stressed liquid crystals: properties and ......dr. philip bos , members, doctoral dissertation...
TRANSCRIPT
STRESSED LIQUID CRYSTALS: PROPERTIES AND APPLICATIONS
A dissertation submitted to Kent State University in partial
fulfillment of the requirements for the degree of Doctor of Philosophy
By
Guoqiang Zhang
August 2007
ii
Dissertation written by
Guoqiang Zhang
B.S. Jilin University, China, 1997
M.S. Jilin University, China, 2000
Ph.D. Kent State University, 2007
Approved by
Dr. John West , advisor, Doctoral Dissertation Committee
Dr. Philip Bos , Members, Doctoral Dissertation Committee
Dr. Dengke Yang ,
Dr. David Allender,
Dr. Christopher Woolverton
Accepted by
Dr. Oleg Lavrentovich , Director, Department of Chemical Physics
Dr. Jerry Feezel , Dean, College of Arts and Sciences
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TABLE OF CONTENTS
LIST OF FIGURES……………………………………………………………………..viii
LIST OF TABLES…………………………………………………………………......xxiv
ACKNOWLEDGEMENTS…………………………………………………………….xxv
Chapter 1 Introduction…………………………………………………………………….1
1.1 General information of liquid crystal devices……………………………………1
1.2 Efforts for speeding up liquid crystal devices……………………………………3
1.2.1 Optimization of intrinsic properties of liquid crystal materials…..................3
1.2.2 Thin cell gap to obtain fast speed………………………………...................3
1.2.3 Novel operation modes of liquid crystal devices………………...................4
1.2.4 Novel driving scheme……………………………………………………….6
1.3 Liquid crystal/polymer composites for large phase modulation…………………7
1.3.1 Polymer dispersed liquid crystal (PDLC)…………………………………..8
1.3.2 Polymer network liquid crystal (PNLC)…………………………………...13
1.3.3 Mechanical deformation in liquid crystal/polymer composites……………16
1.3.4 A Breakthrough on practical fast-switching large-phase-modulation material:
Stressed liquid crystal (SLC)……………………………………………... 22
Chapter 2 General Fabrication and Characterization Procedures….…………….……....28
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2.1 Fabrication of SLCs………………………………………..……………………28
2.1.1 Materials……….…………………………………………………………..28
2.1.2 Fabrication……….………………………………………………………...28
2.1.2.1 Pre-polymerization preparation..………………………….................29
2.1.2.2 Polymerization……..………………………………………………...29
2.1.2.3 Shear process……………..……………………………….................30
2.1.2.4 Final sealing…………..……………………………………………...33
2.2 Characterization description of SLCs………………………………………...….33
2.2.1 Transmittance measurement…………………………………………….…33
2.2.1.1 Transmission at a specific wavelength (λ = 0.633μm)……………....33
2.2.1.2 Visible-near infrared spectra (Vis-NIR)……......................................36
2.2.1.3 Infrared characterizations…..………………………………………..36
2.2.1.3.1 Spectra of pure liquid crystals………………………….............36
2.2.1.3.2 Infrared SLC…………………………………...........................37
2.2.2 Polarizing microscopy………………….……………………………….…37
2.2.3 Fluorescence confocal microscopy..…………………………………..…...37
2.2.4 Scanning electron microscopy (SEM)……………………………………..38
2.2.5 Electro-optical measurements……………..……………………………….38
Chapter 3 Structures of SLCs……………………………………………………………40
3.1 Influence of composition………………………………………………………..40
3.2 Influence of UV intensity and coalescence effect………………………………41
3.3 Cure temperature effect………………………………………………………....47
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3.4 Shear effect………………………………………………………………….…..57
3.5 Stressed liquid crystal model: shaped, close-packed liquid crystal domains inside
a stressed polymer matrix……………………………………………………...63
Chapter 4 Optical Transmission of SLCs………………………………………………..67
4.1 Shear effect……………………………………………………..………………69
4.2 Morphology dependence………………………………………………………..73
4.3 Polarization dependence………………………………………………………..78
4.4 Liquid crystal director ordering…………………………………...…………….82
4.5 Conclusions……………………………………………………………………...86
Chapter 5 Electro-optical Performance of SLCs………………………………………...88
5.1 Definition of switching voltage and response time……………………………..88
5.1.1 Calculation of optical path delay………..…………………………………89
5.1.2 Definition of response time………………………………………………..94
5.2 Experimental investigation of electro-optical performance…………………….96
5.2.1 Shear distance……………………………...………………………………96
5.2.2 Liquid crystal domain size………………………………………………..103
5.3 Electro-optical responses calculation…..……………………………………...105
5.4 Reduced hysteresis.…………………………………………………………….111
5.5 Linearity between OPD and applied voltage……..………………………........120
5.6 Extra-large OPD achieved by thick SLCs…..……………………………........126
5.7 Conclusions…………………………………………………………………….130
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Chapter 6 Stressed Liquid Crystal Based Optical Phased Arrays for Mid-wave Infrared
(MWIR) Beam-steering Application……………..…………………………...………..133
6.1 Introduction…………………………………………………………………….133
6.2 Fabrication of the SLC-OPA device…………………………………………...141
6.3 Beam-steering performance………………………………………………........141
6.4 IR transmission of the designed MWIR SLC-OPA…………………………....148
6.4.1 IR transmittance of the substrates………………………………...............148
6.4.2 IR transmittance of the electrode material……………………………..…148
6.4.3 IR transmittance of the SLC materials…………………………................151
6.4.4 IR transmittance of the SLC-OPA……………………………………….158
6.5 Molecular engineering design to optimize SLC’s IR transmission…………....161
6.6 Conclusions…………………………………………………………………….171
Chapter 7 SLC-OPA for the Application of Tip-Tilt Corrector……………………..…172
7.1 Introduction…..………………………………………………………………..172
7.2 Fabrication of the SLC-OPA…………………………………………………..173
7.3 Electro-optical characterizations of the SLC device…………………………..177
7.4 Characterizations of the performances of a tip-tilt corrector…………………..181
7.4.1 Steering angle and drive methods considerations………………………...181
7.4.2 Beam profile and steering efficiency……………………………………..183
7.4.3 Switching speed of the SLC tip-tilt corrector……………...……………..187
7.5 Conclusions…………………………………………………………………….189
Chapter 8 Photo-patterned SLC Prisms………………………………………………...190
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8.1 Introduction…………………………………………………………………….190
8.2 Experimental setup…………………………………………………………….191
8.3 Characterizations and performance……………………………………………193
8.4 Conclusions……………………………………………………………………202
Chapter 9 Mechanically Patterned SLCs………………………………………………206
9.1 Introduction……………………………………………………………………206
9.2 Experimentals………………………………………………………………….207
9.3 Results and discussions………………………………………………………..209
9.4 Conclusions…………………………………………………………………….222
Chapter 10 SLCs for Fast Display Application……..……………………………….....223
10.1 Introduction…………………………………………………………………..223
10.2 Performance of SLC displays………………………………………………...224
10.3 Conclusions…………………………………………………………………...229
Chapter 11 Conclusions………………………………………………………………...232
Appendix A Components/Chemical Structures of the Materials Used in SLCs….……238
Appendix B Calculations of Electro-optical Responses for Stressed Liquid Crystals
(SLCs)…………………………………………………………………………………..239
Appendix C Jones Matrix Derivation for Light Polarization……………..………….....248
References………………………………………………………………………………252
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LIST OF FIGURES
Fig. 1.1 Comparison between a homogenous cell and a Pi-cell. (a) Homogenous cell with
anti-parallel rubbing alignment; (b) Pi-cell with parallel rubbing alignment…….5
Fig. 1.2 Operation mechanism of a PDLC. I0 is the incident light intensity and IT is the
transmitted light intensity. (a) without an electric field, eff pn n≠ ; light scatters; (b)
with an electric field applied, eff o pn n n= ≈ ; light transmits through…………...10
Fig. 1.3 Illustration of fabrication of a HPDLC sample. A periodical structure of liquid
crystal rich layers and polymer rich layers forms as a result of the interference of
two coherent light beams………………………………………………………..12
Fig. 1.4 Formation of a polymer network inside PNLC. The ellipses represent liquid
crystals while the black rods represent monomer units. (a) Liquid crystalline
monomers align along the liquid crystals’ director controlled by surface alignment
layers; (b) Upon photopolymerization, a polymer network forms when the
monomer units keep their original orientation………………………………….15
Fig. 1.5 Deformation of liquid crystal droplets inside a PDLC during shearing. R is the
radius of original spherical droplet while a, b represent semi-major axis and semi-
minor axis of the formed ellipse………………………………………………...17
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Fig. 1.6 Mechanism of a scattering polarizer built from a stretched PDLC. If no=np and
ne>np, P-polarization of light is scattered while S-polarization of light passes
through without scattering loss…………..………………………………..…….19
Fig. 1.7 Compression of a HPDLC. Compression of a film thickness results in the shift of
the reflection wavelength ( 2 sindλ θΔ = Δ ). Δd is the change of film thickness
and θ is the angle between incident light and the periodic layer normal……...…21
Fig. 1.8 Schematic drawings of a stressed liquid crystal cell: (a) after polymerization; (b)
after shearing; (c) after application of electric field………………..…………….24
Fig. 2.1 The structure of a typical SLC cell and the UV-polymerization setup. …......…31
Fig. 2.2 Structure of a SLC shear device. ……………….………………………………32
Fig. 2.3 Experimental setup for polarization dependent transmittance measurements. The
polarizer is rotated so that the polarization of the incident light is either parallel or
perpendicular to the shear direction ……………………………………………..35
Fig. 2.4 Typical electro-optical measurement setup. The shear direction of a SLC is along
the horizontal direction while the crossed polarizers are at a 45o angle relative to
the shear direction………………….…………………………………………….39
Fig. 3.1 Microscopic graphs of 5CB-SLCs of different LC concentration ratios cured at
60oC. Cure UV intensity is 40 mW/cm2. (a) 60%; (b) 70%; (c) 80%; (d) 90%; (e)
95%. The black bars represent 50 μm in length. …………...…………...............43
x
Fig. 3.2 polarizing microscopic pictures of the SLC samples A1 to A4. (a) A1; (b) A2; (c)
A3; (d) A4. The white bar represents 10 μm in length for all four
graphs…………………………………………………………………………...46
Fig. 3.3 Microscopic pictures of the E7-SLCs cured at different temperatures. (a) 41oC; (b)
50oC; (c) 60oC; (d) 70oC; (e) 80oC; (f) 90oC; (g) 100oC; (h)
110oC. ……………..............................................................................................49
Fig. 3.4 SEM graphs of the E7-SLC system obtained at different cure temperatures: (a)
41oC; (b) 50 oC; (c) 60 oC; (d) 70 oC; (e) 80 oC; (f) 90 oC; (g) 100 oC; (h) 110 oC.
The black bar in (a) is 10 μm in length while the white bars in the rest graphs
represent 2 μm in length…………………………………………………..…….52
Fig. 3.5 SEM graphs of SLCs of which cure temperatures were around the LCs’ TNIs: (a)
E44-SLC cured at 90oC; (b) E7-SLC cured at 50oC; and 70oC; (c) 5CB-SLC cured
at 25oC; (d) E44-SLC cured at 110oC; (e) E7-SLC cured at 70oC; (f) 5CB-SLC
cured at 45oC. The white bar represents 2 μm in length………………………...53
Fig. 3.6 Illustration of upper critical solution temperature phase diagram of cyano-
biphenyl-based-LC/NOA65 system. From D. Nwabunma and T. Kyu, Polymer 42
(2), 801-806 (2001)……………………………….……………………………..56
Fig. 3.7 Microscopic graphs of samples A2 and A3: (a) before-shear state of A3; (b) after-
shear state of A3; (c) before-shear state of A2; (d) after-shear state of A2. The
horizontal black bars represent length scales for the two samples. The shear
direction is depicted by the dark arrow……………………….…….…………...60
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Fig. 3.8 Fluorescence confocal microscopic Z-scan pictures of samples A2 and A3.(a)
before-shear state of A2; (b) before-shear state of A3; (c) after-shear state of A2; (d)
after-shear state of A3…………………………………………………………….61
Fig. 3.9 Sketched polymer network morphologies of two anisotropic gels: (a) type I--
fibrils; (b) type II--sheet structures. From R. A. M. Hikmet and H. M. J. Boots,
Phys. Rev. E 51 (6), 5824-5831 (1995)………………..……………………..….63
Fig. 3.10 Model of shaped, close-packed liquid crystal domains: side views and top
views……………….………….…………………………………………………66
Fig. 4.1 Transmittance of a 12-μm-thick E7-SLC (E7:NOA65=86:14 (weight%);
Tcure=100oC) at various shear distances. A 12-μm-thick pure NOA65 cell was
used as the reference to correct reflection loss…………….…………………….71
Fig. 4.2 Transmittance of a 40-μm-thick 5CB-SLC (5CB/RM82/NOA65: 90/2/8). (a) 0
μm shear; (b) 120 μm shear; (c) 200 V on at the 120 μm shear state. A 12-μm-
thick pure NOA65 cell was used as the reference to correct reflection loss…….72
Fig. 4.3 Transmittance of the series A SLCs of different sizes of liquid crystal domains at
the states of before and after shearing: (a) A1 and A2; (b) A3, A4 and A5. The
hollow and solid symbols represent before-shear and after-shear states,
respectively……………………………………………………………………....74
Fig. 4.4 Transmission spectra of E7-SLC samples cured at different temperatures ranging
from 41oC to 100oC: (a) before-shear state; (b) after-shear state. ………………77
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Fig. 4.5 Measured difference of transmittance at two polarizations. ΔT= T⊥-T‖. (a) 5CB-
SLCs with different compositions: B2(∆); B1(■); B3(○); B4(●). (b) E7-SLCs
polymerized at different temperatures: B6 (■, 100oC); B7 (●, 70oC)…………….79
Fig. 4.6 The absorption spectrum of anthraquinone dichroic dye M483. (From Chen et al.
Mol. Cryst. Liq. Cryst. 433, 129-141 (2005))………………………………........83
Fig. 4.7 Transmittance of B4 and B5 with the incident light’s polarization either parallel or
perpendicular to the shear direction. λ=632.8 nm ………………………………84
Fig. 4.8 Calculated liquid crystal director orderings in a SLC (B5) ……………………..85
Fig. 5.1 Normalized transmittance-voltage curve (T-V curve) of a 40-μm-thick SLC cell
(5CB/NOA65: 90/10) measured between crossed polarizers. The wavelength is
1550 nm. ……..………………………………………………………………….91
Fig. 5.2 Calculated optical path delay for the 40-μm-thick 5CB-SLC according to
formulas listed in Table 5.1. ...…………………………………….…………….93
Fig. 5.3 Definitions of response time for amplitude modulation and phase modulation of
SLCs. (a) τon and τoff for SLC of fast display applications; τon and τoff are
calculated between the 10% and 90% transmittance levels. (b) τon and τoff for
SLCs in the phase modulation mode. τon is defined as the time which OPD drops
to 10%; τoff is defined that OPD increases to 90%. τoff of this 40-μm-thick 5CB-
SLC is 3.0 ms and τon is 0.2 ms………………………………………………….95
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Fig.5.4 T-V curves of a 5-μm-thick 5CB-SLC (5CB/NOA65: 90/10) at different shear
distances: 10, 20, 40, and 60 μm, respectively ………………….………………97
Fig. 5.5 Turn-off time of the 5-μm-thick SLC at different shear distances (10 to 60 μm).
τoff is labeled at the T10…………………………………………………………...99
Fig. 5.6 The turn-on time (τon) of the 5-μm-thick SLC at different shear distances (10 μm,
20 μm, 40 μm and 60 μm). T90 is used to label the τon…………………………100
Fig. 5.7 Shear distance dependence of optical path delay for a 12-μm-thick E7-SLC cured
at 100oC…………………………………………………………………………102
Fig. 5.8 Electro-optical measurements of the four SLC samples at different shear
distances. (a) Shear distance dependence of switching field; (b) shear distance
dependence of relaxation time. ………………………………………………...104
Fig. 5.9 Deformation of liquid crystal droplets during shearing. L is shear distance; D is
cell thickness; R is the radius of original spherical droplet; a, b, and c represent
semi-major axis, semi-minor axis at the direction along shear direction, and semi-
minor axis at the direction perpendicular to shear direction, respectively…..…107
Fig. 5.10 Calculation of the switching fields and response times for a 40-μm-thick SLC.
