Citation
The design, modeling and simulation of an optical logic gate

Material Information

Title:
The design, modeling and simulation of an optical logic gate
Creator:
Rathfon, William Loran
Publication Date:
Language:
English
Physical Description:
x, 117 leaves : illustrations ; 28 cm

Thesis/Dissertation Information

Degree:
Master's ( Master of science)
Degree Grantor:
University of Colorado Denver
Degree Divisions:
Department of Computer Science and Engineering, CU Denver
Degree Disciplines:
Electrical engineering
Computer science

Subjects

Subjects / Keywords:
Logic devices -- Mathematical models ( lcsh )
Genre:
bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

Notes

Bibliography:
Includes bibliographical references (leaf 58).
General Note:
Submitted in partial fulfillment of the requirements for the degree, Master of Science, Department of Electrical Engineering, Department of Computer Science and Engineering.
General Note:
"Support for this work was provided by the Air Force Office of Scientific Research under contract no. 86-0189"--Leaf [iii].
Statement of Responsibility:
by William Loran Rathfon.

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:
19719631 ( OCLC )
ocm19719631

Full Text
THE DESIGN, MODELING, AND SIMULATION OF
AN OPTICAL LOGIC GATE
by
William Loran Rathfon
B.S., University of Colorado at Denver, 1986
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
1988


This thesis for the Master of Science degree by
William Loran Rathfon
has been approved for the
Department of Electrical Engineering and Computer Science
by
Arun K. Majumdar
Date
4-^'-8 8


ACKNOWLEDGMENTS
I would like to thank Rodney Schmidt for his technical assistance and
his commitment to helping me achieve my educational goals. Support for this work
was provided by the Air Force Office of Scientific Research under contract no.
86-0189.


IV
Rathfon, William Loran (M.S., Electrical Engineering)
The Design, Modeling, and Simulation of an Optical Logic Gate
Thesis directed by Professor Aran K. Majumdar
An optical logic gate has been designed that meets the following criteria:
i) the gate functions as a transmission device and does not require rejuvenation at the
output, ii) the inputs and outputs are encoded in horizontally and vertically polarized
light to represent logical true and false, and iii) the outputs are spatially similar, of
the same wavelength, and use the same polarization encoding as the inputs.
The logic gate has been modeled and simulated, and the results have
been correlated to measurements taken from an actual implementation of the gate in
the lab. This initial design of the gate is meant to be a discrete proof-of-principle
version of a future implementation that can be monolithically fabricated in two-
dimensional arrays of many gates. Some preliminary design results for the
monolithic version are presented.
The form and content of this abstract are approved. I recommend its publication.
Signed
Faculty member in charge of thesis


CONTENTS
CHAPTER
1. INTRODUCTION.............................................. 1
2. THEORY OF OPERATION OF THE GATE........................... 3
2.1 General Theory of Operation................... 3
2.2 Absolute Detection Theory of Operation...... 5
2.3 Differential Detection Theory of Operation... 5
2.4 Comparison of the Two Detection Schemes........ 7
3. MODELING OF THE GATE...................................... 9
3.1 Modeling General Approach................... 9
3.2 Representation of the Light................... 11
3.3 FLC Theory........................................ 12
3.3.1 FLC Optical Characteristics...................... 15
3.3.2 Switching of the FLC....................... 17
3.4 Modeling the FLC.................................... 24
3.4.1 Modeling the Molecular Rotation............ 25
3.4.2 Modeling the FLC Optical Effect............ 26
3.4.3 Choosing the FLC Constants....................... 27
3.5 Modeling the Optical Devices........................ 29
3.5.1 Modeling the Beam Splitters...................... 29
3.5.2 Modeling the Microscope Slides................... 30
3.6 Modeling the Electronic and Optoelectronic
Devices............................................. 32


vi
3.6.1 Modeling the Comparator........................ 33
3.6.2 Modeling the Detector.......................... 34
4. IMPLEMENTATION OF THE MODEL........................... 36
4.1 Organization and Data Structures.................. 36
4.2 Libraries and Main Programs....................... 37
5. THE MONOLITHIC OPTICAL LOGIC GATE..................... 40
5.1 Theory of Operation............................... 40
5.2 Layout of the Layers........................... 43
5.3 Conclusions....................................... 43
6. ANALYSIS AND CONCLUSIONS.............................. 47
6.1 Analysis.......................................... 47
6.1.1 Analysis of the FLCs........................... 48
6.1.2 Absolute Detection Gate Analysis............. 49
6.1.3 Differential Detection Gate Analysis... 51
6.2 Conclusions....................................... 56
REFERENCES.................................................... 58
APPENDIXES
A. DATA..............................;............. 59
B. FORTRAN CODE.......................................... 86


vn
TABLES
TABLE
6.1 Horizontal horizontal SNRs.................................. 52
6.2 Vertical horizontal SNRs.................................... 53
6.3 Horizontal vertical SNRs.................................... 53
6.4 Vertical vertical SNRs...................................... 54
6.5 Input-to-output gains......................................... 56


VU1
FIGURES
FIGURE
2.1 Generalized gate, theory of operation........................... 4
2.2 Absolute detection scheme, theory of operation.................. 6
2.3 Differential detection scheme, theory of operation.............. 8
3.1 Classes of liquid crystals..................................... 12
3.2 FLC orientation................................................ 14
3.3 FLC helix....,................................................. 14
3.4 FLC domains.................................................... 15
3.5 90 rotation of polarized light by a half-wave plate... 16
3.6 UP and DOWN domains, no E field applied........................ 17
3.7 Low E field regime........................................... 18
3.8 Intermediate E field regime.................................... 18
3.9 FLC angles..................................................... 20
3.10 FLC operation between polarizer and analyzer................... 21
3.11 Definition of tj, tr, and tf................................... 22
3.12a FLC torques, a > 0............................................. 23
3.12b FLC torques, a < 0............................................. 23
3.13 Non-polarizing and polarizing beam splitters................... 29
3.14 Input/output relationships of non-polarizing and
polarizing beam splitters.................................... 31
3.15 Air-glass-air interface........................................ 32
3.16 Op amp comparator circuit...................................... 33
4.1 FLC rotation conventions....................................... 37


ix
38
41
42
44
45
46
49
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
ROTATELIGHT subroutine conventions
Simplified schematic of the monolithic gate..............
Possible bridge configurations...........................
Monolithic gate, edge view...............................
Monolithic layers 1 through 4, front view..................
Monolithic layers 5 through 8, front view..................
FLC tilted and chevron layer structure...................
Simulation output light paths............................
FLC 1 optical response to an applied voltage, rise time..
FLC 1 optical response to an applied voltage, fall time..
FLC 2 optical response to an applied voltage, rise time....
FLC 2 optical response to an applied voltage, fall time..
FLC D1 optical response to an applied voltage, rise time....
FLC D1 optical response to an applied voltage, fall time.
FLC D2 optical response to an applied voltage, rise time....
FLC D2 optical response to an applied voltage, fall time....
Absolute detection gate, vertical vertical
steady state results.....................................
Absolute detection gate, vertical horizontal
steady state results.....................................
Absolute detection gate, input and output rise times.....
Absolute detection gate, input and output fall times.....
Differential detection,
horizontal horizontal steady state results.............
Differential detection,
horizontal vertical results steady state results.......
Differential detection,
vertical horizontal steady state results...............


X
A. 17 Differential detection
vertical vertical steady state results................... 76
A. 18 Differential detection gate, output rise times
(input 1 switching, input 2 steady)........................ 77
A. 19 Differential detection gate, output fall times
(input 1 switching, input 2 steady)........................ 78
A.20 Differential detection gate, output rise times
(input 1 steady, input 2 switching)........................ 79
A.21 Differential detection gate, output fall times
(input 1 steady, input 2 switching)........................ 80
A.22 Differential detection gate, output 23 rise time,
(both inputs switching)............................................ 81
A.23 Differential detection gate, output 24 rise time,
(both inputs switching)............................................ 82
A.24 Differential detection gate, output 23 fall time,
(both inputs switching)............................................ 83
A.25 Differential detection gate, output 24 fall time,
(both inputs switching)............................................ 84
A.26 Differential detection gate, output 28 fall time,
(both inputs switching)............................................ 85


CHAPTER 1
INTRODUCTION
Digital computer implementations are based upon devices that perform
basic logic functions. The optical logic gate that is the subject of this thesis is a di-
rect result of a research effort to implement an optical computer for artificial intelli-
gence applications [SCHM87]. This computer takes advantage of optical comput-
ing's promise of massive parallelism [GIBB86], thus requiring it to have the ability
to perform large quantities of cascaded boolean operations in parallel. The gate was
designed to meet the following criteria:
a) The gate functions as a transmission device with low enough losses
so that regenerating the optical signal at the output of every gate is not necessary.
The imposition of this criterion is to facilitate the propagation of signals through
several layers of logic before the signal must be pumped, or rejuvenated. The
pumping of the signals at every output would greatly increase the complexity of the
system.
b) Vertically and horizontally polarized light represent "1" and "0"
(logical true and false). Encoding the information in a beam of light of a particular
polarization eliminates the problem of deciding the intensity threshold between
"light" and "dark", a common encoding scheme used in many proposed optical logic
devices [TANI83]. The signal can then propagate through devices that attenuate the
intensity without losing the information or having to rejuvenate the signal after each
gate, as is required in an electronic logic gate.
c) The outputs are spatially similar, of the same wavelength, and of the


2
same polarization encoding as the inputs. This enables the gates to be easily cas-
caded.
The initial design used discrete optical components and was to be used
as a proof-of-principle model, with a future goal being the fabrication of an array of
gates on an optical substrate. To aid in the design and analysis of the gate and ad-
ditional devices for the parallel optical computer, a library of optical devices was
developed and two versions of the discrete gate were simulated. Another activity of
the same research effort was the implementation of the discrete gate on the bench at
the University of Colorado at Boulder. The measurements taken on the actual gate
were then correlated to the simulation results.
The scope of this thesis is the design, modeling, simulation, and corre-
lation to the measurements of the discrete version, with preliminary designs of the
monolithic implementation also included.


