Citation
Experimental study of two-beam coupling in photorefractive barium titanate (BaTiO3) at 442nm

Material Information

Title:
Experimental study of two-beam coupling in photorefractive barium titanate (BaTiO3) at 442nm
Creator:
Vu, Chuong Van
Place of Publication:
Denver, CO
Publisher:
University of Colorado Denver
Publication Date:
Language:
English
Physical Description:
viii, 155 leaves : illustrations ; 29 cm

Subjects

Subjects / Keywords:
Barium compounds -- Experiments ( lcsh )
Photorefractive materials -- Experiments ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references.
Thesis:
Submitted in partial fulfillment of the requirements of the degree, Master of Science, Department of Electrical Engineering, Department of Computer Science and Engineering
Statement of Responsibility:
by Chuong Van Vu.

Record Information

Source Institution:
|University of Colorado Denver
Holding Location:
|Auraria Library
Rights Management:
All applicable rights reserved by the source institution and holding location.
Resource Identifier:
26082193 ( OCLC )
ocm26082193
Classification:
LD1190.E54 1991m .V8 ( lcc )

Downloads

This item has the following downloads:


Full Text
EXPERIMENTAL STUDY OF TWO-BEAM
COUPLING IN PHOTOREFRACTIVE BARIUM
TITANATE (BaTi03) AT 442 nm
by
Chuong Van Vu
B.S., University of Colorado, 1987
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


This thesis for the Master of Science
degree by
Chuong Van Vu
has been approved for the
Department of
Electrical Engineering and Computer Science
by
Arun KL Majumdar

Edward Wall
'Date


Vu, Chuong Van (M.S., Electrical Engineering)
Experimental Study of Two-Beam Coupling in Photorefractive
Barium Titanate (BaTi03) at 442 nm
Thesis directed by Professor Arun K. Majumdar
The objective of this paper was to study photorefractive two-beam
coupling in BaTi03 experimentally. The 442 nm line of a helium cadmium
laser is used as the source. Two-beam coupling gain and time constants
(response time) are analyzed as a function of input angle, input power, and
temperature.
In addition, the two-beam coupling time constant is studied with
focus and nonfocused input beams.
A physical model for two-beam coupling in a photorefractive
material, such as BaTi03, is briefly presented.
The form and content of this abstract are approved. I recommend its
publication.
Signed
Arun K. Majumdar
m


CONTENTS
CHAPTER
1. INTRODUCTION.................................. 1
2. PHYSICAL MODEL DESCRIBING TWO-BEAM
COUPLING IN PHOTOREFRACTIVE MATERIALS ... 5
2.1. The Photorefractive Effect .............. 5
2.2. Two-Beam Coupling in
Photorefractive Materials ................ 9
3. EXPERIMENTAL PROCEDURES AND RESULTS...... 12
3.1. Two-Beam Coupling as a
Function of Input Angle.................... 12
3.2. Two-Beam Coupling as a
Function of Input Power.................... 32
3.3. Two-Beam Coupling as a
Function of Temperature .................. 34
3.4. Two-Beam Coupling Using Focused
and Nonfocused Beams...................... 34
4. CONCLUSION.................................. 118
4.1. Two-Beam Coupling as a
Function of Input Angle .................. 118
4.2. Two-Beam Coupling as a
Function of Input Power................... 119
4.3. Two-Beam Coupling as a
Function of Temperature .................. 125


4.4. Two-Beam Coupling Using Focused
and Nonfocused Beams............... 134
APPENDIX
A. CRYSTAL STRUCTURE OF BARIUM TITANATE___ 140
B. INTERFACE TO DATA ACQUISITION SYSTEM... 143
C. LIST OF EQUIPMENT ..................... 146
D. TEMPERATURE CONTROL AND
MEASUREMENT SYSTEM ..................... 148
E. LASER STABILIZATION
CONFIRMATION EXPERIMENT ................ 151
BIBLIOGRAPHY................................ 154
v


FIGURES
Figure
1.1. Two-beam coupling in a photorefractive crystal............. 3
2.1. Formation of a photorefractive phase grating............... 8
3.1. Experimental configuration used for testing
two-beam coupling for various input angles.............. 13
3.2. Close-up view of crystal/beam interaction.................. 14
3.3 through 3.18. Signal beam Is (L) outputs as a
function of input powers and input angles............... 16-31
3.19. Experimental configuration used for testing
two-beam coupling for various input powers........... 33
3.20. Experimental configuration used for testing
two-beam coupling for various temperatures.............. 35
3.21 through 3.67. Signal beam IS(L) outputs as a
function of temperatures................................ 36-83
3.68. Experimental configuration used for testing
two-beam coupling using focused and nonfocused
beams................................................... 85
3.69 through 3.85. Signal beam Is (L) outputs when
reference beam It(o) is focused........................ 86-100
3.86 through 3.101. Signal beam Is (L) output when
both Is(o) and Ir(o) focused.......................... 101-117


4.1 through 4.5. Coupling gain coefficient versus
grating period at different input angles, input
powers, and temperatures........................................... 120-124
4.6 through 4.13. Coupling time constant versus 1/T
at different grating and input powers..................... 126-133
4.14 through 4.17. Coupling time constant versus
input powers Ir(o) at different input beam focuses........135-138
A. 1. Crystal structure of BaTi03................................. 142
B. l. Data acquisition system..................................... 144
B.2. Low pass filter in data acquisition system.................. 145
B.3. Amplifier in data acquisition system........................ 145
D.l. Heater circuit.............................................. 150
D. 2. Temperature sensor circuit.................................. 150
E. l. Experimental configuration used
to test laser stability. .. .............................. 153
vn


ACKNOWLEDGEMENTS
I am sincerely grateful to Dr. Arun K. Majumdar for his advice,
dedication, and continuous guidance throughout this research. Gratitude is
also extended to Dr. Joe Thomas and Dr. Edward T. Wall for serving on the
examination committee.
Last, but not least, I am very grateful to my brothers and friends
for their patience and support.
vui


CHAPTER 1
INTRODUCTION
When light is transmitted through certain noncentro-symmetric
crystals, it causes a change in the refractive index, which persists for hours or
longer in the dark and can be erased by flooding the crystal uniformly with
light. This is referred to as the photorefractive effect.
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. They are capable of producing the photorefractive effect.
Among these photorefractive materials, barium titanate (BaTi03) has been
the subject of extensive research in recent years.
The photorefractive effect arises from a light-induced migration and
separation of charge in the crystal, which gives rise to internal static electric
fields. These fields produce refractive-index changes via the linear electro-
optic (Pockels) effect [1].
The photorefractive effect is used to describe two-beam coupling, an
optical phenomena that can be observed when two beams incident on a
photorefractive crystal.
In the two-beam coupling technique, the two beam incident on the
photorefractive crystal produces a spatial periodic irradiance pattern. If the


resultant refraction index grating is not in phase with the irradiance grating,
then energy is transferred from one beam to the other, in a direction
determined by the crystal orientation and the carrier with the greater
photoconductivity, but not by the relative power in the beams [2]. The
direction of the crystals C axis determines the direction of power transfers
as shown in Figure 1.1.
The amount of two-beam coupling depends on several parameters
and can be quite large. For the special case of BaTi03, one beam can
transfer its power to the other beam over an interaction distance of only a
few millimeters.
Since the photorefractive effect was discovered in 1966, there are
already many applications of this two-beam coupling in photorefractive
crystals, which include memory devices [3, 4], holographic storage or
interferometry [3, 5], and coherent image processing [6, 7, 8, 9, and 10].
The photorefractive effect in two-beam coupling is being studied extensively
and many more applications are expected.
Rigorous mathematical treatments can be found that analytically
describe two-beam coupling [2], as well as other aspects of the
photorefractive effect. The mathematics involved are complicated and the
results tend to be inaccurate due to the nonuniformities (crystal
abnormalities, optical spectrum differences, etc.) encountered in actual
experimentation. Furthermore, equations describing time constant (response
2


FIGURE 1.1 beamTwo-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 beam are misaligned and do not intersect in the crystal,
therefore no coupling occur. In (c) the crystal is rotated 180 and
the direction of intensity transfer is opposite to (a). (From [1]).
3


time) for two-beam coupling in photorefractive crystals do not exist in
literature to our knowledge.
With these facts in mind, the main goal of this paper is to study the
experimentally obtained gain and time constant of the two-beam coupling
for barium titanate (BaTi03) with the 442 nm line of a helium cadmium
laser as the source. The two-beam coupling gain and time constant are
analyzed as a function of the input angle, input power and temperature.
Additionally, the two-beam coupling time constant is studied with focused
and nonfocused input beams.
A brief explanation of the photorefractive effect and how the effect
leads to two-beam coupling is given. A detailed explanation of these
phenomena is well beyond the scope of this thesis, therefore many
references are given to supplement the omitted material.
4


CHAPTER 2
PHYSICAL MODEL DESCRIBING TWO-BEAM
COUPLING IN PHOTOREFRACTIVE MATERIALS
This chapter presents a brief explanation of the photorefractive
effect, and two-beam coupling in photorefractive crystals.
The derivation of the equation describing the photorefractive effect
and two-beam coupling is somewhat complex; there is no need for
derivation here many articles do this quite elegantly [11].
2.1. The Photorefractive Effect
When two-beam with complex field amplitudes ej = ejEj exp (ikj r)
and e2 = e2 E2 exp (i^ r) intersect in the crystal forming an intensity
interference pattern. This interference pattern is generated [12] and given
by
I(r) = {! + Re [m exP (K r)]} C2-1)
where


Ex (r, t) = E01 cos (kj r wt + Cj)
(2.3a)
E2(r, t) = E02 cos (k2 r wt + Cj)
(2.3b)
and
is the modulation index. The spatial frequency of the grating is given by
If the beam intersection occurs in a crystal which has mobile charge
carrier available [12], the interference pattern described by equation (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 equation (2.1), will produce an electric field -- called space charge field
- that will also vary sinusoidally with equation (2.1), but shifted in phase by
tc/2 radians.
When an electric field is applied to a crystal that does not have
inversion symmetry, there is a change in the indices of refraction. This is
called the electro-optic effect.
6


If the crystal containing the charge distribution does not possess
inversion symmetry [13], the induced space charge field will produce a
change in the refractive index through the linear electro-optic effect. The
entire process is illustrated in Figure 2.1. This process is known as the
photorefractive effect, and crystals capable of producing the effect are called
photorefractive crystals.
The source of the photocarriers is believed to be iron impurities in
most of the photorefractive crystals, which include lithium niobate (LiNb03)
and barium titanate (BaTi03). However, the actual source of the
photocarriers in BaTiOs is still being questioned.
In the absence of an externally applied field, the space charge field
was derived [14] as
where kB T is the thermal energy of the crystal lattice, q is the charge of
the mobile charge carriers, k is the absolute value of ks, and k0 is a
constant of the material that depends on the number density N of charge
carriers available for charge migration according to
E(r) = kB m
v ko =
(2.5)
7


FIGURE 2.1 Formation of a photorefractive 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's) effect. (From [13])
8


Note that upon comparison of equation (2.4) with equation (2.1), we see
I(-j is 90 out of phase with E(-j, as shown in Figure 2.1.
2.2. Two-Beam Coupling in
Photorefractive Materials
In a typical application of the two-beam coupling, at least two
coherent optical beams intersect in the crystal. These beams form an
intensity interference pattern, which then produce an index grating through
the process just described above. The index grating is spatially shifted with
respect to the intensity interference pattern which allows energy to be
diffracted from one beam into the other. The direction of this energy
transfer is determined by the direction of the crystal C axis and the sign of
the photorefractive charge carrier. See Appendix A for a description of the
crystal structure of BaTi03, and a definition of C axis.
The direction of the crystals C axis determines the direction of
energy transfer as shown in Figure 1.1.
The derivation of equations describing two-beam coupling is
complicated and only the results are shown here (see [11] and [14] for
details). The two-beam coupling gain coefficient is
r =
wreff k-B T COS 2 0
ncq cos 0
k;
l +
k20
\
R(ks)
(2.6)
9


where C is the speed of light in vacuum, r is the index of refraction, q is the
carrier charge, re£f is the effective electro-optic coefficient.
In the above equation R(ks) is a variable that is
R(ks) =
(1-C)
1 + C
(2.7)
where C is the variable that contains the hole-electron competition effects
[12].
However, if the intensity of the signal beam Is was made much
smaller than the intensity of the reference beam I so T could be
determined from
r =
IS(L>
IS(D
with Ir 0
with Ir = 0
(2.8)
where L is the interaction length in the crystal.
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 charge is determined by the
direction of two-beam coupling with respect to the crystals 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 a maximum when k = k0 (i.e., since we know the value of k,
10


we can plug it into equation (2.5) and solve for N). These facts are valuable
in understanding the physics involved in the photorefractive process.
11


CHAPTER 3
EXPERIMENTAL PROCEDURES AND RESULTS
This chapter contains descriptions and results of the experiments on
two-beam coupling in BaTi03.
Experimentation was done in the Electro-optics laboratory at the
University of Colorado at Denver.
A description of the data acquisition interface appears in Appendix B.
A list of test equipment used appears in Appendix C.
All data was taken using an helium cadmium laser at k = 442 nm.
In particular, we investigate two-beam coupling as a function of input
angle (Section 3.1), input power (Section 3.2), temperature (Section 3.3),
and with focused and nonfocused input beam.
3.1. Two-Beam Coupling as a
Function of Input Angles
The experimental set-up for these tests is shown in Figure 3.1 and a
close-up of the crystal/beam interaction 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 signal beam Is (o) constant at
0.003W/cm2. A variable neutral density is used to accomplish this.