Liquid crystal domain size and shear distance are varied. Squares, circles,
triangles and reversed triangles represent the calculated data for R=0.2, 0.5, 1, and
2 μm, respectively. (a) Switching field Es; (b) relaxation time τoff; (c) turn-on time
τon……………………………………………………………………………….108
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Fig. 5.11 Comparison between measurement and calculations for a 22-μm-thick 5CB-
SLC. (a) Switching field; (b) turn-on time; (c) turn-off time………………….110
Fig. 5.12 Measured T-V curve showing hysteresis for a 16-μm-thick PDLC cell
(E7/NOA65: 50/50). Hollow triangles represent the ramp from 0 V to 80 V; solid
reverse triangles represent the ramp from 80 V to 0 V. At one transmittance level,
the difference (ΔV) characterizes the hysteresis…………………….………….112
Fig. 5.13 Hysteresis of a 12-μm-thick E7-SLC cured at 100oC. The shear distance was
150 μm………………………………………………………………………….113
Fig. 5.14 OPD-V curves showing no hysteresis for a 5-μm-thick SLC (5CB/NOA65:
90/10) when Lshear = 60 μm. ……………………………………………………114
Fig. 5.15 Hysteresis measurement of two E7-SLC samples B6 and B7 at the different
shear distances…………..……………………………………………………...117
Fig. 5.16 Drzaic’s two-step reorientation mechanism. When an electric field is applied,
liquid crystal molecules in the middle first orient along the field (a to b), then the
molecules at closer to the surfaces (b to d). On the other hand, when the field is
removed, the center molecules again quickly relax (d to c) followed by the
relaxation of the surface area. From Paul S Drzaic, Liq. Cryst. 3 (11), 1543-1559
(1988)……………………………………………………………………..……118
Fig. 5.17 Mechanism on reduction of hysteresis for SLC system. (a) slightly deformed
LC droplet; (b) greatly sheared LC domain; (c) a normal planar LC
cell……………………………………………………………………………...119
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Fig. 5.18 Definition of linear response between OPD and voltage in SLC systems. The
linear region is between A and B: fit function is Y=4.47-0.08X. The change of
OPD in AB region is ~2.5 μm…………………………………………...……..121
Fig. 5.19 Illustration of a driving system using a series of resistors. The voltages applied
on electrodes E1 through E8 are adjusted linearly by simply adjust the voltage at
one end, V0'. If a liquid crystal material has a linear response between OPD and
voltage, different linear phase profiles are obtained when V0'=VL, VM, and VS. VL,
VM, and VS represent large, medium, and small voltages
respectively…………………………………………………………….……….122
Fig. 5.20 Simplified illustration of multi-layer structures of SLCs. It is assumed that the
layer thickness of each layer is slightly varied………………………………....124
Fig. 5.21 Birefringence-voltage plot of a 6-μm-thick liquid crystal/polymer gel. Squares
and crosses indicate experimental data for polymer volume fractions of 0.1 and
0.05, respectively. The dotted line is the calculated result for a cell containing
67% of 0.5 μm thick LC layers. Solid lines are calculated from distributions of
layer thicknesses chosen to obtain reasonable fits to the experimental data. From
R. A. M. Hikmet and H. M. J. Boots, Phys. Rev. E 51 (6), 5824-5831
(1995)…………………………………...............................................................125
Fig. 5.22 OPD versus applied voltage for an 820-μm-thick SLC (5CB/NOA65: 90/10) at
650 μm shear……………………………………………………………………127
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Fig. 5.23 OPD as a function of time of an 820-μm-thick SLC (5CB/NOA65: 90/10) at
650 μm shear after removal of 800 V…………………………………………..128
Fig. 5.24 Measured maximum OPD of SLC cells of different cell gaps (from 22 μm to
820 μm)…….…………………………………………………………………..131
Fig. 5.25 Measured maximum OPD for 12-μm-thick E7-SLCs cured at different
temperatures…………………………………………………………………….132
Fig. 6.1 Operation of a digital light deflector based on LC wedge prism. The incident
light is polarized in the in-plane direction. When the TN cell is not electrically
activated, the incident light rotates its polarization to the parallel direction of the
liquid crystal optical axis inside the LC prism after the switch cell, and then is
steered away. When the TN cell is electrically activated, the incident light keeps
its polarization and passes the LC prism without being steered ………….…....136
Fig. 6.2 Illustration of liquid crystal optical phased arrays. a) Profiled voltage applied to
patterned electrodes; the distance between v0 electrode and vn electrode is the
reset period L. b) The phase profile formed, assuming the maximum phase
retardation achieved for the liquid crystal film is the designed wavelength…...137
Fig. 6.3 Illustration of flyback regions in the liquid crystal based optical phased arrays
due to the fringing field effect. Light blue lines represent the ideal phase profile
while the dark black lines represent the real phase profile. The gaps between these
two profiles are called flybacks………………………..……………………….140
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Fig. 6.4 Configuration of SLC-OPA configuration. Shear direction is orthogonal to the
electrode direction. Each electrode is 97 μm wide and the gap between adjacent
electrodes is 3 μm………………………………………………………………143
Fig. 6.5 Electro-optical measurements of a 22 μm SLC cell: (a) OPD vs. voltage; (b)
OPD vs. relaxation time. A red laser (λ = 632.8 nm) was used……………….144
Fig. 6.6 Illustration of the optical path delay profiles encoded on the SLC-OPA. From top
to bottom, 8, 12, and 16 electrodes are chosen as the reset period, respectively.
From Jianru Shi, Dissertation, Kent State University, 2005………………….145
Fig. 6.7 Experimental setup of the reflective SLC-OPA during a beam steering operation.
The incident light is polarized parallel to the shear direction of the SLC-OPA. A
highly reflective gold mirror is placed behind the SLC-OPA to reflect the light
towards the detector………………………………………………………….....146
Fig. 6.8 The measured maximum steering angles with varied reset periods. On the top the
non-steered wave was plotted. Plots of steering were also provided when the reset
periods are 16, 12, and 8 electrodes, respectively. The corresponding steering
angles (in degree) are 0.115, 0.144, and 0.215, respectively. From Jianru Shi,
Dissertation, Kent State University, 2005……………………………………...147
Fig. 6.9 Transmittance spectra of sapphire in the range of 0.2 to 6 μm. It is measured with
air as the reference………………………………………………………...........149
Fig. 6.10 IR transmittance of an ITO film on sapphire substrate in the 2 to 5 micron
region. It is measured with an uncoated sapphire substrate as the reference…...150
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Fig. 6.11 IR spectra of a 6-μm-thick (dashed line) and a 50-μm-thick (solid line) E7 cells.
The alignment of the two cells is parallel to the polarizer’s transmission axis. The
absorption peak at 4.49 μm represents the cyano band while the peaks between 3
to 4 μm represent the carbon-hydrogen vibration bands…………………..…...153
Fig. 6.12 Calculated coefficients of absorbance for 5CB (a) and NOA65 (b)………….155
Fig. 6.13 Calculated IR transmittance of a 22-μm-thick 5CB-SLC film………………157
Fig. 6.14 Configuration of reflective SLC-OPA………………………………………..159
Fig. 6.15 Comparison between experimental measurement and calculation for a SLC-
OPA with a 22 μm SLC film operating in the reflective mode………………..160
Fig. 6.16 Calculated IR spectrum of an 800-μm-thick SLC……………………………163
Fig. 6.17 IR transmission in 2 – 5 micron region of approximate 5 μm thick layers of 4’-
octyl-4-cyanobiphenyl (8CB) and Deuterated 4’-octyl-4-cyanobiphenyl
(D8CB)………………………………………………………………………….164
Fig. 6.18 Calculated IR transmittance for 820-μm-thick deuterated 8CB film…….......165
Fig. 6.19 The structure of pentafluorophenyl-(2,3,5,6-tetrafluoro-4-trifluoromethoxy-
phenyl)-diazene and the calculated IR absorption bands………………………167
Fig. 6.20 Measured infrared spectra for thin films of cyclohexane, 5CB, PCH5 and
pyridine. Offsets of absorbance are used for easier comparison……………….170
xix
Fig. 7.1 The structure of the SLC tip-tilt corrector with a 24 interdigitally patterned ITO
bottom substrate and a non-patterned ITO top substrate. The width of ITO strips is
412 μm, and the line gap is 5 μm…………………………………..…………..175
Fig. 7.2 The SLC tip-tilt corrector transmittance at the states before and after shear. It is
referenced to transmission of a NOA65-cell to correct the reflection loss……..176
Fig. 7.3 The measured switching times of the SLC tip-tilt corrector. λ = 1.55 μm and V =
200.0 V………………………………………………………………………….178
Fig. 7.4 The measured OPD of SLC tip-tilt corrector as function of voltage. The linear
range is roughly from 67.0V to191.0V…………………………………………179
Fig. 7.5 Measured transmission spectra of SLC Tip-Tilt corrector. It is referenced to a
NOA65 cell……………………………………………………………………..180
Fig. 7.6 Schematic drawings of beam steering effect of a liquid crystal cell at different
voltage driving condition. The drawing on the left side is liquid crystal director
configurations, on the right side is the corresponding optical phase profile. ↔
indicates the beam polarization direction and ↑ indicates the beam propagation
direction. (a) No voltage is applied; (b) Linear voltage ramp is applied, left side
has low voltage and right side has high voltage; (c) Linear voltage ramp is applied,
left side has high voltage and right side has low voltage………………………182
Fig. 7.7 (a) Schematic drawing of the setup for beam profile and switching speed
measurements, BE and BC stand for beam expender and beam compressor. (b)
Three possible positions the beam can be steered to…………………………...184
xx
Fig. 7.8 (a) and (b) are the beam profiles from a reflected reference cell in Z- and Y-
direction. (c) is the SLC steered and non-steered beam profiles in Z-direction. To
compare the beam intensity, the two peaks of the beams are aligned up. The
bottom horizontal axis is for non-steered beam width and position, the top
horizontal axis is for steered beam width and position. (d) is the SLC steered and
non-steered beam profiles in Y-
direction………………………………………………………………………...186
Fig. 7.9 Measured response time of the SLC tip-tilt corrector. Waveform on the top is the
time response of the SLC device, waveform on the bottom is the driving
waveform. The base frequency of the driving waveform is 10.0 KHz and
amplitudes are ±67.0 V and ±191.0 V, respectively...………………………….188
Fig. 8.1 Illustration of polymerization of SLC prism using a UV photo-mask…….......192
Fig. 8.2 UV transmittance measurements of four locations on the photo-mask
corresponding to the four spots, A, B, C, and D, of the SLC prism. The four spots
were round spots of 1 mm diameter, constrained by a pinhole of 1 mm diameter.
Adjacent spots were 5 mm apart from each other. λ=365 nm…………………194
Fig. 8.3 SEM of A, B, C, and D are shown in this graph. The strong UV irradiation
produced the rough polymer matrix (micrograph a) while the weak UV irridiation
produced thin and smooth polymer matrix (micrograph d). For the medium UV
intensity regions, a transition from a coarse network structure to a thin sheet
structure is observed (micrographs b and c)……………………..……………..195
xxi
Fig. 8.4 Optical path delay difference across the gradient SLC prism at the different shear
states…………………………………………………………………….............197
Fig. 8.5 Variation of optical path delay for spots A and D which were at the two ends of
the SLC prism with the change of the voltage. The SLC prism was at the 100 μm
shear state…………………………..……………………………………….…..198
Fig. 8.6 Measured voltage dependent ΔOPD at 0 μm, 30 μm, 100 μm shear states,
respectively……………………………………………………………………..200
Fig. 8.7 Measured turn-off times for spots A and D on the SLC prism………………...201
Fig 8.8 The 2D Birefringence Measurement setup…………………………………….203
Fig. 8.9 Phase profiles across the gradient SLC sample at different voltages λ = 0.633
μm………………………………………………………………………………204
Fig. 8.10 The photo-mask presented on the top was used to demonstrate the SLC lens
concept. The 2-D birefringence pattern measurements of SLC lenses fabricated
with the mask are provided at the bottom………..……………………………..205
Fig. 9.1 (a) Demonstration of twist-shear scheme for the T-SLC; (b) pattern image of the
T-SLC between crossed polarizers; (c) marked six spots along the horizontal line
for measurements of electro-optical properties and transmittance…………..…208
Fig. 9.2 Images of the M483-doped T-SLC taken through a linearly polarized analyzer
horizontally (left) or vertically (right) aligned. Black arrows represent the optical
transmission axis of the analyzer. The pattern rotates when the analyzer rotates.
The real dimension of each area is 20x20 mm2…………………….…….…….212
xxii
Fig. 9.3 Illustration of a pattern shift for T-SLC upon application of a linear shear force.
(a) The angle representation of shear/shift directions; (b) ring pattern obtained
before a linear shear (90o) was applied; (c) the shift of the ring pattern after a 90o
linear shear……………………………………………………………………...214
Fig. 9.4 Mechanism of pattern shift of a T-SLC upon a 90o additional linear shear. The
arrows on the outer circle represent the counterclockwise twist direction……..215
Fig. 9.5 Optical path delay on the different spots of the T-SLC. ……..………………..217
Fig..9.6 Position-dependent transmittance of the T-SLC. The laser’s wavelength is 632.8
nm………………………………………………………………………………218
Fig. 9.7 With the crossed polarizers viewing setup, T-SLC images were recorded in a
voltage ramp: (a) 0 V, (b) 30 V, (c) 50 V, (d) 80 V, (e) 110 V, and (f) 120 V…219
Fig. 9.8 Simplified illustration of distribution of polarization states after a linearly
polarized light (along the X axis) passes through a T-SLC. The large rings are
phase retardation rings; Δnd=λ/4, λ/2, and λ, respectively. Τhe short lines, circles
and ellipses represent linear, circular and elliptical polarizations of light,
respectively…………………………………………………………………..…221
Fig.10.1 Transparency of a 5 μm thick 5CB-SLC: (a) before shear; (b) after shear. The
paper with ‘westlab’ written on was placed 1 cm away from the SLC cell…….225
Fig. 10.2 Response time (τon and τoff): (a) a 5-μm-thick SLC cell switching with 4.7 V; (b)
a 1.7-μm-thick 5CB cell switching with 5 V…………………………………...226
xxiii
Fig. 10.3 The influence of shear distance on switching voltage and total response time
(τon + τoff). The solid round circles represent the switching voltage (axis on the
right). The solid squares are the response time (axis on the left)……………....227
Fig. 10.4 Voltage Holding Ratio measurements for liquid crystals TL205 and ZSM5386
comparing with SLCs based on the corresponding liquid crystals……………..230
Fig. 10.5 Thermal stability test of SLC at three different temperatures: 25 oC, 60 oC, and
100oC……….…………………………………………………………………..231
Fig. B.1 Illustration of liquid crystal director in the spherical coordinates…………….239
Fig. B.2 Illustration of liquid crystal director direction in a liquid crystal droplet before
and after electrical field………………………………………………………...242
Fig. C.1 Illustration of the lab frame coordinates (regular slow and fast axis coordinates)
and the angles used in the Jones Matrix representation. For Point P on the T-SLC,
the angle between the liquid crystal director and X axis, ψ = 2π β+ , where β is
the rotation angle between the lab frame and XY coordinates
(i.e.,∠ POX)…………………………………………………………………….251
xxiv
LIST OF TABLES
Table 3.1 Fabrication conditions of the series A SLC les. Cell gap was 12 μm. A very
small amount of fluorescence dye, ~10-4 by weight, was added to all the samples for the
confocal fluorescence microscopic study ……………………………………………….44
Table 3.2 The cure temperatures for the two steps of polymerization and the clearing
temperatures for the liquid crystals and the mixtures. * The clearing temperatures of the
mixtures were obtained through polarizing microscopy observations…………………..51
Table 4.1 Some physical parameters of the materials used for SLCs……………………68
Table 4.2 Fabrication conditions of the series B SLC samples for polarization dependence
studies on transmittance………………………………………………………………….78
Table 5.1 Formulas for the optical path delay calculation from the T-V curve (Fig.
