liquid crystal waveguide-based non-mechanical beam …
Post on 01-Jun-2022
4 Views
Preview:
TRANSCRIPT
The Pennsylvania State University
The Graduate School
College of Engineering
LIQUID CRYSTAL WAVEGUIDE-BASED
NON-MECHANICAL BEAM STEERING
A Thesis in
Engineering Science and Mechanics
by
Shengshi Liu
© 2017 Shengshi Liu
Submitted in Partial Fulfillment
of the Requirements
for the Degree of
Master of Science
May 2017
ii
The thesis of Shengshi Liu was reviewed and approved by the following:
Jian Xu
Associate Professor of Engineering Science & Mechanics
Thesis Advisor
Osama O. Awadelkarim
Professor of Engineering Science & Mechanics
Samia A. Suliman
Assistant Professor of Engineering Science & Mechanics
Judith A. Todd
Professor of Engineering Science & Mechanics
Head of the Department of Engineering Science & Mechanics
*Signatures are on file in the Graduate School
iii
ABSTRACT
Beam steering technique is widely used in the fields of laser communication, optical
storage, target tracing, etc. Generally, the beam steering technique depends on mechanical
systems for changing the direction of optical axis in order to control the propagating direction of
the laser beam, resulting in complicated structures, substantial masses, high cost, and high energy
consumption. In this work, I present, for the first time, a novel technique of the electro-optic
liquid crystal waveguide-based mechanical laser beam steerer on the fused silica substrate, which
provides unprecedented advantages such as large angular deflection, rapid response, and small
size. This original device is based on the liquid crystal, which is the material of the largest
electro-optic response. The birefringence, Δn, for a typical nematic liquid crystal is around 0.2
over the applied voltage of 5 V, which is several orders of magnitude larger than that of other
materials. When combined with the patterned electrodes, this device is capable of providing an
analog, non-mechanical ‘Snell’s-law-type’ beam steerer. Theoretically, the device could produce
up to 90 degrees of analog electro-optic deflection, which exhibits an extremely large angular
coverage achieved by the non-mechanical ways. Such a device opens up the new opportunities
for applications with traditional LCD structures. In this thesis, the processing technique of liquid
crystal cells will also be introduced, including the cleaning and drying procedure, the
photolithography procedure, the alignment procedure, the cell making procedure, and the LC
filling procedure.
iv
TABLE OF CONTENTS
List of Figures .......................................................................................................................... v
List of Tables ........................................................................................................................... vi
Acknowledgements .................................................................................................................. vii
1 Introduction of Liquid Crystal ......................................................................................... 1
1.1 History of Liquid Crystal Device ............................................................................... 1 1.2 Molecular Structure of Liquid Crystal ....................................................................... 3 1.3 Types of Liquid Crystal ............................................................................................. 7
1.3.1 Nematic Liquid Crystal ................................................................................... 8 1.3.2 Two Kinds of Nematic Liquid Crystal ............................................................ 10
1.4 Brief Introduction of Physical Properties of Liquid Crystal ...................................... 11 1.4.1 Elastic Theory of Liquid Crystal ..................................................................... 11 1.4.2 Optical Anisotropy in Liquid Crystal .............................................................. 13 1.4.3 Dielectric Anisotropy in Liquid Crystal .......................................................... 15
1.5 Applications of Liquid Crystal ................................................................................... 17
2 Theory of the Slab Dielectric Waveguide ........................................................................ 18
2.1 Snell’s Law ................................................................................................................ 19 2.2 Total Internal Reflection ............................................................................................ 20 2.3 Basic Structure of the Slab Dielectric Waveguide ..................................................... 21 2.4 The Analysis Methods of Slab Dielectric Waveguide ............................................... 24
2.4.1 Ray Optics Method .......................................................................................... 25 2.4.2 Wave Equation Method ................................................................................... 29 2.4.3 Mode Field Distribution of TE Modes ............................................................ 34
3 Design and Manufacture the Non-Mechanical Beam Steerer .......................................... 36
3.1 Novelty of the Non-Mechanical Beam Steerer .......................................................... 36 3.2 Design of the Device .................................................................................................. 37
3.2.1 Architecture of the Device .............................................................................. 37 3.2.2 Design of the Deflection Angle ....................................................................... 40 3.2.3 Thickness of the Device .................................................................................. 42
3.3 Production Process of Liquid Crystal Cell ................................................................. 49 3.3.1 Cleaning and Drying Process .......................................................................... 49 3.3.2 Photolithography Process ................................................................................ 50 3.3.3 Alignment Process ........................................................................................... 52 3.3.4 Cell Making and LC Filling Process ............................................................... 54
3.4 Manufacturing of the Beam Steerer ........................................................................... 55
4 Results Achieved by Fabrication and Future Work ......................................................... 59
v
4.1 Quality of Liquid Crystal Cell.................................................................................... 59 4.2 Test Result of Beam Steerer ....................................................................................... 61 4.3 Future Work ............................................................................................................... 67
Appendix .................................................................................................................................. 68
A. TE ............................................................................................................................... 68 B. TM .............................................................................................................................. 69 C. Half Interval: ............................................................................................................... 71
References ................................................................................................................................ 73
vi
LIST OF FIGURES
Figure 1-1 The order of molecules in traditional solid, liquid crystal and traditional liquid
phases. .............................................................................................................................. 4
Figure 1-2 The molecular shape of liquid crystal: rod-like and disk-like molecules. .............. 4
Figure 1-3 Rod-like liquid crystal molecular structure model ................................................. 5
Figure 1-4 The there types of liquid crystal: Smectic, Nematic and Cholesteric.(from left
to right)[7] ........................................................................................................................ 7
Figure 1-5 Diagram of nematic liquid crystal and the director. ............................................... 8
Figure 1-6 Diagram of order para meter changing with temperature.[10] ............................... 9
Figure 1-7 The molecular structure of nematic liquid crystal 5CB. ........................................ 10
Figure 1-8 Three fundamental deformations in uniaxial nematic liquid crystal: twist, bend
and splay.[14] ................................................................................................................... 12
Figure 1-9 The birefringence in nematic liquid crystal. ........................................................... 14
Figure 1-10 The orientation of liquid crystal molecule under the external electric field. (a)
positive dielectric anisptropy (b) negative dielectric anisotropy.[1] ................................ 16
Figure 1-11 The working principle of TN LCD. ..................................................................... 17
Figure 2-1 Refraction of light at the interface between two media of different refractive
indices. ............................................................................................................................. 19
Figure 2-2 Diagram of the total internal reflection. ................................................................. 20
Figure 2-3 The structure of the slab dielectric waveguide. ...................................................... 22
Figure 2-4 Three kinds of waveguide mode: (a) fully waveguide mode, (b) half-leaky
waveguide mode, (c) fully-leaky waveguide mode. ........................................................ 23
Figure 2-5 The numerical aperture of symmetric slab dielectric waveguide. .......................... 25
Figure 2-6 Diagram of the waveguide dispersion equation. .................................................... 26
Figure 2-7 Electric field distribution for TE modes. ................................................................ 34
Figure 3-1 Design drawing of the non-mechanical beam steerer. ........................................... 37
Figure 3-2 The upper ITO glass substrate. ............................................................................... 38
Figure 3-3 The lower ITO glass substrate ................................................................................ 39
vii
Figure 3-4 Schematic diagram of the Snell’s law type beam steerer. ...................................... 39
Figure 3-5 Diagram of waveguide modes for no. ..................................................................... 43
Figure 3-6 Diagram of waveguide modes for ne. ..................................................................... 44
Figure 3-7 Diagram of waveguide modes for no. ..................................................................... 45
Figure 3-8 Diagram of modes for ne. ....................................................................................... 46
Figure 3-9 Diagram of waveguide modes for no. ..................................................................... 47
Figure 3-10 Diagram of waveguide modes for ne. ................................................................... 48
Figure 3-11 Diagram of the photolithography process. ........................................................... 51
Figure 4-1 The bright and dark status of TN LCD (process 1). ............................................... 60
Figure 4-2 The bright and dark status of TN LCD (process 2). ............................................... 60
Figure 4-3 The design drawing of the prism. ........................................................................... 63
Figure 4-4 The working sketch of the beam steerer. ................................................................ 64
Figure 4-5 The waveguide of the beam steerer. ....................................................................... 65
Figure 4-6 Illustration of the new pattern of the ITO electrode. .............................................. 67
viii
LIST OF TABLES
Table 1-1 The table of molecular structure of E7 components.[12] ........................................ 11
Table 3-1 Table of waveguide modes for no. ........................................................................... 42
Table 3-2 Table of waveguide modes for ne. ........................................................................... 43
Table 3-3 Table of waveguide modes for no. ........................................................................... 44
Table 3-4 Table of modes for ne. ............................................................................................. 45
Table 3-5 Table of waveguide modes for no. ........................................................................... 46
Table 3-6 Table of waveguide modes for ne. ........................................................................... 47
Table 4-1 Basic parameters of laser diode. .............................................................................. 61
Table 4-2 Table of waveguide modes for ordinary light.......................................................... 62
Table 4-3 Table of waveguide modes for extraordinary light. ................................................. 63
ix
ACKNOWLEDGEMENTS
Time does fly. It has been nearly three years since I enrolled in the graduate program and
now that is coming to an end. My time here at Penn State University has been filled with
fruitfulness, warmth, and joy. I want to thank my family for their continuous support, my
supervisors for their detailed and careful guide and my classmates for their contagious enthusiasm
that helped me endure this journey.
I want to first express my deepest gratitude to my advisor Prof. Dr. Jian Xu. Dr. Xu has
carefully guided me at each step from research topic selection, design of the experiment method,
progress of the project, to the thesis writing. His rigorous scholarship style and professional
attitude have greatly affected my student career. In addition, he has also cared about my well-
being very much. He has taught me not only professional knowledge and scientific research skills,
but also the meaning and the truth of life. I have no doubt that the knowledge which I obtained
from Dr. Xu will stay with me and continue to guide my path forward in both work and life.
I would also like to thank Professor Chang Min for helping me in experiments. I want to
thank Kandhar K. Kurhade for helping me explore the project at the beginning. I am also much
honored to work together with Chen Mo. Also my sincere and great thanks to Dr. Guanjun You,
Dr. Li Wang, Dr. Mahmoud R. M. Atalla, and Asim M. N. Elahi, for their continuous
encouragements and help to me during the project.
Lastly, I want to especially thank my parents. I could not have achieved what I have done
without their unconditional love, support, words of encouragement and confidence on me.
1
1 Introduction of Liquid Crystal
1.1 History of Liquid Crystal Device
Nowadays, with the rapid development of technology, liquid crystal display has been
common for people. Since liquid crystal devices have many extraordinary advantages such as low
voltage, micro power, flat type structure, no glare, no irritating to the eyes and no electromagnetic
radiation, those devices are used in a wide variety of industrial applications, such as counters,
telephones, mobile phones, digital cameras, TVs, laptops and so on. Generally speaking, liquid
crystal display is closely correlated with people’s daily life. In this section of the thesis, I will
give a brief introduction on the development of liquid crystal display.
Researchers found liquid crystal material in its liquid form as early as 1888.[1] At that
time, liquid crystal material was almost a transparent material, which performed as an
intermediate between liquids and solids. From the shape and appearance point of view, the liquid
crystal is a kind of liquid, however, its crystalline molecule structure as appears to be solid. Like a
metal in the magnetic field, when the metal is influenced by an external electric field, the
molecules are highly ordered. If the molecular arrangement of the liquid crystals is controlled
properly, liquid crystal molecules will allow light to penetrate. The path of light penetration can
be controlled by its molecule structure, which is another important feature of solid.