FIGURE 3.1 Experimental configuration used for testing two-beam
coupling for various input angles
13


FIGURE 3.2 Close-up view of crystal/beam interaction.
Signal beam and refference beam 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.
14


Vary input angles (with constraint ocj = a2= a) from 7.5, 10, 15,
and 20 and record the power Is (L) (i.e., observe beam coupling at various
input angles). Angles are varied by adjusting mirrors M1? M2, and crystal
position. The result is measured by a power meter, then recorded through
data acquisition system.
The experiment will be repeated four times, each time with different
reference beam powers Ir(o) -- 0.28W/cm2, 0.14W/cm2,
0.62 W/cm2, and 0.15W/cm2 -- to see how the result is effected by
different ratio of Is(o)/Ir(o).
Result. Figure 3.3 through Figure 3.18.
Miscellaneous observation.
1. Assume we have constant Is(o) and Ir(o) incident on the
crystal. In the steady state we have coupling from the reference
beam to the signal beam. If we block Is(o), it takes about 50
seconds for Ir (L) to settle into steady state. If instead we block
Ir(), Is (L) settles into steady state almost instantaneously.
Also, if we restore beam Is (o), Ir(L) goes back to its power
in about 10 seconds (note: much faster than decrease this is
probably due to the phase grating already being set-up when Ig (o) is
restored).
15


I (L) (mV)
1.000
ON
a = 7.5
Beam focused : none
2
0.800 \- I (0) = 0.003 W/cm
lr(0) = 0.28 W/cm2
0.600 -
0.400 -
0.200 -
0.000
-I________I________I-------L-
-J________I_______L
_J-------1_______L_
3
TIME (second)
J_______I_______I______1-------I_______L
4
5
FIGURE 3.3 Signal beam IS(L) output as a function of input powers and input angles


(ALU) (1) I
2.000
1.500
1.000
n
Beam focused : None
,2
I (0) = 0.003 W/cm
I (0) = 0.28 W/cm2
0.500 -
0.000
TIME (second)
FIGURE 3.4 Signal beam IS(L) output as a function of input powers and input angles


4
oo
m
1
Beam focused : None
I (0) = 0.003W/cm2
lr(0) = 0.28 W/cm2
j----- .1-----1 I i i i I
1 2 3 4 5
TIME (second)
6
FIGURE 3.5 Signal beam IS(L) output as a function of input powers and input angles


5
a = 20
Beam focused : None
1 I (0) = 0.003 W/cm2
I (0) = 0.28 W/cm2
0 1 2 3 4 5
TIME (second)
FIGURE 3.6
Signal beam IS(L) output as a function of input powers and input angles


0.600
0.500 -
0.400
0.300 -
0.200 -
0.100
a = 7.5
Beam focused : None
I (0) = 0.003 W/cm2
lr(0) = 0.062 W/cm2
0.000
0
2 3
TIME ( second)
FIGURE 3.7 Signal beam IS(L) output as a function of input powers and input angles


I (L) (mV)
0.500
a = 10
to
0.400
Beam focused : None
I (0) = 0.003 W/cm2
lr(0) = 0.062 W/cm2
0.300
0.000 1---11'----1'1----11L
0 1 2
Ji__i__i_il__i__i_i__i_ii__i__i_i_
3 4 5 6
TIME (second)
FIGURE 3.8 Signal beam IS(L) output as a function of input powers and input angles


1.000
0.000 1111i1111I1111I___1_1_1_1__I_1_1_ 1_i_ i i
0 1 2 3 4 5 6
TIME (second)
FIGURE 3.9 Signal beam IS(L) output as a function of input powers and input angles


I (L) (mV)

TIME (second)
FIGURE 3.10 Signal beam IS(L) outputs as a function of input powers and input angles


1.000
0.800
0.600
0.400
0.200
0.000
Beam focused : None
- I (0) = 0.003 W/cm* 2
I (0) = 0.014 W/cm2
J---1--1---1--1__I___l__i__j___i__I__j__a___i__)___
2 3 4 5
TIME (second)
FIGURE 3.11 Signal beam IS(L) outputs as a function of input powers and input angles


I (L) (mV)
1.000
0.800
0.600
0.400
0.200
0.000
0 1 2 3 4 5 6
TIME (second)
FIGURE 3.12 Signal beam IS(L) output as a function of input powers and input angles
a = 10
Beam focused : None
I (0) = 0.003 W/cm2
i i i i----------------------------------------------------------------1-----------------1----------------1-----------------1-----------------1---------------J-------------------1-----------------1 i________________________________i-----------------I-----------------1________________i_________________* i I i_____________________________________________________________________________i________________


2.500
2.000 -
1.500 -
1.000 -
0.500 -
0.000
6
TIME (second)
FIGURE 3.13 Signal beam IS(L) output as a function of input powers and input angles


3.000
2.500
2.000
a = 20
Beam focused : None
I (0) = 0.003 W/cm2
s
1^(0) = 0.14W/cm2
1.500 -
1.000
0.500 -
0.000
0
J____I---1___> ---I I >________I___I___I___I _____I I
2 3 4 5
TIME (second)
FIGURE 3.14 Signal beam IS(L) output as a function of input powers and input angles


0.200
0.150
Beam focused : None
I (0) = 0.003 W/cm2
s 2
I (0) = 0.015 W/cm
0.100
0.050
0.000
TIME (second)
FIGURE 3.15 Signal beam IS(L) output as a function of input powers and input angles


0.150
0.120
0.090
0.060
a = 10
Beam focused : None
I (0) = 0.003 W/cm2
0.030
0.000 L
0
J 1 i | | | 1 i t I i i t t I i i i
2 3 4 5 6
TIME (second)
FIGURE 3.16 Signal beam IS(L) output as a function of input powers and input angles


I (L) (mV)
0.250
w
o
0.200
0.150
0.100
0*050
0.000
0 1 2 3 4 5 6
TIME (second)
FIGURE 3.17 Signal beam IS(L) output as a function of input powers and input angles


I (L) (mV)
0.250
a = 20
Beam focused : None
^ I (0) = 0.003 W/cm2
I^O) = 0.015 W/cm2
0.000 1111'111111111i11___1_I_>_i_!
0 1 2 3 4 5 6
TIME (second)
FIGURE 3.18 Signal beam IS(L) output as a function of input powers and input angles


2. Table vibration changed IS(L) and Ir(L) drastically, whereas
Is(o) and Ir(o) are unaffected by vibration.
3.2. Two-Beam Coupling as a
Function of Input Power
The experimental set-up for these tests is shown in Figure 3.19.
Test Objective. We wish to determine how beam coupling varies as a
function of relative input power.
Procedure. The input angles, ax = a2 = a, and the power in signal
beam Is (o) equals 0.003 W/cm2 will be kept constant throughout the test.
Ir(o) will be varied from 0.28 W/cm2, 0.14W/cm2, 0.062 W/cm2, and
0.015 W/cm2 by adjusting the variable neutral density filter. The result is
measured by the power meter then recorded through the data acquisition
system.
The experiment will be repeated four times at different angles -- 7.5,
10, 15, and 20 for better view of result.
Result. Figure 3.3 through Figure 3.18.
Miscellaneous observation. For the lower powers of Ir (o)
(0.015 W/cm2), the beam coupling is oscillatory.
32


FIGURE 3.19 Experimental configuration used for testing two-beam
coupling for various input powers
33


3.3. Two-Beam Coupling as a
Function of Temperature
The experimental set-up for this test is shown in Figure 3.20 and a
description of the temperature control and measurement system appears in
Appendix D.
Test objective. We wish to determine how beam coupling gain
coefficient and time constant (response time) vary as a function of
temperature.
Procedure. Repeat procedure in Sections 3.1 and 3.2, but this time
use different temperature -- 23C, 28C, 34C and 41C to heat the crystal.
After a preset temperature was reached and sufficient time elapsed for
settling, Is (L) is measured by the power meter, then recorded through the
data acquisition system.
Result. For room temperature 23C Figure 3.3 through Figure
3.18. For other temperatures: Figure 3.21 through Figure 3.67.
Miscellaneous observation. For the higher temperatures applied, the
beam coupling is easier to oscillate.
3.4. Two-Beam Coupling Using Focused
and Nonfocused Beams
The experimental set-up for this test is shown in Figure 3.68.
Test objective. We wish to determine the difference of beam
coupling time constant using focused and nonfocused beams.
34


FIGURE 3.20 Experimental configuration used for testing two-beam
coupling for various temperatures
35


1.000
a = 7.5
0.800 -
,_s 0.600
'
i-
w
o\
0.400 -
T = 28 C
I (0) = 0.003 W/cm
I (0) = 0.28W/cm2
0.200
0.000
J--1--1-1--uL--1__t_i_j__L
~1------1------1______u
Time (second)
FIGURE 3.21 Signal beam IS(L) output as a function of
temperature


1.000
o.aoo
0.600
0.400
0.200
0.000
j__ii--1--!--1--1-1i___1--1-1
i
0 1 2 3 4 5 6 7
Time (second)
FIGURE 3.22 Signal beam IS(L) output as a function of temperature


1.200
oo
1.000
0.800 I-
£
0.600
cr
__01
0.400
0.200
0.000
a = 7.5
T = 41 C
I (0) = 0.003 W/cm
s 2
I (0) = 0.28 W/cm

0
Time (second)
FIGURE 3.23 Signal beam IS(L) output as a function of temperature


0.700
oa
vO
0.600
0.500
> 0.400
E
Ci
ot 0.300
0.200
0.100
0.000
0 1 2 3 4 5 6
Time (second)
FIGURE 3.24 Signal beam IS(L) output as a function of temperatures


1.000
-F^
o
Time (second)
FIGURE 3.25 Signal beam IS(L) output as a function of temperatures


Time (second)
FIGURE 3.26 Signal beam IS(L) output as a function of temperatures


0.500
6
a = 7.5
T = 28 C
t
0.400 \- I (0) = 0.003 W/cm'
S r
I (0) = 0.062 W/cm'
0.300
>
fc

_l
0.200 -
0.100 -
0.000
_J------1_____I______1_
-I-------1------1------1-----1-------L______I______I______L
0
Time (second)
J------1-----1------1-----L------1-----L_____I______L
4
5
FIGURE 3.27 Signal beam IS(L) output as a function of temperatures


0.700
0.600
0.500
0.400
0.300
0.200
0.100
0.000
T = 34 C
; I (0) = 0.003 W/cm2
! I (0) = 0.062 W/cm2
0
2
-i-1--1---1--1--1--1--1--1__i__i___i__i__L
3 4 5
Time (second)
FIGURE 3.28 Signal beam IS(L) output as a function of temperatures


0.200
£
0.160 -
0.120 -
-I
in
0.080 -
I (0) = 0.003 W/cm
lr(0) = 0.015 /cm2
0.040 -
0.000 11L
0
-1-----> I
___________l_________I
J---1--1___i__i___L
Time (second)
FIGURE 3.29 Signal beam IS(L) output as a function of temperatures


L(L) (mV)
£
0.300
0.000 11 1*I1111I1111I> 0 1 2 3 4 5 6 7
Time (second)
FIGURE 3.30 Signal beam IS(L) output as a function of temperatures


0.200
0.160
i >.
0.080
0.040
0.000 L
0
1 2 3 4 5 6 7
Time (second)
FIGURE 3.31 Signal beam IS(L) output as a function of temperatures


lc(L) (mV)
1.800
1.500
1.200
0.900
0.600
0.300
0.000
0 1 2 3 4 5 6 7
Time (second)
FIGURE 3.32 Signal beam IS(L) output as a function of temperatures


2.500
2.000
1.500
1.000
0.500
0.000 l-
0
jiiiiiiiliiiiliiiiiiiiii__i_i_i_i_i
1 2 3 4 5 6 7
Time (second)
FIGURE 3.33 Signal beam IS(L) output as a function of temperatures


I (L) (mV)
2.500
VO
2.000
1.500
1.000
0.500
0.000 L
0
a = 10
T = 41 C
I (0) = 0.003 W/cm2

j_____i_____i_____L
1
J--1--1--1--1--1--1-1__I--1__I__I_I__L
2 3 4
J__i__i__i__i_L
5 6
Time (second)
FIGURE 3.34 Signal beam IS(L) output as a function of temperatures


(AW) (1) |
1.200

0.900 -
fi
I (0) = 0.003 W/cm
lr(0) = 0.14 W/cm'
0.600 -
0.300 -
0.000
3 4
Time (second)
6
FIGURE 3.35 Signal beam IS(L) output as a function of temperatures


L(L) (mV)
2.000
0.000 1111IiLiiliiiiIi i___i il_i_ i_i i_I i_!
0 1 2 3 4 5 6 7
Time (second)
FIGURE 3.36 Signal beam IS(L) output as a function of temperatures


1.500
0.000 i iii l ii i Ii -iiiIi__ii__iI_i__i_ i i i i < i ii i
0 1 2 3 4 5 6 7
Time (second)
FIGURE 3.37 Signal beam IS(L) output as a function of temperatures


0.500
0.000 J11*1
0 1
-1-*--1--1---1--1--1--1-x__j__1___i__i__i__i__L
2 3 4 5
Time (second)
FIGURE 3.38 Signal beam IS(L) output as a function of temperatures


1.000
0.800
a = 10
T = 34 C
I (0) = 0.003W/cm2
lr(0) = 0.062 W/cm2
0.600
0.000 111111111111
0 1 2
i----1____I____k
3
J-----1____I____I----1_____I____I----1____I_____I ...I____I____I____I_____I____L
4 5 6 7
Time (second)
FIGURE 3.39 Signal beam IS(L) output as a function of temperatures


I (L) (mV)
0.500
0.000 1111*1111*1111I1111I1111I111_i _i
0 12 3 4 5 6 7
Time (second)
FIGURE 3.40 Signal beam IS(L) output as a function of temperatures


0.200
0.150
>
E
0.100
__CO
cn
ON
0.050
a = 10
T = 28 C
ls(0) = 0.003 W/cm2
I (0) = 0.015 W/cm2
0.000 111J11'1L--J1
0 1 2
J 1 >1 I I I .1 11 1 4 IJ 1 L 1 I i
3 4 5 6 7
Time (second)
FIGURE 3.41 Signal beam IS(L) output as a function of temperatures


I (L) (mV)
0.300
0.250
0.200
0.150
U\
-j
0.100
0.050
0.000
0 1 2 3 4 5 6 7
Time (second)
FIGURE 3.42 Signal beam IS(L) output as a function of temperatures


I (L) (mV)
0.200
0.150
I (0) = 0.003 W/cm
I (0) = 0.015 W/cm2
0.100
Q
U\
00
0.050
0.000
3 4
Time (second)
FIGURE 3.43 Signal beam IS(L) output as a function of temperatures


VO
>
E
in
5
4
3
2
1
0
a = 15
T = 28 C
/
I (0) = 0.003 W/cm'
I (0) = 0.28 W/cm2
0 1 2 3 4 5 6
Time (second)
FIGURE 3.44 Signal beam IS(L) output as a function of temperatures


0 1 2 3 4 5
Time (second)
FIGURE 3.45 Signal beam IS(L) output as a function of temperatures