CHAPTER 2
THEORY OF OPERATION OF THE GATE
Two designs of the optical logic gate were considered and both were
modeled, simulated, and correlated to measurements made on the actual gates tested
in the lab. In this chapter, a general, idealized description of the operation of the
gate is presented and followed by discussions of each of the two implementations of
the gate. Details on the operation of the individual devices that make up the gate are
contained in Chapter 3.
2.1 General Theory of Operation
The basic gate consists of two beam splitters (one polarizing and one
non-polarizing), two mirrors, a polarization rotator and a device to control the polari-
zation rotator. Two lenses are added at the output to focus the output beams down
into one.
In figure 2.1, two inputs beams of either horizontally or vertically
polarized light enter the gate. The polarizing beam splitter allows the light to
propagate straight through if it is horizontally polarized or reflects it 90 if it is vert-
ically polarized. Without the polarization rotator, light entering the system would
just be channeled along its appropriate route, depending on its polarity, and be split
by the non-polarizing beam splitter, creating two outputs of the same polarity as the
input beams travelling at 90 to each other. The introduction of the polarization
rotator, however, allows for any vertically polarized light to be rotated to
horizontally polarization before it reaches the beam splitter at the output. If


additional output
inputA input B Avl Bvl Av2 Bv2 rotate? Av3 Bv3 Av4 Bv4 Ahl Bhl outputA outputB of output
H H 0 0 0 0 don't care 0 0 0 0 H H H H H
H V 0 V 0 V yes 0 H 0 H H 0 H H H
V H V 0 V 0 yes H 0 H 0 0 H H H H
V V V V V V no V V V V 0 0 V V V
figure 2.1 Generalized gate, theory of operation


5
horizontally polarized light represents logical "false" and vertically polarized light
represents logical "true", the logical operation of AND can be realized if the polari-
zation rotator rotates the light when input A and input B are of opposite polarity and
does not rotate the light when both inputs are vertical. For the case of two horizontal
inputs, the polarization rotator can either rotate or not rotate, because ideally there
would not be any vertical light propagating through it What is required then is a
detection scheme that senses these conditions and rotates the vertical signal accord-
ingly.
2.2 Absolute Detection Theory of Operation
The absolute detection scheme uses a microscope slide, lens,
photodiode detector, comparator and a threshold voltage to detect the proper
condition and operate the polarization rotator (see figure 2.2). A ferroelectric liquid
crystal (FLC) operates as the polarization rotator. The FLC is an optoelectronic
device that can be controlled by an applied voltage to rotate vertically polarized light
to horizontal to perform the proper logic function.
The detection decision is accomplished by using the glass slide to reflect
a small fraction of the horizontal signals, which is focused onto the detector whose
output is proportional to the sum of the intensity of the two horizontal signals
coming out of the polarizing beam splitter. The threshold voltage is set to 1/2 the
voltage out of the detector when inputs A and B are either horizontal-vertical or
vertical-horizontal, which results in the rotation of the vertical light at the proper
time, as shown in the chart at the bottom of figure 2.2.
2.3 Differential Detection Theory of Operation
The second method of detecting the correct condition to rotate the
vertical light to horizontal adds an additional microscope slide, lens, and


additional output
horizontal comparator
detector (Dh) inputs
inputA input B proportional to proportional to + input -input* comparator output polarization of output
H H 21 21 1/2 +Vce H
H V I I 1/2 +Vcc H
V H I I 1/2 +Vcc H
V V 0 0 1/2 - Vcc V
figure 2.2 Absolute detection scheme, theory of operation
as


7
photodetector to sample the vertical signals coming out of the polarizing beam
splitter. Both the vertical and horizontal detectors' outputs are proportional to the
sum of the irradiance, or power, of the vertical signals and horizontal signals,
respectively. As seen is figure 2.3, if the output of the vertical detector is divided in
half and compared to the output of the horizontal detector, the proper rotating of the
vertical light by the FLC is accomplished.
2.4 Comparison of the Two Detection Schemes
The absolute detection scheme has the limitation that the threshold must
be adjusted for different values of irradiance of the polarized logic signals at the
input The differential scheme corrects this problem by comparing the ratio of two
voltages that are linearly related to the power of the two input signals, thus enabling
the gate to function correctly with varying input power. There is, however, a
restriction as to how much the ratio of the irradiance of input A to input B can vary
before the gate stops functioning correctly. This will be discussed further, in the
analysis portion of Chapter 6.


additional output
horizontal vertical comparator
detector (Dh) detector (Dv) inputs
inputA input B proportional to proportional to proportional to + input -input comparator output polarization of output
H H 21 0 21 0 +Vcc H
H V I I I 1/2 +Vcc H
V H I I I 1/2 +Vcc H
V V 0 21 0 I - Vcc V
figure 2.3 Differential detection scheme, theory of operation


CHAPTER 3
MODELING OF THE GATE
3.1 Modeling General Approach
When choosing the mathematical models of the devices to be used in the
simulation of the optical logic gate, the following guidelines were kept in mind: the
particular class of simulation desired, the future use of the simulation, and the accu-
racy verses simulation time constraint
The modeling and simulation of the logic gate, though useful in its own
right, has the greater purpose of eventually being used in the simulation of the opt-
ical computer. This places restrictions on how the components that comprise the
logic gate should be modeled. The optical computing system will be modeled as
deterministic (at this writing) with a fixed increment time advance to move the simu-
lation clock ahead by At. The initial state of the system is calculated, then the next
state at t+At is calculated from the previous state. The optical logic gate's mathemat-
ical description then must be suited for this kind of simulation: time dependent de-
vices with the appropriate state variables updated at each time step.
The size of the simulation into which the model will be incorporated also
has some bearing on the complexity of the mathematical model used. The optical
computer envisioned will have many layers of two-dimensional arrays of logic gates
along with a large number of additional devices, so a very complex model could
make the simulation of a simple operation too long to be of practical value.
To be useful in simulating a large system, the mathematical model of a


10
particular device must be one that can be thought of as a module, with inputs and
outputs. This aids in the ease of changing the simulation to model different systems,
and to assure that a proper balance between accuracy and simulation time is main-
tained. For example, if an optical device consists of several layers of materials with
differing indexes of refraction, the reflection and transmission relationships at each
interface could be recalculated by the simulation at each time increment to determine
the light transmitted out of the final interface. This approach, however, is computa-
tionally expensive if the relationships between the interfaces do not change and the
primary interest is in the final transmission, not the specific amounts reflected and
transmitted at each interface. Thus, if a simple input/output transfer function can be
used instead of recalculating all the internal relationships, it can reduce the complex-
ity and increase the speed of the simulation.
Another factor influencing the complexity of the models is the future
plan to fabricate a monolithic array of gates on an optical substrate. The discrete
version, which is a proof-of-principle implementation, includes devices that will not
be used in the monolithic array. These devices are modeled more ideally while the
devices that will be used in the monolithic version (primarily the FLC) are given
more consideration. The FLC also required more research effort into its theory of
operation because it is a relatively new device technology, and discovering how it
functions is an ongoing effort [CLAR80, HAND82, JIUZ86, JIUZ87]. Its use is
also being considered in the design of several other devices needed for the optical
computing system, so the model of the FLC may find further uses outside of the
logic gate.
With these guidelines and constraints in mind, each device in the gate is
modeled as a device with input and output ports, using elliptically polarized light as


11
the inputs and outputs for the purely optical devices, voltages for the purely elect-
ronic devices, and a combination of the two for optoelectronic devices. Any
changes at the input of the optical devices are instantaneously realized at the output
because of the speed of the propagating light The electronic and optoelectronic
devices are also treated in the same fashion due to their quick response times com-
pared to the time step of the simulation. Details on the theory of operation and the
mathematical model used to represent these devices follow.
It was also assumed that the two inputs originate from sources that are
independent enough that they can be considered incoherent The resulting intensity
of light paths superimposed upon each other that originated from the two inputs can
be analyzed as the sum of the inradiances of each path as if it were acting separately.
3.2 Representation of the Light
The beams of light propagating thorough the device are represented as
elliptically polarized light Two orthogonal optical disturbances can be represented
as
Ex(z,t) = iEoxcos(kz cot) (3.1a)
Ey(z,t) = jEoycos(kz cot + e) (3.1b)
where e is the phase difference between the waves, k is the wave constant and co is
the frequency of the light in radians. At any point z at time t the wave can be ex-
pressed in phasor form: as an amplitude and phase angle relative to some reference
angle. Each light beam in the simulation is described by four parameters: the hori-
zontal and vertical components of its E field, and the phase relationships of the hori-
zontal and vertical components to an arbitrary reference point. Of the most impor-
tance is the phase difference between the horizontal and vertical components of a
particular beam, or plane wave, at a specific point in the system, such as before or


12
after the FLC. Keeping track of the individual phase relationships of every com-
ponent instead of just the phase relationship between the horizontal and vertical
components isn't really critical, but this more general and flexible representation is
used in case these relationships would need to be looked at more closely in the
future. To accurately calculate the phase relationship of any component to the ref-
erence at a given time t at any place in the system, the distances between the devices
would have to be precisely known to within a small percent of the wavelength of the
light. To obtain this degree of accuracy isn't practical. The simulation assumes
arbitrarily that the devices are an integral distance away: the distance between the
output of one device and the input to another is nXQ.
3.3 FLC Theory
There are three classes of liquid crystals: nematic, smectic A and smectic
C (see figure 3.1).
It'wWl) Bfflr n
'AAWiiw 1 1 V \A \
nematic smectic A smectic C
figure 3.1 Classes of liquid crystals [CLAR81]
Liquid crystals have found a place in display technology because of their low voltage
and low power operation. They are limited, however, by their slow response and
insufficient nonlinearity [CLAR81]. Nematic liquid crystals, which are the most
commonly used, have a switching time (x) of:
x = T|L2/K (3.2)
where q is the twist viscosity, L is the thickness of the layer, and K is the curvature


13
elasticity. A typical x for nematic liquid crystal is 10 to 100 msec [CLAR81].
The other two kinds of liquid crystals, smectic A and smectic C, are
referred to as smectic because they are layered. Smectic C, because of its tilt, has a
potential to be ferroelectric. The molecules have an average tilt angle, Qq, between
K, the direction normal to the layers, and n, the molecular director, which
represents the molecule's long axis [CLAR80]. There also exists a dipole density,
P, which is in the direction K X n, or out of the page in figure 3.2 [CLAR81].
In a bulk sample of FLC material, there is a helical pattern in the
molecular tilt from layer to layer which results in an average polarization of zero for
a bulk sample of FLC material, thus eliminating any bulk polarization (see figure
3.3). If the sample did, however, have a bulk polarization, an applied field would
be capable of interacting with the polarization and uniformly changing the orientation
of the molecules. Two ways to break the axial symmetry and cause a net
polarization to occur are to apply a large electric field or to apply a shear. Neither of
these methods produce any faster of a response time than nonferroelectrics
[CLAR81].
The method that is successful in unwinding the helix and creating a
device that switches quickly is to reduce the thickness of the sample until the
thickness is less than the pitch of the helix. This can be accomplished by confining a
thin sample between two optical flats. The plates are treated so that the director, n,
must lie in the plane of the surface. These boundary conditions cause the formation
of regions, or domains, of two possible orientations: UP and DOWN, as seen in
figure 3.4. The only difference between these domains is a it rotation of the
molecules about K [CLAR80].


14
smectic layers
///Hit//
fUH-
///#///
Qq
a r
0 V
\ jf
\ f
figure 3.2 FLC orientation
n
layers
figure 3.3 FLC helix [CLAR81]


15
figure 3.4 FLC domains
In the thin sample, <)> motion is only opposed by very small torques. If
the glass plates are coated with a transparent, conductive material such as indium tin
oxide so that an electric field (E) can be applied across the sample, the interaction
between the P and E will cause homogeneous rotation of the molecules [CLAR81].
3.3.1 FLC Optical Characteristics
As stated in the theory and operation of the gate, the "black box" func-
tion of the FLC is a voltage-controlled light-polarization rotator. Another way to
describe this would be as a voltage-controlled half-wave plate.
Half-wave plates are made from materials that are anistropic: the index
of refraction has two different values; one value for light parallel to the optic axis
(extra-ordinary or e-wave) and another value for light perpendicular to the optic axis
(ordinary or o-wave). The difference in the index of refraction encountered by the
e-wave and the o-wave causes them to be delayed by differing amounts as they
propagate through the material. An ideal half-wave plate has the ability to delay the
e-wave by n radians with respect to the o-wave. Thus light that is polarized strictly
parallel or perpendicular to the optic axis remains unchanged in its polarization, but


16
light that is polarized 45 to the optic axis will have its polarization rotated by 90, as
seen in figure 3.5.
before the half-wave plate
after the half-wave plate
o-wave
e-wave
f 90
/ P
resultant
90 rotation of
. polarization
figure 3.5 90 rotation of polarized light by a half-wave plate
For the difference of the delays between the e-wave and o-wave to be
exactly 7t radians, the condition must be met that
d(ln0 -nel) = (2m + \)XJ2 (3.3)
where d is the thickness of the material, n0 is the index of refraction of the o-wave,
ne is the index of refraction of the e-wave, m = 0,1,2,.... and X0 is the wave-
length of the light in free space.
FLC material is also anistropic. The optic axis of the material can be
represented by the projection of n onto the surface of the glass plates, which in the
two stable states of UP and DOWN, is just n [HAND82]. Therefore, the difference
in optical characteristics between the two possible regions of orientation is the
difference of 2Qq in the direction of the optic axis. If fi0 = 22.5 and d(lnQ -nel) =
(2m + 1)V2, light that is polarized parallel to n in the UP region will have an angle
of 45 (2Q0) to n in the DOWN region. Thus, the light in the DOWN region will
have its direction of polarization rotated by 90. Since these regions can be
electrically controlled, the FLC will act as the needed voltage-controlled polarization
rotator.