5.1). ……..……………………………………………………………………………….92
Table 5.2 Parameters used in the electro-optical response calculations………………..107
Table 6.1 Spectrum branch selection of different materials for the calculation of IR
absorption coefficients (ε)………………………………………………………………154
Table 9.1 Comparison of transmission intensity patterns between radial structure and
azimuthal structure……………………………………………………………………...211
Table 11.1 Comparison between all systems which can switch 55 μm OPD…………..234
xxv
ACKNOWLEDGEMENT
This work is dedicated to my wife, daughter and parents. Their unconditional
support helps me go through these unforgettable years.
I would like to express my great appreciation to my advisor: Dr. John West who
has advised and inspired my research. Without his supervision this dissertation can not be
completed. I would also like to thank my committee members, Dr. Philip Bos, Dr.
Dengke Yang, Dr. David Allender, and Dr. Christopher Woolverton for their insightful
comments and advices. I am greatly indebted to all the faculty and staff in liquid crystal
institute for their help during my study and research. I want to thank Doug Bryant for his
support on cleanroom instruction and substrate fabrication support, Qiu Liou for her
support on SEM characterizations, Ivan Smalukh for his help on fluorescence confocal
microscopy measurement, Jianru Shi for his support on beam steering project, Xinghua
Wang for his support on 2-D phase profile measurement, and Bin Wang for his help on
tip-tilt corrector project.
I am also very grateful for all the great help from Westlab group memembers
including Anatoliy Glushchenko, Linli Su, Ke Zhang, Ebru Buyuktanir, and Fenghua Li.
This work is funded by DARPA 444226 and Samsung Electronics.
1
CHAPTER 1
Introduction
1.1 General Information of Liquid Crystal Devices
Liquid crystal displays are widely used in all types of devices, such as wrist
watches, calculators, TVs, computer monitors, and almost all electronics devices. Liquid
crystals are also applied in many non-display applications such as optical communication
switches, spatial light modulators,[1,2] tunable liquid crystal lenses,[3] non-mechanical
beam-steering devices,[4] and wavefront-control devices. In these applications, large
phase modulation is often required and fast response is always desirable. Especially, fast-
switching large phase retardation is crucial for infrared applications, where the design
wavelength is large (λ =2 to 14 μm). For example, to perform a 2π phase modulation at
wavelength λ =5 μm, a device has to produce 5 μm optical path delay. Optical path
delay (OPD) produced by liquid crystals is calculated as Δnd, where Δn is the
birefringence of liquid crystal, obtained from Eq. 1.2, where ne and no are the
extraordinary refractive index and ordinary refractive index, respectively. The d is the
liquid crystal film thickness.
OPD n d= Δ ⋅ (1.1)
e on n nΔ = − (1.2)
2
For a specific liquid crystal, Δn is constant, thus a thick liquid crystal film is needed to
achieve large phase modulation. However, for most liquid crystal optical modulation
modes, the response times increase quadratically with liquid crystal film thickness. There
are two switching times for liquid crystal devices: turn-on time (τon) and turn-off time
(τoff) .[5,6]
2 2/off d Kτ γ π= (1.3)
12
22 2 1ond VK K
γ ετπ π
−Δ⎛ ⎞= −⎜ ⎟⎝ ⎠
(1.4)
In Equations 1.3 and 1.4, γ, K, Δε are respectively the rotational viscosity, elastic
constant and dielectric anisotropy of a liquid crystal. V is the applied voltage.
For most of the systems, τon is short because of the existence of switching field
during the turn-on process. However, there is no assistance of electric fields during the
turn-off process; therefore, τoff is usually long. Particularly, the cell gap significantly
influences the turn-off time. For example, according to Equation 1.3, a 5 μm thick
homogenously aligned 5CB (4-cyano-4'-pentyl-biphenyl) cell will have τoff about 25 ms,
where γ =0.056 Kg/ms and K = 0.61*10-11 N/m when the maximum OPD (~0.95 μm; Δn
~ 0.19) is switched. However if the cell thickness increases up to 20 μm which produces
3.8 μm maximum optical path delay (2π modulation for λ=3.8 μm in IR region), the
speed becomes very slow: τoff ~ 400 ms.
3
1.2 Efforts for Speeding up Liquid Crystal Devices
Previous efforts towards fast-switching liquid crystal devices include optimizing
liquid crystal materials, reducing cell thickness, constructing novel liquid crystal
operating modes, and adopting complicated driving schemes.
1.2.1 Optimization of Intrinsic Properties of Liquid Crystal Materials
Optimization of liquid crystal materials[7] consists of improvement in the
following three aspects: (1) K: the elastic constant; (2) Δn: the birefringence; and (3) γ:
the rotational viscosity. Wu et al.[8] define a figure of merit evaluation parameter (FoM)
for liquid crystal materials as
FoM=K(Δn)2/γ (1.5)
Large FoM is favorable for practical applications because increasing the ratio of K/γ
reduces response times (as shown by Equation 1.3 and 1.4) and large Δn helps to increase
the OPD. Liquid crystals with high FoM are available such as wide nematic range alkenyl
diphenyldiacetylenes.[9] However, usually thermal or photo stability remain a key issue to
improve in addition to the limitation of narrow nematic range and undesirable high
operating temperatures. Gauza et al.[10] have formulated some isothiocyanato (NCS)
biphenyls and terphenyls of better UV stability and higher FoM.
1.2.2 Thin Cell Gap to Obtain Fast Speed
A straightforward method of improving switching speed is to decrease the cell
thickness because the response times of liquid crystals are proportional to the square of
cell thickness. Thin cell gap approach has been successfully incorporated into a recent
4
popular technology, liquid-crystal-on-silicon (LCoS). LCoS devices are attractive for
virtual displays and rear projectors. LCoS takes advantage of small area (usually less than
1′ in diagonal) and thin cell gap (less than 3 μm) and provides a millisecond range fast
response[11], which is especially desirable for the field sequential color operation scheme
used in projection systems. However, uniform thin cell gap is difficult to achieve in large
area display applications and the liquid crystals are susceptible to external deformations.
Recently, Wang et al.,[12] through a well-controlled phase-separated composite films
method (PSCOF),[13] have fabricated a uniform submicron thin nematic cell. The mixture
of nematic liquid crystal E7 and photocurable prepolymer NOA65 (Norland Optical
Adhesive), capillarily filled in a 3 μm thick cell, undergoes polymerization initiated by
UV light of low intensity (~0.1 mW/cm2). After the phase separation process, a layer of
E7, approximately 0.9 μm thick, separates from the polymer matrix. The device’s total
response time (i.e. τon +τoff) is only 1.3 milliseconds. Theoretically, a series of thin cells
can be stacked together to produce large phase modulation with fast speeds. However,
practically the optical loss of the substrates and related extra cost limit the application.
1.2.3 Novel Operation Modes of Liquid Crystal Devices
Bos et al.[14] invented a Pi-cell (also named optically compensated bend) which
not only decreases the turn-off time as it eliminates backflow in the process of relaxation
but also increases the view angle due to its self-compensated structure. The Pi-cell has a
parallel rubbing alignment on the two substrates while the pretilt of the surfaces point
toward the same direction as shown in Fig. 1.1(b). The formed bend structure prevents
the liquid crystals’ backflow occuring during relaxation in the traditional homogeneously
5
antiparallelly aligned liquid crystal cells. Thus, the Pi-cell reduces the turn-off switching
time. However, it takes longer time for the Pi-cell to adjust from the original splay state
to the operation bend state. A relative high initial voltage pulse is needed to speed up this
process and an offset voltage is usually required to keep the Pi-cell in the operational
bend state, which complexes driving scheme.
Figure 1.1 Comparison between a homogenous cell and a Pi-cell. (a) Homogenous cell
with anti-parallel rubbing alignment; (b) Pi-cell with parallel rubbing alignment.
6
1.2.4 Novel Driving Scheme
The overdrive scheme became a popular method of improving response time of
liquid crystal displays recently driven by the need for fast LCD TVs. Overdrive
techniques have proven to be very promising. Simply put, when a pixel is switching to an
intermediate grey level, a full black/white switch signal is sent first to get a faster
response. Displays using this technology have already been introduced, and have
provided incremental speed improvements. Kawabe et al.[15] describe a dynamic contrast
compensation method utilizing an appropriate voltage to cancel the lack or excess of
luminance which occurs at the transition period in the next couple of frames. Similar
method (Response Time Compensation) is illustrated by McCartney.[16] The overdrive
scheme can reduce response times by a couple of milliseconds, improving the moving
picture quality. However, the undesirable extra cost is added.
Dual frequency liquid crystals[17] can also be used to speed up the switching
process because they change the sign of the dielectric anisotropy at the cross-over
frequency, fc. For example, as a dual frequency liquid crystal has a positive dielectric
anisotropy at frequencies lower than fc, it is switched to the direction of a field upon the
application of a low frequency driving field; then, the driving field is changed to a high
frequency (f > fc), the liquid crystal is reoriented perpendicular to the direction of the
electric field due to its negative dielectric anisotropy at the high frequency. The change of
field frequency simply switches the liquid crystal device. An electric field is present
during both the ‘turn-on’ and ‘turn-off’ process, which reduces the response time.
Schadt[18] obtained dramatically reduced turn-off time in a twisted nematic liquid crystal
7
display based on dual frequency liquid crystal materials (i.e. 10 ms compared to original
168 ms). More recently, devices based on dual frequency liquid crystal materials have
achieved switching speed of 1 ms.[19],[20] However, the complicated driving method and
strict temperature control hinder the extensive applications of dual frequency materials.
1.3 Liquid Crystal/Polymer Composites for Large Phase Modulation
All the above technologies can improve response speed; however, their
applications are limited to the relatively small phase modulation area. There are two
methods to increase phase retardation: increasing the birefringence of a liquid crystal and
increasing the film thickness of a liquid crystal. Unfortunately, until now, the largest
birefringence of liquid crystals is only approximately 0.5, demonstrated by the alkyl
cyclohexane isothiocyanato tolanes, introduced by Wen et al.[21] In addition, Sun et al.
synthesized some azo liquid crystals[22] of high birefringence and tested some mixtures
dissolved in E7 (Δn increases ~20%) based on these pure materials for potential IR
applications.[23,24] In general, the materials of high birefringence tend to have large
viscosity and low photo/thermal stability.[21,23] In addition, the high birefringence liquid
crystals usually have high operating temperatures and narrow nematic ranges. Therefore,
the only feasible way of getting large phase retardation is to use thick liquid crystal film.
However, for devices using pure liquid crystals, when a liquid crystal film is thick, the
response time becomes very long (for example, τoff is over 400 ms for a 20 μm thick pure
5CB cell). Until now, none of current fast-switching systems are feasible for practical
optical large phase modulations.
8
Therefore, the desirable merit of large-phase-modulation material is that a thick
layer of a liquid crystal material with large birefringence has fast response. An alternative
to a single thick liquid crystal film is to use multiple stacks of thin films. A series of thin
fast-switching liquid crystal cells can be stacked to provide the required phase retardation
that a thick cell would produce. Waveguide-like structures can also be applied, where
multi-bounce optical pass is utilized. However, the high optical loss of substrates usually
make them impractical.[25] Thus, there is a critical need to decouple the liquid crystal film
thickness and the switching speed for thick liquid crystal films. It has been revealed that
liquid crystals confined in small complex geometries[26,27] show unique electro-optical
properties, such as fast switching speeds. It is possible that confined liquid crystals can
act as fast-switching large-phase-modulation materials because of the significantly
increased surface to volume ratio, essentially creating an ensemble of thin cells.
1.3.1 Polymer Dispersed Liquid Crystal (PDLC)
The confinement matrix can be membranes,[28] carbon nanotubes,[29] and polymer
binders.[30] Incorporating polymer binders into liquid crystals is more flexible, either
through phase separation methods[31,32] or through emulsion.[33,34] Depending on the
structure of polymer matrices, liquid crystal/polymer composites can be divided into two
categories: composites of droplet morphology and composites of network morphology.
The composites having droplet morphologies include polymer dispersed liquid crystals
(PDLC) from phase separation methods and nematic curvilinear aligned phase (NCAP)
built from emulsion. Very often, when small amount of liquid crystalline monomers are
used, polymer stabilized/network liquid crystals (PSLC/PNLC) of network morphologies
9
are obtained. In this dissertation, PDLC is used to represent both PDLC and NCAP for
the sake of simplicity. Inside the droplets of PDLCs, liquid crystals may have various
director configurations depending on the nature of polymer matrices and liquid crystals.
Figure 1.2 illustrates the bipolar configuration which exists in the E7/NOA65 system.
Normally, PDLCs of nematic droplets with a positive dielectric anisotropy have an
opaque appearance in the unpowered state because of the refractive indices mismatch
between liquid crystal droplets and polymer matrix ( eff pn n≠ ). The effective refractive
index of a droplet is estimated as 2 2 2 2cos sineff e o e on n n n nθ θ= + , where ne and no, θ
are the extraordinary refractive index, ordinary refractive index and the angle between the
liquid crystal director and the light incident direction. With a field applied, the nematic
droplets align along the field direction ( eff on n= ). If no is close to np, PDLCs become
transparent (Fig. 1.2(b)). Upon removal of the field, the nematic droplets return to their
original orientation and PDLCs become opaque again (Fig. 1.2(a)).
10
Figure 1.2 Operation mechanism of a PDLC. I0 is the incident light intensity and IT is the
transmitted light intensity. (a) without an electric field, eff pn n≠ ; light scatters; (b) with
an electric field applied, eff o pn n n= ≈ ; light transmits through.
11
One interesting application of PDLC is the holographic PDLC (HPDLC).[35]
Coherent interference of laser irradiation creates HPDLC structures as shown in Figure
1.3. The interference pattern determines the period of the discrete liquid crystal rich
regions and polymer rich regions due to the difference in the rates of local
photopolymerization. Eventually, the nano-scale periodic spatial gratings form. These
gratings are tunable by electrically varying the average refractive index of the liquid
crystal domains. HPDLCs diffract light when refractive index mismatch occurs.
Therefore, one refractive index of liquid crystals is selected the same as that of polymer
matrix to adjust diffraction efficiency. Compared to conventional nematic liquid crystals,
HPDLCs have very fast switching speeds, dozens of micro seconds, owing to the nature
of nano-scale domains. The tradeoff is the high switching field, usually greater than 10
V/μm.
12
Figure 1.3 Illustration of fabrication of a HPDLC sample. A periodical structure of liquid
crystal rich layers and polymer rich layers forms as a result of the interference of two
coherent light beams.
13
PDLCs have been mainly used for their scattering and diffraction properties.
PDLCs can be used for phase modulation applications as well. The modulation depth is
usually small. Matsumoto et al.[36,37] fabricate a scattering-free nano-PDLC which
significantly reduces the optical loss. However, only a very small amount of phase shift is
obtained and switching voltage is very high: 0.02 μm OPD for a 20 μm thick cell at a
7.5V/μm switching field.
1.3.2 Polymer Network Liquid Crystal (PNLC)
Usually, PDLCs are composed of isotropic polymers and there is no preferential
alignment treatment applied. Therefore, liquid crystals domains inside PDLCs exhibit
macroscopically random orientation without an external field. On the contrary, some
polymer network liquid crystals[38] (or liquid crystal gel[39]) have alignment layers on the
substrate surfaces controlling the orientation of liquid crystals and polymer networks.
They are liquid crystal/polymer composites built with a small amount of liquid crystalline
polymers (usually less than 5%). Before polymerization, liquid crystals are aligned by the
surface alignment, which orients liquid crystalline monomers in the meantime (Fig.
1.4(a)). Upon polymerization, the monomers polymerize according to their original
alignment (Fig. 1.4(b)). As a result, a highly connected polymer network forms and
serves as additional alignment surface. The existence of polymers assists to relax liquid
crystals faster. These composites scatter light due to the formation of microdomains at
either the turn-on state or the turn-off state, depending on the fabrication procedures.[39,40]
Fan et al.[41] increase liquid crystalline monomers’ concentration to 10% and optimize the
fabrication condition to produce a PNLC free of light scattering at the wavelength of near
14
infrared. This near IR scattering-free PNLC achieved a full wave modulation in 2 ms in
the reflective mode. However, besides high switching field, alignment is hard to maintain
for thick cells in this PNLC system.