>
E
a)
5
4
3
2
1
0
T = 41 C
I (0) = 0.003 w/cm2
I (0) = 0.28 W/cm2
0 1 2 3 4 5
Time (second)
FIGURE 3.46 Signal beam IS(L) output as a function of temperatures


I (L) (mV)
o\
to
2.500
2.000
1.500
1.000
0.500
0.000
T = 28 C
I (0) = 0.003 W/cm2
s o
1^(0) = 0.14 W/cm
0 1 2 3 4 5 6
Time (second)
FIGURE 3.47 Signal beam IS(L) output as a function of temperatures


2.500
0.000 ------1--1---1--1---1--1---1--___I--1___1__1___*__I___1__1___1__1___l_____1__1___t
0 1 2 3 4 5
Time (second)
FIGURE 3.48 Signal beam IS(L) output as a function of temperatures


3.000
2.500
2.000
1.500
1.000
0.500
0.000 L
0
T = 41 C
I (0) = 0.003 W/cm2
I (0) = 0.14 W/cm2
J_________1_________L
1
1
-L
2
J----1----1----1----1____
3 4
Time (second)
FIGURE 3.49 Signal beam IS(L) output as a function of temperatures


I (L) (mV)
1.000
ON
a = 15
T = 28 C
/
0.800 I (0) = 0.003 W/cm'
S r
lr(0) = 0.062 W/cm'
0.600
0.400 -
0.200 -
0.000
I \_________I______l_
-j------1______L
i i i i 1 .. i i i i 1
0
Time (second)
FIGURE 3.50 Signal beam IS(L) output as a function of temperatures


L(L) (mV)
1.000
Os
Os
0.800
0.600
n
0.400
0.200
0.000
a = 15
T = 34 C
I (0) = 0.003W/cm2
I (0) = 0.062 W/cm2
T

Time (second)
FIGURE 3.51 Signal beam IS(L) output as a function of temperatures


I (L) (mV)
1.500
1.200
0.900
Ci 0.600
0.500 -
0.000
a = 15
T = 41 C
r
I (0) = 0.003 W/cm'
lr(0) = 0.062 W/cm2

0
J---------1________u
-|-------L-
2 3
Time (second)
FIGURE 3.52 Signal beam IS(L) output as a function of temperatures


I (L) (mV)
0.300
o\
00
0.250
0.200
0.150
0.100
0.050
0.000
I I I .1. J____________U. -I-------t-------1---1-----1-----1----1_____I-----I_____j--------- _l l _i i_ 1 i i i t I _ i_ _i i i_ _\ 1 I i I
01 2345678
Time (second)
FIGURE 3.53 Signal beam IS(L) output as a function of temperatures


I (L) (mV)
0.500
a = 15
0\
VO
0.400 -
T = 34 C
ls(0) = 0.003 W/cm2
lr(0) = 0.015 W/cm'
0.300
o
0.200 -
0.100
0.000
0
Time (second)
8
FIGURE 3.54 Signal beam IS(L) output as a function of temperatures


L(L) (rnV)
-4
O
Time (second)
FIGURE 3.55 Signal beam IS(L) output as a function of temperatures


4
>
E
3 -
a = 20
I (0) = 0.003 W/cm
lr(0) = 0.28 W/cm2
2 -
CO
1 -
4
Time (second)
FIGURE 3.56 Signal beam IS(L) output as a function of temperatures


5
4
a = 20
T = 34 C
I (0) = 0.003 W/cm* 2
lr(0) = 0.28 W/cm2
-j
to
o
>
E
2
0
0
1
-i -_I_ I --* I _l I 1__ I I 1 I I I I_________
2 3 4 5 6
Time (second)
FIGURE 3.57 Signal beam IS(L) output as a function of temperatures


5
a = 20
T = 41 C
0 1 2 3 4 5
Time (second)
FIGURE 3.58 Signal beam Is(L) output as a function of temperatures


(Aw) (1) I
2.500
2.000
a = 20
T = 28 C
I (0) = 0.003 W/cm* 2
1(0) = 0.14 W/cm2
1.500

1.000
0.500
0.000
0
1
J 1 1 1 1 1 I I I I I I I I I
2 3 4 5 6
Time (second)
FIGURE 3.59 Signal beam IS(L) output as a function of temperatures


L(L) (mV)
2.000
Di
1.500
1.000
0.500
0.000 *-
0
a = 20
T = 34 C
I (0) = 0.003 W/cm2
lr(0) = 0.14 W/cm2
Time (second)
J_______L.
FIGURE 3.60 Signal beam IS(L) output as a function of temperatures


2.000
1.500
1.000
0.500
0.000 L
0
a = 20
T = 41 C
I (0) = 0.003 W/cm2
lr(0) = 0.14 W/cm2
j 1------1 1-----1 1-----1 1 1 i i i 1 i i < i i i
2 4 6 8 10
Time (second)
FIGURE 3.61 Signal beam IS(L) output as a function of temperatures


I (L) (mV)
1.000

0.800
a = 20
(0) = 0.003 W/cm
s 2
lr(0) = 0.062 W/cm
0.600
o
0.400 -
0.200
0.000
Time (second)
FIGURE 3.62 Signal beam IS(L) output as a function of temperatures


L(L) (mV)
1.000
<1
oo
0.800 -
0.600 -
o
0.400 -
0.200 -
a = 20
(0) = 0.003 W/cm
lr(0) = 0.062 W/cm2
0.000

0
Time (second)
FIGURE 3.63 Signal beam IS(L) output as a function of temperatures


I (L) (mV)
1.000
-J
VO
0.800
a = 20
T = 41 C
I (0) = 0.003 W/cm2
lr(0) = 0.062 W/cm2
0 1 2 3 4 5 6 7
Time (second)
FIGURE 3.64 Signal beam IS(L) output as a function of temperatures


I (L) (mV)
0.500
0.400
a = 20
T = 28 C
I (0) = 0.003 W/cm2
lr(0) = 0.015 W/cm2
0.300 -
0
00
o
0.200 -
0.100
0.000
8
Time (second)
FIGURE 3.65 Signal beam IS(L) output as a function of temperatures


L(L) (mV)
0.300
0.000
0
2
I t---i i t I __i j - 1 i i
4 6 8 10
Time (second)
FIGURE 3.66 Signal beam IS(L) output as a function of temperatures


I (L) (mV)
FIGURE 3.67 Signal beam IS(L) output as a function of temperatures


Procedure. Repeat procedure in Section 3.2 three times. First time
with no beam focused. Second time with Is (o) focused. Third time with
both Is(o) and Ir(o) focused. Again, the IS(L) is measured by the power
meter, then recorded through the data acquisition system.
Miscellaneous observation. The input powers of Is(o) and Ir(o)
were reduced by the lenses used to focus the beams (due to absorption and
reflection), but the beam coupling is more stable than using nonfocused
beam.
Results. For nonfocused beam: Figure 3.3 through Figure 3.18. For
Is(o) focused: Figure 3.69 through Figure 3.85. For Is (o) and It(o)
focused: Figure 3.86 through 3.101.
84


FIGURE 3.68 Experimental configuration used for testing two-beam
coupling using focused and nonfocused beams
85


I (L) (mV)
0.400
00
ON
0.300
0.200
0.100
Beam focused : I
0.000 1j1^
0 1
-I-1---I--L---1.. I I I I . I I_I_I_1_ - 1- * - -1-
2 3 4 5 6
TIME (second)
FIGURE 3.69 Signal beam IS(L) outputs when refference beam lr(0) is focused


0.250
0.200
0.150
0.100
a = 7.5
o
Beam focused : I
s o
I (0) = 0.003 W/cm
I (0) = 0.14 W/cm2
0.050
0 000 *_1 *- 1-1^11*---1I-1--1-1 1_I--1_-1__-1__i_ i__ i i i-
0 1 2 3 4 5 6
TIME (second)
FIGURE 3.70 Signal beam IS(L) output when refference beam Ir(0) is focused


I (L) (mV)
0.200
0.000 1111I1111I---1111111I___i_1_1__1_I__1_ 1
0 1 2 3 4 5 6
TIME (second)
FIGURE 3.71 Signal beam IS(L) output when refference beam Ir(0) is focused


0.120
0.090
0.060
a. = 7.5
Beam focused : I
s o
I (0) = 0.003 W/cm
lr(0) = 0.015 W/cm2
0.030
0.000 1111*1111*1111I111Ii___i_i_i_i '
0 1 2 3 4 5 6
TIME (second)
FIGURE 3.72 Signal beam IS(L) output when refference beam Ir(0) is focused


I (L) (mV)
0.700
VO
o
0
0.600 -
0.500 -
0.400 -
0.300 -
0.200 -
0.100 -
a = 10
Beam focused : I
I (0) = 0.003 W/cnV
lr(0) = 0.28 W/cm2
0.000
0
TIME (second)
FIGURE 3.73 Signal beam IS(L) output when refference beam Ir(0) is focused


I (L) (mV)
0.400
vo
a = 10
0.300
0.200
0.100
Beam focused : lg
I (0) = 0.003 W/cm2
0.000 - 1
0 1
1 i 1 i I I i i I. i-1- i-_ i-
2 3 4 5 6 7
TIME (second)
FIGURE 3.74 Signal beam IS(L) output when refference beam Ir(0) is focused


L(L) (mV)
S3
0.250
0.200
0.150
0.100
0.050
0.000
0 1 2 3 4 5 6
TIME (second)
FIGURE 3.75 Signal beam IS(L) output when refference beam Ir(0) is focused


I (L) (mVO
0.150
o
a =10
Beam focused : lg
0.030 -
0.000 1111L
0 1
. 1. I -I 1 1 I I I I 1 I I I I I I
2 3 4 5 6
TIME (second)
FIGURE 3.76 Signal beam IS(L) output when refference beam Ir(0) is focused


Full Text

PAGE 1

EXPERIMENTAL STUDY OF TWO-BEAM COUPLING IN PHOTOREFRACTIVE BARIUM TITANATE (BaTi03 ) AT 442 nm by Chuang Van Vu B.S., University of Colorado, 1987 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 1991

PAGE 2

This thesis for the Master of Science degree by Chuong Van Vu has been approved for the Department of Electrical Engineering and Computer Science by Arun K Majumdar Edward Wall =sbr./er; Date

PAGE 3

Vu, Chuong Van (M.S., Electrical Engineering) Experimental Study of Two-Beam Coupling in Photorefractive Barium Titanate (BaTi03 ) at 442 run Thesis directed by Professor Arun K Majumdar The objective of this paper was to study photorefractive two-beam coupling in BaTi03 experimentally. The 442 run line of a helium cadmium laser is used as the source. Two-beam coupling gain and time constants (response time) are analyzed as a function of input angle, input power, and temperature. In addition, the two-beam coupling time constant is studied with focus and nonfocused input beams. A physical model for two-beam coupling in a photorefractive material, such as BaTi03 is briefly presented. The form and content of this abstract are approved. I recommend its publication. iii Signed--------Arun K Majumdar

PAGE 4

CONTENTS CHAPTER 1. INTRODUCTION . . . . . . . . . . . . . . . 1 2. PHYSICAL MODEL DESCRIBING TWO-BEAM COUPLING IN PHOTOREFRACfiVE MATERIALS . 5 2.1. The Photorefractive Effect . . . . . . . . . . . 5 2.2. Two-Beam Coupling in Photorefractive Materials . . . . . . . . . . . 9 3. EXPERIMENTAL PROCEDURES AND RESULTS . . 12 3.1. Two-Beam Coupling as a Function of Input Angle . . . . . . . . . . . 12 3.2. Two-Beam Coupling as a Function of Input Power .................. . . 32 3.3. Two-Beam Coupling as a Function of Temperature . . . . . . . . . . . 34 3.4. Two-Beam Coupling Using Focused and Nonfocused Beams . . . . . . . . . . . . 34 4. CONCLUSION ....... : . . . . . . . . . . . . 118 4.1. Two-Beam Coupling as a Function of Input Angle . . . . . . . . . . . 118 4.2. TwoBeam Coupling as a Function of Input Power . . . . . . . . . . . 119 4.3. Two-Beam Coupling as a Function of Temperature . . . . . . . . . . . 125

PAGE 5

4.4. Two-Beam Coupling Using Focused and Nonfocused Beams ........................ 134 APPENDIX A CRYSTAL STRUCTURE OF BARIUM TITANATE .... 140 B. INTERFACE TO DATA ACQUISITION SYSTEM . . 143 C. LIST OF EQUIPMENT .......................... 146 D. TEMPERATURE CONTROL AND MEASUREMENT SYSTEM . . . . . . . . . . . 148 E. LASER STABILIZATION CONFIRMATION EXPERIMENT .................. 151 BIBLIOGRAPHY ..................................... 154 v

PAGE 6

FIGURES Figure 1.1. Two-beam coupling in a photorefractive crystal. . . . . 3 2.1. Formation of a photorefractive phase grating. 8 3.1. Experimental configuration used for testing two-beam coupling for various input angles. . . . . . 13 3.2. Close-up view of crystal/beam interaction. . . . . . . 14 3.3 through 3.18. Signal beam Is (L) outputs as a function of input powers and input angles. . . . . . 16-31 3.19. Experimental configuration used for testing two-beam coupling for various input powers. ..... . . 33 3.20. Experimental configuration used for testing two-beam coupling for various temperatures. . . . . . 35 3.21 through 3.67. Signal beam Is (L) outputs as a function of temperatures. . . . . . . . . . . . 36-83 3.68. Experimental configuration used for testing two-beam coupling using focused and nonfocused beams. . . . . . . . . . . . . . . . . . . . 85 3.69 through 3.85. Signal beam Is (L) outputs when reference be ani I r ( o) is focused. . . . . . . . . . 86-100 3.86 through 3.101. Signal beam Is (L) output when both Is (o) and Ir(o) focused ..................... 101-117

PAGE 7

4.1 through 4.5. Coupling gain coefficient versus grating period at different input angles, input powers, and temperatures. . . . . . . . . . . . 120-124 4.6 through 4.13. Coupling time constant versus 1/ T at different grating and input powers. . . . . . . . 126-133 4.14 through 4.17. Coupling time constant versus input powers Ir ( o) at different input beam focuses. 135-138 Al. Crystal structure of BaTi03 142 B.l. Data acquisition system. . . . . . . . . . . . . 144 B.2. Low pass filter in data acquisition system. . . . . . . 145 B.3. Amplifier in data acquisition system. . . . . . . . . 145 D.l. Heater circuit. . . . . . . . . . . . . . . . . 150 D.2. Temperature sensor circuit. . . . . . . . . . . . 150 E.l. Experimental configuration used to test laser stability. . . . . . . . . . . . . . . 153 V1l