17
3.3.2 Switching of the FLC
In section 3.3, it was established that the helix can be suppressed by
making the the sample sufficiently thin, and domains of either UP or DOWN or-
ientation are formed. It was also stated that the orientation of these domains can be
controlled.by applying an E field across the sample. To model the FLC in a time-
vaiying simulation, the dynamic operation of the domains must be understood.
Without an E field applied to the FLC, domains of either UP or DOWN
orientation are established with domain walls separating the regions. The domain of
a particular orientation goes through the entire sample thickness, stretching from one
glass plate to the other (see figure 3.6) [CLAR80].
figure 3.6 UP and DOWN domains, no E field applied
Switching occurs when an E field is applied. There are three regimes of
operation: low E field, intermediate E field, and high E field. Typical voltage values
for these regions are : low E field, 0 V to 0.3 V; intermediate E field, 0.3 V to 18 V;
high, 18V and above [HAND82].
In the low E field regime, the switching is accomplished by domain wall
action, with the domains of the favored polarity growing larger. The size, shape and
number of domains growing are affected by defects in the layer structure and surface
[HAND82].


18
5
s\V\\V\V\\\\\VV\\VVVVV\V\\VV\\\\\W
o
Q
O,
P
O
Q
CL,
p
O
Q
V

glass
FLC
material
glass
figure 3.7 Low E field regime
The intermediate E field regime not only has the surface-connected
growth found in the low E field regime, but also has an inner layer of molecules that
rotate homogeneously to the orientation favored by the polarity of the E field, as
seen in figure 3.8 [HAND82].
DOWNy^g X:
glass
DOWN g r
homogeneously rotated inner layer
FLC
material
DOWN -H DOWN !
glass
a,
P

figure 3.8 Intermediate E field regime
In the high E field regime, the E field is strong enough to homogeneously rotate all
the molecules to the favored orientation. This homogeneous rotation has the charac-
teristic switching time of x = rj/PE. This is the preferred regime of operation. Not
only is the switching time the fastest, but the complete switching, or saturation, of
the FLC tends to be bistable [HAND82].
Since the molecules are assumed to be rotating homogeneously, the


19
motion of one molecule can be isolated to describe the motion of all. The geometry
is shown in figure 3.9. The projection of n, the optic axis of the FLC, onto the
glass surface is 0, and <|>0 is the initial position of the director. The angle between P
and E is . As <}> rotates between <|>0 and 7C 0, 0 ranges from Q0 to -Q0. The
value of 0 is equal to
0 = tan^cos^tan^o) (3.4)
The homogeneous motion is described by the equation
T]d + Ae^^s^DQsin^cos^TC (3.5)
where Ae^ is the dielectric anistropy and E and P are the magnitudes of E and P.
The PEsin<|> term is due to the ferroelectric torque and dielectric torque is represented
by the Ae,jcE2sin2Q0 sin<|>cos<|)/47t term. The ferroelectric torque is E and the
dielectric torque is E2. Thus, at low E field magnitudes the ferroelectric torque
dominates, and at higher E fields strengths the dielectric torques become more
important [JIUZ86]. A simplified form of equation 3.5 can be created by setting x =
T|/PE and a = Ae(jcEsin2Q0/4jtP, resulting in:
d<))/dt = sin([)/x + asin(J)cos This form better shows the relationship between the ferroelectric torque and the
dielectric torque with their difference easily identified by the a and the cos<)) terms.
Figure 3.10 illustrates a common use for the FLC, which is to place it
between a polarizer and analyzer. Polarizers are optical devices that only allow a
particular polarization of light to propagate through them, and discard the rest. A
polarizer and analyzer are a pair of polarizers with their favored axes rotated at 90 to
each other. The FLC is positioned so that with the voltage across the FLC at one
polarity, the optic axis of the FLC is parallel to the polarizer and perpendicular to the
analyzer. The light that passes through the polarizer is parallel to the optic axis of


20
glass
front Hew
side view ^ass
figure 3.9 FLC angles


21
the FLC and propagates through the FLC unrotated. When it reaches the analyzer, it
is perpendicular to the direction of the analyzer, and is extinguished. If the polarity
of the E field is reversed, the optic axis of the FLC material is rotated by 2Q0
degrees. In this situation, the light parallel to the polarizer is rotated by 90 as it
propagates through the FLC and is now parallel to the analyzer, giving it maximum
transmission provided 2Q0 = 45.
figure 3.10 FLC operatation between polarizer
and analyzer
If reflection and absorption by the interfaces and polarizers are neglected, the
transmission of the light as a function of <() is
T = irradiance in/ irradiance out (3.7a)
T = C sin2(2Q0 0) (3.7b)
where the irradiance in is the power of the light leaving the polarizer (the vertical
component of the input), the irradiance out is the power of the light leaving the
analyzer (the horizontal component of the output, and C is a constant.
In reference JUIZ86, a delay time (t^) is defined as time between Tmjn and T
= 0.1Tmax, and a rise time (tr) is also defined as the time between 0.1Tmax and T =


22
0.9Tmax. Another helpful time is a finish time (tf), which is the time between T =
0.9Tmax and Tmax (see figure 3.11). The relationship between t dependent on the relationship between the ferroelectric torque and the dielectric
torque. The sign of Ae^ can be positive or negative. For Ae^ > 0, where the
director tends to stay parallel to E, ferroelectric and dielectric torques aid each other
during td and oppose each other after <|> passes 90, thus t^ is shorter than tf (see
figure 3.12). For Ae^ < 0, the dielectric and ferroelectric torques reinforce the UP
and DOWN states, opposing each other during t passes 90, resulting in a longer t between tj and tf to vary because the ferroelectric and dielectric torques are propor-
tional to E and E2, respectively [JIUZ86].
figure 3.11 Definition of t In summary, the FLC material is able to provide domains of opposite ferro-
electric polarization that will respond to E field manipulation. It also has a large opt-
ical response which, under ideal conditions, will act as a quarter wave plate, with the
UP and DOWN domains having optic axes differing by 2Q0 [CLAR80]. If the E
field is strong enough, the switching time, x, is proportional to rj/PE, and for the
FLC materials presently used, should be in the microsecond range [MODD87].


23
+ ferroelectric torque
-dielec trie, torque
motion
+ ferroelectric torque
+ dielectric torque
motion ^
ferroelectric torque
dielectric torque /
K 1 *-4>/\ E
- ferroelectric torque
\+ dielectric torque
0
figure 3.12a FLC torques, a>0
+ ferroelectric torque
+ dielectric torque
motion
+ ferroelectric torque
- dielectric torque
motion ^
- ferroelectric torque
+ dielectric torque /
% 1 K <1) f X ^
- ferroelectric torque
dielectric torque
0
figure 3.12b FLC torques, a < 0


24
3.4 Modeling the FLC
At any given time, the FLC can be thought of as a slab of three dimensional
material divided into volumes of either UP or DOWN orientation. These volumes
are divided by a thin wall of neither orientation in particular. The application of an
electric field will cause the size and shape of these volumes to change. The goal of
the model is to simulate an approximation of the optical effect that these regions
would have on a beam of light emitted from a HeNe laser, which is represented as
an elliptically polarized plane wave.
Of critical importance is the size of the domains in comparison to the spot
size of the light. If the spot size is much, much greater than the size of the domains,
the fraction of total volume in one orientation could be determined and the proper
optical effect calculated. For example, if 1/3 of the total FLC volume was in the UP
configuration and 2/3 in the DOWN, one could assume that 1/3 of the plane wave of
light would be rotated and 2/3 of the plane wave would remain of the same polarity
(given the proper orientation), without concern for the actual distribution in the XY
plane of the different polarities of light (given Z direction propagation). Monitoring
the size and growth would be possible because the rate of growth of a domain's sur-
face area at the glass boundary and its thickness into the bulk are known functions of
the E field [HAND82].
This approach, however, is not valid if the spot size approaches the size of
the domains. If, for example, the domain encompassed the whole spot of light, yet
only 3/4 of the FLC's volume was of the same orientation as the domain, using the
above reasoning would result in a large error. In several conversations with Mark
Handschy [HAND82, JIUZ86, JIUZ87], it was determined that this is indeed the
case for the FLC in the logic gate. The size of the domains can be quite large with


25
respect to a several millimeter in diameter spot It was also learned that the greatest
optical effect is determined by the middle, or inner layer of the sample. The thick-
ness of the sample approaches the wavelength of the light, causing the surface
effects to be minimal. Also, unless the voltage applied to the FLC is in the very
limited range of the low E field regime (0 V to 0.3 V), the inner layer can be con-
sidered to be responding homogeneously to the torques imposed by the applied E
field.
The following assumptions were made in the modeling of the optical effects
of the FLC. The FLC would operate in the intermediate or high regime at all times,
thus the optical effect would be limited to the effect of the molecules rotating homo-
geneously in the bulk. Limiting the FLC to these two regimes of operation in the
logic gate is a reasonable assumption, because the FLC is being driven with an
open-loop comparator that switches very quickly in comparison to x of the FLC. It
is also assumed that the layers are normal to the glass plate.
3.4.1 Modeling the Molecular Rotation
As described in section 3.3.2, the rotation of the FLC molecules can be
described by the differential equation 3.5. Even though E(t) will, in the context of
the logic gate, be very close to an ideal step function because it is the output of the
comparator, solving the differential equation for E(t) = Eu(t) would restrict using the
model elsewhere in the system in different applications. Since a model is desired
that will properly respond to changes in the E field's amplitude, d(|>/dt needs to be a
function of both <(> and E, with all the other parameters remaining constant. Thus, a
numerical method for solving, the differential equation is used.
Euler's method for was chosen for its simplicity and speed. Applying
Euler's method to equation 3.5 yields