In the 1960s, it was found that charging the liquid crystal will change its molecular
arrangement, resulting in distortion or refraction of light. In 1968, a scientist invented the liquid
crystal display device in the United States, and liquid crystal display (LCD) monitors were
officially launched soon. However, since the birth of the first LCD screen, just 30 years ago, the
LCD technology had a quick development. In the early 1970s, the Japanese began to produce
twisted nematic (TN) liquid crystal material, and promoted the application based on TN-LCD;
2
also, in the early 1980s, TN-LCD products were widely used in calculators; in 1984, after the thin
film transistor (TFT) LCD and super twisted nematic (STN) LCD were proposed by Europe and
the United States in the late 1980s, the Japanese mastered the STN-LCD mass production
technology, therefore the LCD industry improved dramatically.[2]
In around 1971, these liquid crystal devices, which were known as original TN-LCDs,
started to be a part of human life. The application of LCD only appeared in some areas such as
medical instrumentation although the production processes were not mature and only
monochrome display was achieved. By the early 1980s, TN-LCD had been used in new computer
products. In 1984, occident proposed the new techniques STN-LCD and TFT-LCD were
proposed at the same time, although the two new techniques were not mature enough. In the late
1980s, because the Japanese mastered the STN-LCD mass production technology, production
lines were finally set up and that was also an important signal that LCD would be commonplace
soon.
In 1993, after the mass production of STN-LCD, new LCD started advancing along two
directions: one direction was to produce low-price and low-cost LCD monitors, so dual-scan
STN-LCD (DSTN-LCD) followed soon to help the costs low down; the other direction was to
develop and researchhigh-quality TFTs. Japanese technicians developed large size TFT-LCD
production line which was represented by 550×670 mm2 large substrate. In the following years,
they cut the cost down by half. Korean and Taiwanese companies had invested a huge sum of
money in building a third generation production line to compete with Japan for world market
after 1996.[3] However, so far, the Japanese has completely quit the large size TV’s LCD panel
throughout the world market, and in stark contrast, a significant number of high-generation LCD
panel production line has put into operation. China has become one of the important global panel
production bases.
3
1.2 Molecular Structure of Liquid Crystal
In general, liquid crystal, which is also called mesogens as well, has many properties and
characteristics such as the arrangement of an organic molecule, strong dipoles and pretty high
birefringence.[4]
The preference of the liquid crystal molecules to point along one common direction is the
most distinctive characteristic of the liquid crystalline state, in which the common direction is
also named the director. In contrast, molecules in the liquid phase have no intrinsic orientation.
However, molecules in the solid phase are highly ordered and have little space to move. The
characteristic molecular arrangement of the liquid crystal is exactly between the normal solid
phase and the normal liquid phase, and this is the reason why it is called mesogenic state, the
synonyms of liquid crystal state. The order of different phases can be roughly described in the
following diagram, as shown in Figure 1-1. Sometimes, only based on the molecular diagram, it
is difficult to distinguish whether a certain material is in a liquid crystal state or not, since all the
crystalline materials have the same key characteristic, long-range periodic order. Liquid crystal
phase only has some degree of order when compared to traditional solid state, not the same order
as the solid state.
4
Figure 1-1. The order of molecules in crystalline solid, liquid crystal and isotropic liquid phases.
Liquid crystal has distinctive physical properties, which are determined by its micro
molecular structure. As shown in Figure 1-2, the group of molecules have special shapes, such as
rod-like or disk-like shapes, also called elongated and flattened shapes. Among them, rod-like
shape molecules are the most common liquid crystal molecules for industrial application.
Figure 1-2. The molecular shape of liquid crystal: rod-like and disk-like molecules.
The model of single liquid crystal molecular structure is shown in Figure 1-3. The model
presents a typical rod-like liquid crystal molecule, which is composed of two parts, one part is
basic mesogenic unit: a central-bridge-bond A and rigid rod benzene ring or other ring structures;
the other part is terminal groups X and Y: usually soft and flexible group. By using this model,
5
the effects of the individual components on the physical properties of the liquid crystals are
summarized as follows.[5]
Figure 1-3. Rod-like liquid crystal molecular structure model
Ring structure: The ring structure varies as both unsaturated ring and saturated ring are
two important compositions of that ring structure. That structure can also be composed of their
derivatives, phenyl group as unsaturated composition and cyclohexyl group as saturated
composition. In the benzene conjugation system, the molecule polarization rate is large in the
direction of the molecular axis. Therefore, increase the number if the aromatic ring can increase
the thermal stability of the liquid crystal, in other words, increase the clear point of the liquid
crystal. The use of polycyclic or fused ring structures to replace the benzene ring could increase
the thermal stability of the liquid crystal as well. The ring structure limits the short-range
intermolecular force, so there is a tendency to form nematic phases.
Electron transitions occur in all molecules no matter whether they have unsaturated or
saturated rings. The electron transition in the pi bond and σ bond occurs at the near UV spectral
and UV spectral region, respectively. Similarly, in the IR spectral region (≥ 9μm), rovibrational
transitions are accompanied by absorption. In summary, the transparency of liquid crystal
molecules is very good in the visible and NIR spectral region. In addition, since different
functional groups have different absorption peaks, at certain wavelengths of light, the photon will
be absorbed by liquid crystal molecules.[6]
Central-bridge-bond A: The groups of central-bridge-bond are always named certain
liquid crystal molecules. In general, those groups are linkage groups, and different groups have a
6
significant influence on the properties of liquid crystal, especially in chemical stability. The
central bridge bond of the benzylidene-type liquid crystal is -CH = N-, which is easily
hydrolyzed or oxidized, and extremely sensitive to water. Accidentally chlorine compounds are
susceptible to oxidation, especially under the light illumination. Liquid crystal molecules contain
stilbene with a double bond, diphenylacetylene with a triple bond, methyl cinnamate and its many
derivatives are poor in chemical stability and will lose their properties due to polymerization or
fracture under the ultraviolet light. If saturated hydrocarbon chain is use as the central bridge
bond, molecules are easy to bend, which can get low-temperature liquid crystal phase and even
non-liquid crystal phase. Generally speaking, central bridge bonds are rigid, facilitating the
formation of liquid crystalline phase, but branched chain compounds are generally less favorable.
For the first time, Gray and his group synthesized a kind of biphenyls liquid crystal without the
central bridge bond, which is more stable than other traditional liquid crystals, indicating that the
central bridge bond is not the indispensable part of the liquid crystal molecule.
Terminal group X: terminal group X, also named side chain, usually consists of alkyl
chain CnH2n+1. Sometimes, side chain groups can have hydroxy or unsaturated double bond. The
length of the side chain X directly determines the clearing point of the liquid crystal molecules,
which means the highest temperature of the liquid crystal molecule to keep the liquid crystalline
phase. When n is smaller than 3, the side chain is very rigid so that it is not conducive to the
formation of liquid crystal phase. Medium-length side chains are the most suitable for forming
liquid crystalline phase, and the value of n ranges from 3 to 8. In industrial production, the higher
the clearing point of the liquid crystal is, the higher the scope of application of the product is.
Therefore, short length side chain liquid crystals tend to have higher clearing point, and have a
wider range of applications.
7
Terminal group Y: side chain Y determines two important physical properties of liquid
crystal, e.g. dielectric anisotropy and birefringence. Two typical terminal group Y are polar group
and nonpolar group. Alkyl chains are typical nonpolar groups and cyano group is a polar group.
Liquid crystal molecules, which have a polar group as a side chain, tend to have a large dielectric
anisotropy. Cyano group can provide an extremely high polarity among those polar groups.[7]
The geometry of the molecule is necessary for the formation of liquid crystal phase. In
order to obtain a rod-like liquid crystal molecule, people always used a method called para-
substituted to synthesis liquid crystal molecule.
1.3 Types of Liquid Crystal
Liquid crystal molecules have several parts which can consist of variety of groups. The
molecules that can form a liquid crystal phase has a high level of geometrical anisotropy in their
molecular shapes, and different molecular structures lead to different arrangement of liquid
crystal molecules. According to the arrangement of liquid crystal molecules, the liquid crystal can
be divided into three types: Nematic, Smectic and Cholesteric. I will focus on the nematic liquid
crystal, which was used in the experiment.
Figure 1-4. Three types of liquid crystals: Smectic, Nematic and Cholesteric.(from left to right)[7]
8
1.3.1 Nematic Liquid Crystal
Nematic liquid crystal is a very popular one. In this type of liquid crystal phase, the
location of the gravity center of the molecules is a chaotic disorder, but the molecular orientation
has a certain degree of order, in other words, the direction of molecular orientation has a
preferential orientation. A vector n is usually introduced to describe the preferential orientation,
which is called liquid crystal director, and it can also be regarded as the orientation direction of
the long axis of the liquid crystal molecules. As shown in Figure 1-5, liquid crystal molecules
have one common direction, i.e. director n . The angle θ is the angle between the long axis of the
liquid crystal molecule and the director.[8]
Figure 1-5. Diagram of nematic liquid crystal and the director.
The introduction of director n allows us to quantitatively describe the physical
characteristics of the liquid crystal. In general, the study of the liquid crystal director distribution,
often determines the specific distribution of liquid crystal molecules in the liquid crystal cell by
measuring the angle of inclination and twist angle. The presence of the director n indicates that
the molecular ratio in the liquid crystal phase is more ordered than that in the isotropic phase. In
order to quantitatively describe the level of order, a new concept called order parameter need to
be introduced, defined as the following equation 1-1.
9
2
2
1(cos ) 3cos 1
2S P
(1.1)
In the equation 1.1, the bracket <> means that all molecules are averaged. However, the
order parameter S is a function of temperature, and the value of S ranges from 0 to 1. Different
values of order parameter S correspond to different phases. When all the long axis of molecules
are perfectly along the director, θ equals to 0 and the value of S equals to 1, which means this
material is a highly ordered material, i.e. a crystal. However, under another boundary condition,
i.e. the value of <cos2θ> is up to 1/3, the value of S equals to 0, which means the material is an
isotropic material. When the value of S is between 0 and 1, the phase of the material is liquid
crystal phase. In the nematic liquid crystal which is aligned inside the liquid crystal cell, the value
of S is around 0.6. As the temperature changes, the value of S changes from 0 to 1, and at the
same time, the liquid crystal molecules change among the crystal, semctic A, nematic and
isotropic phases, shown as in Figure 1-6.[9]
Figure 1-6. Diagram of order para meter changing with temperature.[10]
10
1.3.2 Two Kinds of Nematic Liquid Crystal
A commonly used typical nematic liquid crystal is called 5CB, and it is also used in my
liquid crystal device. 5CB is the commercial name, and the chemical name is 4-Cyano-4'-
pentylbiphenyl with the chemical formula of C18H19N. 5CB was first synthesized at the
University of Hull in 1972.
Figure 1-7. Themolecular structure of nematic liquid crystal 5CB.
5CB is a commonly used liquid crystal monomer. Although this biphenyl cyanide liquid
crystal monomer is now basically out of date, it is still widely used in the laboratory. In addition,
5CB is an important liquid crystal monomer, which can be added to a liquid crystal mixture to
enhance the properties of the mixed liquid crystal. However, this liquid crystal is greatly limited
in industrial use, since the liquid crystal phase exists only between 18 and 35 oC, and this
temperature range significantly limits the work environment of liquid crystal display.
5CB is a kind of medium-sized liquid crystal, and the size of a single molecule is around
2 nm by 0.4 nm. The clearing point of 5CB is 35 degrees.[11]
Unlike liquid crystal monomer, mixed liquid crystals have much wider applications and
better properties in certain aspects, especially in operating temperature. In general, people can
design a mixed liquid crystal with good properties. The clearing point of a mixed liquid crystal is
the average of each component, and the mixture of different liquid crystal monomer will
effectively reduce the minimal temperature limitation for the liquid crystal phase. E7 is a famous
mixed liquid crystal which is very suitable for working at room temperature. In Table 1-1, all the
components and ratio of each component are listed.
11
Table 1-1. The table of molecular structure of E7 components.[12]
Through Table 1-1, 5CB and other three different nematic liquid crystal monomers
(7CB,80CB and 5CT) constitute the liquid crystal mixture together, and E7 have the same
properties as a nematic liquid crystal. The melting point of each liquid crystal monomer is higher
than 20 degrees, but in the E7 liquid crystal mixture, the melting point is only minus 10 degrees.