PAGE 8

ACKNOWLEDGEMENTS I am sincerely grateful to Dr. Arun K Majumdar for his advice, dedication, and continuous guidance throughout this research. Gratitude is also extended to Dr. Joe Thomas and Dr. Edward T. Wall for serving on the examination committee. Last, but not least, I am very grateful to my brothers and friends for their patience and support. viii

PAGE 9

CHAPTER 1 INTRODUCTION When light is transmitted through certain noncentro-symmetric crystals, it causes a change in the refractive index, which persists for hours or longer in the dark and can be erased by flooding the crystal uniformly with light. This is referred to as the photorefractive effect. 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. They are capable of producing the photorefractive effect. Among these photorefractive materials, barium titanate (BaTi03 ) has been the subject of extensive research in recent years. The photorefractive effect arises from a light-induced migration and separation of charge in the crystal, which gives rise to internal static electric fields. These fields produce refractive-index changes via the linear electro optic (Pockels) effect [1 ]. The photorefractive effect is used to describe two-beam coupling, an optical phenomena that can be observed when two beams incident on a photorefractive crystal. In the two-beam coupling technique, the two beam incident on the photorefractive crystal produces a spatial periqdic irradiance pattern. If the

PAGE 10

resultant refraction index grating is not in phase with the irradiance grating, then energy is transferred from one beam to the other, in a direction determined by the crystal orientation and the carrier with the greater photoconductivity, but not by the relative power in the beams [2]. The direction of the crystal's C axis determines the direction of power transfers as shown in Figure 1.1. The amount oftwo-beam coupling depends on several parameters and can be quite large. For the special case of BaTi03 one beam can transfer its power to the other beam over an interaction distance of only a few millimeters. Since the photorefractive effect was discovered in 1966, there are already many applications of this two-beam coupling in photorefractive crystals, which include memory devices (3, 4 ], holographic storage or interferometry (3, 5], and coherent image processing [6, 7, 8, 9, and 10]. The photorefractive effect in two-beam coupling is being studied extensively and many more applications are expected. Rigorous mathematical treatments can be found that analytically describe two-beam coupling [2], as well as other aspects of the photorefractive effect. The mathematics involved are complicated and the results tend to be inaccurate due to the nonuniformities (crystal abnormalities, optical spectrum differences, etc.) encountered in actual experimentation. Furthermore, equations describing time constant (response 2

PAGE 11

(a) (b) c I 1 I 2 I I 2 1 FIGURE 1.1 beam 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 beam are misaligned and do not intersect in the crystal, therefore no coupling occur. In (c) the crystal is rotated 180 and the direction of intensity transfer is opposite to (a) (From [1]). 3 I 2

PAGE 12

time) for two-beam coupling in photorefractive crystals do not exist in literature to our knowledge. With these facts in mind, the main goal of this paper is to study the experimentally obtained gain and time constant of the two-beam coupling for barium titanate (BaTi03 ) with the 442 nm line of a helium cadmium laser as the source. The two-beam coupling gain and time constant are analyzed as a function of the input angle, input power and temperature. Additionally, the two-beam coupling time constant is studied with focused and nonfocused input beams. A brief explanation of the photorefractive effect and how the effect leads to two-beam coupling is given. A detailed explanation of these phenomena is well beyond the scope of this thesis, therefore many references are given to supplement the omitted material. 4

PAGE 13

CHAPTER 2 PHYSICAL MODEL DESCRIBING TWO-BEAM COUPLING IN PHOTOREFRACTIVE MATERIALS This chapter presents a brief explanation of the photorefractive effect, and two-beam coupling in photorefractive crystals. The derivation of the equation describing the photorefractive effect and two-beam coupling is somewhat complex; there is no need for derivation here --many articles do this quite elegantly [11 ]. 2.1. The Photorefractive Effect When two-beam with complex field amplitudes e1 = e1 E1 exp (ik1 r) and e2 = e2 E2 exp (iJs r) intersect in the crystal forming an intensity interference pattern. This interference pattern is generated [12] and given by (2.1) where (2.2)

PAGE 14

(2.3a) (2.3b) and is the modulation index. The spatial frequency of the grating is given by If the beam intersection occurs in a crystal which has mobile charge carrier available [12], the interference pattern described by equation (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 equation (2.1), will produce an electric field --called space charge field --that will also vary sinusoidally with equation (2.1), but shifted in phase by 1i /2 radians. When an electric field is applied to a crystal that does not have inversion symmetry, there is a change in the indices of refraction. This is called the electro-optic effect. 6

PAGE 15

If the crystal containing the charge distribution does not possess inversion symmetry [13], the induced space charge field will produce a change in the refractive index through the linear electro-optic effect. The entire process is illustrated in Figure 2.1. This process is known as the photorefractive effect, and crystals capable of producing the effect are called photorefractive crystals. The source of the photocarriers is believed to be iron impurities in most of the photorefractive crystals, which include lithium niobate (LiNb03 ) and barium titanate (BaTi03). However, the actual source of the photocarriers in BaTi03 is still being questioned. In the absence of an externally applied field, space charge field was derived [14] as (2.4) where k8 T is the thermal energy of the crystal lattice, q is the charge of the mobile charge carriers, k is the absolute value of ks, and is a constant of the material that depends on the number density N of charge carriers available for charge migration according to (2.5) 7

PAGE 16

. I I (X) p (x) E (x) An (X) FIGURE 2.1 Formation of a photorefractive 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 &\ of the crystal by the linear electro-optic (Pockels's) effect. (From [13]) 8

PAGE 17

Note that upon comparison of equation (2.4) with equation (2.1 ), we see l(r) is 90 out of phase with E<"r>, as shown in Figure 2.1. 2.2. Two-Beam Coupling in Photorefractive Materials In a typical application of the two-beam coupling, at least two coherent optical beams intersect in the crystal. These beams form an intensity interference p attern, which then produce an index grating through the process just described above. The index grating is spatially shifted with respect to the intensity interference pattern which allows energy to be diffracted from one beam into the other. The direction of this energy transfer is determined by the direction of the crystal C axis and the sign of the photorefractive charge carrier. See Appendix A for a description of the crystal structure of BaTi03 and a definition of C axis. The direction of the crystal's C axis determines the direction of energy transfer as shown in Figure 1.1. The derivation of equations describing two-beam coupling is complicated and only the results are shown here (see [11] and [14] for details). The two-beam coupling gain coefficient is <..>reff kB T cos 2 e r = _..:..:..::.._:;,. __ ncq cos e 9 (2.6)

PAGE 18

where C is the speed of light in vacuum, r is the index of refraction, q is the carrier charge, rerr is the effective electrooptic coefficient. In the above equation R(k9 ) is a variable that is R(k) = (1-C) 8 1 + c (2.7) where C is the variable that contains the holeelectron competition effects [12]. However, if the intensity of the signal beam Is was made much smaller than the intensity of the reference beam II"' so r could be determined from 1 [ I (L) with Ir ,p. 0 l r = -Ln _::8=------=--L 19(L) with Ir = 0 (2.8) where L is the interaction length in the crystal. 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 charge 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 twobeam coupling strength with the crossing angles of the two beams, because coupling is at a maximum when k = k0 (i.e., since we know the value of k, 10

PAGE 19

we can plug it into equation (2.5) and solve for N). These facts are valuable in understanding the physics involved in the photorefractive process. 11

PAGE 20

CHAPTER3 EXPERIMENTAL PROCEDURES AND RESULTS This chapter contains descriptions and results of the experiments on two-beam coupling in BaTi03 Experimentation was done in the Electro-optics laboratory at the University of Colorado at Denver. A description of the data acquisition interface appears in Appendix B. A list of test equipment used appears in Appendix C. All data was taken using an helium cadmium laser at l = 442 nm. In particular, we investigate two-beam coupling as a function of input angle (Section 3.1), input power (Section 3.2), temperature (Section 3.3), and with focused and nonfocused input beam. 3.1. Two-Beam Coupling as a Function of Input Angles The experimental set-up for these tests is shown in Figure 3.1 and a close-up of the crystal/beam interaction 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 signal beam !9 ( o) constant at 0.003 WI cm2 A variable neutral density is used to accomplish this.

PAGE 21

01-----'.. HeCad Laser ' ' \ \ Ir(O) POWER METER FIGURE 3.1 Experimental configuration used for testing two-beam coupling for various input angles 13

PAGE 22

28 H FIGURE 3.2 Close-up view of crystal/beam interaction. Signal beam and refference beam 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; 14

PAGE 23

Vary input angles (with constraint a; 1 = a;2 = a;) from 7.5, 10, 15, and 20 and record the power Is (L) (i.e., observe beam coupling at various input angles). Angles are varied by adjusting mirrors M1 M2 and crystal position. The result is measured by a power meter, then recorded through data acquisition system. The experiment will be repeated four times, each time with different reference beam powers Ir ( o) -0. 28 W 1 em2 0.14 WI em2 0. 6 2 WI em 2 and 0. 15 WI em 2 --to see how the result is effected by different ratio of Is ( o) I Ir ( o) Result. Figure 3.3 through Figure 3.18. Miscellaneous observation. 1. Assume we have constant Is ( o) and Ir ( o) incident on the crystal. In the steady state we have coupling from the reference beam to the signal beam. If we block Is ( o), it takes about 50 seconds for Ir (L) to settle into steady state. If instead we block Ir (o), Is (L) settles into steady state almost instantaneously. Also, if we restore beam Is (o), Ir(L) goes back to its power in about 10 seconds (note: much faster than decrease --this is probably due to the phase grating already being set-up when Is ( o) is restored). 15

PAGE 24

1.000 I 0 ex= 7.5 Beam focused : none 0.800 I (0) = 0.003 W/cm 2 s 2 I (0) = 0.28 W/cm r ,--.... 0.600 > E '-"' ,--.... _j '-"' Ul 0.400 f-1' 0\ 0.200 0.000 I I I I .L_______l____ _I -L l I 1 )_ __ -1 l I --1 I I 0 2 3 4 5 TIME (second) FIGURE 3.3 Signal beam ls(L) output as a function of input powers and input angles

PAGE 25

-...l ,........_. > E ........... ,........_. _J .......... (/) 2 .000 0 ex = 10 Beam focused : None I (0) = 0.003 W/cm2 s 1.500 I (0) = 0.28 W/cm2 r 1.000 0.500 0.000 0 __ ._ _j_ _l_ _L __J _j I I I 2 3 4 5 TIME (second) FIGURE 3.4 Signal beam 15(L) output as a function of input powers and input angles 6

PAGE 26

4 3 ........... ....__, 2 ........... _J ....__, U) ...... 00 1 0 0 0 ex= 15 Beam focused : None 2 I (0) = 0.003W/cm s 2 I (0) = 0.28 W/cm r 1 2 3 4 5 TIME (second) FIGURE 3.5 Signal beam ls(L) output as a function of input powers and input angles 6

PAGE 27

5 4 3 ..-...... > E '--./ ..-...... _J '-../ ....... (/) 2 \0 0 0 0 ex= 20 Beam focused : None 2 I (0) = 0.003 W/cm s 2 I (0) = 0.28 W/cm r 2 3 4 TIME (second) FIGURE 3.6 Signal beam I5(L) output as a function of input powers and input angles 5

PAGE 28

0 .600 L C( = 7.5 0 Beam focu sed : None 0 .500 2 I (0) = 0.003 W/cm s 2 I (0) = 0.062 W/cm r I 0.400 ,......_.. > E ....__... 0.300 ;,.---.. _J ....__... (/) N 0 0.200 0 .100. 0 .000 l _I l L_ .__ ______j__- I t________._ I I L __ l_ t 0 2 3 4 5 TIME ( second) FIGURE 3.7 Signal beam ls(L) output as a function of input powers and input angles

PAGE 29

0.500 ex = 1 Oo Beam focused : None 0.400 2 I (0) = 0.003 W/cm s 2 I (0) = 0.062 W/ c m r ,--.... 0.300 > E ....._, ,--.... _J ....._, Ill 0.200 N 1-' 0.100 0.000 0 1 2 3 4 5 6 TIME (second) FIGURE 3.8 Signal beam I8(L) output as a function of input powers and input angles

PAGE 30

1.000 I lX = 15 0 Beam focused : None 0.800 1-I (0) = 0.003 W/cm2 s 2 I (0) = 0.062 W/cm r ,..-.... 0.600 > E ...._.., ,..-.... _J ...._.., UJ -0.400 0.200 0.000 0 1 2 3 4 5 6 TIME (second) FIGURE 3.9 Signal beam I5(L) output as a function of input powers and input angles

PAGE 31

1.200 0 .900 ,......... > E '-..-/ 0.600 ,......... _j '-..-/ (/) 0.300. 0 .000 0 0 lX = 20 Beam focused : None 2 I (0) = 0.003 W/cm s 2 I (0) = 0.062 W/cm r 2 3 4 TIME (second) FIGURE 3 10 Signal beam Is(L) outputs as a function of input powers and input angles 5

PAGE 32

1.000 0.800 .,-..... 0.600 > E ....._., .,-..... __J ....._., en 0.400 0.200 0.000 0 0 ex= 7.5 Beam focused : None 2 I (0) = 0.003 W/cm s 2 I (0) = 0.014 W/cm r I I 2 3 4 TIME (second) FIGURE 3.11 Signal beam ls(L) outputs as a function of input powers and input angles 5

PAGE 33

1.000 0 ex = 10 Beam focused : None I (0) = 0.003 W/cm 2 0.800 1s 2 1 (o) = 0.14 W/cm r ,........ 0.600 > E ..__, ,........ _J ..__, U) N U\ 0.400 0.200 0.000 j_ 1 J I I I I 1 I I I I I I 0 1 2 3 4 5 6 TIME (second) FIGURE 3.12 Signal beam Is(L) output as a: function of input powers and input angles

PAGE 34

2.500 2.000 > 1.500 E .........., -::::1 .........., (/) N 1.000 0\ 0.500 0.000 0 0 a= 15 Beam focused : None I (0) = 0.003 W/cm2 s 2 I (0) = 0.14W/cm r 1 2 3 4 5 TIME (second) FIGURE 3.13 Signal beam ls(L) output as a function of input powers and input angles 6