26
t + At = The function, f(JE),is
f( The rotation of <|> is constrained between <)>0 and 7t-0. This not only agrees with the
physical understanding of the rotation of the molecules, it is also clear from the
simplified torque equation that if <|) = 0 or 90, the torque is zero and <|> would re-
main unchanged regardless of E. Each FLC's molecular motion can be charac-
terized with the following group of constants: its polarization density (P), thickness,
viscosity (q), tilt angle (Q0), Ae^, and <|)0.
3.4.2 Modeling the FLC Optical Effect
Though the definition of transmission with the FLC between a polarizer
and an analyzer was introduced to characterize the switching of the FLC, it is not
placed in this configuration in the gate. The unwanted polarities are not blocked by a
set of polarizers, and can not be for the gate to operate correctly. Since the optic axis
of the FLC changes as it rotates between the UP and DOWN state, one must rotate
the representation of the elliptically polarized light along with it in order to determine
the e-wave and the o-wave and the effect that the FLC has on them. First, the vert-
ical and horizontal components must be broken into components parallel and perpen-
dicular to the optic axis. The e-waves and o-waves from the original horizontal and
vertical components are then added together using vectors, taking into account their
phase relationships. The phase change that each wave encounters propagating
through the FLC material is
phase change = 27tdnA0 (3.10)
where d is the distance travelled, n is the index of refraction and X0 is the wave-
length of the light in free space. After the phase change is calculated for the e-wave


27
and the o-wave, the resultant elliptical wave must be transformed back to an elliptical
wave defined by a horizontal and vertical vector with the proper phase relationship.
The FLC material is bounded by two plates of glass that are coated with
ITO. These interfaces (differing indices of refraction) cause reflection losses. These
losses, plus any absorption and scattering losses are treated as one parameter: a frac-
tion of the input power that is transmitted to the output. Given an input of a partic-
ular polarization and measuring the output power when the FLC was rotating or not
rotating the light, the total transmitted power did not vary substantially between
either orientation when measured in the lab, making this assumption feasible.
3.4.3 Choosing the FLC Constants
To model the FLC, there are several physical constants that characterize its
switching and optical performance that must be determined. There are mean, or
typical, values for these constants found in the literature that could be used to model
all the FLCs alike. This would be the best approach for a large system using many
FLCs. However, after observing the vastly different operating characteristics of the
FLCs that were used in the gate being constructed on the bench at CU-Boulder, it
was decided for this simulation that the constants would be chosen to characterize
each unique FLC as closely as possible. This in itself is a good exercise for check-
ing the validity of the model instead of just correlating the performance of the simu-
lation of the entire gate using mean, or typical, values with the measurements of the
actual gate on the bench. Some of the characteristics can be measured directly, but
others must be ascertained from the measurements.
The process of determining the constants is one of educational trial and error
due to the number of unknowns and available relationships. There are seven
constants that must be determined: the polarization density (P), thickness, viscosity


28
(H), tilt angle (Q0), x, Aedc, and <)>0. The thickness of the sample is used to deter-
mine the delay of the e-wave and o-wave through the FLC material, and the value of
E due to an applied voltage (E = V/d). The thickness is not easily measured, and is
not uniform due to the method of manufacture of the FLC, which results in a sample
that is actually wedge-shaped with a typical thickness of approximately 1 |im
[HAND82]. For the model, it is assumed to be the correct thickness for half-wave
plate operation, given the wavelength of the propagating light The tilt angle, Q0> is
measurable on the bench, along with t [JIUZ86], with its sign yet to be determined. The four measurable quantities, O0,
t(j, tr and tf, along with the assumed thickness, the typical value of Aedc, and the am-
plitude of the applied voltage when the actual FLC was measured, are used to
determine P, tj, x, the sign of Aedc, and <|)0..
A simplified simulation of the FLC model that uses equation 3.6 is used to
determine what value of a will best approximate the relationship that exists between
td, t,. and tf for the particular FLC being modeled. This not only requires determining
the magnitude of a, which ranges from 0 to 1.0, but also its sign, which is a func-
tion of whether Aedc is positive or negative. The sign of is quickly determined by
observing the relationship between td and tf: if tj is less than tf, Aedc is positive; if td
is greater than tf, it is negative. The value of <|>0 also affects the relationship of td, tr,
and tf and must be determined. This is where the trial and eiror enters the problem,
because there may be more than one unique solution to the problem, or, in trying to
characterize some of the actual FLCs, the proper relationship between td, tr, and tf
could not be reached. (Reasons for this can be found in chapter 6, Analysis and
Conclusion.) Once the best a and and T| by the following relationships:


P = Ae,jcEsin2Q0sin<()cos<|)/oc47t
T| = xPE
29
(3.11a)
(3.11b)
3.5 Modeling the Optical Devices
3.5.1 Modeling the Beam Splitters
Beam splitters are used to split one light beam into two beams: one beam
is transmitted straight ahead and a second beam is reflected at 90 to the original
beam. There are two different kinds of beam splitters used in the logic gate:
polarizing and non-polarizing (see figure 3.13). The non-polarizing beam splitter
divides the input light into two beams that are a fixed fraction of the input's
irradiance, regardless of its polarity. Different ratios of transmitted to reflected light
are available. The polarizing beam splitter, however, transmits the horizontal
component and reflects the vertical component of the input light.
top view
input
transmitted
^ output
reflected
output
non-polarizing beam splitter
input
transmitted
output
horizontally polarized
T reflected
output
vertically polarized
polarizing beam splitter
figure 3.13 Non-polarizing and polarizing beam splitters
The beam splitters are modeled as single input, double output devices using
the light representation discussed in section 3.2 as inputs and outputs. The
reflection, absorption and scattering losses are taken into account as one parameter
by assuming that the outputs are linearly related to the inputs by a constant, or


30
coefficient, of less than one. These constants were measured in the lab to match the
beam splitters used in the actual test gate to the simulated gate, but mean values
could also be used.
The non-polarizing beam splitter needs only two coefficients to relate the
outputs to the input because of its disregard for the polarity of the light (see figure
3.14). The phase relationships of the output components to the input components
are considered equal except for the vertical component of the reflected beam, which
has a 7t phase shift with respect to the vertical input component. This occurs be-
cause it is perpendicular to the plane of incidence with an angle of incidence of 45
to the internal boundary inside the beam splitter which causes the splitting of the
light [HECH79].
The polarizing beam splitter is a more complex device because it does not do
a perfect job of splitting the two components; there is a leakage of horizontally pol-
arized light into the vertical output and vertically polarized light into the horizontal
output Figure 3.14 shows the additional coefficients that were used experimentally
obtained and incorporated into the model. Care must be taken to observe the proper
relationship between the E field magnitude modeled and the intensity measurements
made to characterize the beam splitters.
3.5.2 Modeling the Microscope Slides
The microscope slides are modeled as the optical effect that two interfaces,
air-to-glass and glass-to-air (see figure 3.15), have on elliptically polarized light.
The coefficients of reflection and transmission are calculated using the Fresnel
equations:
rj_ = sin(0i Q^/sin^ + 0^
r|| = + tan(0j 0t)/tan(0j + 0j)
(3.12a)
(3.12b)



figure 3.14 Input/output relationships of non-polarizing
and polarizing beam splitters


32
tj_ = + 2sin(0t)cos(0{)/sin(0i + 0t) (3.12c)
t|| = + 2sin(0t)cos(0i)/sin(0i + 0t)cos(0j 0t) (3.12d)
and Snell's Law:
njsin(0j) = ntsin(0t) (3.13)
The choice of 0^ was made graphically [HECH73], with the criteria being a large
enough 0j to allow adequate physical space between the optical components, yet
small enough that the transmitted light would be large compared to the reflected
light, thus not decreasing the output of the gate substantially.
3.6 Modeling the Electronic and Optoelectronic Devices
The models of the electronic and optoelectronic devices are ones of
simplicity: they use as ideal a representation of the devices that provides reasonable
accuracy. The reason for this is twofold: to maintain the balance between model
accuracy and reasonable simulation time, and to not expend a large amount of time
and effort modeling a very specific devices that will not be used in the monolithic


33
version of the gate. The models for the comparator and detector follow, but the
attenuator, which just divides the voltage out of the vertical detector in half, is ex-
cluded because of its simplicity.
3.6.1 Modeling the Comparator
The comparator is modeled as an ideal operational amplifier (op amp)
operated in an open loop configuration with the exception that the output is limited
to, or "rails", at = Vcc of the op amp (see figure 3.16).
If V+ > V_, then Vout is equal to if V. > V+, the output is -Vcc. Any change of
the condition of V+ or V. is felt instantaneously at the output The only limitations
that could cause the output to act non-ideally would be too slow of a slew rate, too
much power demand placed upon the output of the op amp by the FLC, or too high
of an RC time constant at the output.
An op amp with a slew rate of 36V/|isec, which is readily available, could
change from -18V to + 18V in 1 fisec, or 1 time step of the simulation. Therefore,
the assumption that the slew rate has little effect on the response of the output is
reasonable.
The FLC is a low-power device, with the power being dissipated during
switching equal to T|d/T2 = 45mW for an FLC with typical values of T| = 50cP, d =


34
l|im and x = lOOjisec, and a typical surface area of 3cm x 3cm [MODD87]. This
power demand would easily be met by a typical op amp.
The RC time constant of the output would be Rout of the op amp and the
capacitance of the FLC, with a typical value of capacitance for an FLC being
7nF/cm2 [MODD87]. For with a surface area of 3cm x 3cm and an op amp with the
output resistance of 10£2, the RC time constant would be 0.63 (isec, thus placing its
time constant very close to the time step of the simulation.
The model of the op amp could be made more accurate by including some of
these non-ideal characteristics, but the gain in accuracy would be small in compar-
ison to the increased simulation time of calculating the device's time-dependent re-
sponse.
3.6.2 Modeling the Detector
This optoelectronic device is modeled as a very idealized detector which
produces an output voltage that responds linearly to the light incident on its input, or
Vout = Constant Ijncident (3.14)
The detectors that were used in the actual test gate were a unit consisting of a re-
versed biased photodiode and an amplifier circuit. The use of the photodiode gives
the detector the ability to respond linearly and quickly; it is also.more stable and has
a good dynamic range [WILS83]. The response time of these detectors is 100 to
1000 times faster than the time step of the simulation, thus assuming an immediate
response at the output to a given input is reasonable. The gate being modeled is a
predecessor to a monolithic version of an optical gate using the same principles, so
modeling these particular detectors in detail would not be that useful, especially since
the detection in the monolithic version would involve the use of amorphous silicon
photoconductors (see Chapter 5), not PIN photodiodes.


35
The detector model in the simulation is capable of two inputs of ellip-
tically polarized light and assumes that they are incoherent. The total iiradiance that
the detector responds to is the sum of the squares of the individual components. The
output is a voltage directly proportional to that sum. A calibration could be perform-
ed to relate the intensity of the light at the input to the output voltage, but in all of the
applications of the detectors in the simulation, the absolute output of the detector is
not critical. In the absolute detection scheme, the threshold is set to one half the out-
put of the detector given a specific input state, and in the differential scheme it is im-
portant that the gain of each detector is equal, but its actual value is unimportant.
The detectors included to make measurements are used to determine the relative gain
between points in the simulation.


