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

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