PAGE 35

3.000 ex= 20 0 Beam focused : None 2.500 1-I 2 I (0) = 0.003 W em s . 2 I (0) = 0.14W/cm r I 2 .000 _..... > E ..__, 1.500 _..... _J ..__, (/) N --..l 1 .000 0.500 0 .000 0 1 2 3 4 5 TIME (second) FIGURE 3.14 Signal beam ls(L) output as a function of input powers and input angles

PAGE 36

0.200 0.050 0.000 0 0 ex = 7.5 Beam focused : None 2 I (0) = 0.003 W/cm s 2 I (0) = 0.015 W/cm r --'--'_I _ _L .... L>. .. I I _ _ _. __l _ _. ____ ..J...._ --'---'---'---'--...1.--'---l 1. 2 3 TIME (second) I I -1--4 5 FIGURE 3.15 Signal beam I5(L) output as a function of input powers and input angles 6

PAGE 37

0.150 0.120 ,--... 0.090 > E ............ ,--... _J ............ 1/) N 0.060 \0 0.030 0.000 0 0 a= 10 Beam focused : None 2 I (0) = 0.003 W/cm s 2 I (0) = 0.015 W/cm r 1 2 3 4 5 TIME (second) FIGURE 3.16 Signal beam Is(L) output as a function of input powers and input angles 6

PAGE 38

0.250 a= 15 0 Beam focused : None 2 0.200 1-I (0) = 0.003 W/cm s 2 I (0) = 0.015 W/cm r ,...._ 0.150 > E ...._ ,...._ _J ............ fl) -0.100 Vl 0 0.050 0.000 0 1 2 3 4 5 6 TIME (second) FIGURE 3.17 Signal beam ls(L) output as a function of input powers and input angles

PAGE 39

0.250 0.200 ,.--.. 0.150 > E ..__, ,.--.. _J ..__, Ul 0.100 Vl 0.050 0.000 0 0 a= 20 Beam focused : None 2 I (0) = 0.003 W/cm s 2 I (0) = 0.015 W/cm r 1 2 3 4 5 TIME (second) FIGURE 3.18 Signal beam ls(L) output as a function of input powers and input angles 6

PAGE 40

2. Table vibration changed Is (L) and Ir (L) drastically, whereas Is ( o) and Ir ( o) are unaffected by vibration. 3.2. Two-Beam Coupling as a Function of Input Power The experimental set-up for these tests is shown in Figure 3.19. Test Objective. We wish to determine how beam coupling varies as a function of relative input power. Procedure. The input angles, a 1 = a2 = a, and the power in signal beam Is (o) equals 0.003 WI cm2 wiil be kept constant throughout the test. Ir(o) will be varied from 0.28Wicm2 0.14W/cm2 0.062Wicm2 and 0.015 WI cm2 by adjusting the variable neutral density filter. The result is measured by the power meter then recorded through the data acquisition system. The experiment will be repeated four times at different angles--7.5, 10, 15, and 20 --for better view of result. Result. Figure 3.3 through Figure 3.18. Miscellaneous observation. For the lower powers of Ir ( o) (0.015 WI cm2), the beam coupling is oscillatory. 32

PAGE 41

HeCad Laser \. \. !5(0) \. ' \. \. Ir(O) DErECI'CR POWER METER FIGURE 3.19 Experimentalconfiguration used for testing two-beam coupling for various input powers 33

PAGE 42

3.3. Two-Beam Coupling as a Function of Temperature The experimental set-up for this test is shown in Figure 3.20 and a description of the temperature control and measurement system appears in Appendix D. Test objective. We wish to determine how beam coupling gain coefficient and time constant (response time) vary as a function of temperature. Procedure. Repeat pro cedure in Sections 3.1 and 3.2, but this time use different temperature -23C, 28C, 34C and 41 oc --to heat the crystal. After a preset temperature was reached and sufficient time elapsed for settling, Is (L) is measured by the power meter, then recorded through the data acquisition system. Result. For room temperature -23C --: Figure 3.3 through Figure 3.18. For other temperatures: Figure 3.21 through Figure 3.67. Miscellaneous observation. For the higher temperatures applied, the beam coupling is easier to oscillate. 3.4. Two-Beam Coupling Using Focused and Nonfocused Beams The experimental set-up for this test is shown in Figure 3.68. Test objective. We wish to determine the difference of beam coupling time constant using focused and nonfocused beams. 34

PAGE 43

HeCad Laser HEATER ' ' ' ' Ir(O) DETECTOR POWER METER FIGURE 3.20 Experimental configUration used for testing two-beam coupl.irig for various temperatures 35

PAGE 44

w 0\ 1.000 0 ex = 7.5 T = 28 C 2 0.800 1-I (0) = 0.003 W/cm s 2 I (0) = 0.28W/cm r _.-, 0.600 ...... ,_ .. .. ............. _j ...__, CJl 0.400 0.200 0.000 0 1 .J __ ___. ___ _. --1 __J 2 3 4 Time (second) FIGURE 3.21 Signal beam ls(L) output as a function of temperature 5 6

PAGE 45

w -.....) 1.000 0.800 0.0(11) .. : r: . . / _...-.... _J ....._, (I) 0.400 0.200 0 ex = 7.5 T = 34 C 2 I (0) = 0.003 W/crn s 2 I (0) = 0.28 Wjr:;rn r 0.000 "--'---''--'---'--..L-..1---'---'--'--L__.___.__ ____.__ -..__.___.__ .'--1--' .__1-......J 0 2 3 4 5 6 7 Time (second) FIGURE 3.22 Signal beam I8(L) output. as a function of temperature

PAGE 46

w 00 ,... ... .. E ,....-, _J -._/ (/) 1.200 1.000 0.800 0.600 -0.400 0.200 0 a= 7.5 T = 41 C 2 I (0) = 0.003 W/cm s 2 I (0) = 0.28 W/cm r ---------------------0.000 --'---L-.L-1 --L---'---'--_..__ ___ ,___. ___ !.___.___ 0 2 3 4 5 6 7 8 Time (second) FIGURE 3.23 Signal beam I8(L) output as a function of temperature

PAGE 47

(;) "' 0.700 0.600 0.500 -::;.-0.400 t _.--, _J ....__,(/) 0.300 0.200 0.100 0.000 0 0 ex = 7.5 T = 28 C 1 (o) = o.003 W/crr? s 2 I (0) = 0.14 W/ em r l 1 1 _j___ t J I 2 3 4 5 Time (second) FIGURE 3.24 Signal beam I5(L) output as a function of temperatures 6

PAGE 48

> E '-"" ,.--... _J ..... __, (;) 1.000 0.800 0.600 0.400 0.200 0.000 0 ex = 7.5 T = 34 C 2 I (0) = 0.003 /em s 2 I (0) = 0.14 W/cm r '---''--1'---i-..!-l.---'---.-l __ L__.__._ _._ I I I I .1--..J. --l--l..--1--i--L.---1-L-l-.i-J 0 2 3 4 5 6 Time (second) FIGURE 3.25 Signal beam Is(L) output as a of temperatures 7

PAGE 49

1-' .......... > E 0.800 0.600 ,_.... 0.400 /---. ,__, en 0.200 0.000 0 0 ex= 7.5 T = 41 C 2 I (0) = 0.003 W/cm s . 2 I (0) = 0.14 W/cm r 1 I I 2 3 Time (second) FIGURE 3.26 Signal beam Is(L) output as a function of temperatures 4

PAGE 50

0.500 0 ex = 7.5 T = 28 C 2 0.400 '"-' I (0) = 0.003 W/cm s 2 r--.. 0.300 > E ......_, "-" _.I ,_, {/) t:s 0.200 0.100 0.000 0 I (0) = 0.062 W/cm r _j_ __J_ __ i___ I l I I I J -1I L I 2 3 4 5 Time (second) FIGURE 3.27 Signal beam I5(L) output as a function of temperatures 6

PAGE 51

.p. C,;l 0.700 0.600 0.500 0 400 r.: "' _J 0.300 0.200 0.100 0.000 0 0 ex = 7.5 T = 34 C 2 I (0) = 0.003 W/cm s 2 I (0) = 0.062 W/cm r 2 3 4 5 Time (second) FIGURE 3.28 Signal beam I8(L) output as a function of temperatures . 6

PAGE 52

t 0.200 0 C( = 7.5 T = 28 C 2 0.160 1-I (0) = 0.003 W/cm s 2 ,.. 0.120 __ ... ,r.: .... _, ,__, (J) 0.080 0.040 0 .000 0 I (0) = 0.015 /em r I 1 --I I 2 I I I I I I_ I .1______ 1 I I 3 4 5 Time (second) FIGURE 3 .29 Signal beam ls(L) output as a function of temperatures 6

PAGE 53

0.300 0.240 ,.-.,. 0. 180 > E '--' ,.-.,. _J '--' U) 0.120 0.060 0 a= 7.5 T = 34 C 2 I {0) = 0.003 W/cm s 2 I {0) = 0.015 W/cm r o.ooo0 1 2 3 4 5 6 7 Time (second) FIGURE 3.30 Signal beam I5(L) output as a function of temperatUres

PAGE 54

0.200 0.040 0.000 0 ex = 7.5 0 T = 41 C ? I (0) = 0.003 W/ erns I (0) :.-::: 0.01S W/cmr. . L---L---L-.L .-L---L-.L-. ___L--' ----1--. J ---l.-l __ __.__...__'-----.1.. 0 2 3 4 5 6 Time (second) FIGURE 3.31 Signal beam I5(L) output as a function of temperatures 7

PAGE 55

1.800 I a= 10 0 0 T = 28 C 2 1.500 1 (0) = 0.003 W/cm s 2 1 (0) = 0.28 W/cm r r 1.200 ........... > E ..._ 0.900 ........... _J ........... (IJ """" 0.600 0.300 0.000 0 1 2 3 4 5 6 7 Time (second) FIGURE 3.32 Signal beam I6(L) output as a function of temperatures

PAGE 56

2.500 2.000 > 1.500 E ...._ '.:J' ...._ ._UJ 1.000 0.500 0.000 0 0 a= 10 T = 34 C I (0) = 0.003 W/cm s 2 I (0) = 0.28 W/cm r 2 1 2 3 4 5 6 Time (second) FIGURE 3.33 Signal beam Js(L) output as a function of temperatures 7

PAGE 57

\0 2.500 2.000 > 1.500 E .....__, ,--.... _J (I) 1.000 0.500 0.000 0 0 a= 10 T = 41 C 2 I (0) = 0.003 W/cm s 2 I (0) = 0.28 W/crn r 2 3 4 5 6 Time (second) FIGURE 3.34 Signal beam I5(L) output as a function of temperatures 7

PAGE 58

1.200 0.900 > E ...._, 0.600 -:J ...._, Vl (I) 0 0.300 0.000 0 0 a= 10 T = 28 C 1 (o) = o.oo3 W/crr? s 2 I (0) = 0.14 W/cm r 1 2 3 4 5 6 Time (second) FIGURE 3 35 Signal beam I5(L) output as a function of temperatures 7

PAGE 59

Vl ..... > E 2.000 1.500 ...._ 1.000 ,....., _J ...._ (I) 0.500 0.000 0 0 a= 10 T = 34 C 2 I (0) -: 0.003 W/cm s 2 I (0) = 0.14 W/cm r 1 2 .3 4 5 6 Time (second) FIGURE 3.36 Signal beam 18(L) output as a function of temperatures 7

PAGE 60

V\ N ,.--..,. > E '--' ,.--..,. _j '--' Ill 1.500 1.000 0.500 0.000 0 0 ex = 10 T = 41 C 2 I (0) = 0.003 W/cm s 2 I (0) = 0.14 W/cm r 1 z 3 4 5 6 Time (second) FIGURE 3.37 Signal beam ls(L) output as a function of temperatures 7

PAGE 61

V\ Vl 0.500 0.400 0 .. ::: ..__..,. ......--.. _J '--" (/) 0.200 0.100 0.000 0 a= 10 T = 28 C 2 I (0) = 0.003 W/cm s ? I (0) = 0.062 W/ ernr L--'--'---....!---' __ ._ .__ ___ ._ _.L _j_.__ _J__.l __ _,___L_, __ __. __ _.___, ____ .L__... --'---'--......___. 0 1 2 3 4 5 6 Time (second) FIGURE 3.38 Signal beam I5(L} output as a fu..."'1ction of temperatures

PAGE 62

1.000 0.800 S' 0.600 E ..._ -::J ..._ CIJ 0.400 0.200 0.000 0 0 a= 10 T = 34 C 2 I (0) = 0.003W/cm s 2 I (0) = 0.062 W/cm r 1 2 3 4 5 6 Time (second) FIGURE 3.39 Signal be.am I8(L) output as a function of temperatures 7

PAGE 63

0.500 I C( = 10 0 T = 41 C 2 0.400 1-I (0) = 0.003 W/cm s 2 I (o) = 0.062 W/cm r _.... 0.300 > E _.... _j VI Ill VI 0.200 0 .100 0.000 0 2 3 4 5 6 7 Time (second) FIGURE 3.40 Signal beam Is(L) output as a function of temperatures

PAGE 64

U\ "' > E 0 .200 0.150 ..._ _, 0.100 ,.--.,. _J ...._, Ul 0.050. 0.000 0 a= 10 0 T = 28 C 2 I (0) = 0.003 W/cm s 2 I (0) = 0.015 W/cm r L-..-..1-..-.i --1.-.t _L---.1. I I I I I I I I I I I I I I I I I I 0 2 3 4 5 6 7 Time (second) FIGURE 3.41 Signal beam 15(L) output as a function of temperatures

PAGE 65

0.300 I 0( = 10 0 0 T = 34 C 2 0.250 1-1 (0) = 0.003 W/cm s 2 1 (0) = 0.015 W/cm r I" 0.200 ,---.._ > E ...__, 0 .150 ,---.._ _j ...__, Ul IJ\ -....I 0.100 0.050 0.000 0 2 3 4 5 6 7 Time (second) FIGURE 3.42 Signal beam ls(L) output as a function of temperatures