CHAPTER 4
IMPLEMENTATION OF THE MODEL
4.1 Organization and Data Structures
The models and simulations are implemented in Fortran 77 on a Sun
workstation. The modeling of the devices as modules naturally leads to each device
model being a subroutine with inputs and outputs of light or voltages passed in and
out as parameters.
The four part representation of the light consists of a vertical electric
field component, its phase relationship to a reference point, a horizontal electric field
component, and its phase. These parameters are passed in and out of the device
subroutines as individual real values, but because of the large number of points in
the simulation where the value of the light must be known, these values are stored in
arrays in the main program and passed as arrays by many of the higher level sub-
routines. The arrays index numbers correspond to unique light paths in the sim-
ulation.
The FLCs are individually characterized to match the performance of
actual devices in the gates that were tested in the lab, thus requiring unique constants
for each FLC. These constants are stored in a two-dimensional array of real
numbers and passed to the subroutines that require them.
Three common blocks of information are available to subrountines.
GLOBALS includes the time information, T and DELTAT, for the subroutines that
need it. ARRAYSIZE is a group of integers that include the sizes of all the arrays
used throughout the simulation so that the size of individual arrays that are passed as


37
parameters can be changed in the main program. Control of the output is commun-
icated with the common block PRINTOPTTONS.
4.2 Libraries and Main Programs
A group of libraries was created that contains the modeled devices:
FLCMODEL, GATEMODEL, OPTICDEVICES, ELECTDEVICES and OPTIC-
MATH.
FLCMODEL contains two subroutines: UPDATEFLCSTATE, FLC-
OPTEFFECT and the function PETOOTTCAXIS. FLCOPTEFFECT determines the
affect that the FLC will have on the elliptically polarized light as it propagates
through the FLC, given the angle between P and E, or the PEANGLE, and UP-
DATEFLCSTATE updates the present PEANGLE, given the applied voltage. Both
routines use an array of FLC constants for the appropriate FLC. A convention was
adopted, as seen in figure 4.1, that a negative voltage applied to the FLC would
cause 0 to rotate so that it is equal to the reference angle (usually 90, or vertical),
and a positive applied voltage would cause 0 to rotate to 2Q0 + reference angle. This
is in agreement with how the FLC's are oriented in the lab. Function PETOOPTIC-
AXIS returns the value of the FLC optic axis projected onto the surface of the con-
fining glass plates, given the PEANGLE, Q0 and the reference angle.
figure 4.1 FLC rotation conventions


38
GATE and PRINTGATE comprise the GATEMODEL library. GATE
is the subroutine that actually connects the inputs and outputs that function together
as the gate, and PRINTGATE prints out, at any time T, all the light paths of a gate:
the E field values and phases and their intensity, which is proportional to E2.
The optical and electronic devices are all included in the OPTTCDE-
VICES and ELECTDEVICES libraries, respectively. Some of the devices were
characterized to closely match devices in the lab implementation. Their name in-
cludes a number to specify which device they represent, but a non-specific routine is
also included for each model.
A group of basic mathematical functions needed to solve some of the
phasor problems is included in OPTICMATH. The most complex is ROTATE-
LIGHT, which is used to rotate the horizontal and vertical components of the light
so that one of the vectors is parallel to the optic axis of the FLC and the other is
peipendicular, enabling the effects on the e-wave and o-wave to be readily calculated
(see figure 4.2).
Two main programs were used: one to characterize the FLC model to a
specific FLC, and a much large one, DGATE, which is the simulation of the gate
with differential detection, a dual FLC element that controls the inputs to the gate,


39
and additional polarizers and detectors to simulate the measurements taken in the lab.
Several upper level subrountines were used to help organize the simulation. Code
for the libraries and DGATE is included in Appendix B and the results are discussed
in Chapter 6, with the data that accompanies the results in Appendix A.


CHAPTER 5
THE MONOLITHIC OPTICAL
LOGIC GATE
The discrete implementation of the optical logic gate was meant to be a
proof-of-principle model of a monolithic implementation of optical logic gates cap-
able of being fabricated in two-dimensional arrays. Preliminary designs of how to
lay out the layers of the device are presented in this chapter.
5.1 Theory of Operation
Figure 5.1 illustrates a simplified drawing of the monolithic gate. A
birefringent crystal has replaced the polarizing beam splitter of the discrete imple-
mentation to separate the vertically and horizontally polarized input light As with
the discrete version, the detector senses when to cause the FLC to rotate any vert-
ically polarized light to horizontally polarized light to create the proper logic func-
tion.
Schematic diagrams of two proposed detection schemes to substitute for
the two PIN photodetectors, attenuator, and op amp in the discrete version are
shown in figure 5.2. The light impinging on the hydrogenated amorphous silicon
(a-Si:H) will cause its resistance to decrease, thus the voltage at point A of figure 5.2
will swing either positive or negative, depending on the situation, resulting in the
switching of the FLC. The difference in the two bridges is that the resistor R2 is not
illuminated in the resistor-photoconductor version, but is illuminated in the
photoconductor-photoconductor implementation. Two possible schemes are
proposed in case R2's resistivity, which is a function of its size, is such that a bias,


birefringent crystal
detector
11
12
inputs
top view

figure 5.1 Simplified schematic, of the monolithic gate


resistor-photoconductor bridge photoconductor-photoconductor bridge
figure 5.2 Possible bridge configurations


43
or reference illumination, is necessary to adjust R2 to the proper value of resistance
for the bridge to operate correctly.
5.2 Layout of the Lavers
The layers would be deposited on a piece of birefiingent crystal. In-
dium tin oxide (ITO), which acts as an transparent conductor, would be used to
route the needed bias voltages to the gate and make the proper connections between
layers. SiC>2 would be used to perform the function of a tranparent insulator, and
the a-Si:H would be deposited to create the two photoconductors. A back-plane of
ITO-coated glass would be separated from the rest of the material by a thin layer of
the necessary FLC material, creating the FLC light polarization rotator. Figures 5.3,
5.4, and 5.5 illustrate a possible layout for the proposed gate.
5.2 Conclusions
In discussions with Professor Garret Moddel, University of Colorado at
Boulder, who is a fellow researcher in the same research effort, it was decided that,
though the actual fabrication of the monolithic version of the gate would be possible,
the effort would be large with many difficulties to overcome, and would not be in
the scope of the present research grant. Other possible ways of fabricating the logic
gate are being explored, along with other implementations of optical logic.


figure 5.3 Monolithic gate, edge view
4^
4^



birefringent
crystal
layer 1
ITO (+V)
layer 2
figure 5.4 Monolithic layers 1 throught 4, front view
4^


layer 5 layer 6

r:il££:££:::£i£:£5£ rro :
I (GND) ; glass

layer 7 layer 8
figure 5.5 Monolithic layers 5 through 8, front view
4^
On


CHAPTER 6
ANALYSIS AND CONCLUSIONS
6.1 Analysis
Both the absolute and differential versions of the gate were implemented
in the lab and simulated, and the results are found in Appendix A. The measure-
ments of the differential detector gate are more complete than those of the absolute
detector gate due to gained expertise and an improved input stage, which is ex-
plained in section 6.3. The lenses on the output of the device that focus the light
down to one beam were not implemented in order to better analyze the various light
paths.
Two basic kind of measurements were made on the laboratory gate and
also simulated: steady state intensity readings with constant voltages applied to the
FLCs so that they would not switch, and dynamic readings to observe the switching
characteristics. The switching characteristics of the FLCs were also measured out-
side of the gate to supply the necessary data to match the FLC models to the actual
devices before placing them in the gate and the gate simulation.
Of primary concern in the modeling and analysis is the amount of ellip-
tical polarization that is introduced into the signals. As the waves of light propagate
through the gate, a component of the light normal to the ideal component can be
introduced by the non-ideal characteristics of the devices. This degradation of the
signal can be viewed as noise, and if the amplitude of the unwanted component
approaches the amplitude of the component that truly represents that logical value of
the signal, its logical value may be indiscernible. The intensities of the horizontal
and vertical components of the inputs and outputs can be observed in the steady state


48
measurements and simulation results.
The dynamic measurements and simulation results are normalized to
their peak values with any "dc" intensity levels subtracted out so that just the timing
relationships are evident The relationships between the intensity levels that were
measured and simulated can be studied in the steady state measurements. It should
be pointed out that when viewing the graphs of the switching of both gate imple-
mentations, the output that switches first can also be thought of as one of the inputs,
since it is a result of the path that propagates straight through the gate from the
horizontal output of the polarizing beam splitter (see figures A.1 and A. 10) and not
through FLC 2, the polarization rotator of the gate.
6.1.1 Analysis of the FLCs
The FLCs that were used in the the two gates were first placed between
a polarizer and an analyzer and their optical response to an applied step voltage was
recorded (see figure 3.10). These results were used to adjust the constants of the
models so that their operation matched as closely as, possible the switching char-
acteristics of the actual FLCs, as described in section 3.4.3. They could then be
incorporated into the simulations of the two versions of the optical logic gate.
The success of matching the model to the actual device varied from FLC
to FLC. The major factor that affected how closely the actual operation could be
matched by the model was the symmetry between the rise and fall curves of the
FLCs molecular motion, which can be observed in the graphs of the FLCs
switching characteristics (see figures A.2 through A.9). The more symmetric the
switching, the closer it could be modeled. For example, the rise time of FLC 2
(figure A.4) is much slower than its fall time (figure A.5). A compromise was made
so that the model has a shorter rise time than the actual FLC and a longer fall time.
One of the assumptions made in modeling the FLCs is that the layers are normal to


49
the glass surfaces [JIUZ86]. This is usually not the case: they can be uniformly
tilted, or even in a chevron shape (see figure 6.1). This will result in asymmetric
switching [JIUZ87].
tilted structure chevron structure
figure 6.1 FLC tilted and chevron layer structure
As explained in section 3.4.3, the procedure used for matching the mod-
el's characteristics to the actual FLC is trial and error, and finding the right combin-
ation of constants can be difficult Obtaining the ratios of tj, tr, and tf for the model
that closely match those of actual FLCs may not result in a switching curve with the
same shape as the actual FLC, even though the total switching time (tj + tr + tf) for
the model may be about equal.
6.1.2 Absolute Detection Gate Analysis
Figures A. 10 through A. 13 contain the steady state and dynamic meas-
urements and simulation results of the absolute detection gate. As seen in figure
A. 10, an additional number of devices were needed to create and control the inputs.
The light source was a HeNe laser. FLC 1 was used to control the polarization of
one of the inputs, and the other input remained constant and vertically polarized.
The beam splitter used to create the two input beams was a 60:40 beam splitter: 60%
of the light from the laser was reflected to FLC 1 to create the switching input, and
the other 40% was transmitted straight ahead to the gate input to be the constant
input. This was done to compensate for the loss of intensity of the light as it passed
through FLC 1, thus assuring fairly equal intensities for the two inputs as they


50
entered the gate. The portion of the system that created and controlled the inputs
was not rearranged to switch the second input because small changes in the align-
ment of the front end of the system can sometimes necessitate realignment of the the
whole gate. In addition, switching of the other input would not have revealed a
great deal more about the operation of the absolute detection gate because of its
simple detection scheme.
The steady state measurements and simulation results correlated fairly
well (see figures A. 10 and A. 11). Some of the actual measurements are higher than
the simulation results, especially the paths that have low intensities of light at that
particular state. There are two possible reasons for this difference: one due to meas-
urement error and one due to modeling error. The lower the intensity being meas-
ured, the more susceptible the measurements are to the effects of ambient light.
Though the measurements were done in the dark, the environment was such that not
all ambient light could be removed, which included the light necessary to read the
equipment.
The steady state error between the model and the measurements could
also be caused by too ideal of an FLC model. The FLC is the primary device that
introduces noise, or unwanted polarization, into a signal by not acting as an ideal
half wave plate. Creation of this noise by the FLC can happen in two ways: either
by the FLC not having a perfect 22.5 tilt angle, or by the FLC not being of the
correct thickness. The model does properly represent the imperfect tilt angle and
how this affects the polarization of the light, but the thickness is assumed to be
correct for half wave plate operation for the given wavelength.
As seen in figure A. 10, the horizontal and vertical components of the
outputs were measured to observe the amount of elliptical light introduced by the
gate. The amount of light of the unwanted polarization at the outputs is greater in the