15
Figure 1.4 Formation of a polymer network inside PNLC. The ellipses represent liquid
crystals while the black rods represent monomer units. (a) Liquid crystalline monomers
align along the liquid crystals’ director controlled by surface alignment layers; (b) Upon
photopolymerization, a polymer network forms when the monomer units keep their
original orientation.
16
1.3.3 Mechanical Deformation in Liquid Crystal/Polymer Composites
In addition to variation of monomer categories and compositions, mechanical
modifications are also applied to liquid crystal/polymer composites, introducing unique
properties, such as alignment of liquid crystals,[42],[43] macroscopic birefringence,[44] and
improved electro-optical performance.[45] There are mainly three types of mechanical
deformation applied to the liquid crystal/polymer composites: (1) shear deformation; (2)
stretch deformation; and (3) compress deformation. Wu et al.[45] have demonstrated that
shear force can produce alignment to liquid crystal droplets inside PDLCs and improve
response speed. Amundson et al.[44] find that sheared PDLC samples of high liquid
crystal concentration (~80 wt%) exhibit large birefringence due to the uniform alignment
of liquid crystals induced by shear force. Other groups have used shear stress during the
phase separation process to align liquid crystals in many liquid crystal polymer composite
systems. For instance, Sixou et al.[46-48] build sheared polymer dispersed nematic liquid
crystals (PDNLC) and sheared polymer dispersed cholesteric liquid crystals (PDCLC)
and demonstrate the elliptical shape of liquid crystal droplets formed by the shear using
scanning electron microscopy. The characterized electro-optical performance of the
PDNLC is consistent with the theoretical prediction. Sheared PDCLC shows a correlation
between ellipticity and reflectivity: larger ellipticity produces blue-shifted and narrower
reflection band. Kitzerow et al.[49,50] successfully achieve prealignment for ferroelectric
liquid crystals inside a polymer matrix by applying shear force during polymerization,
avoiding the difficulty of building surface stabilized ferroelectric liquid crystal devices of
which the cell gap is usually thinner than 2 μm.
17
Figure 1.5 Deformation of liquid crystal droplets inside a PDLC during shearing. R is the
radius of original spherical droplet while a, b represent semi-major axis and semi-minor
axis of the formed ellipse.
18
Another mechanical modification is through stretching. Stretching PDLC[51,52] has
become one standard method for fabricating scattering polarizers. Polymer content is
usually over 50% to make a stand-alone film. After the stretch, liquid crystal droplets
align along the direction of stretch, and the refractive index mismatch between liquid
crystal droplets and polymer matrix occurs for only one polarization of the incident
light.[53] Figure 1.6 demonstrates the polarization dependence of light scattering for
stretched PDLC. Figure 1.6(a) is a PDLC film before stretching. Upon stretching, shown
by the horizontal arrows, the liquid crystal droplets inside the PDLC become elliptical
and liquid crystals align along the direction of stretching to minimize elastic free energy.
When a light with a pair of polarizations is shed on the stretched PDLC film, the light of
in-plane polarization (P-polarization) ‘sees’ the ne (extraordary refractive index) of the
liquid crystal droplet which is different from the np, thus, light scattering occurs. On the
other hand, the light of polarization perpendicular to the plane (S-polarization) ‘sees’ the
ordinary refractive index of the liquid crystal droplet which is close to np, therefore, the
light transmits without scattering.
19
Figure 1.6 Mechanism of a scattering polarizer built from a stretched PDLC. If no=np and
ne>np, P-polarization of light is scattered while S-polarization of light passes through
without scattering loss.
20
The third mechanical deformation is through compression. Crains et al.[54] have
studied the influence of compressive stress on PDLC. They observed amplified strain-rate
dependence: PDLC material has much higher modulus than the pure polymer matrix
material. A micromechanical model was proposed to explain the phenomena and estimate
the change of aspect ratio of the liquid droplet inside a PDLC during compression.
Holmstrom et al.[55] successfully tune the reflection band of HPDLC over 120 nm in the
visible spectral range by changing film thickness from compression. The compression
scheme is illustrated in Fig. 1.7. When the thickness of the HPDLC film reduces from d
to d', the period of the diffraction layer structure is reduced, giving rise to shift of
reflection bands.
21
Figure 1.7 Compression of a HPDLC. Compression of a film thickness results in the shift
of the reflection wavelength (roughly 2 cosdλ θΔ = Δ ⋅ ). Δd is the change of film
thickness and θ is the angle between incident light and the periodic layer normal.
22
1.3.4 A Breakthrough on Practical Fast-switching Large-phase-modulation Material:
Stressed Liquid Crystal (SLC)
Liquid crystal/polymer composites significantly increase surface to volume ratio.
Polymer dispersed liquid crystal (PDLC) and polymer network liquid crystal (PNLC) can
switch faster compared to pure liquid crystal cells due to the assistance of large areas of
polymer matrix during the liquid crystals’ reorientation process, and it’s possible for
them to provide large phase modulation because thick samples are producible and
operatable in theory. However, PDLCs have very low phase modulation efficiency due to
the large amount of polymer matrices and the curved interface of liquid crystal droplets.
PNLC have high concentration of liquid crystals, but the high operation fields and light
scattering in thick samples greatly limit their applications for large phase modulation.
During the search for an ideal fast-switching large phase modulation material,
West et al. have found interesting light modulating properties rising from a sheared liquid
crystal/polymer composite. The sheared samples become scattering free and can
modulate large phase retardation at fast speeds.[56] They are essentially different from
conventional deformed PDLCs because of the absence of light scattering in any
polarization. This system decouples the speed and liquid crystal film thickness and it is
named stressed liquid crystal (SLC).[57],[58]
SLCs are fabricated through a photo-polymerization procedure. No alignment
layers are needed. Shear force is applied to the polymer matrix and introduce
unidirectional alignment to the embedded liquid crystal domains. Figure 1.8 shows the
configuration and operation of a SLC cell. After polymerization, liquid crystal domains
23
are randomly oriented (Fig. 1.8(a)). When shear stress is applied, the polymer matrix is
stretched and the liquid crystal domains align along the direction of shear force (Fig.
1.8(b)). For a liquid crystal of positive dielectric anisotropy, all the domains will orient
along the electric field direction upon application of an external field (Fig. 1.8(c)). Then,
liquid crystals will relax back to their original shear-aligned position after the removal of
the electric field.
24
Figure 1.8 Schematic drawings of a stressed liquid crystal cell: (a) after polymerization;
(b) after shearing; (c) after application of electric field.
25
My dissertation is focused on the fundamental understanding of SLCs and further
exploring and optimizing SLCs for various applications. Chapter 1 discusses the
background of developing fast large-phase-modulation liquid crystal materials. Chapter 2
covers the basic fabrication and characterization techniques of SLCs. The fabrication
conditions, such as composition, UV intensity, and cure temperature, greatly influence
the morphologies and the performance of SLCs. In Chapter 3, the structures of SLCs are
studied using scanning electron microscopy (SEM) and non-destructive characterizations
such as polarizing microscopy and fluorescence confocal microscopy. Upon shearing, it
is observed that polymer matrix is stretched along the shear direction and liquid crystal
domains wrapped by the sheets adopt elliptical shape. During this process, liquid crystals
orient along the shear direction due to the shape anisotropy of liquid crystal domains.
Based on the microscopic study, a simplified model of SLCs is developed. SLCs are
proposed to exist as close-packed and shaped liquid crystal domains inside a stressed
polymer matrix. Chapter 4 discusses the optical transmittance characterization of SLCs.
Light scattering of SLCs decreases dramatically upon shearing. In Chapter 5, the electro-
optical performance of SLCs is discussed in detail. The electro-optical performance of
SLCs depends on not only liquid crystal domain size but also the aspect ratio of the liquid
crystal domains. Small liquid crystal domains require high switching fields and they
produce fast speed. In addition, the switching field rises with the increase of shear
distances and both the relaxation time and the rise time declines with the increase of the
shear distance because the aspect ratio of the elliptical domains increases. With
modification of Wu’s model of elliptical droplets inside PDLC, formulas are derived for
26
switching electrical fields and response times of SLC systems. The calculated electro-
optic responses of the SLC samples are consistent with experimental results. In addition,
thick SLC films capable of switching optical path delay as large as 55 microns are
demonstrated. This large OPD has not been obtained through a single cell of any tradition
liquid crystal material. SLCs not only can switch large OPD in very short amount of time,
they also have linear response between phase shift and applied voltage, which simplifies
driving electronics. In addition, SLCs essentially have no hysteresis.
Chapter 6 through Chapter 10 discuss the various applications of SLCs. In
Chapter 6, mid-wave IR SLC optical phase array non-mechanical beam-steering devices
have been fabricated and characterized. SLC beam-steering devices which switch 4.5 μm
in 2 ms have demonstrated continuous beam steering for an IR laser of (λ=3 μm) as well
as visible and NIR laser wavelengths. Chapter 7 demonstrated ultra-fast tip-tilt correctors
based on SLC-OPAs. Designed according to SLC’s linear response between optical path
delay and voltage, a SLC based tip-tilt corrector can switch 1.55 μm OPD as fast as 100
μs. SLCs are patternable, either through photo-mask or by mechanical approach. In
Chapter 8, photo patterned SLC prisms are described. SLC prisms and lenses were made
by polymerizing SLC films through various photo-masks. These devices have great
potential for fast tunable lenses of large aperture because the phase retardation of SLCs
can be increase as large as needed without sacrificing switching speed. In Chapter 9, a
twist-SLC was made when a twist shear (instead of a linear shear) was applied to a SLC
film. It has large OPD at the edges and small OPD in the center, resulting in a negative
lens. This device is not only electrically tunable but also mechanically adjustable. In
27
addition to the twist shear, an extra linear shear can shift the lens structure to create
asymmetric phase profile in the active area of the device, opening opportunities for novel
devices. Chapter 10 discusses SLCs’ potential for fast display applications. Low voltage
SLC devices with response time less than 2 ms have been demonstrated. With further
modification of materials and fabrications, fast low-voltage SLCs of high voltage-
holding-ratio are promising for the development of fast displays. Chapter 11 concludes
this dissertation.
28
CHAPTER 2
General Fabrication and Characterization Procedures
2.1 Fabrication of SLCs
2.1.1 Materials
In these experiments, the cyanobiphenyl based liquid crystals from Merck
including 5CB (4-pentyl-4'-cyanobiphenyl), E7, and E44 were used. The prepolymer,
NOA65, from Norland Optical Adhesive, Inc. was used to form the polymer solution.
Another monomer, RM82, a reactive mesogen is diacrylate from Merck, was utilized in
some samples. The photo initiator, Irgcure651, was added when RM82 was used. The
chemical structures of the above mentioned compounds are listed in Appendix A. The
indium-tin-oxide (ITO) glass substrates are 1.1 mm thick and are from Colorado Concept
Coatings and the spacers are from EM Industry.
Liquid crystals and prepolymers were weighted to produce specific ratios and
then mixed together in amber vials to minimize light exposure. The room light was
shielded by UV filters in order to avoid unwanted polymerization. All mixtures were
vigorously shaken by a Fisher Vortex Genie 2 Mixer for 20 minutes. After shaking, the
mixtures were heated for 5 to 10 minutes on a hot plate at a temperature above the
nematic-isotropic transition of the liquid crystals.
2.1.2 Fabrication
29
2.1.2.1 Pre-polymerization preparation
The mixtures were drop-filled between two ITO glass substrates before
polymerization. First, spacers (glass fiber or plastic) in isopropanol solutions
(approximately at a volume ratio of 5 x 10-5) were spin-coated on a clean ITO glass
substrate (The spin-coater, EC101DT-R485, is from Headway Research Inc.). No
alignment layer was applied. Then, the substrate was placed on the top of a hotplate with
controlled temperature. Second, the liquid crystal-prepolymer mixture was heated above
the isotropic temperature of the liquid crystal to ensure homogeneity and was dropped on
the ITO glass. Another ITO glass was aligned with the first ITO glass substrate with the
ITO side facing down to form a cell for the mixture. Finally, the top substrate was
pressed to expel extra solutions and air bubbles, if any, and to maintain a uniform cell gap.
Figure 2.1 illustrates the structure of such a cell and the polymerization setup.
2.1.2.2 Polymerization
The polymerization of SLC samples consists of two steps: (1) high temperature
polymerization (The cure temperature in the first step, 1cureT , is greater than the clearing
temperature of the mixture); and (2) low temperature polymerization (The cure
temperature in the second step, 2cureT , is room temperature, ~20 oC). Two separate heating
stages are used to control 1cureT and 2
cureT , respectively. The metal halide UV lamp, ELC-
2540, is from Electro-Lite Inc. It has a maximum emission peak at 365 nm. The UV
intensity was adjusted according to the distance between the lamp and samples. It is in
the range of 6~50 mW/cm2, measured by a UV meter, IL 1350 Radiometer/Photometer
30
from International Light. The cure time depends on the cell thickness of the samples. In
practice, when thickness, d, is equal or less than 50 μm, 30 minutes’ cure for each step is
applied. When d is greater than 50 μm, the cure time is increased to over 60 minutes. For
example, two hours’ cure was used to polymerize an 820-μm-thick SLC sample.
2.1.2.3 Shear Process
Figure 2.2 demonstrates the shear device and its shear mechanism. When a SLC was
placed on a shear device, one substrate was fixed and against a metal plate (Plate 1), and
the other substrate was against another metal plate (Plate 2). The displacement was
controlled by a micrometer. The rotation of micrometer in one direction caused the top
substrate to move towards the other end of the shear device, producing the shear. When
the micrometer was rotated in the reverse direction, the shear force was reduced. To
obtain uniform shear deformation, it is critical that both top and bottom substrates have
flat straight sharp edges and stay in full contact with the metal plates. In addition, the
bottom substrate has to stay flat on the support base. There is a 1 in2 hole cut on the
support base for light to pass through to perform optical characterizations. During
shearing, the micrometer knob was rotated to control shear distances. The accuracy was
approximately 5 μm.
31
Figure 2.1 The structure of a typical SLC cell and the UV-polymerization setup.
32
Figure 2.2 Structure of a SLC shear device.
33
2.1.2.4 Final Sealing
To avoid the contamination of moisure and hold the shear force, a SLC cell was
perimeter-sealed either by NOA81 (from Norland Optical Adhesive) or by 5-minute
epoxy (from Devron) after a SLC sample was sheared to a desired shear state. First, the
edges of the cell were cleaned by isopropanol and dried. Then the sealants were applied
at the four edges. Twenty minutes’ UV cure (IUV = 20 mW/cm2) finished the final sealing
when NOA81 was used. If an epoxy was used, longer time (over two hours) was needed
for the glue to solidify.
2.2 Characterization Description of SLCs
Transmittance was measured to characterize the optical transparency (Vis-NIR,
IR) and the shear effects of SLCs. The polarizing microscopy and fluorescence confocal
microscopy were used to observe the morphologies of polymer matrices inside SLCs and
the shear deformation upon shearing. Scanning electron microscopy was used to
determine the polymer matrix morphologies in detail. The electro-optical measurements
characterized the performance of SLCs. The general characterization techniques are
described in the following text.
2.2.1 Transmittance Measurements
2.2.1.1 Transmission at a specific wavelength (λ = 0.6328 μm)
The polarization dependence for transmittance of SLCs was measured at a
wavelength of 632.8 nm with a He-Ne laser source. The setup is demonstrated in Fig. 2.3.
34
The unpolarized laser passing through a rotatable polarizer became linearly polarized and
transmitted through a SLC cell before reaching a visible-light detector with a red filter.
The transmittance value was then captured by the detector and processed by a PC. The
polarizer was rotated to achieve different polarizations, either parallel or perpendicular to
the shear direction of the SLC. This setup was used to characterize the fundamental
difference between SLCs and PDLCs. The liquid crystal domain ordering inside a SLC
was obtained through this setup as well.
35
Figure 2.3 Experimental setup for polarization dependent transmittance measurements.
The polarizer is rotated so that the polarization of the incident light is either parallel or
perpendicular to the shear direction.