PAGE 66

0.200 0.150 ......-.. > E .....__, 0.100 ......-.. _j .....__, en V\ 00 0.050 0.000 0 0 ex = 10 T = 41 C 2 I (0) = 0.003 W/cm s 2 I (0) = 0.015 W/cm r 2 3 4 5 6 Time (second) FIGURE 3.43 Signal beam I8(L) output as a function of temperatures 7

PAGE 67

5 I 0( = 15 0 T = 28 C I (0) = 0.003 W/cm 2 4 Is 2 I (0) = 0.28 W/cm r r---3 > t '---' ,.-... _J ......__, (fJ -2 VI \0 1 0 0 2 3 4 5 6 Time (second) FIGURE 3.44 Signal beam Is(L) output as a function of temperatures

PAGE 68

4 3 .......--.. > E ..__, 2 .......--.. -' ..__, (/) 0\ 0 1 0 0 0 a= 15 T = 34 C 2 I (0) = 0.003 W/cm s 2 I (0) = 0.28 W/cm r 1 2 3 4 Time (second) FIGURE 3.45 Signal beam I5(L) output as a function of temperatures 5

PAGE 69

5 4 ,--., 3 > E -.....J ,........_ _J -.....J (/) 0\ 2 1-' 1 0 0 0 a= 15 T = 41 C 2 I (0) = 0.003 W/cm s 2 I (0) = 0.28 W/cm r 1 2 3 4 Time (second) FIGURE 3.46 Signal beam ls(L) output as a function of temperatures 5

PAGE 70

2.500 2.000 .-... 1.500 > E .-... _j ___. U) Rj 1.000 0.500 0.000 0 0 a=15 T = 28 C 2 I (o) = 0.003 W/cm s 2 I (0) = 0.14W/cm r 2 3 4 5 Time (second) FIGURE 3.47 Signal beam ls(L) output as a function of temperatures 6

PAGE 71

0\ (.U 2.500 2.000 .....--.. 1.500 > E '-../ ,--. _J -....J (I) 1.000 0.500 0.000 0 0 a= 15 T = 34 C 2 I (0) = 0.003 W/cm s 2 I (0) = 0.14W/cm r 1 2 3 4 TiJTle (second) FIGURE 3.48 Signal beam I5(L) output as a function of temperatures 5

PAGE 72

3.000 I 0 a= 15 0 T = 41 C 2 2.500 1 (0) = 0.003 W/ em s 2 1 (0) = 0.14 W/cm r r 2.000 ----> E "-" 1.500 -----_J ...._, en 1.000 0.500 0.000 0 2 3 4 Time (second) FIGURE 3.49 Signal beam I5(L) output as a function of temperatures

PAGE 73

0\ lJl 1.000 0.800. ,_..._ 0.600 > E ...__, ,.----_ _J ...__, (/) 0.400 0.200 0.000 0 0 a= 15 T = 28 C 2 I (0) = 0.003 W/cm s 2 I (0) = 0.062 W/cm r 1 2 3 4 5 Time (second) FIGURE 3.50 Signal beam 15(L) output as a function of temperatures 6

PAGE 74

1.000 .0.800 ,.-.,. 0.600 > E '--' ,.-.,. _J '--' en 0\ 0.400 0\ 0.200 0.000 0 0 ex= 15 T = 34 c I (0) = 0.003W/cm2 s 2 I (0) = 0.062 W/cm r 1 2 3 4 5 Time (second) FIGURE 3.51 Signal beam I8(L) output as a function of temperatures 6

PAGE 75

0'\ -.....1 1.500 1.200 ,....._ 0.900 > E ......__, ,....._ _J ......__, en 0.600 0.300 0.000 0 0 ex= 15 T = 41 C 2 I (0) = 0.003 W/cm s 2 I (0) = 0.062 W/cm r 1 2 3 4 Time (second) FIGURE 3.52 Signal beam I8(L) output as a function of temperatures 5

PAGE 76

0.300 L ex= 15 0 0 T = 28 C 2 0 .250 1-1 (0) = 0.00.3 W/cm2 ls(O) = 0.015 W/cm r I 0.200 > E '--' 0.150 __J '--' Ul 0\ 00 0.100 0.050 0.000 L_______l___l I I I I ,____1___1______1 __ .__ I _f __ ,_l_ ____._._ J _t I I I I I I J I I I 0 1 2 3 4 5 6 7 8 Time (second) FIGURE 3.53 Signal beam I5(L) output as a function of temperatures

PAGE 77

0\ \0 0.500 0.400 ---. 0.300 > E ---. __J en 0.200 0.100 0.000 0 0 ex= 15 T = 34 C 2 I (0) = 0.003 W/cm s 2 I (0) = 0.015 W/cm r 2 4 6 Time (second) FIGURE 3.54 Signal beam Is(L) output as a function of temperatures 8

PAGE 78

c! _.... > c: 0.400 0.300 .... '---' 0.200 _.... _J ....._, (/) 0.100 0.000 0 0 ex = 15 T = 41 C 2 I (0) = 0.003 W/cm s 2 I {0) = 0.015 W/cm r 2 3 4 5 Time (second) FIGURE 3.55 Signal beam I5(L) output as a function of temperatures 6

PAGE 79

4 3 ,.-... > E ...._, 2 -:1 ...._, ...,J _VJ .... 0 0 0 a= 20 T = 28 C 2 I (0) = 0.003 W/ em s 2 I (0) = 0.28 W/cm r 1 2 3 4 5 Time (second) FIGURE 3.56 Signal beam Js(L) output as a function of temperatures 6

PAGE 80

5 I a= 20 0 T = 34 C I (0) = 0.003 W/cm 2 4 s 2 I (0) = 0.28 W/cm r 0 3 > E ......_, ,..-... .....J ......_, _rn 2 -l N 1 0 0 1 2 3 4 5 6 Time (second) FIGURE 3.57 Signal beam ls(L) output as a function of temperatures

PAGE 81

5 I a= 20 0 T = 41 C . 2 4 I (0) = 0 .003W/cm s 2 lr(O) = 0.28 W/cm t r--. 3 > E ......_, r--. __J ......_, rn ...J -2 w 1 0 0 1 2 3 4 5 Time (second) FIGURE 3.58 Signal beam Is(L) output as a function of temperatures

PAGE 82

2 .500 2.000 > 1.500 E ....._, ,..-.._ _J ....._, en 1.000 0.500 0.000 0 0 a = 20 T = 28 C 2 I (0) = 0.003 W/cm s 2 I (0) = 0.14 W/cm r 2 3 4 5 Time (second) FIGURE 3.59 Signal beam ls(L) output as a function of temperatures 6

PAGE 83

2.000 1.500 _....... > E ..._... 1.000 _....... _J ..._... (/) 0.500 0.000 0 0 ex= 20 T = 34 C 2 I (0) = 0.003 W/cm s 2 I (0) = 0.14W/cm r 1 2 3 4 5 Time (second) FIGURE 3.60 Signal beam Is(L) as a function of temperatures 6

PAGE 84

-...1 0\ > E ..__ S' ..__ (I) 2.000 1.500 1.000 0.500 0.000 0 0 a= 20 0 T = 41 C 2 I (0) = 0.003 W/ em s 2 I {0) = 0.14 W/cm r 2 4 6 8 Time (second) FIGURE 3.61 Signal beam I5(L) output as a function of temperatures 10

PAGE 85

1.000 0.800 ,-.... 0.600 > E ............. ,-.... _J ............. en :j 0.400 0.200 0.000 0 0 a= 20 0 T = 28 C 2 I (0) = 0.003 W/cm s 2 I (0) = 0.062 W/cm r 1 2 3 4 5 Time (second) FIGURE 3.62 Signal beam I5(L) output as a function of temperatures 6

PAGE 86

....:I 00 S' E ......._, ,....... _J ......._, (/) 1.000 0.800 0.600 0.400 0.200 0.000 0 0 a= 20 T = 34 C 2. I (0) = 0.003 W/cm s 2 I (0) = 0.062 W/cm r 1 2 3 4 5 Time (second) FIGURE 3;63 Signal beam I5(L) output as a function of temperatures 6

PAGE 87

-.1 \0 1.000 0 a= 20 T = 41 C 2 0.800 1-I (0) = 0.003 W/cm s 2 ....0.600 > E ...._, ...._J ...._, (/) -0.400 0.200 0.000 0 I (0) = 0.062 W/cm r 1 2 3 4 5 6 Time (second) FIGURE 3.64 Signal beam I5(L) output as a function of temperatures 7

PAGE 88

00 0 0.500 0.400 _.... 0.300 > E ......_, -::1 ......_, (I) 0.200 0.100 0.000 0 0 ex= 20 T = 28 C 2 I (0) = 0.003 W/cm s 2 I (o) = 0.015 W/cm r 2 4 6 Time (second) FIGURE 3.65 Signal beam Is(L) output as a function of temperatures 8

PAGE 89

00 ...... ,-.... > E ..._... ,-.... _j ..._... Ul 0.300 0.200 0.100 0.000 0 0 a= 20 0 T = 34 C I (o) = 0.003W/cm2 s 2 I (0) = 0.015 W/cm r 2 4 6 8 Time (second) FIGURE 3.66 Signal beam I8(L) output as a function of temperatures 10

PAGE 90

' 0.250 0.200 S' 0.150 E '--' ,--.... _J '--' UJ 0.100 0.050 0.000 0 0 a= 20 T = 41 C 2 I (0) = 0.003 W/cm s 2 I (0) = 0.015 W/cm r 2 4 6 8 Time (second) FIGURE 3.67 Signal beam ls(L) output as a fm1ction of temperatures 10

PAGE 91

Procedure. Repeat procedure in Section 3.2 three times. First time with no beam focused. Second time with Is ( o) focused. Third time with both Is ( o) and Ir ( o) focused. Again, the Is ( L) is measured by the power meter, then recorded through the data acquisition system. Miscellaneous observation. The inpu t powers of Is ( o) and Ir ( o) were reduced by the lenses used to focus the beams (due to absorption and reflection), but the beam coupling is more stable than using nonfocused beam. Results. For nonfocused beam: Figure 3.3 through Figure 3.18. For I, ( o) focused: Figure 3.69 through Figure 3.85. For Is ( o) and Ir ( o) focused: Figure 3.86 through 3.101. 84

PAGE 92

lsCO> DETECTOR POWER METER FIGURE 3.68 Experimental configuration used for testing two-beam coupling using focused and nonfocused beams 85

PAGE 93

0.400 0.300 ,........ > E '--" 0.200 ,........ _J '--" fl) 00 0\ 0.100 0.000 0 0 ex= 7.5 Beam focused : I s 2 I (0) = 0.003 W/cm s 2 I (0) = 0.28 W/cm r I I I ' I 1 2 I I I I I I I J I 3 4 5 TIME (second) FIGURE 3.69 Signal beam I5(L) outputs when refference beam Ir(O) is focused 6

PAGE 94

0.250 0.200 ,........ 0.150 > E '-" ,........ _j '-" {/) 00 0.100 -.....) 0.050 0.000 0 0 a= 7.5 Beam focused : I s 2 I (0) = 0.003 W/cm s 2 I (0) = 0.14 W/cm r 1 2 3 4 5 TIME (second) . FIGURE 3.70 Signal beam I8(L) output when refference beam Ir(O) is focused 6

PAGE 95

0.200 0.150 ,........._ > E ........., 0.100 _.. _J ........., (/) 00 00 0.050 0.000 0 0 ex = 7.5 Beam focused : I s 2 I (0) = 0.003 W/cm s 2 I (0) = 0.062 W/cm r 2 3 4 5 TIME (second) FIGURE 3.71 Signal beam I5(L) output when refference beam lr(O) is focused 6

PAGE 96

00 \0 ,....,. > E ......__, ,....,. __J ......__, rn 0.120 0.090 0.060 0.030 0.000 0 . 0 ex = 7.5 Beam focused : 1 s 2 I (0) = 0.003 W/cm s 2 I (0) = 0.015 W/cm r 1 2 3 4 5 TIME (second) FIGURE 3.72 Signal beam I5(L) output when refference beam Ir(O) is focused 6

PAGE 97

0.700 0.600 0.500 ,.-..._ 0.400 > E .....__, ,.-..._ _J .....__,Ul 0.300 \0 0 0.200 0.100 0.000 0 0 X= 10 Beam focused : 15 2 I (0) = 0.003 W/cm 5 2 I (0) = 0.28 W/cm r 1 2 3 TIME (second) FIGURE 3.73 Signal beam Is(L) output when refference beam Ir(O) is focused 4

PAGE 98

.,.-.... > E ........., -:J ........., (/) \0 '""""" 0.400 0 a= 10 Beam focused : 15 2 I (0) = 0.003 W/cm s 2 0.300 I (0) = 0.14 W/cm r 0.200 0.100 0.000 0 1 2 3 4 TIME (second) 5 6 FIGURE 3.74 Signal beam. I5(L) output when refference beam Ir(O) is focused 7

PAGE 99

0.250 0.200 S' 0.150 E ........, ___, ........, UJ t8 0.100 0.050 0.000 0 0 ex= 10 Beam focused : Is 2 I (0) = 0.003 W/cm s 2 I (0) = 0.062 W/cm r 1 2 3 4 5 TIME (second) FIGURE 3.75 Signal beam I5(L) output when refference beam Ir(O) is focused 6

PAGE 100

0.150 0.120 0 0.090 > E ........., ':J ........., \0 1/) w 0.060 0.030 0.000 0 0 a= 10 Beam focused : Is I (0) = 0.003 W/cm2 s I (0) = 0.015 W/cm2 r 1 2 3 4 5 TIME (second) FIGURE 3 76 Signal beam ls(L) output when refference beam Ir(O) is focused 6

PAGE 101

1.000 0.800 ,......_ 0.600 > E ..._, -::J ..._, Ul '() 0.400 0.200 0.000 0 0 a= 15 Beam focused : Is I (0) = 0.003 W/cm2 s I (0) = 0.28 W/cm2 r 2 3 4 5 TIME (second) FIGURE 3.77 Signal beam Is(L) output when refference beam Ir(O) is focused 6

PAGE 102

0.600 a= 15 0 Beam focused : 15 2 0.500 1-I (0) = 0.003 W/cm s 2 I (0) = 0.14 W/cm r 0.400 ,-.. > E -....J 0.300 ,-.. _J -....J (/) -\0 lJ\ 0.200 0.100 0.000 0 1 2 3 4 5 6 TIME (second) FIGURE 3.78 Signal beam 15(L) output when refference beam Ir(O) is focused