51
vertical horizontal case than in the vertical vertical case because of the non-ideal
behavior of the FLCs, which are both rotating light during the vertical vertical case.
In figure A. 11, the ratio of wanted-to-unwanted components is better for paths 25
and 26 than paths 24 and 27. This occurs because paths 25 and 26 were rotated by
FLC 1, while paths 24 and 27 were rotated by FLC 2, and FLC l's optical
characteristics were more ideal than FLC 2's characteristics.
The dynamic results of the simulation and the measurements are
presented in figures A. 12 and A. 13. The fall time results were more closely
matched than the rise time results because the models of FLC 1 and FLC 2 being
used at the time were more accurately matched to their fall times than to their rise
times. The constants associated with FLC 2 were later changed to more closely
match the model to the device. Those results are graphed in figures A.4 and A.5.
6.1.3 Differential Detection Gate Analysis
Along with the changes to the detection scheme, another change was
made to the system when the differential detection gate was implemented and sim-
ulated (see figure A. 14). A dual FLC was obtained so that both inputs could be
switched without making major changes to the input portion of the system. The dual
FLC is constructed in the same manner as the single FLC, except that the ITO that is
deposited on the plates is divided into two regions which can be independently
addressed with voltages. Not only can both inputs be switched simultaneously
using the dual FLC, but it also supplies the gate with non-ideal inputs to better test
the gate's operation.
All four possible steady state input combinations were measured and
simulated (figures A. 14 through A. 17). The results were very similar to those of the
absolute detection scheme, with a little more error in the low intensity readings.
Along with the two possible reasons for error given in the previous section, a dif-


52
ference in measurement techniques between how the absolute detection gate and the
differential detection gate were measured could also be a factor. When making the
steady state measurements on the absolute detection gate, an iris, or stop, was placed
in front of the detector of the intensity meter, blocking much of the scattered light
produced by the FLCs and the other devices. The second implementation was meas-
ured without the iris, and the extra power from the scatter and ambient light meas-
ured by the meter has a greater affect on the lower intensity readings than on the
higher readings. The charts in the following discussion show the measured results.
The simulated results indicate the same basic relationships and trends, but they are
more ideal.
As with the absolute detection gate, the more times that the signals were
rotated by an FLC, the more unwanted polarization component, or noise, was
introduced into the elliptical light The signal-to-noise ratio (SNR) can be defined as
SNR = 10 logO^vanted^imwanted) (6.1)
where 1^,^^ is the intensity of the desired component and Iunwante{i is the intensity
of the undesired component. The SNR of the outputs can easily be obtained by
taking the difference in the dB gains in figures A. 14 through A. 17 of the two com-
ponents of the path of interest.
In the horizontal horizontal input condition (figure A. 14), there is
actually on improvement in the SNR of all the outputs when compared to the SNRs
of the input signals at paths 1 and 2 (see table 6.1).
input 1 input 2 output 21 output 22 output 23 output 24
16.2dB 12.7dB 24.4dB 24.2dB 25.4dB 25.1dB
table 6.1 Horizontal horizontal SNRs
This is a result of the polarizing beam splitter separating the wanted horizontal and


53
unwanted vertical components of both input signals, and FLC 2 rotating the un-
wanted vertical to horizontal before it reaches the output to recombine with the
original horizontal components.
In the vertical horizontal case (figure A. 16), the same improvement in
the SNR can be seen in the outputs that are results of the horizontal input (paths 21
and 24), but the outputs that are a result of the vertical input rotated to horizontal by
FLC 2 (paths 22 and 23) have a reduced SNR because of the non-ideal behavior of
FLC 2 (table 6.2).
input 1 input 2 output 21 output 22 output 23 output 24
17.2dB 10.7dB 26.9dB 7.3dB 7.6dB 15.8dB
table 6.2 Vertical horizontal SNRs
The horizontal vertical input case produced similar results as the
vertical horizontal case, but now paths 22 and 23 have better SNRs than 21 and 24
(see table 6.3).
input 1 input 2 output 21 output 22 output 23 output 24
13.2dB 21.6dB 8.7dB 13.1dB 23.6dB 8.5dB
table 6.3 Horizontal vertical SNRs
In the vertical vertical case (figure A. 17), the SNRs lie in between the
best and worst of the three other input combinations (see table 6.4). The polarizing
beam splitter separates the vertical components of each input from the horizontal
noise component. The vertical light must travel the path through FLC 2, and is
rejoined at the output beam splitter with any horizontal noise component that was
part of the input. The extra losses that the vertical components incur as they travel
their own route reduce the SNR at the output.


54
innut 1 innut 2 outnut 21 output 22 outnut 23 outnut 24
18.1dB 23.8dB 15.7dB 19.2dB 16.3dB 15.9dB
table 6.4 Vertical vertical SNRs
Three different cases were used to test the switching characteristics of
the gate: switching input one while input two was held constant, switching input two
while input one was held constant, and switching both inputs at the same time. The
comparison of switching characteristics between the measurements and the simu-
lation results shows a greater variation for the differential detection scheme than the
absolute detection scheme (see figures A. 18 through A.26). This was expected,
since the differential detection scheme is more complex. The comparator switched
later in the simulation than it did in the lab because the models of the two halves of
the dual FLC (D1 and D2) switched slower than the actual FLC.
A major cause of the differences between the measured and simulated
results was a decrease in the switching time of FLC 2 between when it was meas-
ured for characterization and when the gate itself was measured. For some reason
FLC 2 was switching in about 30% less time when it was operating in the gate then
when it was measured outside of the gate. Care was taken to make sure that the
same amplitude of square wave was used for all switching measurements, but
perhaps the amplitude was not maintained. Another possible cause for error could
be a change in temperature of the FLC, which will change its viscosity and in turn,
its switching time.
The detection scheme of using a horizontal and vertical detector did not
work as symmetrically in the lab as it did in the simulation. This could be due to
differences in the gains of the detectors, or differences in the angle of incidence of
the light on the microscope slides, resulting in unequal amounts of reflected light


55
going to the detectors. This asymmetry in the detection scheme also causes dif-
ferences between the actual gate and the simulation concerning when the comparator
switches the FLC.
Of special interest is the graph of the horizontal component of output 28
(figure A.26) as the inputs are both switching from horizontal back to vertical. As
the vertical components increase on paths 5 and 6, FLC 2 is continuing to rotate the
polarization of any impinging vertically polarized light, and rotates the growing
vertical light to horizontal, which can be seen increasing in figure A.26. The
detection scheme soon senses that the inputs are now vertical-vertical and switches
the FLC accordingly. As the FLC switches, it now stops rotating the vertical to
horizontal, and the horizontal component at the output then decreases, thus sup-
pressing the transient
In the ideal operation of the differential detection gate as described in
Chapter 2, the differential detection scheme stops working properly if the irradiance
of the horizontal input approaches half the value of the vertical input. When consid-
ering how this relates to inputs of non-ideal, elliptically polarized light, the gate will
stop functioning correctly when the sum of the irradiances of the horizontal com-
ponents of the inputs approaches one half of the sum of the irradiances of the vertical
components. This condition can manifest itself in an infinite number of input com-
binations of varying elliptical ratios and total signal intensities.
One of the criteria used in the design was that it was to be a transmission
device with low enough losses so that the gates could be cascaded for several layers
before the signal had to be rejuvenated. If the total irradiance of the desired pol-
arization at one of the outputs is compared to the irradiance of one of the input sig-
nals, the gains were measured to be:


56
V-V inputs V-H inputs H-V inputs H-H inputs
-2.8dB -1.5dB -2.2dB -l.ldB
table 6.5 Input-to-output gains
It must be remembered that the gate is providing two outputs, or a fan-out of two. If
the two inputs were somehow combined, the gate would actually have a positive
gain.
The switching time of the gate is dependent on the switching time of
FLC 2. The switching times of the gate averaged 390 |i.sec rise times and 342 (isec
fall times. The rise time is defined as the time between when the comparator
changes and when the output reaches 0.9 of its final value, and the fall time is
defined as the time between when the comparator changes and when the output falls
to 0.1 of its final value. An additional delay of from 125 to 230 |isec occurs
between when the inputs begin to change and the detection scheme senses the new
input state and switches the comparator.
The gate can only operate efficiently if the wavelength of the input light
is correct for the FLCs to operate as half wave plates. Any variation from this freq-
uency of input light will cause reductions in the SNRs at the output.
The assumption that the two inputs are incoherent was valid. There was
no indication during the measurements that the superimposed beams were adding
coherently, such as the fringing effects one sees in association with interferometers.
6.2 Conclusions
The optical logic gate performed as specified both in actual implement-
ation and when simulated The model simulated the actual gate well enough so that
its use in a large system would be justified.
The discrete version of the gate, however, was meant to prove in prin-


57
ciple that a polarization-encoded logic gate would work. The shortcomings of the
discrete gate are obvious: its size and speed. The gate itself takes up one half of a
lab table when actually assembled, and the average switching time is over 360 jisec.
Clearly, a monolithic version of the gate that operates on the same principles is
needed to reduce the size and offer the possibility of two dimensional arrays of the
devices. FLC switching speeds, though orders of magnitude smaller than nematic
liquid crystals, must also decrease to make this a viable technology.
The FLC model that was developed, along with some of the basic
optical devices, may find more uses as additional devices are proposed within the
present research. Many of the devices being proposed use the FLC, but as more is
learned about the nature of the FLC, such as the layer structure, the model should be
improved to incorporate this new knowledge.
In a larger sense, the scientific community has been looking at optical
computing because of the promise it shows in speed, massive parallel operations,
and connectivity. The value of research into basic optical logic gates could extend
beyond this specific application.


REFERENCES
[CLAR80]
[CLAR81]
[GIBB 8 6]
[HAND82]
[HECH79]
[JIUZ86]
[JIUZ87]
[MODD87]
[SCHM87]
[TANI83]
[WILS83]
Noel A. Clark and Sven T. Lagerwall, "Submicrosecond Bistable
Electro-optic Switching in Liquid Crystals," Applied Physics Letter.
36(11), June 1,1980, pp. 889-901.
N. A. Clark and S. T. Lagerwall, "Physics of Ferroelectric Fluids:
The Discovery of a High-Speed Electro-Optic Switching Process in
Liquid Crystals," Recent Developments in Condensed Matter
Physics. Vol. 4,1981, pp. 309-319.
Hyatt M. Gibbs, "Approaching the All-Optical Computer," Optics
News. April 1986, pp. 21-23.
M. A. Handschy and Noel A. Clark, "Stroboscopic Microscopy of
Fast Electro-optic Switching in Ferroelectric Smectic C Liquid
Crystals," Applied Physics Letter. 41(1), July 1,1982, pp. 39-41.
Eugene Hecht and Alfred Zajac, Optics. Reading, Massachusetts:
Addison-Wesley Publishing Company, 1979.
Xue Jiu-Zhi, M. A. Handschy, and N. A. Clark, "Electrooptic
Response During Switching of a Ferroelectric Liquid Crystal Cell
with Uniform Director Orientation," Ferroelectrics. Vol. 73,1986,
pp. 305-314.
Xue Jiu-Zhi, M. A. Handschy, and N. A. Clark, "Electrooptical
Switching Properties of Uniform Layer Tilted Surface Stablized
Ferroelectric Liquid Crystal Devices," Liquid Crystals. Vol. 2,
1987, pp. 1-4.
Garret Moddel, Kristina M. Johnson, and Mark A. Handschy,
"Photoaddressing of High Speed Liquid Crystal Spatial Light
Modulators," Proceedings of SPIE. Vol. 754, January 1987,
pp. 207-213.
Schmidt, Rodney A. and W. Thomas Cathey, "Implementations of
Optical Mathematical Resolution," Applied Optics. Vol. 26, May
15,1987, pp. 1852-1858.
J. Tanida and Y. Ichioka, "Optical Logic Array Processor,"
Proceedings of SPIE. Vol. 422, January 1983, pp. 18-23.
J. Wilson and J. F. B. Hawkes, Optoelectronics: An Introduction.
Englewood Cliffs, New Jersey: Prentice/Hall, 1983.