36
2.2.1.2 Visible-Near Infrared Spectra (Vis-NIR)
The spectrometer is Perkin-Elmer Lambda 19. The light sources have a
wavelength range between 100 to 2500 nm. For each measurement, the reference for the
spectra measurement was a fully-cured pure NOA65 cell, which consisted of the cured
NOA65 sandwiched between two ITO-glass substrates. During the measurement, a
background was first scanned without any sample inside the spectrometer chamber. Then,
a reference cell and a SLC were inserted into the reference channel and the sample
channel, respectively, to obtain the transmissive Vis-NIR spectrum of the SLC sample.
Scanning wavelength range and speed were controlled through the system program.
2.2.1.3 Infrared Characterizations
2.2.1.3.1 Spectra of Pure Liquid Crystals
Sodium chloride substrates were used because of their good transparency in the
IR range. First, a thin film of polyimide 2555 (PI-2555) was spin-coated on a NaCl
substrate, prebaked for 1 minute at 90 oC and then baked in an oven at 270oC for an hour.
Second, it was rubbed with a linen cloth 8 times to obtain alignment. With a mylar film
controlling the cell gap, two NaCl substrates were stacked together while keeping the
rubbing directions antiparallel. Liquid crystals were capilarily filled on a hot-plate at a
temperature 20oC higher than the TNI of the liquid crystals. Five-minute epoxy was used
to seal the cells.
During the IR spectrum measurement, one PI coated NaCl substrate was used as
the reference to scan the background to correct for reflection and absorption of the
37
substrates. Then the liquid crystal cell was put into the chamber to measure its IR
spectrum. A wired grid polarizer (ZnSe polarizer from Spectra-Tech Inc.) was used to
obtain linearly polarized IR light.
2.2.1.3.2 Infrared SLC
ITO coated sapphire substrates were used to build IR SLC samples because of
their high transparency at both UV and IR ranges. The rest of the fabrication procedure of
sapphire SLCs are the same as in Section 2.1.
2.2.2 Polarizing Microscopy
Most SLC samples were observed between crossed polarizers and micrographs
were taken correspondingly. However, in order to clearly demonstrate detailed structures,
some graphs were shot without polarizers. During the imaging of shearing processes for
SLC samples, the shear device was fixed on the rotating object stage of the microscope.
Then, when the shear force was applied, the real-time shearing process was recorded with
a video camera and snapshots at different states of shearing were extracted from the video.
2.2.3 Fluorescence Confocal Microscopy
The fluorescence confocal microscopy was used to visualize the structure of SLCs
non-invasively. Olympus Fluoview BX-50 confocal microscope was used. A minimal
concentration of fluorescence dye (Fluorescein acrylate, λmax~ 490 nm) (10-4 by weight)
was added to SLC solutions before polymerization. The dye selectively accumulated in
the polymer matrix during polymerization. Thus, upon the excitation of the laser light (λ
= 488 nm), polymer matrices appeared much brighter than liquid crystals. The image data
were collected by scanning the tightly focused laser beam in the vertical cross-section of
38
the samples, thus providing side views of the polymer morphology between the two
bounding plates. The confocal graphs at different shear states were taken. In addition to
the vertical cross-section images (in Z direction), the fluorescence images in the X-Y
plane were recorded as well.
2.2.4 Scanning Electron Microscopy (SEM)
SEM is used for identifying detailed polymer matrix morphologies. The substrates of
the SLC samples were pulled apart after the treatment of liquid nitrogen. Liquid crystals
were washed out by methanol. After the evaporation of methanol, a thin layer of gold
film was sputtered on the remaining polymer networks for the SEM measurements. The
sputter machine is Hummer VI-A from Anatech Ltd. The SEM machine is Hitachi
S2600N.
2.2.5 Electro-optical Measurements
The electro-optical measurement setup is shown in Fig. 2.4. The measurements
were carried out mainly by the software “Electro Optical Measurement” developed in
Boslab of Liquid Crystal Institute at Kent State University. The square waveforms were
generated through the software and increased by an amplifier (7602M wideband
amplifier from Krohn-Hite Corporation). The amplitude was calibrated by an
oscilloscope, Tektronix TDS210. The laser wavelength was either 0.6328 μm or 1.55 μm.
A SLC cell was placed between two crossed polarizers (one is called polarizer and the
other is called analyzer). The shear direction was aligned horizontally, at 45o angle to
each polarizer.
39
Figure 2.4 Typical electro-optical measurement setup. The shear direction of a SLC is
along the horizontal direction while the crossed polarizers are at a 45o angle relative to
the shear direction.
40
CHAPTER 3
Structures of SLCs
The morphology of liquid crystal-polymer composites is greatly varied. It usually
strongly depends on the nature of polymers and liquid crystals, the concentration ratios,
and the fabrication conditions. It is very important to understand the relationship between
structures and performance for a LC/polymer composite to optimize for applications.
Drzaic[27] described in detail the different structures of PDLCs which originate from
different fabrication conditions and the performance of different structures.
Dierkings[38,59,60] particularly illustrated the relationship between structure and
performance in PNLC systems. Currently SLC systems are fabricated from a
photopolymerization-induced phase-separation process. The influencing factors include
materials and compositions,[61],[62] cure temperature,[62,63] and UV intensity.[61],[62],[63],[64]
In this chapter, the factors influencing SLCs’ morphologies are discussed and the
corresponding morphologies are characterized and studied. In addition, a model of SLC
structure is proposed to understand SLC.
3.1 Influence of Composition
Mixtures of 5CB/NOA65 with different LC concentrations (50% to 95%) were
prepared. It has been found that the cure temperatures have to be greater than the TNI of
the liquid crystal to achieve SLCs with optimized electro-optical performance; therefore,
41
the fabrication followed the procedures described in Chapter 2 while cure temperatures
were controlled at 60oC and 20oC at the two cure steps, respectively. Macroscopic phase
separation was observed for the three samples with relatively low liquid crystal
concentrations (50%, 60%, and 70% in wt%) as shown in Fig. 3.1(a), (b), (c). Conversely,
mixtures of higher LC concentrations (80% and 90%) demonstrated more uniform phase
separation as well as favorable SLC electro-optical properties. SLC samples of higher
liquid crystal concentration showed relatively larger liquid crystal domains which is
consistent with the observation of Nwabunma and Kyu[65]: photopolymerization rate is
slower at higher liquid crystal concentration; thus, there is more time for liquid crystal
molecules to separate out and form large liquid crystal domains. However, when 5CB’s
concentration increases up to 95%, the macroscopic phase-separation occurs again.
Probably there were not sufficient polymers inside the system to form a continuous
matrix. Thus, the optimized concentration range for 5CB-SLC is approximately from
80% to 90%. When additional reactive mesogen RM82 was used, the liquid crystal
concentration can be increased up to 94% while maintaining good shearability and
electro-optical performance. Similarly, E7-SLC and E44-SLC systems have an optimized
concentration range: 80%-88%.
3.2 Influence of UV intensity and Coalescence Effect
UV intensity[66] and coalescence effect[62] also play very important roles in the
formation of polymer network morphology. With fixed cure temperature and composition,
UV intensity was varied to obtain SLC samples of different liquid crystal domain sizes
(2~40 μm). As observed in most UV-curable liquid crystal-polymer composites, low UV
42
intensity cure allows slower polymerization and therefore larger liquid crystal domains.
In addition, slow cooling favors coalescence of liquid crystal domains which gives rise to
large droplets too. Table 3.1 lists the fabrication conditions for the series A SLC samples.
43
Figure 3.1 Microscopic graphs of 5CB-SLCs of different LC concentration ratios ( in
weight percentage) cured at 60oC. Cure UV intensity is 40 mW/cm2. (a) 50%; (b) 60%;
(c) 70%; (d) 80%; (e) 90%; (f) 95%. The black bars represent 50 μm in length.
44
5CB/RM82/NOA65
94/2/4
5CB/RM82/NOA65
90/2/8
Sample
A1 A2 A3 A4 A5
UV intensity (mW/cm2) 6.0 6.0 22 40 40
Cooling rate (oC/min) 0.4 4 4 10 10
LC domain size:
(diameter in μm)
30-40 10-20 5-8 ~2 < 1
Table 3.1 Fabrication conditions of the series A SLC samples. Cell gap was 12 μm. A
very small amount of fluorescence dye, ~10-4 by weight, was added to all the samples for
the confocal fluorescence microscopic study.
45
Liquid crystal domain sizes of samples A1 to A4 are estimated from the polarizing
microscopic pictures shown in Fig. 3.2. The domain size A5 is too small to be shown
clearly by microscopic graphs. But its optical properties and electro-optical performance
are studied in following chapters. All the samples show relatively uniform polyhedral
droplet structure, indicating the phase separation occurred through spinodal
decomposition process. When liquid crystal domains become smaller, the borders
between them turn less obvious. During a spinodal decomposition phase separation, the
two phases develops at the beginning in the format of bicontinuous phases. If it is
controlled to proceed slowly, such as through using low UV intensity and slow cooling,
one continuous phase can break up and form droplets inside the other continuous phase
(Fig. 3.2(a), (b)). On the other hand, if the phase separation proceeds fast enough that the
two continuous phases are frozen upon the separation, then the final structure is one
continuous phase, interconnected liquid crystal domains, dispersed in the other
continuous phase, polymer matrix (Fig. 3.2(c), (d)).
46
Figure 3.2 Polarizing microscopic graphs of the SLC samples A1 to A4. (a) A1; (b) A2; (c)
A3; (d) A4. The white bar represents 10 μm in length for all four graphs.
47
3.3 Cure Temperature Effect
Cure temperatures plays different roles for different LC/polymer composite
systems. In some acrylate/LC systems, increasing cure temperatures results in coarser
network structure[67] and large liquid crystal domains.[59] Carter et al.[62] attribute the large
liquid crystal domain size to the existence of the coalescence effect in higher cure
temperatures. It is also evaluated by Murashige et al.[68] that, in their acrylate/LC system,
higher cure temperature induces a lower degree of polymerization, and hence producing
coarser polymer networks with large liquid crystal domains. In other LC/acrylate
systems,[66],[69] high cure temperatures favor smaller domain size, possibly due to the high
reaction rate at high temperature for their monomers.
In the thiolene/LC system, thiolenes tend to have higher conversion rate at higher
cure temperatures. The conversion rate, theoretically, can be as high as 100% for a
LC/polymer system; however, it is hard to achieve full polymerization due to the
decreased diffusion rate as the degree of polymerization increases. In practice, conversion
rate as high as 93% was observed by Smith.[64] Nwabunma et al.[70] and Bhargava et al.[71-
73] both found that, in cyano-biphenyl based liquid crystal/NOA65 systems, at higher
temperatures, the maximum converstion rate of NOA65 is higher than that of lower
temperatures, which is possiblely attributed to the increase of mobility at high
temperatures. In addition, the reaction rate of NOA65 rises drastically at the onset of the
reaction, quickly reaching the maximum rate, within a few seconds. The subsequent drop
in the reaction rate may be due to the reduced mobility of polymer radicals and monomer
depletion.
48
Currently, SLC systems mainly utilize thiolene/LC materials. RM82 was only
added to a few samples while thiolene was still present. A few series of SLCs (5CB-SLC,
E7-SLC, and E44-SLC) were made at different cure temperatures (Table 3.2). The
micrographs of the series of E7-SLC are shown in Fig. 3.3.
49
Figure 3.3 Microscopic pictures of the E7-SLCs cured at different temperatures. (a) 41oC;
(b) 50oC; (c) 60oC; (d) 70oC; (e) 80oC; (f) 90oC; (g) 100oC; (h) 110oC.
50
It can be seen that, as the cure temperature increases, the phase separation
becomes more uniform. This is also observed from the SEM micrographs. Figure 3.4
illustrates SEM graphs of E7-SLCs cured at different temperatures.
Samples cured at temperatures lower than 60oC exhibit a polymer-ball-like
structure (Fig. 3.4(a), (b), (c)) whereas, at temperatures higher than 60oC, a polymer-
sheet-like structure is achieved (Fig. 3.4(d), (e), (f)). With the increase of the cure
temperature, the size of liquid crystal domain decreases and the polymer matrix becomes
thinner. In addition, it is observed that liquid crystal domains are interconnected and
dispersed in polymer matrices. When the cure temperature is higher than 90oC, liquid
crystal domains are in submicron range and polymer sheets are too thin and soft to hold
the actual structure during the process of SEM sample preparation. Therefore, the
micrographs demonstrated actual collapsed structures which still clearly show that the
liquid crystal domains become smaller and the polymer sheets become thinner and
smoother as the cure temperature increases.
51
SLC materials
(weight ratio)
TNI (oC) Tclear * (oC) 1CureT (oC) 2
CureT (oC)
E7/NOA65
(86:14)
61 ~40 41, 50, 60, 70, 80, 90,
100, 110
20
5CB/NOA65
(90:10)
35 ~20 20, 30, 40, 50, 60 20
E44/NOA65
(86:14)
100 ~80 80, 90, 100, 110, 120 20
Table 3.2 The cure temperatures for the two steps of polymerization and the clearing
temperatures for the liquid crystals and the mixtures. * The clearing temperatures of the
mixtures were obtained through polarizing microscopy observations.
52
Figure 3.4 SEM graphs of the E7-SLC system obtained at different cure temperatures: (a)
41oC; (b) 50 oC; (c) 60 oC; (d) 70 oC; (e) 80 oC; (f) 90 oC; (g) 100 oC; (h) 110 oC. The black
bar in (a) is 10 μm in length while the white bars in the rest graphs represent 2 μm in
length.
53
Figure 3.5 SEM graphs of SLCs of which cure temperatures were around the LCs’ TNIs:
(a) E44-SLC cured at 90oC; (b) E7-SLC cured at 50oC; and 70oC; (c) 5CB-SLC cured at
25oC; (d) E44-SLC cured at 110oC; (e) E7-SLC cured at 70oC; (f) 5CB-SLC cured at
45oC. The white bar represents 2 μm in length.
54
In addition to E7-SLC system, the effect of cure temperatures on 5CB/NOA65
and E44/NOA65 systems was also investigated through SEM. Similar to the E7-SLC
system, a transformation of polymer network structure around the nematic-isotropic
temperatures of these two cyanobiphenyl liquid crystals is also observed (Fig. 3.5).
Figure 3.5(a), (b), (c) demonstrated the polymer-ball-like structures which were obtained
at cure temperatures of 10 degrees lower than the TNIs of E44, E7, and 5CB, (100oC,
61oC, and 35oC) respectively. In contrast, Figure 3.5(d), (e), (f) illustrated the polymer-
sheet-like structure achieved at cure temperatures of 10 degrees higher than the TNIs. For
all these SLC samples, when cure temperatures are higher than their TNIs, they exhibited
good shear abilities and greater transmittances at the after-shear state which will be
discussed in Chapter 4. Therefore, cure temperatures play a significant role in final
morphologies of SLCs made of cyanobiphenyl-based-LCs/NOA65. Specifically, if the
cure temperature is lower than TNI of a cyanobiphenyl-based liquid crystal, a polymer-
ball-like structure is achieved; if the cure temperature is higher than TNI of a
cyanobiphenyl-based liquid crystal, a polymer-sheet-like structure is obtained. At cure
temperatures close to TNIs, an intermediate state between the ball-like structure and the
sheet-like structure is obtained. The polymer-sheet-like structure favors superior shear
ability, uniform shear-induced alignment of liquid crystals and fast response, which
represents the optimized structures of SLCs.
As discussed before, Bhargava et al.[73] found that at high temperatures, the
prepolymer material not only reacts faster but also achieves higher conversion rates. In
addition, phase separation starts late in the curing process. Based on Smith[74] and
55
Nwabunma et al.[65]’s work, a sketch of phase diagrams for cyano-biphenyls/NOA65
systems is plotted in Fig. 3.6. As the polymerization advances, the upper critical solution
temperature curve shifts to a higher temperature progressively as demonstrated by the
dashed lines in Fig. 3.6. Therefore, Low temperature cured SLCs’ phase separation starts
before the gelation point is reached; the conversion rate of polymer is less than that of
high temperature cured SLCs. The polymer shows coarser structure: the polymer ball
structure and liquid crystal domains remain large. High temperature cured SLCs do not
phase separate until the second step low temperature cure starts; the deep quenching (e.g.,
cure temperature drops from 100oC to 20oC) induces the gelation and locks in the
bicontinuous phases of small length scales, i.e. small liquid crystal domains and thin
polymer sheets.
