wave. We therefore concluded that the oscillation of the phase conjugate wave is not due to an unstable laser source. It is possible, however, that an oscillation could be seen in the laser cavity with more sophisticated equipment that was not available to us. Finally, it should be noted that an optical isolator could be used if there is any doubt as to laser instability due to optical feedback into the cavity. Unfortunately, such a device was not available to us during the testing reported on in this paper.

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+ argon detector 1 input beam power meter 1 e polarization rotator variable neutral density filter phase conjugate beam 87 detector 2 power meter 2 FIGURE C-1 Experimental configuration used to test laser stability. Detector 1 monitors the laser cavity output while detector 2 monitors the oscillating phase conjugate wave.