In addition, the clearing point of E7 is up to 60 degrees.
1.4 Brief Introduction of Physical Properties of Liquid Crystal
1.4.1 Elastic Theory of Liquid Crystal
According to the continuum theory of the uniaxial nematic liquid crystal phase, the state
of liquid crystal is described by the director n. If there is no other external field or boundary
12
disturbance, the director n of this nematic phase is a constant, which means the director n does
not vary with spatial position. However, under the external field or due to the existence of
boundary conditions, n can be changed with the spatial position. Assuming that some
singularities in the liquid crystal are removed, the director n is a continuous function of the
position vector r. When the director of liquid crystal deviates from the original direction (when
the director n is a constant), the deformation of liquid crystal occurs. The deformation of liquid
crystal will produce a restoring force against the deformation, or more specifically a restoring
torque, which is similar to the elastic deformation in the solid phase.[13]
The elastic continuum theory assumes that the rotation of liquid crystal molecules in the
direction of torque is the only physical quantity which can be changed by external
perturbations.[5] Therefore, the deformations of the liquid crystal can be divided into three types:
splay, bend, and twist (as shown in Figure 1-8).
Figure 1-8. Three fundamental deformations in uniaxial nematic liquid crystal: twist, bend, and
splay.[14]
The feature of splay is: 0n ;
The feature of twist is: n is parallel to n;
The feature of bend is: n is perpendicular to n.
And the related formulas of free energy density are listed,
13
Splay: 2
1 11
1( )
2F K n (1.2)
Twist: 2
2 22
1( )
2F K n n (1.3)
Bend: 2
3 33
1( )
2F K n n (1.4)
If the surface elastic energy is neglected, the expression of Frank elastic free energy
density of the uniaxial nematic liquid crystal is
2 2 2
11 22 33
1 1 1( ) ( ) ( )
2 2 2elasf K n K n n K n n (1.5)
The three terms in the above equation 2.5 describe the free energy density of the splay,
twist, and bend, respectively. K11, K22, and K33 represent the splay, twist, and bend elastic
constant, respectively. The elastic constant of the uniaxial nematic liquid crystal is very small
relative to the solid phase. Therefore, the uniaxial nematic liquid crystal director is susceptible to
external perturbations.[15]
1.4.2 Optical Anisotropy in Liquid Crystal
Liquid crystal molecules have uniaxial anisotropy, so that they have many unique optical
properties. The unpolarized light passing through the uniaxial liquid crystal molecules is divided
into two polarized light (extraordinary light and ordinary light), and this phenomenon is called
birefringence of the liquid crystal. The anisotropy of the nematic liquid crystal causes light in
which polarization parallel to the director is propagated at a refractive index while light
perpendicular to the director is propagated at another refractive index. Here, as shown in Figure
1-9, n∥ corresponds to the uniaxial crystal ne (refractive index of extraordinary light), while n⊥
corresponds to its no (refractive index of ordinary light).
14
Figure 1-9. The birefringence in nematic liquid crystal.
In the direction of arrangement of nematic liquid crystal molecules, which is the direction
of the molecular long axis, the arrangement of molecules is dense. However, in the direction
perpendicular to the arrangement of liquid crystal molecules, molecular arrangement is loose and
has a lower density. Because the liquid crystal has birefringence, in the liquid crystal, different
directions of polarized light propagate at different velocities. Thus, after entering the liquid
crystal, as the distance to the liquid crystal increases, the two vertical components of the light will
gradually deviate from the phase. This appearance of optical delay is very important.[16]
In the overwhelming majority of cases, the light wave oscillating in the long axis
direction of the nematic liquid crystal has a maximum refractive index ne and the light wave
oscillating in the direction perpendicular there to has a minimum refractive index no. The
anisotropy of refractive index is
e on n n n n (1.6)
LCD generally has positive uniaxial crystal optical properties, which can change the polarization
state and direction of the incident light. For example, the extraordinary and ordinary refractive
15
index of E7 liquid crystal at 550 nm is 1.7497 and 1.5261, respectively. The refractive index
birefringence Δn is up to 0.2236.[17]
1.4.3 Dielectric Anisotropy in Liquid Crystal
Similar to the optical anisotropy in the liquid crystal, the liquid crystal has dielectric
anisotropy, which is another important property in the display. Dielectric properties of the liquid
crystal are connected to the response of liquid crystal molecule to the application of an electric
field. In electromagnetics, the measure of resistance when the dielectric response to an applied
external electric field is called the permittivity. The liquid crystal molecule has two different
relative permittivities, the relative permittivity parallel to the director ε∥ and the relative
permittivity perpendicular to the director ε⊥. Considering the normal uniaxial liquid crystal
molecule in a Cartesian coordinate, and the z-axis is exactly parallel to the director. Then, these
two different refractive indices can then be quantitatively analyzed.
z , 1
( )2
x y (1.7)
The dielectric anisotropy is defined as
(1.8)
The value of the dielectric anisotropy can be positive and negative, and this positive or negative
value directly determines the orientation of the liquid crystal molecule under the external electric
field.[5]
16
Figure 1-10. The orientation of liquid crystal molecule under the external electric field. (a)
positive dielectric anisptropy (b) negative dielectric anisotropy.[1]
When the dielectric anisotropy is positive and applied the voltage higher than the
threshold voltage of liquid crystal molecule, as shown in Figure 1-10 (a), the liquid crystal
molecules tend to orient parallel to the electric field direction. On the contrary, when the
dielectric anisotropy is negative, the liquid crystal molecules tend to orient perpendicular to the
electric field direction.[18] The threshold voltage Vth is given by
12
iith
KV
(1.9)
In the above formula, Kii is the elastic constant of liquid crystal molecule. When the initial
molecular orientation is oriented in parallel, Kii is equal to K11; for vertical orientation, Kii is
equal to K33; when the parallel orientation is distorted into a spiral orientation,
11 33 22
1( 2 )
4iiK K K K (1.10)
17
1.5 Applications of Liquid Crystal
This chapter introduces the distinctive molecular structure and some important special
physical properties of liquid crystal. Based on its special properties, the liquid crystal is widely
used, especially in the flat panel display.
The TN (twisted nematic) liquid crystal cell is a kind of basic and common device to
achieve LCD. The liquid crystal is sealed between two pieces of glass which are platinized
electrode. The material of electrode must be transparent, for example, ITO. The thickness of
liquid crystal cell is controlled by the size of the spacer material. Attach polarizers to the outer
surface of the upper and lower glass substrate, in which one polarizer serves as a polarizer and the
other polarizer is used as a polarization analyzer. The two polarizers are perpendicular to each
other. When connecting this liquid crystal cell to a circuit control panel, a simple TN liquid
crystal display is made. The diagram of LCD is shown in Figure 1-11.
Figure 1-11. The working principle of TN LCD.
The circuit control panel is used to control the power on and off. When the power is
turned on, i.e. add a voltage between the liquid crystal molecules, the liquid crystal molecules
18
within the box will reorient, deviating from its original direction. When the power is off, i.e.
remove the voltage on the cell, under the elastic force, the liquid crystal molecules within the box
will restore its original orientation. Natural light through the polarizer will become linearly
polarized light, and linearly polarized light in the liquid crystal will be along the direction of the
long axis of liquid crystal molecules. For a TN liquid crystal cell, the long axis of the liquid
crystal molecules are rotated by exactly 90 degree between two pieces of glass substrates, so that
the direction of vibration of the linearly polarized light is also rotated by 90 degree. Therefore, the
light passes through the liquid crystal cell and becomes the bright status. When applying an
external electric field, the direction of liquid crystal molecules is changed to the direction of
electric field, therefore, in combination with polarizers, the light cannot pass through the liquid
crystal cell and turns to the dark status. This is the basic working principle of twisted nematic
LCD.[19]
2 Theory of the Slab Dielectric Waveguide
In this part of the thesis, I introduce the basic theory of the slab dielectric waveguide. The
using of slab dielectric waveguide theory is the core technique to achieve the non-mechanical
19
beam steering. When combined with the tremendous electro-optic response material liquid crystal
and the patterned electrodes ITO glass substrate, it is capable of manufacturing a unique
geometry liquid crystal based analog non-mechanical “Snell’s Law Type” beam-steerer.
2.1 Snell’s Law
When light travels in different media with different refractive indices, it generally bends,
or refracts. Refraction is the bending of the path of the incident light wave as it passes through the
boundary separating two media with different refractive indices. Refraction is caused by the
change in speed when the light propagates in two different media. Snell’s law is an important
formula used to describe the relationship between the angles of incidence and refraction when a
light passes through the interface between two media (shown in Figure 2-1).
Figure 2-1. Refraction of light at the interface between two media of different refractive indices.
In Figure 2-1, the relationship between the angles of incidence and refraction is given by
Snell’s law,
20
1 1 2 2sin sinn n (2.1)
where each θ is the angle measured from the normal of the boundary and n1 and n2 are the two
refractive indices of two different media in which the light passes through.[20]
2.2 Total Internal Reflection
Total internal reflection is a special optical phenomenon. In general, when the light
passes through two different media with different indices, part of the incident light will be bent by
refraction at the interface between two media, while the rest is reflected. However, when light
across from the optically denser medium to the optically thinner medium, the refracted light will
deviate from the normal of the interface between two media, as shown in Figure 2-2.
Figure 2-2. Diagram of the total internal reflection.
When the incident angle θ is gradually increased to a certain point (as shown in the
second case of Figure 2-2), the refracted light is extended to the interface, that is, the refracted
angle is exactly 90 degrees, which is called the critical angle. If the incident angle increases
continuously and is greater than the critical angle, and all the light reflects back to the optically
denser medium, and there is no refracted light in the optically thinner medium, but there is still an
21
evanescent wave which enters the optically thinner medium, as shown in the third case in Figure
2-2. This phenomenon is called total internal reflection (TIR).[20]
To find the critical angle, one needs to find the incident angle θi when exiting angle θt is
equal to 90 degrees. The resulting value of incident angle θi is equal to the value of critical angle
θc. The equation of the critical angle is
2
1
arcsinc
n
n
(2.2)
In equation (2.2), n2 is the refractive index of the optically thinner medium, while n1 is the
refractive index of the optically denser medium. For example, if the light is traveling through a
common glass substrate with a refractive index approximately 1.50 into the vacuum with a
refractive index 1.00, the critical angle is 41.8 degrees. In this case, when the incident angle is
greater than 41.8 degrees, the total internal reflection occurs.
2.3 Basic Structure of the Slab Dielectric Waveguide
Compared with other kinds of the waveguide, the structure of the slab dielectric
waveguide is very simple. As shown in Figure 2-3, the slab dielectric waveguide has a three-layer
structure. The middle layer is the guiding layer, and the refractive index of the guiding layer (n1)
is larger than that of the surrounding layers. The upper layer is the cladding layer, and the lower
layer is the substrate layer. The refractive index of the cladding layer and substrate layer are n3
and n2 respectively.[21]
22
Figure 2-3. The structure of the slab dielectric waveguide.
If the refractive index n2 is equal to n3, it is called symmetric slab dielectric waveguide.
On the contrary, if n2 and n3 values are different, it is called asymmetric slab dielectric waveguide.
The slab dielectric waveguide is a typical one-dimensional waveguide, because when the light is
confined in the middle layer by total internal reflection, the extension of the X axis direction, that
is, the thickness of the guiding layer, is the only condition to limit light beam. In practice, a slab
waveguide is not infinite in the direction of Y and Z axis, but if the typical size of the designed
device is far greater than the thickness of the guiding layer, the slab waveguide device will be an
excellent approximation.