56
0.0 0.2 0.4 0.6 0.8 1.0
Tem
pera
ture
LC volume fraction
TNI
Figure 3.6 Illustration of upper critical solution temperature phase diagram of cyano-
biphenyl-based-LC/NOA65 system. From D. Nwabunma and T. Kyu, Polymer 42 (2),
801-806 (2001).
57
The final LC domain morphology may not only depend on thermodynamic phase
equilibrium of the LC/polymer mixture, but also depend on the liquid crystal ordering. It
is possible the dramatic change of polymer morphologies below and above TNIs can be
attributed to the difference of dragging force in nematic and isotropic phases of liquid
crystals. West et al.[75] demonstrated the difference between the dragging forces in
nematic and isotropic phases of liquid crystals are large. The interface region between
nematic and isotropic phases during phase transition can drag isotropic particles along.
During NOA65’s polymerization, the polymer grows into larger isotropic media
gradually; the liquid crystal starts to expel the polymers after they reach sizes larger than
the critical size. In nematic phase, liquid crystals have much stronger expelling force to
push out other isotropic materials in addition to solubility-driven force, so that phase
separation proceeds faster, then the polymer ball structure forms. On the other hand, in
isotropic phase, liquid crystals does not expel polymer. As the spinodal decomposition
phase separation starts, the bicontinuous phases form: small interconnected liquid crystal
domains and thin polymer sheets.
3.4 Shear Effect
Many studies have been done on the investigation of shear deformation in
stretched/sheared-PDLCs. Sixou et al.[46] applied vibrational shear deformation during the
photopolymerization of PDLCs based on nematic LC and cholesteric LC/NOA and SEM
micrographs showed the elliptical droplet shape. Leader et al.[76] applied unidirectional
shear deformation during the polymerization of a smectic-LC/NOA65 system; significant
elongated droplets were observed based on microscopy. Zhao et al.[77] used infrared
58
dichroism to monitor the nematic liquid crystal’s orientation for stretched PDLC films.
The liquid crystals tended to align along the stretch direction while the liquid crystal
droplets adopted elliptical shape. Order parameter of the liquid crystals increased in the
draw ratio of the PDLC films and the maximum value was as high as ~0.55 when the
draw ratio was 4. The draw ratio is defined as Lstretch/L0, where Lstretch and L0 are the
lengths of the PDLC film after and before stretching. SEM micrographs of stretched
PDLC films also demonstrated clearly the elliptical shape of liquid crystal droplets after
stretch.[53]
Non-invasive methods such as polarizing microscopy and fluorescence confocal
microscopy were used to study the shear process of SLCs. Samples A2 and A3 with
relatively large liquid crystal domains were investigated. The liquid crystal domain
dimensions of A2 and A3 were approximately 10~20 μm and 5~10 μm in diameter,
respectively. Figure 3.7 displayed microscopic views of these two samples. The dark
lines are polymers and the light regions are liquid crystals confined between the polymer
sheets. Comparing the before-shear and the after-shear states of sample A3 (Fig. 3.7(a),
(b)), it is clearly seen that, after shear, dark lines became parallel to each other along the
shear direction which demonstrated that polymer matrices are stretched during shearing.
Liquid crystal domains in sample A2 showed a hexagonal tube shape before shearing (Fig.
3.7(c)). After the shear, the liquid crystal domains were elongated as seen in Fig. 3.7(d).
Therefore, two major shear effects on SLCs’ structures were observed: stretching of
polymer matrices and elongation of liquid crystal domains.
59
Fluorescence confocal micrographs confirmed these two shear effects. Figure 3.8
shows fluorescence confocal microscopic textures of the vertical optical scans of samples
A2 and A3. The image data were collected by scanning the tightly focused laser beam in
the vertical cross-section of the sample, providing the side view of the polymer
morphology between the two bounding plates; the plates are seen as dark top and bottom
regions in Fig. 3.8. Figure 3.8(a) and (c) were taken before shearing samples A2 and A3,
while Fig. 3.8(b) and (d) were taken after shear. The shear direction was from right to left.
The white color represents the polymer matrix and the gray color inside the white is the
liquid crystal domain. One can see that, during shearing, polymer matrices in both SLC
samples are stretched along the shear direction and liquid crystal domains adopt an
elongated shape. In addition, it is also observed that the size of liquid crystal domains
inside the A2 is not uniform: the domains close to the bottom substrate have larger size
while domains close to the top substrate have smaller size. This is due to the decay of the
cure UV intensity: both the monomer and liquid crystals inside SLC materials absorb
some UV radiation. Besides, phase separation results in additional UV intensity losses
due to scattering. Thus, the SLC materials on the bottom part receive less UV light
compared to those on the top part of the cell, which gives rise to the variation of liquid
crystal domain size. To avoid incomplete polymerization in thick SLCs (thicker than 200
μm), reflective curing setup was used. Reflective mirrors were placed underneath cells to
reflect UV light to the bottom substrate when UV light was shed from above.
60
Figure 3.7 Microscopic graphs of samples A2 and A3: (a) before-shear state of A3; (b)
after-shear state of A3; (c) before-shear state of A2; (d) after-shear state of A2. The
horizontal black bars represent length scales for the two samples. The shear direction is
depicted by the dark arrow.
61
Figure 3.8 Fluorescence confocal microscopic Z-scan pictures of samples A2 and A3.(a)
before-shear state of A2; (b) before-shear state of A3; (c) after-shear state of A2; (d) after-
shear state of A3.
62
The shear distance of a SLC can be as long as 10 times of the cell thickness
before the sample is broken. The strain, defined as the ratio of increase of film length
over original length, is approximately 900%. In this dissertation, Rshear is used to
represent shear capability: Rshear = Lmax/d, where Lmax is the maximum shear distance
beyond which a SLC cell will break and d is the thickness of the SLC film. Higher value
of Rshear ( > 6 ) is preferred for optimized SLC system. Rshear depends on SLC materials
and fabrication conditions. For example, in 5CB-SLC system, Rshear decreases as the
amount of RM82 inside a SLC is increased for cells of same thickness due to the rigidity
of mesogenic monomers. Also, Rshear decreases as cure temperature of SLCs decreases.
The extraordinary strain in SLCs is due to the rubbery nature the polymer and has
been observed before. De Rosa et al.[48] demonstrated over 200 μm displacement on a
15-μm-thick E7/NOA65 based holographic PDLC film (Rshear > 10). When fully cured,
the NOA65 in SLCs becomes a film with rubbery mechanical properties at room
temperature, which makes it possible to mechanically deform the composite. Smith[78]
estimated through DSC studies that in E7/NOA65 system of 50/50 volume ratio the
amount of E7 separated out after phase separation is about 50% and Bhargava et al.[73]
utilized infrared microspectroscopy to obtained similar result (30%). Bhargava et al also
pointed out that E7/NOA6 system cured at high temperatures tends to have high liquid
crystal solubility in the polymer matrix. For the SLC systems polymerization starts at
temperatures much higher than room temperature and quenching occurs at room
temperature, the percentage of liquid crystals dissolved and trapped by quench in the
63
polymer matrix would be even higher. With significant amount of liquid crystals
dissolved inside, NOA65 is plasticized and capable of long stretching without fracture.
3.5 Stressed Liquid Crystal Model: Shaped, Close-packed Liquid Crystal Domains
inside a Stressed Polymer Matrix
Hikmet et al.[79] proposed two type of polymer network morphology for different
anisotropic gels: 1) polymer fibrils and 2) liquid crystal domains separated by thin walls
of polymer network. For the type II gel, the polymer sheets are oriented along the
substrate plane due to the alignment layer on both substrates.
Figure 3.9 Sketched polymer network morphologies of two anisotropic gels: (a) type I--
fibrils; (b) type II--sheet structures. From R. A. M. Hikmet and H. M. J. Boots, Phys. Rev.
E 51 (6), 5824-5831 (1995).
64
In contrast to their model, polymer sheets inside SLCs can be oriented in any
direction before shear; however, after shear the polymer sheets are stretched along the
shear direction and oriented along the substrate plane. The degree the polymer sheets
orient depends on the original orientation and the shear extent (Lshear/d), where Lshear is
the shear distance and d is the cell gap.
Based on the microscopic studies and above discussion, a simplified model of
stressed liquid crystals was proposed: close-packed liquid crystal droplets inside a
sheared polymer matrix. In this model, SLCs are composed of multiple stacks of liquid
crystal hexagonal tubes separated by thin polymer sheets. The tilt angle of each
hexagonal tube depends on the shear extent and the height of each stack can be different.
The model is illustrated in Fig. 3.10. Both the side view and the top view are presented in
order to demonstrate the shear mechanism.
65
3.6 Conclusions
SLC is a unique LC/polymer composite existing in a narrow composition regime
and requires high cure temperatures (30oC or more higher than TNI of LCs used). The
nature of spinodal decomposition phase separation determines the bicontinuous phase
structures. Optimized SLCs consist of interconnected liquid crystal domains of
submicron dimension dispersed in stressed/stretched polymer matrices in the form of
polymer sheets. Liquid crystal domains have a size distribution instead of unidispersion
as confirmed by microscopic observations and SEM characterizations. Based on
microscopic studies, a shaped, close-packed liquid crystal domain model is proposed for
SLCs.
66
Figure 3.10 Model of shaped, close-packed liquid crystal domains: including side views
and top views.
67
CHAPTER 4
Optical Transmission of SLCs
Most liquid crystal/polymer composites scatter light and the field-controlled light
scattering mechanism is used to produce displays,[80] shutters,[81] etc. There are many
factors influencing the light scattering: liquid crystal domain size,[82] domain shape,[42]
domain density,[83] and the liquid crystal and polymer refractive indices.[84],[85] In addition,
light scattering depends on the characterizing wavelength[82],[83] and liquid crystal
ordering[85] inside the domains.
There has not been a generally suitable theory developed for the light scattering
characteristics of all the liquid crystal/polymer composites. Most theories are simplified
to analyze systems of low liquid crystal domain densities. When it comes to a system of
high liquid crystal concentration, multiple scattering is the most import factor in the light
scattering characteristics. It is difficult to make a complete description of light scattering
in multiple scattering liquid crystal/polymer composite systems. Among high LC%
systems, there are two main sources for light scattering: (1) refractive index mismatch
between liquid crystal and polymers; (2) refractive index mismatch between liquid crystal
domains. Drzaic[83,86] pointed out that when liquid crystal concentration is high (greater
than 80%), the light scattering between liquid crystal domains is dominant.
68
LC’s concentrations in SLCs are greater than 80%. Before shear, each liquid
crystal domain is surrounded by and connected to other randomly-oriented liquid crystal
domains. The refractive index mismatch between adjacent domains causes major light
scattering. When shear deformation aligns liquid crystal domains in the same direction,
the light scattering of the film are reduced drastically as the mismatch of effective
refractive index between liquid crystal domains disappears. The light scattering resulting
from refractive index mismatch between liquid crystal and polymer matrix is less
significant.
No Ne Δn TNI (oC) Δε
5CB 1.533 1.724 0.191 35 12.0
E7 1.522 1.746 0.225 61 13.8
E44 1.528 1.790 0.262 100 16.8
RM82 1.532 1.656 0.124 N/A N/A
NOA65 1.524 N/A N/A N/A
Table 4.1 Some physical parameters of the materials used for SLCs.
69
4.1 Shear Effect
The transmittance of a 12-μm-thick E7-SLC sample (E7/NOA65: 86/14) is
presented in Fig. 4.1. The reference used to correct reflection loss was a fully-cured 12-
μm-thick NOA65 film sandwiched between two ITO glasses. With the increase of shear
distance from 10 μm to 150 μm, transmittance of the SLC sample increased gradually.
After the sample was sheared over 100 μm, transmittance level did not change any more.
In the model of shaped, close-packed liquid crystal domain of SLCs, the hexagonal tubes
can be simplified to spheres and tilted hexagonal tubes can be treated as ellipsoids.
Liquid crystal droplets inside SLCs have bipolar configuration as shown by the
micrographs in Fig. 3.2 which is consistent with the observation and simulations of
Crawford et al.[87] When shear deformation is first applied, the bipolar structure inside a
domain becomes stretched and adjacent domains orient to the same direction. As the
shear force increases, the orientation of the liquid crystal domains becomes more uniform;
thus, light scattering is reduced gradually and transmittance becomes higher.
Light scattering decreases as wavelength increases and becomes essentially zero
at near IR range for all SLCs. However, residual light scattering still existed in the short
wavelength of visible region after shear force was applied. For example, a 40-μm-thick
5CB-SLC was characterized (Fig. 4.2). At λ=400 nm, TL=0μm =0% (L is the shear
distance); after 120 μm shear, further shear did not change the transmittance any more,
TL=120μm=72%. The transmittance loss at after-shear state comes from two possible
sources: the refractive mismatch between liquid crystals and polymers and the distorted
70
liquid crystal orientation caused by curvatures inside liquid crystal domains. Plot (c) in
Fig. 4.2 shows that when a strong enough electric field is applied to a SLC the residual
light scattering disappears. Mostly because the mismatch of refractive index between
liquid crystal and polymers and the distorted liquid crystal orientation were eliminated.
71
Figure 4.1 Transmittance of a 12-μm-thick E7-SLC (E7:NOA65=86:14 (weight%);
Tcure=100oC) at various shear distances. A 12-μm-thick pure NOA65 cell was used as the
reference to correct reflection loss.
72
Figure 4.2 Transmittance of a 40-μm-thick 5CB-SLC (5CB/RM82/NOA65: 90/2/8). (a) 0
μm shear; (b) 120 μm shear; (c) 200 V on at the 120 μm shear state. A 12-μm-thick pure
NOA65 cell was used as the reference to correct reflection loss.
73
4.2 Morphology Dependence
For a LC/polymer composite, transparency significantly depends on the liquid
crystal droplet/domain sizes and the polymer network structures. It is no exception for
SLCs. At first, transmittances of samples in series A were studied. They were fabricated
from varying UV intensity and cooling rate. The fabrication conditions are listed in Table
3.1. Their liquid crystal domain sizes varied from 2 to 40 μm. The transmittances were
examined at the two states: before-shear and after-shear. The shear distance, Lshear, for the
after-shear state is at the saturation point, beyond which further shearing will not reduce
light scattering any more. It is found that there is little difference (Fig. 4.3(a)) between
the states of before-shear and after-shear for both samples A1 and A2. This is due to
inferior shear capability: Rshear < 4 (Lmax is less than 40 μm while d is 12 μm) for these
two samples. Rshear is defined in Chapter 3 as Lmax/d, where Lmax is the maximum shear
distance beyond which a SLC cell will break and d is the thickness of the SLC film.
Rshear is so small for A1 and A2 that the domain deformation is not enough to influence the
liquid crystal orientation; thus, scattering between liquid crystal domains does not change.
In contrast, shear is more effective on the samples A3, A4 and A5 as seen in Fig. 4.3(b):
transmittance increases for all three samples. In particular, A5 of the smallest of the liquid
crystal domains has the best shear capability (Rshear ~= 9) and the most significant
increase of transmission at the after-shear state.
74
Figure 4.3 Transmittance of the series A SLCs of different sizes of liquid crystal domains
at the states of before and after shearing: (a) A1 and A2; (b) A3, A4 and A5. The hollow
and solid symbols represent before-shear and after-shear states, respectively.
500 1000 1500 20000
20
40
60
80
100
A2 after-shear A2 before-shear A1 after-shear A1 before-shear
T%
wavelength (nm)
500 1000 1500 2000
0
20
40
60
80
100
A5 after-shear A5 before-shear A4 after-shear A4 before-shear A3 after-shear A3 before-shear
T%
wavelength (nm)
(a)
(b)
75
Secondly, the transmittance spectra of E7-SLCs polymerized at different
temperatures were investigated. The fabrication conditions are listed in Table 3.2. Liquid
crystal domain sizes vary from submicron to ~20 μm and the polymer matrix experiences
a transformation from polymer structure to polymer sheet structure. As cure temperature
increases, transmittance increases in general as shown in Fig. 4.4(a). In addition, as cure
temperatures were higher than 60oC, the TNI of E7, transmittance is significantly higher
then those SLCs cured below 60oC. This is due to the change of polymer matrix structure:
polymer balls exist in larger dimension than polymer sheets; therefore, refractive index
mismatch between liquid crystal domains and polymer matrix is more significant,
scattering more light. Shear deformation improves light transmittance for all the E7-SLC
samples in the Vis-NIR spectra range (Fig. 4.4(b)). In particular, E7-SLCs cured at
temperatures higher than 90oC are free of light scattering in the near infrared region.