PAGE 103

0.300 ex= 15 0 Beam focused : 15 2 0.250 1 (0) = 0.003 W/cm 5 2 1 (0) = 0.062 W/cm r 0 .200 .,...... > E ..._, 0.150 .,...... _J ..._, II) \0 0\ 0.100 0.050 0.000 0 1 2 3 4 5 6 TIME (second) FIGURE 3.79 Signal beam 15(L) output whE=n reffere&lce beam Ir(O) is focused

PAGE 104

1.0 -...! .. E .....__, ,..-, _J ....._ (/) 0.150 0.120 0.060 0.030 0.000 0 0 ex= 15 Beam focused : Is 2 I (0) = 0.003 W/cm s 2 I (0) = 0.015 W/cm r 2 3 4 5 TIME (second) FIGURE 3.80 Signal beam ls(L) output when refference beam Ir(O) is focused 6

PAGE 105

1.800 lX = 20 0 Beam focused 1 s 1.500 1-ls(O) = 0.003 W/cm2 1/0) = 0 .28 W/cm2 1.200 ,-... > E ...._... 0.900 ,-... _J .........., \0 C/l 00 0.600 0.300 0.000 0 1 2 3 4 5 6 TIME (second) FIGURE 3.81 Signal beam 18(L) output when refference beam Ir(O) is focused

PAGE 106

0.200 0.000 0 1 2 3 4 5 6 TIME (second) FIGURE 3.82 Signal beam ls(L) output when refference beam Ir(O) is focused

PAGE 107

0.500 0.400 r-... 0.300 > E .........., r-... _J .........., Ul 0 0.200 0 0.100 0.000 0 0 oc = 20 Beam focused : Is 2 I (0) = 0.003 W/cm s 2 I (0) = 0.062 W/cm r 1 2 3 4 TIME (second) FIGURE 3.83 Signal beam I8(L) output when refference beam Ir(O) is focused 5

PAGE 108

0.150 0.120 r-... 0.090 > E ......., "'""' _J ......., (/) ..... 0.060 0 ..... 0.030 0.000 0 0 ex= 20 Beam focused : Is 2 I (0) = 0.003 W/cm s 2 I (0) = 0.015 W/cm r 1 2 3 4 5 TIME (second) FIGURE 3.84 Signal beam Is(L) output when refference beam Ir(O) is focused 6

PAGE 109

;---... > E ........., ;---... __J ........., (I) 0 N 1.000 0.800 0.600 0.400 0.200 0 a= 7.5 Beam focused : I & I s 2r I (0) = 0.003 W/cm s 2 I (0) = 0.28 W/cm r 0.000 0.500 1.000 1.500 TIME (second) 2.000 2.500 FIGURE 3.86 Signal beam I5(L) outputs when both 15(0) & Ir(O) are focused 3.000

PAGE 110

..... 0 W 0.600 l 0.500 1-I 0.400 ,.--... > E ......., 0.300 ,.--... _J ......., en 0.200 0.100 0.000 0.000 a= 7.5 0 Beam focused : & lr 2 I (0) = 0.003 W/cm s 2 I ( 0) = 0. 1 4 W /em r 0.500 1.000 1.500 TIME (second) 2.000 2.500 FIGURE 3.87 Signal beam I5(L) out:put when both !5(0) & lr(O) are focused 3.000

PAGE 111

_.. > E _.. _J (/) ...... 0 0.400 0.300 0.200 0.100 0.000 0.000 0 ex = 7.5 Beam focused : 15 & lr 2 I (0) = 0.003 W/cm s 2 I (0) = 0.062 W/cm r 0.500 1.000 1.500 TIME (second) 2.000 2.500 FIGURE 3.88 Signal beam ls(L) output when both ls(O) & Ir(O) are focused 3.000

PAGE 112

...... ,-.... > E 0.200 0 a= 7.5 Beam focused : & lr 2 I (0) = 0.003 W/cm s 2 0.150 1 (0) = 0.015 W/cm r ._.. 0.100 ':J' ._.. UJ 0.050 0 .000 0 1 2 3 TIME (second) FIGURE 3.89 Signal beam I8(L) output when both 18(0) & Ir(O) are focused 4

PAGE 113

...... 0 0\ 0.250 0.200 S' 0.150 E .._.. ':J .._.. Ul 0.100 0.050 0.000 0.000 0 a= 10 Beam focused : 15 & lr I (0) = 0.003 W/cm2 s I (0) = 0.28 W/cm2 r 0.500 1.000 TIME (second) 1.500 FIGURE 3.90 Signal beam Is(L) output when both Is(O) & Ir(O) are focused 2.000

PAGE 114

0.250 0 X= 10 Beam focused : 15& lr 0.200 I (0) = 0.003 W/cm2 s _._ 0.150 > E '-" _._ _J ...._, U) b -0.100 -...l 0.050 0.000 0.000 I (0) = 0.14 W/cm2 r 0.500 1.000 1.500 2.000 TIME (second) FIGURE 3.91 Signal beam I5(L) output when both 18(0) & Ir(O) are focused 2.500

PAGE 115

0.200. 0 a= 10 Beam focused : 15 & lr I {0) = 0.003 W/cm2 5 0.150 1-I (0) = 0.062 W/cm2 r 0.000 0.000 0.500 1 .000 1.500 2.000 TIME (second) FIGURE 3.92 Signal beam I5(L) output when both 15(0) & Ir(O) are focused 2.500

PAGE 116

-0 1.0 0 .120 0.090 > E '-" 0.060 _J '-" UJ 0.030 0.000 0.000 0 a= 10 Beam focused : 1 5 & lr I (0) = 0.003 W/cm2 s 1 (o) = o.o1s w;--L2 r 0.500 1.000 1.500 2.000 TIME (second) FIGURE 3.93 Signal beam I8(L) output when both 18(0) & Ir(O) are focused 2.500

PAGE 117

............ > E ..._., ,.......... 0 ..._., en ..... ..... 0 0.250 0.200 0.150 0.100 -o.o5o 0.000 0.000 0 ex = 15 Beam focused : Is & lr 2 I (0) = 0.003 W/cm s 2 I (0) = 0.28 W/cm r 0.500 1.000 1.500 2.000 TIME (second) FIGURE 3.94 Signal beam I5(L) output when both 15(0) & Ir(O) are focused 2.500

PAGE 118

> E ...__, _J ...__, Ul ...... ...... ...... 0 .200 0 ex= 15 Beam focused : 15 & lr I (0) = 0.003W/cm2 s 0.150 l(0)=0.14W/cm2 r 0.100 0.050 0.000 0.000 0.500 1.000 1.500 2.000 TIME (second) FIGURE 3.95 Signal beam I5(L) output when both I5(0) & Ir(O) are focused 2 .500

PAGE 119

N ,...--... > E ...._, ,--.... _j ...._, rn 0.200 0.150 r 0.100 0.050 0.000 0.000 a. = 15 Beam focused : Is & lr I (0) = 0.003 W/cm2 s 1 (0) = 0.062 W/c-2 r 0.500 1.000 1.500 2.000 TIME (second) FIGURE 3.96 Signal beam I8(L) output when both 18(0) & Ir(O) are focused 2.500

PAGE 120

,--.... > E .....__, ,--.... _J .....__, .Ill ,__. ,__. w 0.120 0 a= 15 Beam focused : 15 & lr I (0) = 0.003 W/cm2 s 0.090 I (o) = 0.015 W/cm2 r 0.060 0.030 0.000 0 .000 0.500 1.000 1.500 TIME (second) 2 .000 2.500 FIGURE 3.97 Signal beam I5(L) output when both 15(0) & Ir(O) are focused 3.000

PAGE 121

,-.... > E ,-.... _J UJ 0.300 0.250 1-. 0.200 0.150 0.100 0.050 0.000 0.000 a= 20 0 Beam focused : 15 & lr 1 (0) = 0.003 W/cm2 ls(O) = 0.28 W/cm2 r 0.500 1.000 1.500 2.000 2.500 TIME (second) FIGURE 3.98 Signal beam I8(L) output when both I8(0) & Ir(O) are focused

PAGE 122

,..... > E ....._ ,..... _J ....._ fl) ..... ..... V\ 0 .200 0 a= 20 Beam focused : Is & lr I (0) = 0.003 W/cm2 o.15o 1;(o) = 0.14 W/cm2 0.100 0.050 0.000 0.000 0.500 1.000 TIME (second) 1.500 FIGURE 3.99 Signal beam I5(L) output when both 15(0) & Ir(O) are focused 2.000

PAGE 123

,..... > E ....._, ,..... _J ....._, (I) 0\ 0.200 0.150 0 .100 0.050 0 .000 0.000 0 a= 20 Beam focused : Is & lr I (0) = 0.003 W/cm2 s I (0) = 0.062 W/cm2 r 0.500 1 .000 TIME (second) 1 .500 FIGURE 3 100 Signal beam I5(L) output when boi:h 15(0) & Ir(O) are fo.:used 2.000

PAGE 124

....... ....... -.....1 .........._ > 0.120 0 a= 20 Beam focused : Is & lr 1 (o) = o.ooJ W/cm2 s 0.090 1-I (0) = 0.015 W/cm2 r $0.060 .........._ _J ...._., 0.030 0.000 0.000 0.500 I 1.000 TIME (second) 1.500 FIGURE 3.101 Signal beam I5(L) output when both 15(0) & Ir(O) are focused 2.000

PAGE 125

CHAPTER4 CONCLUSION This chapter is divided into four main sections. The first, second and third sections discuss the results found during the experimental studies of the gain coefficient two-beam coupling as a function of input power, input angle, and temperature, respectively. The fourth section discusses the two beam coupling time constant responses to the focused and nonfocused input beams. 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. 4.1. Two-Beam Coupling as a Function of Input Angle Again, we use Figure 4.1 through Figure 4.5 of two-beam coupling gain coefficient r versus the grating period A to provide a whole view of results in Section 3.2. Some conclusions are made here: 1. Two-beam coupling power trarisfer is largest for

PAGE 126

2. All crystal interactions are sensitive to vibration. 3. Phase grating is stayed in the crystal after it is set-up until erased. 4. Coupling is oscillatory for input angles greater than 20. 4.2. Two-beam Coupling as a Function of Input Power The results of Section 3.1 is described by plotting the two-beam coupling gain coefficient versus the grating period A inside the crystal. The grating period A corresponding to the measured value of r was found in terms of the external incident angle using A = l /2 sin where l = 442 nm. By changing r was plotted versus A in Figure 4.1 through Figure 4.5. Each plot has a difference in input power Ir ( o) and temperature to provide a general view of the results. Some conclusions of the experiment in Section 3.1 is drawn here: 1. Two-beam coupling power transfer is larger for higher input power lr (o). 2. All crystal interactions are sensitive to vibration. 3. Once a phase grating is set-up in a crystal it remains there until it is erased (for approximately a day). 4. Two-beam coupling is oscillatory for input power Ir ( o) less than 0. 0 15 W 1 em 2 119

PAGE 127

.......... E 0 .......... r-....._ 1-' L t-.) 0 16 12 8 4 0 0.500 0 0 ----- 2 I (0) = 0.003 W/cm s T = 23 C 0 0 0 lr(O) = .28 W/cm2 A .& e 1,.:(0) = .14 W/cm2 ). lr(O) = .062 W/cm2 A lr(O) = .015 W/cm2 1.000 1.500 A (;u,m) FIGURE 4.1 Coupling gain coefficient versus grating period at different input angles, input powers, Cll1d temperatures 2.000

PAGE 128

....... N ....... 16 12 E 0 .......... 8 .--....__ L 4 0 0.500 0 D. .. 0 0 ----. 0 2 I (0) = 0.003 W/cm s T = 28 C A .. .. lr(O) -:.28 W/cm2 lr(O) = .14 W/cm2 lr(O) = .062 W/crri2 lr(O) = .015 W/cm2 1.000 D. .. .. 1.500 A (JLm) FIGURE 4.2 Coupling gain coefficient versus grating period at different input angles, input powers, and temperatures 2.000

PAGE 129

16 12 r ,........., r E u ........... 8 __, L. ....... N N 1-4 0 0.500 0 ... 0--0-.----o 2 I (0) = 0.003 W/cm s T = 34 C --i ... -----... --------------.&--.& lr(O) = .28 W/cm2 lr(O) = .14 W/cm2 lr(O) = .062 W/cm2 lr(O) = .015 W/cm2 1 .000 1.500 1\ (JLm) FIGURE 4 3 Coupling gain (:oefficient versus grating period at different input angles, input powers, and temperatures 2.000

PAGE 130

16 12 1-,-.. a E 0 .......... r-........, """"' L I 4 1-0 0.500 0 ---./-----o ls(O) = 0.003 W/cm2 T = 41 c -/6--.........0 ... -----0 1r(O) = .28 W/cm2 1r(o) = .14 W/cm2 ----. 1r(o) = .062 W/cm2 .A 1r(O) = .015 W/cm2 1.000 1.500 1\ (,um) FIGURE 4.4 Coupling gain coefficient versus grating period at different input angles, input powers, and temperatures 2.000

PAGE 131

17 L 15 r ,._ 13 tE u "-.. r ....___, L 11 [ t-.) 9 1r 7 0.500 I (0) = 0.003 W/cm 2 s 2 I (0) = 0.28 W/cm r .... ""' ,, 0 .... !:::. .... T = 41 C !:::. T = 34 C T = 28 C 0 T = 23 C 1.000 1.500 2.000 A (,urn) FIGURE 4.5 Coupling gain coefficient versus grating period at different input 3.ngles, input powers, and temperatures

PAGE 132

4.3. Two-Beam Coupling as a Function of Temperature The results in Section 3.3 are studied in two parts: two-beam coupling gain coefficient and two-beam coupling time constant (response time). In the first part, the two-beam coupling gain coefficient responses to the temperature applied on the crystals is plotted in Figure 4.1 through Figure 4.5. In the second part, a conclusion for two-beam coupling time constant is desired. Here time constant (response time) is defined as the time for 18 (L) to rise to 63.2% of the final value. By changing temperature T applied on the crystal, the time constant 't is plotted versus 1/ T in Figure 4.6 through Figure 4.13. Each plot has a difference in input angle ex and input power Ir ( o) to provide a whole view of the results. Following are some conclusions from the experiment in Section 3.3: 1. The higher the temperature applied on the crystal, the larger the two-beam coupling gain coefficient. 2. The higher the temperature applied on the the smaller the two-beam coupling time constant. 125