In an actual slab dielectric waveguide structure, the refractive index of the three materials
must satisfy n1> n3, and n1> n2. In order to facilitate future discussion, suppose those three
refractive indices n1> n2> n3. Assuming a light beam propagates along the direction of Z axis and
only be confined in the guiding layer, a fully waveguide occurs when the inner angle β is satisfied
β>θc and β>θs. θc and θs are the critical angles of the cladding layer and substrate layer,
respectively. According to Snell’s law, the critical angles of the upper and lower interfaces are
given by following formulas:
3
1
arcsinc
n
n
(2.3)
23
2
1
arcsins
n
n
(2.4)
Because n2 is greater than n3, θs is greater than θc. From the relationship between the
inner angle β and the critical angles θs and θc, there are three kinds of the possible waveguide
modes in the slab dielectric waveguide structure. (Figure 2-4)
Figure 2-4. Three kinds of waveguide mode: (a) fully waveguide mode, (b) half-leaky waveguide
mode, (c) fully-leaky waveguide mode.
(a) Fully waveguide mode
When the inner angle βsatisfies the equation θs<β<π/2, the light propagating in the
guiding layer will be totally reflected in the upper and lower interfaces, as shown in Figure 2-4 (a),
which corresponds to the fully waveguide mode. Even if the light beam is totally reflected in the
24
guiding layer, light is not completely confined within the guiding layer due to the existence of an
evanescent field in the cladding layer and the substrate layer.
(b) Half-leaky waveguide mode
When θc<β<θs, the total internal reflection only occurs at the interface between the
guiding layer and the cladding layer. In this mode, part of the light beam leaks out from the
guiding layer and enters the substrate layer. The light beam is transmitted from one side of the
slab dielectric waveguide structure, so this case corresponds to the half-leaky waveguide mode, as
shown in Figure 2-4 (b).
(c) Fully-leaky waveguide mode
When inner angle β is smaller than θc, the light beam will leak out from both interfaces,
as shown in Figure 2-4 (c). This mode is referred to as a fully-leaky waveguide mode in which
the light propagating in the guiding layer becomes very weak.[22]
2.4 The Analysis Methods of Slab Dielectric Waveguide
In general, there are two effective methods that can be used to analyze a slab dielectric
waveguide, which are namely the ray optics method and wave equation method. The ray optics
method, that is, the geometrical optics method, is simple, intuitive, clear physical concept, and
can get some basic transmission characteristics of the light beam in the waveguide. However, the
wave equation method, which uses Maxwell’s equations, is a good way to describe the mode field
distribution in the waveguide, but it needs to use strict electromagnetic field theory to analyze.
25
2.4.1 Ray Optics Method
In the optical waveguide theory, only propagation light enters the guiding layer within a
certain angle, and the half-angle of this total angle is called the acceptance angle, θmax. As shown
in Figure 2-5, the numerical aperture of this symmetric slab dielectric waveguide is
2 2
max 1 2sinNA n n n (2.5)
The equation 2.5 can be approximated as the following equation (2.6),
1 2NA n , where 1 2
1
n n
n
(2.6)
Figure 2-5. The numerical aperture of symmetric slab dielectric waveguide.
From the section 2-3, we have known that only the total internal reflection of the light
beam can achieve the stable transmission in the waveguide. However, to maintain the light wave
transmission in the guiding layer, it is necessary to satisfy the dispersion equation of slab
dielectric waveguide (2.7).
1 0 12 132 cos 2n k t m (2.7)
26
Figure 2-6. Diagram of the waveguide dispersion equation.
To maintain the light wave transmission in the guiding layer, after a round trip between
the upper the lower interface of the guiding layer, the total phase shift of the light wave must be
an integer multiple of 2π. The total reflection phase shift of upper and lower interface are ϕ13 and
ϕ12, respectively.[23] In the equation (2.7), m is an integer, which represents a different mode of
the waveguide, and wave vector in vacuum k0= 2π/λ. The first term in the equation (2.7) is the
phase change in the process of the light wave moving forward. ϕ13 and ϕ12 are the phases
produced by the light wave at the interface. The unit of phase is 2mπ.
exp ( )E A j k r
(2.8)
According to the plane wave equation (2.8), the phases are continuous. Phase can only be
changed in one way, that is, the wave light transmits a section of distance. When the total internal
reflection occurs, the actual incident light will partially enter the optically thinner medium, and
the form is equivalent to the point of reflection relative to the incident point that has an offset
distance. This area has a higher attenuation and the offset distance is called Goos-Hanchen shift.
27
Therefore, the cladding layer and substrate layer need to have a certain thickness to confine the
light wave in the guiding layer.
In order to describe the phase shift of a light which moves from a medium of a given
refractive index, n1, into another medium with a refractive index, n2, the first thought must be the
Fresnel equations. When the Fresnel equations are used to describe the reflected light between
two media, the equations assume the interface between the media is flat and that the media are
homogeneous. In addition, the incident light is always considered as a plane wave, and will not be
affected by the edge effect.
The results directly depend on the polarization of the incident light, which can be
generally separated into two cases, S polarization and P polarization.
In order to describe two different modes clearly, define a plane which contains the
incident light, reflected light and refracted light, and this plane is also called the plane of
incidence. The incident light polarized with its electric field perpendicular to the plane of
incidence is called s-polarized. On the contrary, the incident light is polarized with electric field
parallel to the plane of incidence. Such light is described as p-polarized. S polarization
corresponds to the transverse electric (TE) modes which means there is only a magnetic field and
no electric field in the direction of propagation, while P polarization corresponds to the transverse
magnetic (TM) modes means no magnetic field in the direction of propagation.[24]
The Fresnel equations describe what fraction of the incident light is reflected. The
equations are as follows.
1 1 2 2
1 1 2 2
cos cos( )
cos cosTE s
n nr r
n n
(2.9)
2 1 1 2
1 2 2 1
cos cos( )
cos cosTM p
n nr r
n n
(2.10)
28
In the Fresnel equations, n1 and n2 are the refractive indices of media. θ1 and θ2 are the incident
angle and refraction angle respectively. Replace the refraction angle θ2 with Snell’s law (2.1).
Take the TE mode as an example,
2 2 2
1 1 2 1 1
2 2 2
1 1 2 1 1
cos sin
cos sinTE
n n nr
n n n
(2.11)
In the slab dielectric waveguide, the refractive indices of media must satisfy n1> n2. When the
total reflection occurs, the root number is an imaginary number, so the reflection coefficient at
this time is a complex number.
exp( 2 )r i (2.12)
Under this circumstance, we can find the phase angle by using formula (2.12) and solve the value
of ϕ12 and ϕ13.
1/22 2 2
1 212 2 2
1
sin2arctan
cos
n n
n
(2.13)
1/22 2 2
1 313 2 2
1
sin2arctan
cos
n n
n
(2.14)
Similarly, the total reflection phase shift for TM mode can be derived in the same method.
The total reflection phase shifts for TM mode as shown in the formula (2.15) and (2.16),
1/22 2 2 2
1 1 212 2 2 2
2 1
sin2arctan
cos
n n n
n n
(2.15)
1/22 2 2 2
1 1 313 2 2 2
3 1
sin2arctan
cos
n n n
n n
(2.16)
By returning the above phase angles back to the waveguide dispersion equation (2.7), the
eigen equations of the slab dielectric waveguide can be obtained. All the modes for both TE
29
modes and TM modes cases can be solved by these eigen equations, and the value of each m
corresponds to the solution of an incident angle (m is an integer, m= 0, 1, 2, 3…). The eigen
equations are as follows,
1/2 1/22 2 2 2 2 2
1 2 1 31 0 2 2 2 2
1 1
sin sin: cos arctan arctan
cos cos
n n n nTE n k t m
n n
(2.17)
1/2 1/22 2 2 2 2 2 2 2
1 1 2 1 1 31 0 2 2 2 2 2 2
2 1 3 1
sin sin: cos arctan arctan
cos cos
n n n n n nTM n k t m
n n n n
(2.18)
Longitudinal propagation constant and effective refractive index are two important
parameters of the waveguide. They can be defined by the following formulas,
1 1 0 sinzk n k (2.19)
1
0
sineffn nk
(2.20)
β is the longitudinal propagation constant of waveguide and k0 is the magnitude of the wave
vector of the plane wave in a vacuum. neff is the effective refractive index of the waveguide. The
conditions of the waveguide exists are the wave vector k1 is much greater than k2 and the value of
neff is between the refractive indices n2 and n1.
2.4.2 Wave Equation Method
Based on Maxwell’s equations, the electromagnetic wave distribution equation (wave
equation) of the light wave in the dielectric waveguide is established, and the characteristic
equation of the propagation mode can be derived by combining the boundary condition. Then
discuss the characteristics of light propagation in slab dielectric waveguides. The wave equation
method can accurately describe the mode distribution of light waves in the waveguide, and all the
30
derivation begins with the Maxwell’s equations of the harmonic electromagnetic field. The
equations are as follows,
0E i H (2.21)
H i E (2.22)
To extend all the components of the vector, the y axis is approximated to infinity, that is, all the
components in y direction are uniform,
0y
Assume the wave light propagates along the z direction, so the change in the z direction can be
expressed by a transfer factor,
exp( )i z
Here, β is the longitudinal propagation constant of the waveguide. We can obtain two groups of
equations for TE mode and TM mode respectively.
For TE mode: 0
y xE H
0
y
z
Ei H
x
zx y
Hi H i E
x
(2.23)
And for TM mode:
y xH E
y
z
HiE
x
31
0z
x y
Ei E i H
x
(2.24)
Take the TE mode as an example. The above group of equations (2.23) can be written as
2
2 2 2
02( ) 0
y
y
Ek n x E
x
(2.25)
This equation (2.25) is a wave equation, and it is also called Helmholtz equation. The above
equation (2.25) provides all the information of light wave in the slab dielectric waveguide, and
we can replace the value of n(x) to describe the distribution of light wave in each layer of the slab
dielectric waveguide. n1 is the refractive index of the guiding layer, and n2 is the refractive index
of the substrate layer, as well as n3 is the refractive index of the cladding layer.[21] The wave
equation is an important second order linear partial differential equation to describe the light
wave, and there are several kinds of general solution for the wave equation. The general solutions
are as follows,
1 2cos( ) sin( )y T TE k x k x
1 cos( )Tk x
1 exp[ ( )]Tj k x (2.26)
where,
2 2 2
0 1Tk k n
kT is usually called transverse wave vector, β is the longitudinal propagation constant of the
waveguide, and k0 is is the magnitude of the wave vector of the plane wave in vacuum. α1 and α2
are two undetermined coefficients.
According to the physical meaning, one can be expected that there is a standing wave
solution in the guiding layer, that is, cosine function can be used, while in the cladding layer and
32
the substrate layer, they are evanescent waves which should be decay solution, so expressed by
the exponential function. The following equations express the solutions of cladding layer, guiding
layer and substrate layer in turn.
3 3( ) exp ( )yE x E x a ( )x a
1 cos( )xE k x ( )a x a
2 2exp ( )E x a ( )x a (2.27)
In this group of solutions (2.28), the undetermined coefficients are
2 2 2 2
0 1xk k n
2 2 2 2
3 0 3k n
2 2 2 2
2 0 2k n
If the solution of the equation is present, then all the undetermined coefficients, kx, α3 and α2 must
be real numbers. Therefore, the condition of the presence of the guided mode is
0 1 0 3 0 2max( , )k n k n k n (2.28)
By comparison, using the wave equation method to derive the condition of the presence of guided
mode gives the same result by using ray optics method.[25]
At the boundary, it can be seen from the equation (2.23) that the component of Ey is
continuous. Similarly, the component of Hz is continuous as well. Combined with boundary
conditions, the result of equation (2.27) yields
2tan( )x
x
k ak
( )x a
3tan( )x
x
k ak
( )x a
Thus, the characteristic equation of TE mode is
33
2 3: 2 arctan( ) arctan( )x
x x
TE k a mk k
(2.29)
And the characteristic equation of TM mode can be derived use the same method.