In addition, the samples cured at temperatures higher than the TNI of E7 (60oC)
had much better shear capability (Rshear) than other samples cured at lower temperatures.
For example, Rshear for E7-SLC samples cured at temperatures higher than 70oC is greater
than 10. However, Rshear for E7-SLC samples cured at temperatures lower than 60oC is
less than 2. The E7-SLC cured at 60oC broke as long as shear force was applied. There
are two reasons: (1) compared to SLC cured at lower temperatures, SLCs cured at higher
temperatures phase separate at the late stage of polymerization; thus the degree of
conversion is higher and crosslink density of the polymer work is higher too. The
elasticity of the network is higher. Therefore, the maximum shear distance is larger. (2)
the extent of plasticization caused by liquid crystal dissolved inside the polymer matrix is
76
much higher for SLCs cured at higher temperature (> 70oC) due to the better solubility
and deeper quenching compared with SLCs cure at lower temperatures (< 60oC).
77
Figure 4.4 Transmission spectra of E7-SLC samples cured at different temperatures
ranging from 41oC to 100oC: (a) before-shear state; (b) after-shear state.
500 1000 1500 20000
20
40
60
80
100
T%
Wavelength (nm)
100dg 90dg 80dg 70dg 41dg 60dg 50dg
500 1000 1500 20000
20
40
60
80
100
T%
Wavelength (nm)
100dg 90dg 80dg 70dg 50dg 41dg
(a)
(b)
78
4.3 Polarization Dependence
Series B of SLCs were made to investigate the polarization dependence of
transmittance and liquid crystal orderings inside SLCs. The fabrication conditions are
tabulated in Table 4.2. RM82 was added to enhance the strength of polymer network. The
initiator (Irgcure 651) is 0.1 weight percent of the whole mixture. The samples of B series
were used to investigate the influence of composition and curing temperature on
polarization dependence of light transmission properties and particularly calculate liquid
crystal orderings with the help of a dichroic dye, M483. With fixed liquid crystal
concentration, the ratio of RM82 and NOA65 was varied among 5CB-SLCs samples: B1
through B5. Sample B6 and B7, the two E7-SLCs, have different cure temperatures: 100oC
and 70oC.
SLC Sample # B1 B2 B3 B4 B5 B6 B7
Materials 5CB/RM82/NOA65 E7/NOA65
Composition (weight ratio) 90/0/10 90/2/8 90/2/8 90/6/4 90/6/4/dye
(0.15)
86/14 86/14
Cell gap (μm) 12 12 12 12 12 12 12
Tcure( oC) 60 60 60 60 60 100 70
UV intensity (mW/cm2) 40 15 40 40 40 40 40
Quenching 60oC to 20oC 100oC to 20oC 70oC to 20oC
DLC (μm) 1~2 submicron submicron 1~3
Table 4.2 Fabrication conditions of the series B SLC samples for polarization dependence
studies on transmittance.
79
Figure 4.5 Measured difference of transmittance at two polarizations. ΔT= T⊥-T‖. (a)
5CB-SLCs with different compositions: B2(∆); B1(■); B3(○); B4(●). (b) E7-SLCs
polymerized at different temperatures: B6 (■, 100oC); B7 (●, 70oC).
0 20 40 60 80 100 120
0
10
20
30
40
B4
B2 (Weak UV)
ΔT,
%
Shear distance (μm)
B3
B1
0 20 40 60 80 100 120
0
10
20
30
40
B6
ΔT,
%
Shear distance (μm)
B7
(a)
(b)
80
The single rotatable polarizer setup depicted in Fig. 2.3 was used to measure the
polarization dependent transmittance. A NOA65 cell was used as the reference to correct
reflection loss. The wavelength is 632.8 nm. Shear direction was along the horizontal
direction. First, the transmittances at two polarizations, horizontal (∥) and vertical (⊥),
were measured at different shear distances for each SLC cell. Then, the transmittance
difference was calculated as ΔT= T⊥-T‖. The measurement error is about ±5%. The
discrepancy between the transmittance measured at the two polarizations arises from the
refractive index mismatch as discussed in Chapter 1 (Fig. 1.6).
Figure 4.5(a) plotted the transmittance difference for B1, B2, B3 and B4. At zero
shear distance, there is no polarization dependence for all the samples because both
polymer matrices and liquid crystals are randomly aligned. When shear distance increases,
ΔT for B1 and B2 start to increase while ΔT for B3 and B4 are less than ±5%. In addition,
ΔT(B2) is much greater than ΔT(B3), which demonstrates that strong UV cure intensity is
favorable to reduce polarization dependence. It is also found that addition of RM82 gives
rise to less polarization dependence (i.e. ΔT(B3,B4)< ΔT(B1)). Fig. 4.5(b) compares B6 and
B7 which were cured at different temperatures. B6, cured at higher temperature (100oC),
has no polarization dependence while B7, cured at lower temperature (70oC), shows
strong polarization dependence.
Liquid crystal director ordering increases when shear distance increases.
Refractive indices mismatch between liquid crystal domains and polymer matrix
increases along the horizontal direction (i.e. when the polarizer is at the parallel position).
81
On the other hand, refractive indices mismatch between LC domains and polymer matrix
along the vertical direction does not change much. If the dimensions of LC domains and
polymer sheets are large enough to be comparable to a specific wavelength, T‖ decreases
due to the mismatch mentioned above and T⊥ stays unchanged. Thus, ΔT (T⊥-T‖ )
increases; i.e., polarization dependence increases. UV intensity to cure B2 was only 15
mW/cm2, less than half of that of B3 ( 40 mW/cm2). Both liquid crystal domain size and
polymer film thickness of B2 are larger than that of B3, causing more significant
polarization dependence. Similarly, B7 has large LC domains and thicker polymer sheets
than B6 as shown in Chapter 3; therefore, B7 shows strong polarization dependence.
Inside a SLC system with RM82, RM82 is possibly aligned along the shear direction
upon shearing. ne of RM82 is 1.656, closer to ne of 5CB (1.72) compared with isotropic
polymer NOA65 (n=1.524); no of RM82 is 1.532, close to no of 5CB (1.533). Therefore,
when RM82 is added, the refractive index mismatch between liquid crystal and polymer
is reduced, which helps to reduce the polarization dependence (e.g. ΔT(B3,B4)< ΔT(B1)).
It is worthy to note that optimized SLCs have no polarization dependence in
contrast to stretched or sheared PDLCs of which light scattering are strongly polarization
dependent. In addition, the polarization dependence is wavelength dependent as well, For
example, B1 shows polarization dependence at 632.8 nm but not at the near infrared 1550
nm, which again, is related to the structure of the sample.
82
4.4 Liquid Crystal Director Ordering
Approximately 0.15 wt% of dichroic dye, M-483, was mixed into B4 solution to
fabricate B5. The dye orients its molecules along the directors of surrounding liquid
crystals so that its ordering can be taken as liquid crystals’ director ordering.[88] M483’s
absorption spectrum is plotted in Fig. 4.6.[89] The two polarization transmittance
measurements of samples B4 and B5 are plotted in Fig. 4.7. B4 was used as the reference
to calculate the absorbance of M-483 of sample B5 according to equation (4.1). There is
no polarization dependence for B4; therefore, the difference of light transmittance is only
attributed to the dichroism of M-483 inside the sample B5.
Then, according to Eqs. 4.2 and 4.3, the dichroic ratio and the liquid crystal
director ordering S were calculated.
, 10 , 10 , ,log ( ) log ( )dye dye SLC dye SLCA T I I+⊥ ⊥ ⊥ ⊥= − = − (4.1)
10 10log ( ) log ( )dye dye SLC dye SLC SLC dye SLCD A A T T T T+ +⊥ ⊥ ⊥= = (4.2)
12
DSD
−=
+ (4.3)
Figure 4.8 demonstrated liquid crystal director orderings inside B5 increases
gradually from essentially zero to about 0.5 with the increase of shear distance, which is
the result of liquid crystal alignment induced by shearing. It is noticed that the liquid
crystal director ordering is saturated after about 80 μm shear distance for B5, Lshear/d ~=7.
83
Figure 4.6 The absorption spectrum of anthraquinone dichroic dye M483. (From Chen et
al. Mol. Cryst. Liq. Cryst. 433, 129-141 (2005))
84
Figure 4.7 Transmittance of B4 and B5 with the incident light’s polarization either parallel
or perpendicular to the shear direction. λ=632.8 nm.
85
0 20 40 60 80 100
0.0
0.2
0.4
0.6Li
quid
Cry
stal
Dire
ctor
Ord
erin
g
Shear distance (μm)
Figure 4.8 Calculated liquid crystal director orderings in a SLC (B5).
86
4.5 Conclusions
Conventional LC/polymer composites operate based on field controlled light
scattering. A normal PDLC scatters light in the field OFF state and becomes transparent
in the field ON state, depending on the refractive index matching between liquid crystal
droplets and polymer matrix (Fig. 1.2). On the contrary, a normal PNLC transmits light in
the field OFF state and scattering light in the field ON state depending on the refractive
index match between adjacent liquid crystal domains.[39] In contrast, SLCs combines the
light transmitting properties of both PDLC and PNLC: SLCs are transparent in both field
on and field off states. Before shear deformation is applied, SLCs behave as a PDLC.
However, after shear, most liquid crystals orient along the shear direction, eliminating the
scattering between liquid crystal domains; SLCs act as a PNLC. When field is applied,
the polymer matrix in SLCs is flexible enough to allow the liquid crystals to align along
the field without forming micro-domains existing in PNLC with field on; SLCs behave as
PDLC again. SLCs are highly transparent in visible-NIR wavelength range at both the
field on and off states. In addition, SLCs differ from the conventional mechanically
deformed liquid crystal/polymer composites in light polarizing abilities. When stretched,
a PDLC becomes a polarizer which transmits light with polarization perpendicular to the
stretching direction and scatters light with polarization parallel. In contrast, SLCs do not
scatter with polarization anisotropy. Rather, light of any both polarizations is transmitted.
Shear deformation helps on the alignment of liquid crystal domains and improves light
transmittance. The transparency of SLCs strongly depends on the morphologies which
derives from different fabrication conditions. To reduce residual light scattering, small
87
liquid crystal domains and thin polymer sheets are favorable. Liquid crystal director
ordering in SLCs is also characterized: ~0.5.
88
CHAPTER 5
Electro-optical Performance of SLCs
SLCs decouple the cell thickenss and speeds so that they can modulate extra large
phase shift at fast speeds. This characteristic is very important in many phase modulation
applications, such as liquid crystal based optical phased arrays. The electro-optical
response of LC/polymer composites has been investigated extensively based on the
variation of materials and composition,[30],[90],[91],[66] droplet shape,[85] and network
morphologies.[44],[61] In this chapter, the factors influencing SLCs such as shear
deformation and network morphology are discussed. In addition, the electro-optical
performance of SLCs is studied and compared with calculations based on the previously
proposed model for sheared PDLC.[45]
5.1 Definition of Switching Voltage and Response Time
For phase modulation devices, switching voltage is optical path delay (OPD)
relevant so that it is defined as a voltage level for switching a specific OPD. At first, the
calculation of OPD based on transmittance-voltage curve (T-V curve) obtained from
crossed polarizers setup is demonstrated.
89
5.1.1 Calculation of Optical Path Delay
A continuous ramp of voltages was applied to a 40-μm-thick SLC cell to measure
the switching fields using the crossed polarizer setup shown in Fig. 2.4. The
transmittance intensity, I, in this setup is calculated as follows:
2max sin ndI I π
λΔ⎛ ⎞= ⋅ ⎜ ⎟
⎝ ⎠ (5.1)
Imax represents the maximum intensity on the transmittance-voltage curve (T-V curve). λ
is the characterization wavelength. The maximum and minimum intensities are obtained
when Δnd/λ equals to k/2 and (k+1)/2 (k is an odd integer), respectively. The optical path
delay (OPD, i.e. Δnd) between each adjacent maximum and minimum is λ/2.
Figure 5.1 demonstrated the normalized T-V curve of the 40-μm-thick SLC cell.
Based on Eq. 5.1, OPD is derived as follows:
max
sin IOPD nd m aI
λλπ
⎛ ⎞= Δ = ± ⋅ ⎜ ⎟
⎝ ⎠ 0,1,2m = ⋅⋅ ⋅ (5.2)
To determine the exact formula for each point on the T-V curve, the T-V curve is divided
into five branches: OA, AB, BC, CD, and DE. On the OA branch, most liquid crystals
were oriented along the electric field direction at point O, thus, OPDO ~= 0 (neff~=no).
Point A is the first maximum next to the point O, therefore, OPDA=λ/2. Thus, at any
point on OA branch, OPDOA=max
sin IaI
λπ
⎛ ⎞⎜ ⎟⎝ ⎠
, which is a value between 0 and λ/2. On
AB branch, the value of OPD is from λ/2 to λ, and calculated as
90
max
sinABIOPD a
Iλλπ
⎛ ⎞= − ⋅ ⎜ ⎟
⎝ ⎠. Similarly, the calculation formula of OPD for the points
on branches BC, CD, and DE are derived and listed in Table 5.1. Therefore, this 40-μm-
thick SLC had a total OPD approximately two and a half waves. The calculated results
are plotted in Fig. 5.2.
91
0 20 40 60 80 100 120 1400.0
0.2
0.4
0.6
0.8
1.0
(IMin)
Nor
mal
ized
Inte
nsity
Voltage (V)
A
B
C
D
E
(IMax)
Figure 5.1 Normalized transmittance-voltage curve (T-V curve) of a 40-μm-thick SLC
cell (5CB/NOA65: 90/10) measured between crossed polarizers. The wavelength is 1550
nm.
92
Branch of T-V curve Optical Path Delay Formula
OA
max
sinOAIOPD a
Iλπ
⎛ ⎞= ⋅ ⎜ ⎟
⎝ ⎠
AB
max
sinABIOPD a
Iλλπ
⎛ ⎞= − ⋅ ⎜ ⎟
⎝ ⎠
BC
max
sinBCIOPD a
Iλλπ
⎛ ⎞= + ⋅ ⎜ ⎟
⎝ ⎠
CD
max
2 sinCDIOPD a
Iλλπ
⎛ ⎞= − ⋅ ⎜ ⎟
⎝ ⎠
DE
max
2 sinCDIOPD a
Iλλπ
⎛ ⎞= + ⋅ ⎜ ⎟
⎝ ⎠
Table 5.1 Formulas for the optical path delay calculation from the T-V curve (Fig. 5.1).
93
0 40 80 120 160
0
1
2
3
4O
PD (μ
m)
Applied Voltage (V)
10%
Vs
Figure 5.2 Calculated optical path delay for the 40-μm-thick 5CB-SLC according to
formulas listed in Table 5.1.
94
In this dissertation, switching voltage is defined for switching 90% of the total
OPD that a SLC cell can provide unless specified. When the voltage increases to a value
at which OPD is at its 10% value, this voltage is the switching voltage (Vs), shown in Fig.
5.2. The total OPD of this cell is about 3.5 μm. Then, switching voltage is 71 V for this
SLC cell. The switching field was calculated as Es = Vs /d, where d is the thickness of a
SLC cell.
5.1.2 Definition of Response Time
Conventional liquid crystal displays operate in the light amplitude modulation
mode. The response time is defined as τ=τoff+τon, where τoff and τon are calculated as the
time intervals between two transmittance levels (T10 and T90) in a T-V curve (turn-off and
turn-on processes) as shown in Fig. 5.3(a). In contrast, for phase modulations, the
response time is defined as the time required switching a specific amount of OPD.
Corresponding to the definition of switching voltage, the response time of SLCs is
defined by the switching time for the 90% of total OPD that a cell can produce unless
specifically defined. The voltage applied for the τon and τoff is the voltage for switching
the total OPD. For instance, Figure 5.3(b) illustrates these definitions. The voltage used
was 120 V.