APPENDIX A
DATA
Appendix A contains the data from the measurements and simulations of
the FLCs (figures A.2 through A.9), and the steady state and dynamic results of the
absolute and differential detection implementations (figures A. 10 through A.26).
The numbering of the light paths is identical in the simulation and the
recording of the differential detector measurements, but because each of the four
outputs is really two outputs superimposed on one another, the simulation represents
them as seen in figure A.l. The exaggeration of the angle of propagation of four of
the beams in figure A.l is to indicate that they are reflected beams, which is in con-
trast to the beams which propagate straight through the beamsplitter. For example,
beams 24 and 25 are the result of the splitting of beam 20. Beam 25 is actually
reflected approximately normal to beam 20, while beam 24 is the other half of beam
20 propagating straight through. The superimposed output beams can be separated
in the lab by blocking the undesired beam of light just before the final beam splitter,
which was done to record the various outputs during the dynamic measurements.


60


horizontal component of FLC output,
note: step voltage to switch ELC lime (usec) meas,ure^ ^P0
is applied at t = 0 * simulated response
figure A.2 FLC 1 optical response to an applied step voltage, rise time
o\


note: step voltage to switch FLC time (usee) measured response
is applied at t = 0 simulated response
figure A.3 FLC 1 optical response to an applied step voltage, fall time
o\
to


horizontal comDonent of FLC ou
note: step voltage to switch FLC dme (usec) measured response
is applied at t = 0 * simulated response
o\
figure A.4 FLC 2 optical response to an applied step voltage, rise time


horizontal component of FLC output,
normalized to its maximum value
note: step voltage to switch FLC drae (usec) measured response
is applied at t = 0 simulated response
figure A.5 FLC 2 opitical response to an applied step voltage, fall time


note: step voltage to switch FLC time is applied at t = 0 m simulated response
figure A.6 FLC D1 optical response to an applied step voltage, rise time


note: step voltage to switch FLC toe (usee) measured response
is applied at t = 0 simulated response
figure A.7 FLC D1 optical response to an applied step voltage, fall time
Os
Os


horizontal component of FLC output,
normalized to its maximum value
note: step voltage to switch FLC dme (usec) measured response
is applied at t = 0 simulated response
figure A.8 FLC D2 optical response to an applied step voltage, rise time


horizontal component of FLC output,
normalized to its maximum value
note: step voltage to switch FLC dme is applied at t = 0 " simulated response
o\
00
figure A.9 FLC D2 optical response to an applied step voltage, fall time


POSITION MEASURED GAIN (dB)* SIMULATED GAIN (dB) POSITION MEASURED SIMULATED GAIN (dB)* GAIN (dB) POSITION MEASURED GAIN (dB)* SIMULATED GAIN (dB)
1 0.00 0.00 13 -5.10 -4.40 24 horz -32.3 -37.5
2 -2.35 -2.92 14 -39.9 -43.8 24 vert -11.7 -10.5
3 -4.85 -4.28 15 < -50.0 -42.2 25 horz -34.0 -58.4
4 -2.63 -3.54 16 -5.64 -5.02 25 vert -11.2 -12.1
5 -4.40 -4.66 17 -5.36 -7.77 26 horz -31.6 -68.2
6 -4.62 -5.29 18 -32.4 -31.8 26 vert -10.1 -11.8
7 -5.36 -5.92 19 -30.4 -30.2 27 horz -32.6 -57.2
8 -32.0 -41.6 20 -6.61 -7.77 27 vert -10.8 -10.1
9 -29.6 -30.2 21 -7.86 -6.13
10 -40.4 -43.2 22 -8.95 -6.76 . * all gains are relative to position 1
11 < -50.0 -41.6 23 -7.40 -8.40 gain n = 10 * log(intensily n / intensity 1)
12 -5.36 -6.03
Q\
VO
figure A. 10 Absolute detection, vertical vertical steady state results


POSITION MEASURED GAIN (DB)* SIMULATED GAIN (DB) POSITION MEASURED GAIN (DB)* SIMULATED GAIN (DB) POSITION MEASURED GAIN (DB)* SIMULATED GAIN (DB)
1 6.66 0.00 13 -4.46 24 Korz -10.5 -10.6
2 -2.14 -2.94 14 -9.60 -21.0 24 vert -22.0 -25.2
3 -4.20 -4.28 15 < -50.0 -42.2 25 horz -10.2 -11.5
4 -2.22 -3.54 16 -13.9 -30.7 25 vert -30.2 -36.2
5 -3.98 -4.66 17 -4.95 -5.0 26 horz -9.7 -11.6
6 -4.95 -5.29 18 -6.99 -6.1 26 vert -26.2 -35.9
7 -5.38 -5.92 19 -30.0 -30.2 27 horz -11.0 -10.2
8 -6.20 -5.93 20 -14.9 -31.8 27 vert -20.5 -24.9
9 -29.2 -28.0 21 -6.78 -6.13
10 -20.0 -20.4 22 -7.70 -6.7
11 < -50.0 -41.6 23 -16.6 -35.8 * all gains are relative to position 1
12 -13.37 -30.0 gain n = 10 * log(intensity n / intensity 1)
figure A.l 1 Absolute detection, vertical horizontal steady state results


iiradiance of vertical component,
note: step voltage to switch input FLC (usec) * rcsPonse
is applied at t = 0 * simulated response
figure A. 12 Absolute detection gate, input and output rise times


note: step voltage to switch input FLC dme (usec) meas,ur| resPnse
is appUed at t = 0 simulated response
figure A. 13 Absolute detection gate, input and output fall times


horizontal horizontal input flc Di
Vin 1 = + 20 V
Vin 2 = + 20 V
measured
intensity in (db) Vout
Hdet
Vdet
All gains are relative to position 25 and 26, horz
gain n = 10 log(intensity n / intensity 25 horz)
-11.49 .817
-23.94 .002
measured simulated measured simulated measured simulated
position gain (db) gain (db)___________________position gain (db) gain (db) position gain (db) gain (db)
1 horz -1.30 -1.11 10 -14.12 -23.37 21' horz -5.37 -4.91
1 vert -17.51 -34.48 11 -18.38 -25.73 21 vert -29.79 -30.71
2 horz -0.60 -1.12 12 -14.31 -24.00 22 horz -5.88 -4.91
2 vert -13.30 -26.82 13 -20.52 -26.84 22 vert -30.06 -31.30
3 -1.90 -1.13 14 -15.62 -25.11 23 horz -5.37 -4.94
4 -1.11 -1.14 15 -16.31 -25.74 23 vert -30.14 -30.97
5 -17.13 -24.78 16 -20.52 -27.47 24 horz -4.70 -4.95
6 -13.45 -23.01 17 -13.61 -15.56 24 vert -29.79 -30.37
7 -28.15 -39.36 18 -13.15 -15.89 25 horz -37.13 -37.13
8 -24.70 -37.11 19 -2.42 -1.42 25 vert 0.00 0.00
9 -17.17 -25.10 20 -2.01 -1.43 26 horz 26 vert -34.91 0.00 -34.91 0.00
figure A. 14 Differential detection, horizontal horizontal steady state results
-j
u>


horizontal vertical input
Vin 1 = + 20 V
Vin 2 = 20 V
measured
intensity in (db) Vout
Hdet
Vdet
All gains are relative to position 25 and 26, horz
gain n = 10 log(intensity n / intensity 25 horz)
-14.31 .390
-13.01 .522
measured simulated
position gain (db) gain (db)
measured simulated
position gain (db) gain (db)
measured
position gain (db)
simulated
gain (db)
1 horz -1.30 -1.11 10 -1.49 -1.67 21 horz -7.51 -7.865
1 vert -14.50 -34.48 11 -18.38 -25.73 21 vert -16.16 -22.73
2 horz -22.48 -36.03 12 -1.96 -2.31 22 horz -5.88 -4.903
2 vert -0.85 -1.11 13 -19.47 -26.84 22 vert -19.00 -31.30
3 -1.85 -1.13 14 -3.01 -3.42 23 horz -5.37 -4.94
4 -22.24 -24.53 15 -3.77 -4.05 23 vert -29.18 -30.97
5 -16.95 -24.78 16 -20.14 -27.47 24 horz -7.51 -7.52
6 -0.98 -1.22 17 -13.30 -15.885 24 vert -16.16 -22.48
7 -27.92 -39.56 18 -34.50 -37.90 25 horz -37.13 -37.13
8 -12.30 -14.50 19 -2.13 -1.42 25 vert 0.00 0.00
9 -17.92 -25.10 20 -23.94 -24.98 26 horz 26 vert -34.91 0.00 -34.91 0.00
figure A. 15 Differential detection, horizontal vertical steady state results
-j


position measured gain (db) simulated gain (db) position measured gain (db) simulated gain (db) position measured gain (db) simulated gain (db)
1 horz -18.79 -40.28 10 -14.70 -23.37 21 horz -5.14 -4.91
1 vert -1.39 -1.11 11 -3.01 -2.31 21 vert -32.01 -30.71
2 horz -0.60 -1.12 12 -15.25 -24.00 22 horz -8.10 -7.67
2 vert -11.30 -26.82 13 -4.12 -3.42 22 vert -15.37 -22.74
3 -18.38 -24.66 14 -16.78 -25.11 23 horz -8.33 -7.52
4 -1.49 -1.14 15 -17.13 -25.74 23 vert -15.88 -22.49
5 -1.80 -1.22 16 -4.50 -4.15 24 horz -4.31 -4.95
6 -14.12 -23.01 17 -31.11 -38.00 24 vert -20.14 -30.37
7 -12.74 -15.5 18 -13.15 -15.89 25 horz -37.13 -30.13
8 -25.14 -37.1 19 -19.17 -25.10 25 vert 0.00 0.00
9 -2.36 -1.67 20 -1.74 -1.43 26 horz 26 vert -34.91 0.00 -34.91 0.00
figure A1.16 Differential detection, vertical horizontal steady state results


position measured gain (db) simulated gain (db) position measured gain (db) simulated gain (db) position measured gain (db) simulated gain (db)
1 horz -19.35 -38.24 10 -1.90 -1.68 21 horz -22.87 -39.00
1 vert -1.30 -1.11 11 -3.01 -2.31 21 vert -7.13 -7.73
2 horz -24.91 -36.03 12 -2.18 -2.31 22 horz -27.14 -40.72
2 vert -1.11 -1.11 13 -3.86 -3.42 22 vert -7.93 -7.40
3 -20.93 -24.66 14 -3.53 -3.42 23 horz -23.45 -40.64
4 -23.94 -24.53 15 -3.94 -4.05 23 vert -7.13 -7.392
5 -1.80 -1.22 16 -4.12 -4.05 24 horz -22.36 -38.97
6 -1.39 -1.22 17 -32.74 -38.00 24 vert -6.46 -7.729
7 -12.74 -14.50 18 34.50 -38.00 25 horz -37.13 -37.13
8 -13.69 -14.50 19 -21.90 -25.10 25 vert 0.00 0.00
9 -2.36 -1.676 20 -24.70 -24.98 26 horz 26 vert 34.91 0.00 34.91 0.00
figure A. 17 Differential detection, vertical vertical steady state results
as