2 2
1 2 1 3
2 2
2 3
: 2 arctan( ) arctan( )x
x x
n nTM k a m
n k n k
(2.30)
The result is consistent with the result obtained by the ray optics method.
Consider the case of symmetric slam dielectric waveguide for TE mode, and we can get
the characteristic equation for it.
2 tan( )2
x x
ma k a k a
(2.31)
2 2 2 2 2 2
0 1 2( ) ( ) ( )xa k a k a n n (2.32)
In order to obtain the order of the modes, we can use the graphical method to solve the
characteristic equation, and the number of intersections of two equations (2.31) and (2.32) is the
number of TE mode. In addition, the order of modes can also be calculated by the following
formula
2 2 2 2
0 1 22 ( )k a n nM
(2.33)
The equation (2.32) rounds down to the nearest integer. For the symmetric slam dielectric
waveguide, the zero order of mode always exists. Once the waveguide parameters are determined,
the number of corresponding modes are determined. When the value of m is 0, the longitudinal
propagation constant is the largest, and the longitudinal propagation constant decreases as m
increases. The characteristic equation represents the TE mode wave (S polarization wave), and
the order of the mode is used as the index of the polarized light, such as TE0 mode, TE1 mode and
so on.[26]
34
2.4.3 Mode Field Distribution of TE Modes
The solution of the characteristic equation is substituted into the equation (2.27) and the
coefficients are determined, so the function of Ey can be derived. According to the equation set
(2.23), we determine all the remaining field components. Therefore, we can get the mode field
distribution of TE modes in symmetric slab dielectric waveguide. The diagram of electric field
distribution is shown as follows,
Figure 2-7. Electric field distribution for TE modes.
In Figure 2-7, the horizontal direction is the z-axis, and the vertical direction is the x-axis.
The curves are the function of electric field distribution, Ey for first three TE modes in symmetric
slab dielectric waveguide.[26]
The electric field is attenuated by an exponential function in the cladding layer and the
substrate layer, and the decay rate is determined by the attenuation coefficients α2 and α3,
respectively. The larger the values of α2 and α3 are, the faster the attenuation of the electric field
35
is, and the penetration depths of 1/α2 and 1/α3 are shallow, indicating that the electric field is
mainly confined in the guiding layer of the waveguide. On the contrary, if the values of α2 and α3
are getting smaller, the field attenuation becomes slower and the depth of penetration is deeper,
which indicates the poor ability of the waveguide to confine the electric field. The value of α2 and
α3 is related to the refractive indices of the cladding layer and the substrate layer, and is also
closely related to the order number m of the mode. From the mode eigen equation, we can know
that if the order number m is bigger, then the longitudinal propagation constant β becomes
smaller, and two coefficients α2 andα3 become smaller. This indicates that the electromagnetic
field of the higher order mode can extend a long distance away from the guiding layer of slab
dielectric waveguide.[27]
36
3 Design and Manufacture the Non-Mechanical Beam Steerer
3.1 Novelty of the Non-Mechanical Beam Steerer
In this chapter of the thesis, I present a novel technique electro-optic liquid crystal
waveguide non-mechanical laser beam steerer with fused silica substrate for the first time, which
provides unprecedented advantages such as rapid response time, large angular deflection and
small size. The refractive index of general optical glass is around 1.50, while the typical fused
silica has the extremely low refractive index, 1.44. This low refractive index provides a small
critical angle, so it is easier to couple the laser beam into the guiding layer of device. This original
device is based on the liquid crystal, which is the world largest electro-optic response material,
for example, the birefringence, Δn for a typical nematic liquid crystal is around 0.2 when applied
over 5 volts, which corresponds to several orders of magnitude larger than any other materials.[28]
In addition, I use the liquid crystal as the guiding layer of the slam dielectric waveguide to
circumvent some traditional liquid crystal limitations. When combined with patterned electrodes,
this device is capable of providing an analog, non-mechanical ‘Snell’s-law-type’ beam steerer,
since the liquid crystal in the patterned area work as an electro-optic prism to refract incident light
beam. In addition, this beam steerer has a simple structure. In other words, this beam steerer is
also a new application of traditional LCD structure. For the preliminary experimental stage, we
used a simple ITO pattern. However, theoretically, if we use more complex ITO pattern, we can
achieve up to 90 degrees field of view with two control electrodes.[29]
37
3.2 Design of the Device
3.2.1 Architecture of the Device
Liquid crystal is one of the most successful techniques in the world for the past decades.
This distinctive material has the largest known electro-optic response and this material is
technical mature, price moderate and environmentally stable.[28]In part 1- 4, I have introduced
the basic structure of a typical TN liquid crystal display. A thin liquid crystal layer is put between
two transparent electrodes, and the basic principle is used to control the voltage between the
liquid crystal molecules which in combination with two polarizers (one is polarizer, the other is
polarization analyzer) to block and transmit the light so as to achieve the display. As shown in the
Figure 3-1, I used the same structure to make a slab dielectric waveguide which can circumvent
some traditional liquid crystal limitations, and at the same time, utilize the large electro-optic
response of liquid crystal.
Figure 3-1Design drawing of the non-mechanical beam steerer.
38
For the typical TN LCD structure, there is a significant limitation: the electrodes must be
transparent, because the light must transmit through both liquid crystal layer and the electrodes,
which limits the total optical power and the material of the electrodes. However, with this new
method, the liquid crystal layer is equivalent to the guiding layer of the slam waveguide, which
means the light beam will never transmit the entire device, but only transmit the liquid crystal
layer. Although in this thesis, I still use the ITO glass as the transparent electrode and substrate of
the device, the liquid crystal waveguide can be built on any conductive and low refractive index
material, for example, silicon is a good choice for electrode because it is easy to be integrated
with other electronic components.
Figure 3-2. The upper ITO glass substrate.
39
Figure 3-3. The lower ITO glass substrate
The above design drawings (Figure 3-2 and Figure 3-3) are the two ITO glass substrate of
the non-mechanical beam steerer, and the blue area is the ITO area. The size of the lower glass
substrate is 45mm by 24mm, and one side has high quality ITO transparent conductive film,
while the size of the upper glass substrate is 30mm by 20mm and has a distinctive ITO electrode
pattern. The pattern of the ITO electrode is important for the device. In this device, the pattern of
the upper glass makes the device perform as a triangular electro-optic prism when combined with
liquid crystal, shown as in Figure 3-4.
Figure 3-4. Schematic diagram of the Snell’s law type beam steerer.
40
When we apply the voltage higher than the threshold voltage of liquid crystal molecule,
the liquid crystal molecules tend to orient parallel to the electric field direction so that the
refractive index will change at the same time. The part that changes the refractive index is just
like a prism. Since the incident light beam transmits from the right-angled edge of the prism, the
light is still propagating in a straight line, i.e. without deflection. However, when transmitting
through the hypotenuse of the prism, the light beam will be bent by refraction and follow the
Snell's law (2.1), thereby achieving the steering of the beam. It is worth noting that ITO
electrodes need to use high quality lithography to make sure the device has good optical
properties. If the edge of the ITO pattern is not smooth enough, it will affect the performance of
the device, or even cannot make the light beam deflection.
Due to the limitations of the manufacturing process, the length of the working area of the
device should not be too long, so that the energy loss of light beam in the waveguide is reduced.
The material that makes up the waveguide will absorb a portion of the light beam, and the liquid
crystal molecules cause different degrees of scattering loss of the light beam. Therefore, I
designed the length of working area as 20mm. After these two sets of ITO glass substrate are
made into a liquid crystal cell, as shown in Figure 3-1, it is convenient to connect the beam steer
to the power supply. In addition, the lower substrate has enough space to place prism which is
used to couple the light beam into the beam steerer.
3.2.2 Design of the Deflection Angle
Since the structure of this beam is the same with the structure of a symmetric slab
dielectric waveguide, and I plan the working mode of the waveguide in fully waveguide mode,
the choice of material of the guiding layer is critical. The magnitude of the birefringence of the
41
liquid crystal determines the magnitude of the deflection angle. For ease of coupling, I used a
kind of fused silica with low refractive index. The model of the silica glass is JGS2 and in room
temperature, the refractive index is 1.444687 at 1500nm wavelength and 1.443492 at 1600nm
wavelength. Compared with the normal optical glass, the fused silica significantly reduces the
critical angle of the guiding layer.
The refraction is followed by Snell’s law,
1 1 2 2sin sinn n (2.1)
Use the positive nematic liquid crystal,which the liquid crystal with positive dielectric anisptropy
and positive dielectric anisotropy as the material of the guiding layer. By the surface treatment
(rubbing), make the long axis direction of the nematic liquid crystal molecules parallel to the
propagation direction of the light beam, and at this time, if the direction of polarization of the
incident light is perpendicular to the device, the refractive index of the liquid crystal to the light
beam is no. When adding a voltage to the electrodes, the refractive index of the liquid crystal to
the light beam becomes ne. Then, we can calculate the deflection angle of the beam steerer.
sin45arcsin( ) 45e
o
n
n
(3.1)
If the beam steerer is placed as shown in Figure 3-1, and the light beam is propagated
from left to right, then the light beam will deflect upward. If we use liquid crystal monomer 5CB
(refractive indices are ne=1.71 and no= 1.53), the deflection angle is 7.19 degrees. If use mixed
liquid crystal E7 (refractive indices are ne=1.7497 and no= 1.5261), then the deflection angle is
9.09 degrees.[30]
42
3.2.3 Thickness of the Device
The thickness of the device directly determines the number of modes of the waveguide,
and it is an important part of the device design. Here, I usedthe ray optic method to analyze the
number of modes and incident angles of the light beam in different thickness of beam steerer. All
the modes for both TE modes and TM modes cases can be solved by the following eigen
equations,
1/2 1/22 2 2 2 2 2
1 2 1 31 0 2 2 2 2
1 1
sin sin: cos arctan arctan
cos cos
n n n nTE n k t m
n n
(2.17)
1/2 1/22 2 2 2 2 2 2 2
1 1 2 1 1 31 0 2 2 2 2 2 2
2 1 3 1
sin sin: cos arctan arctan
cos cos
n n n n n nTM n k t m
n n n n
(2.18)
The number of modes can be calculated by the following formula
2 2 2 2
0 1 22 ( )k a n nM
(2.33)
We use the same silica glass as the substrate, so the materials of the cladding layer and substrate
layer are the same, that is, n2= n3. For the sake of discussion, the ITO layer and the alignment
layer are not considered for the time being. The wavelength is 1550nm, the refractive indices of
liquid crystal are ne=1.74 and no=1.52 and the refractive index of silica glass, n2 and n3 are 1.44.
Then, we can analyze the thickness of 5μm, 10μm and 15μm, respectively.
In the case of the thickness of 5μm,
Table 3-1. Table of waveguide modes for no.
m TE TM
0 85.21523438 85.00546875
1 80.33818359 80.18085938
2 75.49609375 75.49609375
43
Figure 3-5. Diagram of waveguide modes for no.
Table 3-2. Table of waveguide modes for ne.
m TE TM
0 85.26523438 85.26523438
1 80.69667969 80.49804688
2 76.02880859 75.59766159
3 71.26162109 70.73193359
4 66.39511719 65.86542969
5 61.42929688 60.89960938
75
80
85
90
0 1 2
TE TM
44
Figure 3-6. Diagram of waveguide modes for ne.
In the case of the thickness of 10μm,
Table 3-3. Table of waveguide modes for no.
m TE TM
0 87.24296875 87.24296875
1 84.65585938 84.65585938
2 82.0425293 81.96386719
3 79.41171875 79.41171875
4 76.82460938 76.61484375
5 74.18505859 74.02773438
60
65
70
75
80
85
90
0 1 2 3 4 5
TE TM
45
Figure 3-7. Diagram of waveguide modes for no.