PAGE 133

..... tv 0\ 2.500 2.000 ,.-.... "U c 0 0 Q) (/). ...._, 1.500 1z en z 0 0 1.000 w 1-l-0.500 0.000 3 .150 2 I {0) = 0.003 W/cm s 2 I (0) = 0.28 W/cm r 3.200 0 l:l. A=1.27JLm .. 3.250 3.300 3.350 -3 0 -1 1 /T (1 0 K degree) 0 6 .... A= 1.69,u.m 1\ = 0.85 ,u.m A= 0.65 ,u.m 3.400 FIGURE 4.6 Coupling time constant versus 1/T at different grating periods and input powers 3.450

PAGE 134

N 2.500 I -;;' 2.100 c 0 u Q.) (/) '--' 1.700 1z (f) z 0 0 w 1-l-1-1.300 0.900 0.500 3.150 I (0) = 0.003 W/cm 2 s 2 I (0) = 0.14 W/cm r A 3.200 3.250 A 3.300 e A= 1.27,um o A= 1.69 ,um L:.. A= 0.85 ,um A A= 0.65 ,um 3 .350 3.400 -3 0 -1 1 /T (1 0 K degree) FIGURE 4.7 Coupling time constant versus 1 /T at different grating periods and input powers 3.450

PAGE 135

....... 3.000 c 0 u Q.) (/) ...._, 2.200 1z (/) z 0 1.800 0 w 1l1.400 1.000 3 .150 2 I {0) = 0 .003 W/cm s 2 1/0) = 0.062 W/cm 0 f). 3.200 -----0 0-----t::. 0 t::. 0 t::. 3.250 3.300 3.350 -3 0 -1 1 /T ( 1 0 K degree) A =1.27 J.Lm A = 1.69 J.Lm A= 0.85 J.Lm A= 0.65 J.Lm 3.400 FIGURE 4.8 Coupling time constant versus 1 /T at different grating periods and input powers 3.450

PAGE 136

4.000 I U'3.500 c 0 u Q) rn .....__., 3.000 Iz <( I-U1 z 1-l 8 2.500 N '0 w ::2 I1:-2.000 I I 1.500 3.150 2 I (0) = 0.003 W/cm s 2 I (0) = 0.015 W/cm r .---' 0----0 1\ = 1.27 J.Lm 6. 0 1\ = 1.69 J.Lm ... 6 1\ = 0.85 J.Lm 0 ... 1\ = 0.65 J.Lm 3.200 3.250 3.300 3.350 3.400 -3 0 -1 1/T(10 K degree) FIGURE 4 9 Coupling time constant versus 1/T at different grai:ing periods and input powers 3.450

PAGE 137

w 0 4.500 -;)3.700 c 0 u QJ en ___. 2.900 1z (/) z 0 2.100 u w I-t:-= 1.300 0.500 3.150 ... A 0 I (0) = 0.015 W/cm 2 r I (0) = 0.062 W/cm 2 r 2 ... I (0) = 0.14 W/cm r 2 ... I (0) = 0.28 W/cm r -----6. ... A ::-----a =7.5,1\ = 1.7 JJ.m I (0) = 0.003 W/cm2 s 0 3.200 3.250 3.300 3.350 3.400 3.450 -3 0 -1 1 /T (1 0 K degree) FIGURE 4.10 Coupling time constant versus 1/T at different grating periods and input powers

PAGE 138

-o c 0 (.) (I) ""--/ 2.900 1z (f) z 0 2.100 t;; 0 w 11.300 2 A I (0) = 0.015 W/cm r 2 I (0) = 0.062 W/cm r 2 I (0) == 0.14 W/cm r 2 0 I (0) = 0 .28 W/cm r 0 ... ... 0 ex = 1 0 1\ = 1 2 7 J..Lm 2 I (0) = 0.003 W/cm s 3 .150 3 .200 3.250 3.300 3.350 3.400 3.450 -3 0 -1 1 /T (1 0 K degree) FIGURE 4.11 Coupling time constant versus 1 /T at different grating periods and input powers

PAGE 139

....... w N 3.000 ,--..,. 2.500 -o c 0 u Q) (f) '"'-...-/ 2.000 1z <(' I(/) z 0 1.500 u w 2 Il-1.000 0.500 3 .150 2 I (0) = 0.015 W/cm r 2 b. I (0} = 0.062 W/cm r 2 I (0) = 0.14W/cm r 2 o 1/0) = 0.28. W/cm .... --------.... / /:).----/:). .... 0 0 0----------0 a = 15 1\ = 0.854 J..Lm 2 I (0) = 0.003 W/cm s 3.200 3.250 3.300 3.350 3:400 3.450 -3 0 -1 l/T ( 10 K degree) FIGURE 4 12 Coupling time constant versus 1/T at different grating periods and input powers

PAGE 140

...... 3.000 2.500 ,.....,.. Ll c 0 u 2.000 ..._ z 1.500 (/) z 0 u w 1.000 L ..._ 0.500 0.000 3.150 2 A I (0) = 0.015 W/cm r 2 t:::. I (0) = 0.062 W/cm A r 2 I (0) = 0.14 W/cm r 2 o 1 (0) = 0.28 W/cm r .A --------------A_/ ( -.A . l::. --------------0 ------------0 0 0 a = 20 1\ = 0.650 J-Lm 2 I (0) = 0.003 W/cm s 3.200 3.250 3.300 3.350 3.400 -3 0 -1 1/T.(10 K degree) FIGURE 4.13 Coupling time constant versus 1/T at different grating periods and input powers 3.450

PAGE 141

The second conclusion is a very encouraging one for studying of optical high-speed switching: 4.4. Two-Beam Coupling Using Focused and Nonfocused Beams The results of Section 3.4 is summarized by plotting the two-beam coupling time constant versus the input power Ir ( o). Again, the two:beam coupling time constant (response time) is defined as the time for Is (L) to rise to 63.2% of the final value. The plots are shown in Figure 4.14 through Figure 4.17. Each plot has a difference in input angle ex to provide a more general view of the results. Some conclusions of the experiment in Section 3.4 is drawn here: 1. By focusing the signal beam Is (o) and the reference beam Ir (o), the two-beam coupling time constant is much faSter than that of Is (o) focused only. 2. By focusing the beam I8 (o) only, the two-beam coupling time constant is faster than that of Is ( o) or Ir ( o) focused. 3. The stability is the best when both Is (o) and Ir (o) are focused. It is probably because when we focused the beams the intensities were increased following the formula of intensity I = power I area. 134

PAGE 142

,..-... "'0 r::: 0 0 Q) fl) ...._, 1z (/) z ...... 0 w VI () w 1-. 5 I 4 [ 3 2 1 0 0.000 T = 23 C Beam focused : None 0 ex= 20 .... Beam focused : Is ls(O) = 0.003 W/cm2 Beam focused : Is & lr .... I . ----------------------0.050 0.100 0.150 0.200 0.250 0.300 I (0) (W/cm2 ) r FIGURE 4.14 Coupling time constant versus input power Ir(O) at different beams focused

PAGE 143

5 I T = 23 C Beam focused : None a= 15 0 Beam focused : Is 4 r I (0) = 0.003 W/cm2 Beam focused : Is & lr s ,-... "'0 c 0 0 Q) rn 3 ...._, 1z (/) z 0 ..... u 2 w w 0\ ::::! 1-"I I t-o 1 0 . 0.000 0.050 0.100 0.150 0.200 0.250 0.300 lr(O) (W/cm2 ) FIGURE 4.15 Coupling time constant versus input p 'ower Ir(O) at different beams focused

PAGE 144

5 I T = 23 C Beam focused : None a= 7.5 0 A Beam focused : Is 4 t I (0) = 0.003 W/cm2 Beam focused : Is & lr s ...-.. "'C c 0 0 Q) en 3 ..._.... ...._ z (f) z 0 ...... u 2 w -..l w :::!: ...._ A-A-t-1 1. A 0 0.000 0.050 0.100 0.150 0.200 0.250 0.300 I {0) {W/cm2 ) r FIGURE 4.16 Coupling time constant versus input power lr(O) at different beams focused

PAGE 145

FIGURE 4.17 Coupling time constant versus input power Ir(O) at different beams focused

PAGE 146

4. The results from the experiment in Section 3.4 are very encouraging. It probably could contribute a great deal to improving the switching time in optical high-speed switching and phase conjugation research. 139

PAGE 147

APPENDIX A CRYSTAL STRUCTURE OF BARIUM TITANATE

PAGE 148

BaTi03 has tetragonal crystal structure between 5 and 120C. As shown in Figure A1(a) it has one Ti4+ ion at the body center, Ba2+ ions at the corners, and 02 ions at the face centers. Below the Curie temperature the 02 ions are displaced slightly relative to the Ba2+ and Ti4+ ions as shown in Figure A1(b ). This produces a dipole moment. .l3aTi03 has one axis of rotational symmetry. This axis is called the crystal axis or C axis and is also shown in Figure A1(b). Since the 02 ions are displaced along the same axis the crystal structure does not have inversion symmetry along the C axis. The lack of inversion symmetry allows us to define a unique direction associated with the C axis. This direction is also indicated in Figure A1(b). 141

PAGE 149

a b 9 9 T.4+ I o Ba2+ oo2 -l C-AXIS FIGURE A.l (a) Crystal structure of BaTi03 (b) Crystal structure of BaTi03 showing displacement of Q2 ions and direction of c axis. 142.

PAGE 150

APPENDIX B INTERFACE TO DATA ACQUISITION SYSTEM

PAGE 151

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 hoard X 40 1-----1 0-4 v digital computer FIGURE B-1 Computer interface for phase conjugation experiments. 144

PAGE 152

v in 2.67 k v out '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 amplifier. +V in +V out v = 40 v out in FIGURE B-3 Amplifier used to increase 0-100 mV signal to 0-4 V signal for increase resolution of AID converter. 145

PAGE 153

APPENDIX C LIST OF EQUIPMENT

PAGE 154

The following is a list of equipment that was used in the experiments described within this thesis. CRYSTAL : Melt single domain BaTi031 2.5 ,. 2.5 ,. 2.5 mm3 LASER : Uconix Series 4214N helium cadmium1 A.= 442 nm. POWER METER : Newport Research Corporation model 820. DATA ACQUISffiON SYSTEM : Data Translation DT2814 AID converter board -Zenith AT compatible Op-amp circuit with Tl081 -Low pass filter VARIABLE NEUTRAL DENSITY FILTER : By Oriel ROTATOR : Two plain mirrors oriented at 450 with respect to each other 147

PAGE 155

APPENDIX D TEMPERATURECONTROLAND MEASUREMENT SYSTEM

PAGE 156

The circuit used for heating and monitoring the crystal temperature are shown in Figures D-1 and D-2. The heater circuit in Figure D-1 uses a DC power supply to drive the heater. This circuit uses a transistor to covert the voltage input to a current output that is pulled through a 10 watt resitor. The energy dissipated in this resistor used to heat the crystal. Figure D-2 shows the schematic for the temperarure sensor and support electronics. It uses an LM335 temperature sensor which is actually a zener diode with a breakdown voltage that changes linearly 10 m V per degree centigrade. The op-am is used as both an amplifier and a zero-adjust. The output of the amplifier goes directly to a voltmeter to monitor the applying temperature. More detail about calibration of temperature is found in [11]. 149

PAGE 157

IN 2N3055 FIFURE D-1 Heater circuit for heating the crystal oven. 100 K 2,2 K OUT LM335 100 K FIGURE D-2 Temperature sensor for measuring the crystal temperature. 150

PAGE 158

APPENDIX E LASER STABILIZATION CONFIRMATION EXPERIMENT

PAGE 159

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 E-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. 152

PAGE 160

HeCad Laser detector 1 power meter 1 input beam e polarization rotator variable neutral density filter bs (50%) phase conjugate beam detector 2 power meter 2 FIGURE E-1 Experimental configuration used to test laser stability. Detector 1 monitors the laser cavity output while detector 2 monitor the oscillating phase conjugate wave. 153

PAGE 161

BffiLIOGRAPHY [1] Feinberg, J., D. Heiman, AR. Tanguay, Jr. and R.W. Hellwarth. 1980. Photorefractive effects and light-induced charge migration in barium titanate. J. Appl. Phys. 51(3): 1297-1305. [2] Klein, M.B. and G.C. Valley. 1985. Beam coupling in BaTi03 at 442 nm. J. Appl. Phys. 57(11): 4901-4905. [3] Chen, F.S. 1969. Optical induced change of refractive indices in LiNb03 and LiTa03 J. Appl. phys. 40(8): 3389-3396. [4] Thaxter, J.B. 1969. Electrical control of holographic storage in strontium barium niobate. Appl. Phys. Lett. 15(7): 210-212. (5] Glass, AM. 1978. Optical induced change of refractive indices in photorefractive materials. Opt. Eng. 17: 470. [6] White, J.Q. and A Yariv. 1980. Real-time image processing via four-wave mixing in a photorefractive medium. Appl. Phys. Lett. 37(1): 5-8. [7] Fischer, B., M. Cronin-Golomb, J.O. White and A Yariv. 1984. Theory and applications of four-wave mixing in photorefractive media. IEEE J. of O.E. vol. QE-20: 12-30. [8] Cronin-Golomb, M., 1.0. White, B. Fischer and A Yariv. 1982. Four-wave mixing in photorefractive medium. Opt. Lett. 7: 313. (9] Feinberg, J. and R .W. Hellwarth. 1980. Photorefractive effect and light induced charge migration in BaTi03 Opt. Lett. 5: 519. [10] Feinberg, J. 1983. Continuous-wave self-pumped phase conjugator with wide field of view. Opt. Lett. 8: 480-482. [11] Motes, R.A. 1987. Two-beam coupling in photorefractive barium titanate. Ph.D. Dissertation, University of New Mexico, Albuquerque, N.M., pp. 18-28.

PAGE 162

[12] Klein, M.B. and R.N. Schwartz. 1986. Photorefractive effect in BaTi03 : microscopic origins. J. Opt. Soc. Am. B. vol. 3, no. 2: 293305. [13] Yariv, A 1985. Optical Electronics. HRW, Ch. 9. [14] Fischer, R.A 1983. Optical Phase Conjugation. Academic Press, Ch. 11. .. 155