comparator
switching
note: step voltage to switch input FLC **me ^usec^ measured response
is applied at t = 0 simulated response
figure A. 18 Differential detection gate, output rise times
(input 1 switching, input 2 steady)


comparator
switching
note: step voltage to switch input FLC
is applied at t = 0
time (usee)
measured response
simulated response
figure A. 19 Differential detection gate, output fall times
(input 1 switching, input 2 steady)


comparator
switching
note: step voltage to switch input FLC tinK (uSec) measured response
is applied at t = 0 simulated response
figure A.20 Differential detection gate, output rise times,
(input 1 steady, input 2 switching)


iiradiance of horizontal
comparator
switching
time
note: step voltage to switch input FLC time (uSec) measured response
is applied at t = 0 simulated response
figure A.21 Differential detection gate, output fall times,
(input 1 steady, input 2 switching)
OO
O


comparator
switching
time
note: step voltages to switch input FLCs
are applied at t = 0
time (usee)
measured response
simulated response
figure A.22 Differential detection gate, output 23 rise time,
(both inputs switching)
OO


comparator
switching
time
note: step voltages to switch input FLCs t*me (usec) measured response
are applied at t = 0 * simulated response
figure A.23 Differential detection gate, output 24 rise time,
(both inputs switching)
oo
N>


comparator
switching
time
note: step voltages to switch input FLCs
are applied at t = 0
time (usee)
measured response
simulated response
figure A.24 Differential detection gate, output 23 fall time,
(both inputs switching)
OO


iiradiance of horizontal component,
comparator
switching
time
note: step voltages to switch input FLCs
are applied at t = 0
time (usee)
measured response
simulated response
figure A.25 Differential detection gate, output 24 fall time,
(both inputs switching)


comparator
switching
note: step voltages to switch input FLCs tfme(usec> measured response
are applied at t = 0 " simulated response
figure A.26 Differential detection gate, output 28 fall time,
(both inputs switching)
Ul


APPENDIX B
FORTRAN CODE
Appendix B contains the Fortran 77 code of the simulations. It was it
implemented on a Sun/UNIX workstation. Sun/UNIX Fortran 77 allows for
lines of greater that 72 characters, which is reflected by some of the lines of code
that wrap around onto a second line and occupy columns 1 through 6.
cccccccccccccccccccccccccccccccccc
c program DG ATE (dual gate) cc
cccccccccccccccccccccccccccccccccc
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c This program is used to simulate the optical logic gate
c with the dual FLC controlling the inputs.
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
program dgate
cccccccccccccccccccccccccccccccccccccccceccccccccccccccccccccccccccccccccccccccc
c These are the common blocks that will be used by the program,
c The first group includes the variables that are constants.
cccccccccccccccccccccccccccccccccccccccccccccccccccceccccccccccccccccccccccccccc
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c Common block ARRAYSIZES are the sizes of the various arrays that
c are to be used.
c
c
c
c
c
c
c
c
c
c
c
c
pathnum
pathsets
gatenum
flcnum
measdetnum
flcconstnum
the number of light paths in a gate
the number of arrays of path numbers, usually gatenum+1
the number of gates in the simulation
the number of Acs in the simulation
(it can be larger than gatenum if there are other
flcs used to control the input light
the number of detectors being used to measure at various
spots in the simulation (they do not include the
detectors in the gate)
the number of constants that are used to describe
each FLC


87
c flclibnum the number of FLCs unique characterized in the FLC
c library
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
common / arraysizes/ pathnum,pathsets,gatenum,flcnum,measdetnum,
flcconstnum,flclibnum
integer pathnum,pathsets,gatenum,flcnum,measdetnum,flcconstnum, flclibnum
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c common block GLOBALS includes the global variables
c that are time related and should be known throughout the system,
c t the simulation clock
c deltat time increment of the simulation
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
common/ globals/1, deltat
real t, deltat
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c common block PRINTOPTIONS contains the options so that various degrees
c of output can be obtained. It also includes the variable COHERENT ADD,
c which controls the adding of the outputs either coherently or
c incoherently.
prints out the light paths of the simulation
after the gate has completely switched
prints all the paths if true, but only prints
the input and output paths if false
adds outputs coherently or incoherently, and
prints them out if allpaths is true
steadystate
allpaths
coherentadd
c
c
c
c
c
c
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
common/ printoptions/ steady state,allpaths .coherentadd
logical steadystate,allpaths,coherentadd
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
c MAIN PROGRAM
c Below are the variables used in the main program:
c
c
c
c
c
c
c
c
c
c
c
c
horz(pathnum,pathsets) the horizontal component of the path light
vert(pathnum.pathsets) the vertical component of the path light
the phase angle of the horz. component
the phase angle of the vert, component
the angle between the polarization vector the and
the E field for a particular flc
the output of the comparator for a particular gate
the gate detector outputs (there are two) for
a particular gate
the controlling voltage of the 2 input flcs
real array that holds the value of the output of
the measurement detectors
ph(pathnum,pathsets)
pv(pathnum,pathsets)
peangle(flcnum)
compoutfgatenum)
gatedetout(2,gatenum)
vin(2)
measdet(12)


88
a 2-D array of FLC constants
Subroutines called:
initflcconst initializes a 2-dimensional array that holds the
values of the FLC constants. The array is
flcconstnum by flclibnum and these values must
agree with the initialized values of the
common block ARRAYSIZE values
initlookup This initializes an array of numbers that are
used by the output routine PRINTGATE to
match the output of the simulation with the
data taken in the lab.
dosimulation A helper subroutine that simulates the switching
of die gate for different voltages that control
the rotation of the input FLCs.
c flcconstant
c
c
c
c
c
c
c
c
c
c
c
c
c
c
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
real horz(28,2),vert(28,2),ph(28,2),pv(28,2),peangle(3),compout(l),
gatedetout(2,1 ),vin(2) ,measdet( 12),flcconstant( 10,4)
print *, '************* doing dual FLC input gate simulation **********
$$$$$$ I
deltat= 1.0e-6
pathnum = 28
pathsets = 2
gatenum = 1
flcnum = 3
measdetnum = 8
flcconstnum = 10
flclibnum = 4
call initlookup
call initflcconst(flcconstant)
steadystate = .false.
allpaths = .true.
coherentadd = .false.
peangle(l) = flcconstant(5,2)
peangle(2) = flcconstant(5,3)
peangle(3) = flcconstant(5,4)
compout(l) = -15
horz(l,2) = 8.34730e-3
vert(l,2) = .6
ph(l,2) =0.0
pv(l,2) =0.0
horz(2,2) = 10.7763e-3
vert(2,2) = .6
ph(2,2) =0.0
pv(2,2) =0.0
vin(l) = -20.0
vin(2) = -20.0


89
call dosimulation(horz,vert,ph,pv,peangle,compout,gatedetout,vin,measdet,
flcconstant)
vin(l) = -20.0
vin(2) = 20.0
call dosimulation(horz,vert,ph,pv,peangle,compout,gatedetout,vin,measdet,
flcconstant)
vin(l) = -20.0
vin(2) = -20.0
call dosimulation(horz,vert,ph,pv,peangle,compout,gatedetout,vin,measdet,
flcconstant)
vin(l) = 20.0
vin(2) = -20.0
call dosimulation(horz,vert,ph,pv,peangle,compout,gatedetout,vin,measdet,
flcconstant)
vin(l) = -20.0
vin(2) = -20.0
call dosimulation(horz,vert,ph,pv,peangle,compout,gatedetout,vin,measdet,
flcconstant)
vin(l) = 20.0
vin(2) = 20.0
call dosimulation(horz,vert,ph,pv,peangle,compout,gatedetout,vin,measdet,
flcconstant)
vin(l) = -20.0
vin(2) = -20.0
call dosimulation(horz,vert,ph,pv,peangle,compout,gatedetout,vin,measdet,
flcconstant)
stop
end
cccccccccccccccccccccccccccccecccccccccccccccccccccccccccccccccccccccccccccccccc
c Subroutine DOSIMULATION is a helper to the main program that calls the
c simulation of the system with various input voltages. All the output
c is called from this routine,
c
c Imports:
c h(pathnum,pathsets)
c v(pathnum,pathsets)
c ph(pathnum,pathsets)
c pv(pathnum,pathsets)
c peangle(flcnum)
c
c compout(gatenum)
c gatedetout(2,gatenum)
c
c vin(2)
c measdet(12)
c
c flcconstant
c
c Subroutines called:
c printsimheader prints the header for the dynamic simulation
c printsim prints out information of the dynamic simulation
the horizontal component of the path light
the vertical component of the path light
the phase angle of the horz. component
the phase angle of the vert, component
the angle between the polarization vector the and
the E field for a particular flc
the output of the comparator for a particular gate
the gate detector outputs (there are two) for
a particular gate
the controlling voltage of the 2 input flcs
real array that holds the value of the output of
the measurement detectors
a 2-D array of FLC constants


90
c printgate prints out the light paths of the gate
c printextrapaths prints out the extra light paths used to create
c the front end of the system
c simusystem defines the system to be simulated
cccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccccc
subroutine dosimulation(h,v,ph,pv,peangle,compout,gatedetout,vin,measdet,
flcconstant)
real h(pathnum,pathsets),v(pathnum,pathsets),ph(pathnum,pathsets),
pv(pathnum,pathsets)
real peangle(flcnum),compout(gatenum),gatedetout(2,gatenum),vin(2),
measdet(measdetnum),flcconstant(flcconstnum,flclibnum)
common / arraysizes/ pathnum,pathsets,gatenum,flcnum,measdetnum,
flcconsmum, flclibnum
integer pathnum,pathsets,gatenum,flcnum,measdetnum,flcconstnum,flclibnum
common/ globals/t, deltat
real t, deltat
common/ printoptions/ steadystate,allpaths,coherentadd
logical steadystate,allpaths,coherentadd
integer i
t = 0.0
print *,'
print *,'llllllllllllllllllllllllllllllllllllllllllllllllllllllllllir
print '
print *,'Vin 1 is now ',vin(l),' and Vin 2 is ',vin(2)
if (.not.steadystate) then
call printsimheader
end if
do 16, i = 0,1149
call simusystem(h,v,ph,pv,peangle,compout,gatedetout,vin,measdet,
flcconstant)
if ((mod(i,25).eq.0).and.(.not.steadystate)) then
call printsim(peangle,compout,measdet)
end if
t = t + deltat
16 continue
if (steadystate) then
print *,''
print *,'These are the paths in the gate.'
call printgate(h( 1,1 ),v( 1,1 ),ph( 1, l),pv( 1,1 ),peangle( l),compout( 1),
gatedetout( 1,1),allpaths,flcconstant( 1,1))
print '
print *,'These are the extra paths.'
call printextrapaths(h(l ,2),v( 1,2),ph( 1,2),pv(l ,2))
end if
return