Table 3-4. Table of modes for ne.
m TE TM
0 87.58261719 87.58261719
1 85.26523438 85.03349609
2 82.61679688 82.61679688
3 80.26630859 79.96835938
4 77.84960938 77.61787109
5 75.20117188 75.20117188
6 72.75136719 72.55273438
7 70.2519043 69.90429688
8 67.78554688 67.25585938
9 65.13710938 64.80605469
10 62.48867188 62.15761719
11 59.84023438 59.50917969
70
75
80
85
90
0 1 2 3 4 5
TE TM
46
Figure 3-8. Diagram of modes for ne.
In the case of the thickness of 15μm,
Table 3-5. Table of waveguide modes for no.
m TE TM
0 88.16943359 88.16943359
1 86.33398438 86.33398438
2 84.44609375 84.44609375
3 82.76796875 82.76796875
4 80.84511719 80.84511719
5 79.06210938 78.85234375
6 77.17421875 77.17421875
7 75.49609375 75.3300293
8 73.57324219 73.46835938
55
60
65
70
75
80
85
90
0 1 2 3 4 5 6 7 8 9 10 11
TE TM
47
Figure 3-9. Diagram of waveguide modes for no.
Table 3-6. Table of waveguide modes for ne.
m TE TM
0 88.44335938 88.44335938
1 86.70946045 86.6722168
2 85.03349609 85.03349609
3 83.34511719 83.34511719
4 81.75605469 81.55742188
5 79.96835938 79.96835938
6 78.37929688 78.37929688
7 76.79023438 76.6081543
8 75.0439209 74.87011719
9 73.28105469 73.08242188
10 71.49335938 71.49335938
11 69.90429688 69.67255859
12 68.1331543 67.98417969
13 66.39511719 66.19648438
14 64.60742188 64.37568359
15 62.78662109 62.48867188
16 60.89960938 60.89960938
17 59.1532959 58.97949219
70
75
80
85
90
0 1 2 3 4 5 6 7 8
TE TM
48
Figure 3-10. Diagram of waveguide modes for ne.
The code of Matlab is attached in the appendix.
By comparing the mode distribution at different thickness, the thicker device has more
mode orders than the thinner device. The number of modes is advantageous for coupling the light
beam into the beam steerer. At the same time, need to take into account the size of the light spot
of the semiconductor laser, so the larger thickness will also facilitate coupling. However, as a
liquid crystal device, the common thickness ranges from 5 to12 microns.[19] In addition, only the
liquid crystal adjacent the alignment layer are highly ordered because of rubbing, which means
high responding speed and low scattering loss. Increasing the device thickness also increases the
threshold voltage of the liquid crystal and reduces the sensitivity of the device. In summary, in
this thesis, I chose to make the beam steerer with a thickness of 10 microns.
55
60
65
70
75
80
85
90
95
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
TE TM
49
3.3 Production Process of Liquid Crystal Cell
After completing the core part of the device design, it is necessary to understand the
technological process of liquid crystal cell. The liquid crystal cell is mainly composed of ITO
glass, liquid crystal, spacer, sealing material, an alignment layer and so on. The technological
process can be divided into five main parts: cleaning and drying process, photolithography
process, alignment process, cell making process and LC filling process.[31]
3.3.1 Cleaning and Drying Process
In the experiment, the ITO coating was formed on the fused silica by magnetron
sputtering. The thickness of ITO coating is 200nm, and the square resistance is 40 Ω/sq. Testing
ITO side is very important in the experiment, because we need to clean the impurities on the ITO
surface, the easiest way to check the ITO side is using the ohm gauge of the multimeter to
measure the side which has the resistance value is the ITO surface.
For ITO glass, the main pollutants are dust and grease, while for the glass substrate, the
pollution type can be divided into grease, other organic matter, and ash layer of adhesion.
Detergent is a surfactant that changes the incompatible liquid into a stable emulsion. Detergent
through the role of emulsifying, to achieve the effect of decontamination. After the glass is
washed with detergent and then rinsed with deionized water, it is possible to achieve the purpose
of cleaning the glass surface. Grease and some other organic matter are not soluble in water, but
can be dissolved in some organic solvents. Acetone is a good organic solvent, which has strong
ability to remove grease. However, acetone cannot remain on the glass surface, either. Also,
because acetone is soluble in isopropanol, it can continue to be washed with isopropanol.
Isopropanol can be miscible with water, and finally, a large amount of deionized water is used to
50
remove isopropanol. Therefore, use those reagents: acetone, isopropanol and DI water in turn and
combined with ultrasonic cleaning to finish the cleaning process.
After cleaning the substrate will remain a lot of water, which in the air environment can
easily be contaminated. Use nitrogen to treat the cleaned glass substrate and quickly blow dry the
residual moisture on the glass substrate. And then put the glass substrate into the oven, and adjust
the temperature inside the oven slightly higher than 100 degrees, so that the residual moisture on
the glass substrate turns into steam and be removed. The residual is a small amount of DI water,
so will not leave water stains on the glass substrate.
3.3.2 Photolithography Process
Photolithography, also called optical lithography or ultraviolet lithography, is an
important process for fabricating the specific pattern on the thin file or the bulk of the substrate of
microelectronic devices. The process of photolithography combines several steps in sequence,
which make this procedure to be comparable to a high precision version of the method used to
make printed circuit boards. The basic procedure of photolithography includes photoresist coat,
prebake, exposure, develop, main cure, etching and photoresist removal.[32]
51
Figure 3-11. Diagram of the photolithography process.
There is no doubt that the key step of photolithography is exposure. The quality of
exposure directly decides the performance of microelectronic devices. What’s more, the solution
of pattern, which has a big effect on the size of the device, depends on the process of exposure. It
is obvious that a small device with the same function has more widespread application in the
modern world. Exposure systems typically produce an image on the wafer using a photomask,
and it can be classified by the optics that transfers the image from the mask to the wafer, contact
printing, proximity printing and projection printing.
Due to process conditions, the patterned ITO electrode used at the beginning of the
experiment was not very effective. Therefore, we prepared ITO fused silica, and sent to
manufacturers to help to process, then, got the high precision ITO electrode pattern.
52
3.3.3 Alignment Process
In the liquid crystal display manufacturing process, the alignment process is a key
process. The TN (twisted nematic) type requires that the alignment of the liquid crystal molecules
on the inner surface of the two glass substrate must be 90 degrees. The designed beam steerer,
requires the alignment of the liquid crystal molecules on the inner surface of the two glass
substrate are parallel to each other.
The response time of the signal is undoubtedly an important parameter for the beam
steerer. In addition to the properties of the material itself, the alignment of the liquid crystal
material in the liquid crystal device of the electrode surface is an important external factor. Liquid
crystal alignment technology is to make the liquid crystal molecules neatly align at the electrode
interface, and form a certain pretilt angle. It is not only related to the response speed of liquid
crystal device, but also directly affect the display quality.
The friction alignment technique was discovered by Maugin in 1911, which rubs the
coated inorganic or organic covering film on the surface of the glass substrate in a certain
direction so that the liquid crystal molecules are aligned and highly ordered in the rubbing
direction. Friction can produce enough anchoring energy on the substrate surface to align the
liquid crystal molecules. The process is simple, easy to operate, low cost, and easy to achieve a
large area of friction alignment and LCD mass production.[33]
In rubbing alignment technology, although the number and the intensity of friction will
affect the anchoring energy on the glass substrate, the material of the alignment layer takes the
decisive position. Polymeric materials used in liquid crystal display alignment layer are
polystyrene (PS) and its derivatives, polyvinyl alcohol (PVA), polyester (PE), epoxy resin (ER),
polyurethane, polyimide (PI) and so on. Polyimide (PI) is a high temperature resistance, corrosion
resistance, high hardness, good insulation, easy to form film, and low production cost among
53
polymer materials, which is widely used in LCD production and laboratory research.[34]
However, the raw material PA which is used to produce PI must be stored in the environment
below 4 degrees, and need to buy in bulk, so we use the PVA as the material of the alignment
layer. PVA is a common water-soluble polymer, and just put into DI water to dissolve to get a
stable solution. The alignment agent may be applied by spin coating, which is simple way to get
the uniform thin film in the laboratory. After the substrate is coated with the alignment material,
prebake is carried out in order to remove the solvent from the alignment material. The prebaked
material is also cured at a certain temperature for a certain period of time to obtain a stable
alignment layer which is suitable for rubbing. Finally, use nylon, fiber or cotton and other
materials to rub the alignment layer in a certain direction, t the film surface condition changes,
and the liquid crystal molecules have the uniform anchoring energy, so that the liquid crystal
molecules will neatly align on the two glass substrate. Therefore, we can choose the direction of
rubbing as needed, and then the liquid crystal molecules will align in the direction of our design.
The traditional rubbing alignment technology also exposed some limitations. For
example, the alignment layer on the substrate will create a trench in the direction of rubbing, the
liquid crystal molecules are aligned along the trench during the filling process, but the scale of the
trench is much larger than the linearity of the liquid crystal molecules, so that the liquid crystal
molecules in these trenches cannot be completely consistent, part of the liquid crystal molecules
may not be strictly in accordance with the direction of rubbing.
In the experiment, we used a PVA solution with a mass fraction of 4%, and set the spin
coating to 2500 rpm. The thickness of the alignment layer is 300nm.
54
3.3.4 Cell Making and LC Filling Process
In the manufacture of liquid crystal devices, the liquid crystal layer needs to have a
certain thickness, and this thickness is usually called cell gap. In order to make such a small cell
gap, and to ensure its uniformity, it is necessary to add some spacer in the frame sealant, or
evenly spread some of the spacer in the display area.
We have developed three methods of cell making.
(1) In the professional LCD laboratory use equipment to manufacture liquid crystal cell.
The spacer is mixed with the thermosetting adhesive and then applied to the edge of the glass
substrate. Aligned the two glass substrates of the liquid crystal cell and then thermally cured. This
method produces the high quality liquid crystal cell, but in the absence of equipment need to
improve the process.
(2) In our laboratory, handmade liquid crystal cell. The spacer was uniformly dispersed in
ethanol and then uniformly sprayed on the glass substrate. After the evaporation of ethanol,
aligned with another piece of substrate glass, and then seal the frame. During the period, the
substrate glass can be fixed with a weight or clip instead of the equipment. This method can also
obtain a uniform cell gap, however, due to some of the spacer being spread in the working area of
beam steerer, these ten micron spacers will cause the scattering of the light beam. Therefore, I
came up with the third method of process.
(3) We use UV adhesive, Norland NOA 63, as the frame sealant. The spacer was mixed
with UV adhesive, and then applied to the edge of the glass substrate. Aligned with another piece
of substrate glass, and then the frame was sealed with UV light. The liquid crystal cell produced
by this method ensures that the light is not scattered by the spacer, and uniformity of the cell gap
can also be ensured in the small-sized device. It is worth noting that the UV adhesive is mobile,
55
so only paint a small amount of UV adhesive on the edge of glass substrate, otherwise the
working area of the device will be too small.
The LC Filling Process is relatively simple in the laboraatory. Only need to drop a small
amount of liquid crystal in the gap of liquid crystal cell and put up the device, then the liquid
crystal molecules will fill the entire device by capillary force and gravity. In order to adapt to a
wider working temperature, and have better birefringence, we used E7 mixing liquid crystal in the
experiment.
3.4 Manufacturing of the Beam Steerer
In this section, I will describe the steps of manufacturing the beam steerer. In the
experiment, we used the patterned ITO glass substrate, so we skipped the steps of the
photolithography.
Cleaning: This is one of the most important and the main steps.
It consists of three steps
(A) Ultrasonic bath (B) Bake (C) Ultraviolent (UVO) cleaning
Steps involved in an ultrasonic bath. Focus on the ITO side of the glass substrate.
(1) Rinse the two glass substrates in DI water for at least 30 seconds.
(2) Put the substrate in detergent and use an ultrasonic bath for 15 minutes.
(3) Rinse them in DI water for 1 minute.
(4) Put the substrate in an ultrasonic bath with DI water for 15 minutes.
(5) Put the substrate in an ultrasonic bath with acetone for 15 minutes to remove organic
impurities.
(6) Put the substrate in an ultrasonic bath with IPA for 15 minutes to dissolve acetone.
(7) Rinse with DI water to dissolve IPA and visually examine the surface of substrate
56
(8) Blow dry the substrates with nitrogen.
(9) Bake the substrates for about 10 minutes in the baking oven to remove any residual
water, and the temperature is set at 120 degrees. (baking)
(10) Examine the substrate by visual inspection to make sure there is no spot on the glass
substrate.
Steps involved in UVO cleaning:
(Generally used for energizing the substrate and it improves adhesion of photoresists and
polymers. After the removal of the contaminant, the contact angle will be reduced to that
characteristic of contact with the pure substrate, which is an effective way to assess the
cleanliness.)[34]
(1) Place the ITO side face up in the UVO cleaning machine.
(2) Turn on the air knob by a quarter rotation.
(3) Keep the substrate in the machine for around 15-20 minutes.
Spin Coating:
Used to uniformly coat the surface of a glass plate with a polymer. The quality of the
alignment layer takes the decisive position for alignment of liquid crystal molecules.
(1) Prepare the PVA solution with a mass fraction of 4%.
(2) Place the clean substrate on the spinner, centered on the chuck with the side to be
coated up (the ITO side).
(3) Turn on the vacuum knob and press the vacuum button on the spin coats.
(3) Check if the substrate is tightly attached and is not moving (if it moves try a different
chuck). It is important that the substrate should not move as it spins at a very high speed.
57
(4) Fill a clean syringe with PVA solution and pour it uniformly on the substrate.
(5) Turn on the spin coater for 30 seconds at 2500 rpm.
Annealing:
(1) Carefully move the substrate to a hot plate and heat it at 120 degrees for 100 seconds.
(2) Then bake the substrate at 120 degrees in the baking oven for 1 hour.
(3) Store the substrates in a clean and dry place.
Rubbing:
According to actual condition, we used a manual rubbing technique. The steps of rubbing
process are as follows:
(1) Put the glass substrate on a stage or a flat surface for rubbing. Make sure the
alignment layer is facing up.
(2) Mark the rubbing direction with a mark or a pen on the glass side of the substrate. We
plan to make two kinds of liquid crystal cell: TN (twisted nematic) liquid crystal cell (the
alignment of the liquid crystal molecules on the inner surface of the two glass substrates must be
90 degrees) and the beam steerer (the alignment of the liquid crystal molecules on the inner
surface of the two glass substrate are parallel to each other).
(3) Prepare a piece of professional fiber friction cloth and fixed on a weight like objects
to replace the machine friction roller. The width of this object needs to be greater than the width
of the substrate glass. Before using, blow some try N2 to clean the friction cloth.
(4) Rub on unidirection once or twice. The number of rubbing depends on the material of
the friction cloth.
(5) Blow some clean dry N2 to remove the remaining fibers.
58
LC Cell Making:
(1) Clean the substrate assembly and the substrate of any dust particles.
(2) Mix the silicon dioxide spacer (diameter of 10 microns) in the NOA-63 ultraviolet
adhesive and take it in a clean syringe.
(3) Apply two lines of the mixture on the lower glass substrate. Glue to complete the
closure of the two edges, but the amount of glue being as little as possible.
(4) Liquid crystal cell assembly: follow the design drawing and press the substrate
together. To avoid any deformation, use a uniform object, such as a Petri dish, to press on two
glass substrate to apply an adequate pressure to the spacer.
(5) At this time, the empty liquid crystal cell will appear some interference fringes.
Check these interference fringes. The wider the interference fringes, the more uniform the cell
gap of the liquid crystal cell.
(6) Cure the adhesive with a UV light.
LC Filling:
(1) Take the LC bottle out of the refrigerator around 5 minutes before filling.
(2) With a sharp and a clean needle put only one drop of liquid crystal near the edge of
two substrates.
(3) Slowly erect the liquid crystal cell. Now, due to capillary action and gravity, the LC
will gradually fill the gap between two glass substrates.
(4) Wait until the LCD filled the entire device, and then wipe off the excess LC.
From the fabrication of liquid crystal cell, we can successfully get the device we want. I
will discuss the result in the next chapter.
59
4 Results Achieved by Fabrication and Future Work
4.1 Quality of Liquid Crystal Cell
In general, to obtain accurate information of the liquid crystal cell, one needs to use
aapolarizing microscope and pretilt angle measuring instrument. Polarizing microscopes are used
to detect the alignment of liquid crystal molecules, and pretilt angle measuring instrument can
measure the pretilt angle of liquid crystal molecules, then through the liquid crystal model,
measure the thickness of cell gap. In the absence of professional equipment, the visual inspection
can also judge the quality of the liquid crystal cell. As I mentioned in section 3.3.4, I used a
different cell making process to fabricate TN liquid crystal cell. One process is completed in a
professional laboratory, and has a pretty high quality when tested by professional equipment, the
other process was completed in our laboratory. Therefore, different liquid crystal cells can be
compared by visual inspection, and then can draw the conclusion.[35]
Visual inspection focus on the changing of bright and dark, and TN LCD can achieve the
changing of bright and dark, so we can detect the quality of TN LCD. If we can get high quality
TN LCD, and then only change the direction of rubbing, we can get high quality beam steerer.
The steps of visual inspection are simple. Firstly, the two glass substrates is affixed to the
polarizer, and the directions of polarization are the same as the rubbing directions of the two glass
substrates,respectively. Secondly, use the power supply to drive the device. The drive voltage is
slightly higher than twice the threshold voltage of liquid crystal molecule. When the voltage is
twice the threshold voltage, the long axis of the liquid crystal molecule will be aligned along the
direction of the electric field. It is best to use a square wave of 50 Hz to drive the LCD, however,
in this experiment, we used a DC power supply. When using DC power supply, the operation
60
time should not be too long, so as not to damage the device, and often swap the positive and
negative electrode to remove the residual charge. Finally, place the device on the backplane to
observe the bright and dark variations of the device.
(1) Use PI as the material of alignment layer. Sealed with a thermosetting adhesive which
is mixed with spacer. The thickness of cell gap is 10 microns.
Figure 4-1. The bright and dark status of TN LCD (process 1).
(2) Use PVA as the material of alignment layer. Sealed with UV adhesive which is mixed
with spacers. The thickness of cell gap is also 10 microns.
Figure 4-2. The bright and dark status of TN LCD (process 2).
61
By comparing two different TN LCDs, It can be seen that the laboratory made device
also have a significant variation of bright and dark. Through the colors that liquid crystal shows,
the thickness of cell gap is basically uniform. If the thickness of cell gap is absolutely uniform,
liquid crystal will show the same color. In addition, patterned ITO electrode is also very effective,
so that the device could work as an electro-optic prism to refract incident light beam. However, it
also has some serious drawbacks. There are some small bubbles in the solution, which are caused
by dissolving PVA powder, resulting in the uneven surface of the alignment layer. Combined
with the possibilities pollutants on the alignment layer, the working area of device leaves some
tiny stripes during the LC filling process. There are two possibility at the stripes, one may be
filled with liquid crystal molecules but don’t have highly order, the other may not be filled with
liquid crystal molecules. In any case, it will affect the performance of the device.
Change the direction of rubbing, and then we can fabricate beam steerer.
4.2 Test Result of Beam Steerer
To test the beam steerer for light modulation, we need to select a suitable light source. I
used a semiconductor laser diode with a wavelength of 1550 nm as a light source. The module
type is Mitsubishi FU-636SDF-F1M1, which is an InGaAsP DFB laser diode with single mode
fiber pigtail. The basic parameters are listed in the following table (Table 4-1).
Table 4-1. Basic parameters of laser diode.
Maximum output power from fiber end 5 mW
Maximum working voltage 1.2 V
Maximum operating current 60 mA
Operating case temperature 0-85 ℃
Central wavelength 1550 nm
62
It is necessary to consider how to couple the laser into the guiding layer of the beam
steerer, since it is difficult for the laser to directly enter the guiding layer. The beam steerer can be
considered as a symmetric slab dielectric waveguide, and any mode that can be propagated in the
guiding layer must satisfy the condition of total internal reflection. For any light refracted from
the glass substrate into the guiding layer, the refraction angle must be less than the total reflection
critical angle, so can only form full-leaky waveguide mode, but cannot form full waveguide mode
as we expected. Therefore, we use two prisms to couple the laser into the guiding layer. In order
to design the apex angle of prism, we must know the modes of the waveguide to design the
incident angle of laser. Here, we use the average refractive index to calculate.
In practice, the guiding layer is not entirely composed of liquid crystal, as well as ITO
layer and alignment layer. The refractive index of ITO film is 1.80 and the refractive index of
PVA film ranges from 1.51 to 1.53. According to the refractive index recursive formula of E7
liquid crystal, calculate the average refractive indices are no= 1.514 and ne= 1.691 at 1550nm. The
thickness of guiding layer is 11μm (including LC layer, ITO layer). The modes of waveguide are
listed in following tables.
Table 4-2. Table of waveguide modes for ordinary light.
m TE TM
0 87.5723 87.5723132
1 85.0362 85.03617683
2 82.8127 82.64769223
3 80.2418 80.24183684
4 77.8099 77.80992526
5 75.5865 75.39538447
63
Table 4-3. Table of waveguide modes for extraordinary light.
m TE TM
0 87.75232134 87.75232134
1 85.45890734 85.38987481
2 83.15015278 83.15015278
3 80.87974962 80.69566288
4 78.56332478 78.42525972
5 76.27758106 76.06281319
6 73.82309116 73.82309116
7 71.552688 71.36860126
8 69.19024148 68.91411136
9 66.78177326 66.45962146
10 64.36755234 64.18921831
11 62.04153965 61.73472841
Figure 4-3. The design drawing of the prism.
It is calculated that the use of high refractive index materials is easier to achieve the
coupling, so we used ZF-52A optical glass as the material of the prism. The refractive index of
ZF-52A optical glass is around 1.80 at an incident light wavelength of 1550nm. The apex angle of
64
the prism is 80 degrees, and the length of two base lines are 5mm, as shown in Figure 4-3.
Therefore, we have two experimental schemes, one is that the laser is an incident in the horizontal
direction, and the other is that the laser is incident in the direction perpendicular to the
hypotenuse of the prism. The first scheme has an incident angle of 84.46 degrees, and the position
of the incident spot should be 0.48mm to 0.49mm from the bottom of the prism. The advantage of
the first scheme is easy to adjust the optical path. The second scheme has an incident angle of 80
degrees, and the position of the incident spot should be 0.85mm to 0.86mm. The second scheme
has the advantage of reducing the reflection of the prism to the incident light beam. In the
experiment, the angle of incidence should be fine-tuned according to the actual situation.
Figure 4-4. The working sketch of the beam steerer.
Place the two prisms as shown in Figure 4-4. Before coupling, since the laser diode has
single mode fiber pigtail, and the laser emitted by the fiber will undergo a strong diffraction, so it
is necessary to converge the laser. Here, we use a matching fiber optic adapter to converge laser
beam. Also, because the light source is invisible infrared light, so we use the IR sensor card and
IR viewer to observe the laser spot.
The steps of the test are as follows. Firstly, the laser and matching fiber optic adapter are
adjusted on the same optical axis, and the laser is converged to reduce the spot area. Secondly,
65
use a certified refractive index liquids with a refractive index of 1.80 to eliminate the air between
the prism and the glass substrate, and the prism and the liquid crystal layer. And then, couple the
laser into the liquid crystal layer. Thirdly, use IR sensor card and IR viewer to find the spot of the
emergent light of slab dielectric waveguide, then add voltage to the beam steerer and observe the
deflection of the spot. The voltage is slightly higher than twice the threshold voltage of liquid
crystal molecule. Finally, record the deflection distance of the spot on the IR sensor card, and
then calculate the deflection angle.
Figure 4-5. The waveguide of the beam steerer.
Through this picture one can clearly see the spot on the IR sensor card, and this photo
was taken with the iPhone through the IR viewer. However, when adding voltage to the beam
steerer, we don’t see the deflection of the spot. Therefore, it is necessary to prove that the laser is
propagated in the liquid crystal layer. Now that we can see the spot on the IR sensor card, then
there are only three possible laser propagation paths: (1) The laser does not enter the device, but
only pass through the air and two prisms. (2) The laser enters the device, but the slab waveguide
is in full-leaky waveguide mode, and total reflection occurs between the glass substrate and the
air, so the laser is still confined in the device. (3) The laser only propagates in the guiding layer.
66
Measure the location of the incident laser, and then use the IR sensor card to detect
whether there is a spot behind the first prism. Found no spot behind the first prism, so the first
case can be excluded. The refractive index of the prism is 1.80, while the refractive index of the
glass substrate is 1.44, so the value of the critical angle is 53.1 degrees. The incident angles of the
two schemes are 84.46 degrees and 80 degrees, so the laser cannot enter the lower glass substrate.
It is difficult to determine whether the laser enters the upper glass substrate or not, so I designed
an experiment. Directly stick the two glass substrate together with UV adhesive, and ensure the
UV adhesive layer is very thin which can be ignored. Try to couple the laser beam into the device
in the same way, and cannot observe the spot on the IR sensor card, so the laser does not enter the
upper glass substrate. In summary, the laser only propagates in the LC (guiding) layer.
Therefore, we need to improve the technological process of the LCD. The biggest
problem is that the working area of the liquid crystal cell has many small stripes, which can be
observed by visual inspection. As I mentioned in section 4.1, there are some small bubbles in the
PVA solution, which are caused by dissolving PVA powder, resulting in the uneven surface of
the alignment layer. In addition, the rubbing process may increase the damage of the alignment
layer, and at the same time, remain some pollutants on the surface of the alignment layer.
Rubbing is an indispensable step in the manufacture of liquid crystal devices. If the conventional
rubbing leaves a deeper scratch on the alignment layer, it indicates that the alignment layer is too
soft. The uneven surface of the alignment layer has a big effect on the LC filling process, so that
the deflection of the beam cannot be achieved. The current best improvement is to replace the
material of alignment layer with PI, which is the most popular material. According to the
concentration of PI solution concentration, control the PI layer at 120nm, then we can get an
effective alignment layer. In addition, the quality of the rubbing process directly determines the
order of the liquid crystal molecules on the surface of the alignment layer. Manual rubbing
technique limits the quality of the device to a certain extent.
67
4.3 Future Work
Up to now, we have made a clear LCD cell, and passed the visual inspection. However,
we also need to improve and perfect the technological process of the liquid crystal cell, gradually
introduce some new equipment, and propose a new experimental scheme according to practical
needs. Among them, the replacement of the alignment layer material is particularly important,
and PI is the best choice of alignment layer material.
After observing the deviation of the coupled light, we can integrate the blue LED and the
beam steerer together to achieve the visible light scanning. As shown in Figure 4-6, change the
pattern of the electrode to achieve the beam scanning.
Figure 4-6. Illustration of the new pattern of the ITO electrode.
Using this pattern, we can achieve beam scanning, that is, the beam can be deflected in
both up and down directions. In theory, this non-mechanical beam steerer has more than 90
degrees angular coverage. It is worth noting that must alternately drive the two regions of the
substrate, so that the light beam will be deflected to different directions and achieve large angular
deflection of the light beam.
68
Appendix
Code for calculating modes of waveguide.
A. TE
clc
clear;
symssita phi12 phi13
eps=0.01;
pi=4*atan(1.0);
k0=2*pi/1.55;
t=11.0;
n1=1.691;
n2=1.44;
n3=n2;
a=t/2;
M=fix(2*(k0^2*a^2*(n1^2-n2^2))^0.5/pi);
for m=0:(M-1)
%function
phi12=2*atan((((sin(sita))^2-(n2/n1)^2)/(cos(sita))^2)^0.5);
phi13=2*atan((((sin(sita))^2-(n3/n1)^2)/(cos(sita))^2)^0.5);
69
f=n1*k0*t*cos(sita)-0.5*phi12-0.5*phi13-m*pi;
%initial values
a1=(asin(n2/n1)/pi*180+0.1)/180*pi;
b1=89.9/180*pi;
%result
angel=HalfInterval(f,a1,b1,eps);
angel=angel/pi*180.0;
disp(m)
disp(angel)
re(m+1,1)=m;
re(m+1,2)=angel;
end
re
B. TM
clc
clear;
symssita phi12 phi13
eps=0.01;
pi=4*atan(1.0);
70
k0=2*pi/1.55;
t=11.0;
n1=1.691;
n2=1.44;
n3=n2;
a=t/2;
M=fix(2*(k0^2*a^2*(n1^2-n2^2))^0.5/pi);
for m=0:(M-1)
%function
phi12=2*atan((n1/n2)^2*(((sin(sita))^2-(n2/n1)^2)/(cos(sita))^2)^0.5);
phi13=2*atan((n1/n2)^2*(((sin(sita))^2-(n3/n1)^2)/(cos(sita))^2)^0.5);
f=n1*k0*t*cos(sita)-0.5*phi12-0.5*phi13-m*pi;
%initial values
a1=(asin(n2/n1)/pi*180+0.1)/180*pi;
b1=89.9/180*pi;
%result
angel=HalfInterval(f,a1,b1,eps);
angel=angel/pi*180.0;
disp(m)
disp(angel)
re(m+1,1)=m;
71
re(m+1,2)=angel;
end
re
C. Half Interval:
function root=HalfInterval(f,a,b,eps)
if(nargin==3)
eps=1.0e-4;
end
f1=subs(sym(f),symvar(sym(f)),a);
f2=subs(sym(f),symvar(sym(f)),b);
if(f1==0)
root=a;
end
if(f2==0)
root=b;
end
if(f1*f2>0)
disp('The product of two ends > 0!');
return;
72
else
root=FindRoots(f,a,b,eps);
end
function r=FindRoots(f,a,b,eps)
f_1=subs(sym(f),symvar(sym(f)),a);
f_2=subs(sym(f),symvar(sym(f)),b);
mf=subs(sym(f),symvar(sym(f)),(a+b)/2);
if(f_1*mf>0)
t=(a+b)/2;
r=FindRoots(f,t,b,eps);
else
if(f_1*mf==0)
r=(a+b)/2;
else
if(abs(b-a)<=eps)
r=(b+3*a)/4;
else
s=(a+b)/2;
r=FindRoots(f,a,s,eps);
end
end
end
73
References
1. Li, Q., Liquid crystals beyond displays: chemistry, physics, and applications. 2012: John
Wiley & Sons.
2. Schadt, M., Liquid crystal materials and liquid crystal displays. Annual review of
materials science, 1997. 27(1): p. 305-379.
3. Kawamoto, H., The history of liquid-crystal displays. Proceedings of the IEEE, 2002.
90(4): p. 460-500.
4. Wojtowicz, P.J., P. Sheng, and E. Priestley, Introduction to liquid crystals. 1975:
Springer.
5. Khoo, I.-C., Liquid crystals: physical properties and nonlinear optical phenomena. Vol.
64. 2007: John Wiley & Sons.
6. Collyer, A.A., Liquid crystal polymers: from structures to applications. Vol. 1. 2012:
Springer Science & Business Media.
7. Yeh, P. and C. Gu, Optics of liquid crystal displays. Vol. 67. 2010: John Wiley & Sons.
8. Wu, S.-T., Nematic liquid crystals. OPTICAL ENGINEERING-NEW YORK-MARCEL
DEKKER INCORPORATED-, 1994. 47: p. 1-1.
9. Ikeda, T. and O. Tsutsumi, Optical switching and image storage by means of azobenzene
liquid-crystal films. Science, 1995. 268(5219): p. 1873.
10. Heinekamp, S., et al., Smectic-C* to Smectic-A transition in Variable-Thickness Liquid-
Crystal films: Order-Parameter measurements and theory. Physical review letters, 1984.
52(12): p. 1017.
11. Seo, D.-S., K.-I. Muroi, and S. Kobayashi, Generation of pretilt angles in nematic liquid
crystal, 5CB, media aligned on polyimide films prepared by spin-coating and LB
techniques: effect of rubbing. Molecular Crystals and Liquid Crystals, 1992. 213(1): p.
223-228.
12. Woolverton, C.J., et al., Liquid crystal effects on bacterial viability. Liquid crystals, 2005.
32(4): p. 417-423.
13. Frank, F.C., Liquid crystals on the theory of liquid crystals, in Crystals That Flow:
Classic Papers from the History of Liquid Crystals. 2004, CRC Press. p. 389-399.
14. Stewart, I.W., The static and dynamic continuum theory of liquid crystals: a
mathematical introduction. 2004: Crc Press.
15. Ericksen, J.L., Continuum theory of liquid crystals of nematic type. Molecular crystals
and liquid crystals, 1969. 7(1): p. 153-164.
16. Catanescu, C., L.-C. Chien, and S.-T. Wu, High birefringence nematic liquid crystals for
display and telecom applications. Molecular Crystals and Liquid Crystals, 2004. 411(1):
p. 93-102.
17. Jia, D., et al., Wide-angle switchable negative refraction in high birefringence nematic
liquid crystals. Liquid Crystals, 2013. 40(5): p. 599-604.
18. Schiekel, M. and K. Fahrenschon, Deformation of nematic liquid crystals with vertical
orientation in electrical fields. Applied Physics Letters, 1971. 19(10): p. 391-393.
19. Lueder, E., Liquid crystal displays: Addressing schemes and electro-optical effects. 2010:
John Wiley & Sons.
20. Akhmanov, S.A. and S.Y. Nikitin, Physical optics. 1997: Clarendon Press.
21. Adams, M.J., An introduction to optical waveguides. Vol. 14. 1981: Wiley New York.
22. Hu, J. and C.R. Menyuk, Understanding leaky modes: slab waveguide revisited.
Advances in Optics and Photonics, 2009. 1(1): p. 58-106.
74
23. Croswell, W.F., O.M. Bucci, and G. Pelosi, From wave theory to ray optics. IEEE
Antennas and Propagation Magazine, 1994. 36(4): p. 35-42.
24. Born, M. and E. Wolf, Principles of optics: electromagnetic theory of propagation,
interference and diffraction of light. 1980: Elsevier.
25. Marcuse, D., Theory of dielectric optical waveguides. 2013: Elsevier.
26. Okamoto, K., Fundamentals of optical waveguides. 2010: Academic press.
27. Snyder, A.W. and W.R. Young, Modes of optical waveguides. JOSA, 1978. 68(3): p.
297-309.
28. Davis, S.R., et al. Analog, non-mechanical beam-steerer with 80 degree field of regard.
in SPIE Defense And Security Symposium. 2008. International Society for Optics and
Photonics.
29. Kim, J., et al. Wide-angle, nonmechanical beam steering using thin liquid crystal
polarization gratings. in Proc. SPIE. 2008.
30. Li, J., et al., Infrared refractive indices of liquid crystals. Journal of Applied Physics,
2005. 97(7): p. 073501.
31. Yamada, S. and H. Matsukawa, Production process of liquid crystal display panel, seal
material for liquid crystal cell and liquid crystal display. 1999, Google Patents.
32. Lee, J.-g., J.-H. Lee, and H.-r. Nam, Method for manufacturing a liquid crystal display.
1999, Google Patents.
33. Sato, Y., K. Sato, and T. Uchida, Relationship between rubbing strength and surface
anchoring of nematic liquid crystal. Japanese journal of applied physics, 1992. 31(5A): p.
L579.
34. Ishihara, S., et al., The effect of rubbed polymer films on the liquid crystal alignment.
Liquid Crystals, 1989. 4(6): p. 669-675.
35. Kumagai, E., et al., Liquid crystal panel inspection method. 1994, Google Patents.
top related