95
Figure 5.3 Definitions of response time for amplitude modulation and phase modulation
of SLCs. (a) τon and τoff for SLC of fast display applications; τon and τoff are calculated
between the 10% and 90% transmittance levels. (b) τon and τoff for SLCs in the phase
modulation mode. τon is defined as the time which OPD drops to 10%; τoff is defined that
OPD increases to 90%. τoff of this 40-μm-thick 5CB-SLC is 3.0 ms and τon is 0.2 ms.
0 1 2 3 4 5
0
1
2
3
4
0%
10%
90%
τon
OP
D (μ
m)
Time (ms)
τoff
100%
(a)
(b)
96
5.2 Experimental Investigation of Electro-optical Performance
5.2.1 Shear distance
First, experimental T-V curves of a 5-μm-thick 5CB-SLC cell (Fig. 5.4) are used
to investigate the influence of shear distance on Vs. The experimental setup was the
crossed polarizers setup (Fig. 2.4). In addition, a compensator was inserted between
crossed polarizers. The compensator was used to compensate the OPD of the SLC cell at
the 0 V. Thus, at any shear distance, the T-V curve will start from a minimum, which
makes the comparison of Vs easy. To make the comparison straightforward, Vs for half
wave retardation is used. As discussed early, in a T-V curve, phase shift between a
minimum and maximum is exactly half wave. Since at 0 V the transmittance was always
compensated to zero (minimum), the voltage values corresponding to the first maxima on
the T-V curves are exactly the Vs for half wave OPD (VOPD=λ/2). Therefore, comparison
is made between these VOPD=λ/2 s. Figure 5.4 demonstrates that VOPD=λ/2 increases in
shear distance, from 5.6 V at 10 μm shear to 9.2 V at 60 μm shear.
97
0 2 4 6 8 10
0.0
0.2
0.4
0.6
0.8
1.0N
orm
aliz
ed In
tens
ity
Voltage (V)
10 μm 20 μm 40 μm 60 μm
VOPD=λ/2
Figure 5.4 T-V curves of a 5-μm-thick 5CB-SLC (5CB/NOA65: 90/10) at different shear
distances: 10, 20, 40, and 60 μm, respectively.
98
With the same setup, the response times of half wave OPD for the 5-μm-thick
5CB-SLC cell were measured. Corresponding VOPD=λ/2 at different shear distances were
applied. T10 and T90 of the definitions for display applications are used to determine turn-
off time and turn-on time, respectively. As shown by Fig. 5.5 and 5.6, both the turn-off
time and turn-on time curves shift to the left as the shear distance increases, implying
switching times reduce in shear distances. τoff decreases from 6.5 ms at 10 μm shear to
1.5 ms at 60 μm shear. τon decreases from 4.5 ms at 10 μm shear to 0.8 ms at 60 μm shear.
99
Figure 5.5 Turn-off time of the 5-μm-thick SLC at different shear distances (10 to 60 μm).
τoff is labeled at the T10.
100
Figure 5.6 The turn-on time (τon) of the 5-μm-thick SLC at different shear distances (10
μm, 20 μm, 40 μm and 60 μm). T90 is used to label the τon.
101
In addition to the effects on switching voltage and response times, shear increases
OPD for a SLC cell. Upon shearing, polymer matrix is stretched along the shear direction
and the submicron liquid crystal domains adopt elliptical shape. Liquid crystals inside
domains become more and more oriented as demonstrated in Chapter 4: liquid crystal
director ordering increases in shear distance. Figure 5.7 demonstrates that OPD of a 12-
μm-thick E7-SLC cured at 100oC increases in shear distance.
102
0 50 100 150
0.0
0.4
0.8
1.2O
PD
(μm
)
Shear Distance (μm)
Figure 5.7 Shear distance dependence of optical path delay for a 12-μm-thick E7-SLC
cured at 100oC.
103
5.2.2 Liquid Crystal Domain Size
The series A, A1, A2, A3, and A4, of which liquid domain size ranges from 2 μm to
40 μm, were characterized to investigate the influence of domain size on the electro-
optical performance (Fabrication conditions of A series are listed in Table 3.1 in Chapter
3). The setup was the crossed polarizer setup (Fig. 2.4). SLC samples were placed
between two crossed polarizers. The shear direction is aligned at 45o angle to each
polarizer. The laser wavelength was 632.8 nm. Figure 5.8(a) shows the measured Es. The
diameter of liquid crystal domains of sample A1 was approximately 30~40 μm and it
broke when shear distance was 40 μm. The required switching field remained unchanged,
~1.5 V/μm. In contrast, Es was increasing in shear distance for the rest of the series A
samples. At the same shear distance, Es is larger for the SLCs with smaller domains.
When the shear distance increases, Es grows at a higher rate for the SLCs with smaller
domains. All observations agree with the calculated trends based on the proposed SLC
model.
τoffs for all the samples at different shear distances are shown in Fig. 5.8(b).
Relaxation time decreases when shear distance increases except for A1. Comparing these
four samples, samples of the smallest liquid crystal domain, has the shortest τoff at any
shear distance.
104
Figure 5.8 Electro-optical measurements for samples A1, A2, A3, and A4 at different shear
distances. (a) Shear distance dependence of switching field; (b) shear distance
dependence of relaxation time.
105
5.3 Electro-optical Responses Calculation
B-G Wu et al.[45] built a model for sheared PDLCs and derived formulas for the
electro-optical performance based on the balance of elastic torque and electric field
torque. They demonstrated that aspect ratio, droplet size, and intrinsic properties of liquid
crystal and polymer are important factors affecting the electro-optical performance.
Based on their model with proper simplification and approximation, prediction of SLCs’
performance is achieved. As shown by the model in Chapter 3 SLCs can be treated as
close-packed, stacked hexagonal liquid crystal domains dispersed inside a stressed
polymer matrix. Furthermore, the hexagonal tubes are simplified into spherical droplets
in the before-shear state and ellipsoids in the after-shear state (Fig. 5.9). In addition, the
interaction between adjacent droplets is neglected. Then switching electrical fields and
response times of a SLC system at different shear distances are derived.
As depicted in Fig. 5.9, when a spherical liquid crystal droplet is sheared it
deforms to an ellipsoid. Geometrically the semi-major axis can be obtained as
2 21( ) 1 ( ) 1La R R L
d= ⋅ + = ⋅ + where
1L L d= . It is assumed that the volume of liquid crystal
droplets does not change during a shear process so that 3abc R= . From the microscopic
study, it is observed that c R= (the width of droplet does not change as shown in Fig. 3.6
(c), (d)). Thus, b is obtained as 2 21( ) 1b R a R L= = + . Then the aspect ratio (l) is as follows:
21( ) 1al L
b= = + . The formulas based on B-G Wu et al.’s model are derived as follows:
(details are included in Appendix B)
Relaxation time (τoff):
106
2 2
2 2( 1) ( 1)offa R l
K l K lγ γτ = =
− − (5.3)
where γ is rotational viscosity of the liquid crystal, a is the long axis of a liquid crystal
droplet, K is the bend elastic constant K33 of the liquid crystal.
Rise time (τon):
( ) ( ) ( )22 2
33 332 22 2
1 1 4 4
on
K l K lE E
R l R l l
γτ
ε ε
=⎛ ⎞ ⎛ ⎞− − ⎛ ⎞⎜ ⎟ ⎜ ⎟+ Δ + ⋅ Δ ⋅ −⎜ ⎟⎜ ⎟ ⎜ ⎟ ⎝ ⎠⎝ ⎠ ⎝ ⎠
(5.4)
where Δε is the dielectric anisotropy of a liquid crystal, E is the strength of an applied
electric field.
Switching field (Eswitch):
( ) ( )1 1
2 22 233 332 2
1 1
1 11 12 23 3
switchswitch
K l K lVEd a Rl
σ σσ ε σ ε
⎛ ⎞ ⎛ ⎞− −⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟= = + = +⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟Δ Δ⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠
(5.5)
where σ1 and σ2 are the conductivities of the polymer matrix and the liquid crystal,
respectively.
During the derivation of all the formulas, the liquid crystal directors are
considered to be fully oriented by the electric field during switching.
107
D
L
b
acD
L
b
acD
RD
RAfter shearing
D
L
b
acD
L
b
acD
RD
RAfter shearingAfter shearing
Figure 5.9 Deformation of liquid crystal droplets during shearing. L is shear distance; D
is cell thickness; R is the radius of original spherical droplet; a, b, and c represent semi-
major axis, semi-minor axis at the direction along shear direction, and semi-minor axis at
the direction perpendicular to shear direction, respectively.
γ (kg/ms) σ2/σ1 K33 (10-11 N) Δε R1 (μm)
0.056 20 0.61 12 0.2, 0.5, 1, 2
Table 5.2 Parameters used in the electro-optical response calculations.
108
Figure 5.10 Calculation of the switching fields and response times for a 40-μm-thick SLC.
Liquid crystal domain size and shear distance are varied. Squares, circles, triangles and
reversed triangles represent the calculated data for R=0.2, 0.5, 1, and 2 μm, respectively.
(a) Switching field Es; (b) relaxation time τoff; (c) turn-on time τon.
109
According to the formulas (Eqs. 5.3, 5.4, 5.5) and the parameter listed in Table
5.2, the electro-optical responses are calculated and the results are plotted in Fig. 5.10.
The switching field increases with the increase of shear distances, and both the relaxation
time and the rise time decrease with the increase of the shear distance. As such, this
model provides a tool to predict electro-optic performance of SLCs. It is observed that
the turn-on time, τon, is dependent on the Es and its variations are insignificantly small
compared with the variations of the turn-off time, τoff: 0~4 ms compared to 0~160 ms.
Therefore, in this dissertation only τoff is used to evaluate the response time unless SLCs
are operated in fast display mode which require low voltage operation (less than 10 V).
Electro-optical responses of a 22-μm-thick 5CB-SLC were measured and the
measurements were compared with calculations in Fig. 5.11. It is rather consistent
between each other. It should be noted that the measured switching voltages were
voltages to switch over 98% of OPD the cell can provide. It is consistent with the
assumption in the calculation: the liquid crystal directors are considered to be fully
oriented by the electric field during switching. The liquid crystal domain size of this 22-
μm-thick 5CB-SLC is estimated to be between 0.2 μm and 0.5 μm. In reality, the size is
likely a distribution between 0.2 μm and 0.5 μm instead of unidispersed one, which
agrees with the SEM and fluorescence confocal microscopic observations.
110
Figure 5.11 Comparison between measurement and calculations for a 22-μm-thick 5CB-
SLC. (a) Switching field; (b) turn-on time; (c) turn-off time.
0 20 40 60 800
5
10
15
E switc
h (V/μ
m)
Shear distance (μm)
R= 0.2 μm R= 0.5 μm Eswitch-measured
0 20 40 60 800
1
2
3
τ on (m
s)
Shear distance (μm)
0 40 80 120
0
10
20
30
τ off (m
s)
Shear distance (μm)
R=0.2 μm R=0.5 μm toff-measured
(a)
(b)
(c)
111
5.4 Reduced Hysteresis
For a liquid crystal cell to be hysteresis-free, the liquid crystal molecules have to
be strongly anchored by the alignment layers which precisely control the reorientation of
the liquid crystal molecules during the application of electric fields. However, hysteresis
is common in liquid crystal/polymer composite systems.[92],[93],[94],[95] Hysteresis is
measured by applying voltage ramp for a liquid crystal/polymer film up and down and
comparing the optical response at each voltage. For example, a typical hysteresis
characteristic of a PDLC film is demonstrated in a T-V curve (Fig. 5.12). At a specific
optical transmission level, the difference in voltage between the curves ramping up and
down is calculated as the hysteresis, shown as ΔV. For instance, in Fig. 5.12, the
hysteresis is approximately 8 V (defined at 50% transmittance level). In this dissertation,
the hysteresis is defined as the maximum voltage difference of OPD-V curves measured
for the two ramping processes. Generally speaking, SLCs have essentially no hysteresis
or much smaller hysteresis than traditional liquid crystal/polymer composites. Figure 5.13
demonstrates the OPD-V curve of a 12-μm-thick E7-SLC at 150 μm shear distances. The
hysteresis at 150 μm is less than 0.5 V. The OPD-V curve for a 5-μm-thick 5CB-SLC at
the 60 μm shear state is plotted in Fig. 5.14. It is seen that for this SLC cell hysteresis is
essentially zero.
112
0 20 40 60 80
0
1
2
3In
tens
ity (a
.u.)
Voltage (V)
ΔV
Figure 5.12 Measured T-V curve showing hysteresis for a 16-μm-thick PDLC cell
(E7/NOA65: 50/50). Hollow triangles represent the ramp from 0 V to 80 V; solid reverse
triangles represent the ramp from 80 V to 0 V. At one transmittance level, the difference
(ΔV) characterizes the hysteresis. Generally, the ΔV at 50% transmittance level is used.
113
0 10 20 30 40 50 60
0.0
0.2
0.4
0.6
0.8
1.0
1.2 150 μm shear, decreasing voltage 150 μm shear, increasing voltage
OPD
(μm
)
Voltage (V)
Figure 5.13 Hysteresis of a 12-μm-thick E7-SLC cured at 100oC. Shear distance was 150
μm.
114
0 2 4 6 8 100.0
0.2
0.4
0.6
OPD
(μm
)
Voltage (V)
0V to 10V 10V to 0V
Figure 5.14 OPD-V curves showing no hysteresis for a 5-μm-thick SLC (5CB/NOA65:
90/10) when Lshear = 60 μm.
115
In SLCs, hysteresis decreases with shear distance. Hysteresis of samples B6 and
B7 were measured and compared (Fig. 5.15). By comparison, B6 is a 12-μm-thick E7-
SLC cell fabricated at 100oC while B7 is a 12-μm-thick E7-SLC cell fabricated at 70oC,
which actually behaves as a PDLC as shown by the transmittance polarization
dependence experiment. Upon shearing, hysteresis of both samples reduces. B6 has
smaller hysteresis than B7, and the ΔVB6 at 100 μm shear state is reduced to less than 0.3
V.
So far it is not completely understood on the origin of hysteresis and the
mechanism of reducing it in SLC systems. However, it is apparently structure dependent.
The possible influencing factors include defect structures of liquid crystal director
configuration at the connection regions for interconnected domains, surface anchoring,
and shape of the liquid crystal domains. Drzaic divided the switching process of PDLCs
to a two-step process.[94] Basically, the nematic near the wall of the droplet cavity is
constrained to reorient more slowly than the molecules in the center of the droplet. In Fig.
5.16, the process (1) and (2) are the switching on progress while the process (3) and (4)
are the switching off progress. It is assumed that during the on and off processes the
liquid crystal molecules experience different director configurations, resulting in different
transmittance level/phase shift, i.e., hysteresis. Hikmet et al.[79] fabricated liquid crystal
gels which exhibited essentially no hysteresis. The polymer network consisted of an
anisotropic matrix which was assumed to exist in continuous sheet structure. Hikmet et
al. proposed that the polymer sheets separated a liquid crystal gel into multiple layers of
thin cells with strong uniaxial anchoring at the two surfaces parallel to the substrates of
116
the liquid crystal gel. SLCs have small hysteresis which decreases to zero essentially with
the increase shear distance. It can be assumed that as SLCs’ polymer films are stretched
the aspect ratio of the ellipsoidal liquid crystal domains becomes greater, which to some
extent reduces the proportion of the liquid crystal molecules confined in the round
curvatures. The liquid crystal domains more and more resemble pure nematic liquid
crystal cells (illustrated in Fig. 5.17). The polymer sheets inside SLCs act as the
alignment layers in regular nematic liquid crystal cells.
117
0 20 40 60 80 100
0
1
2
3
4Δ
V hyst
eres
is (V
)
Lshear (μm)
B7
B6
Figure 5.15 Hysteresis measurement of two E7-SLC samples B6 and B7 at the different
shear distances.
118
Figure 5.16 Drzaic’s two-step reorientation mechanism. When an electric field is applied,
liquid crystal molecules in the middle first orient along the field (a to b), then the
molecules at closer to the surfaces (b to d). On the other hand, when the field is removed,
the center molecules again quickly relax (d to c) followed by the relaxation of the surface
area. From Paul S Drzaic, Liq. Cryst. 3 (11), 1543-1559 (1988)
119
Figure 5.17 Mechanism on reduction of hysteresis for SLC system. (a) slightly deformed
LC droplet; (b) greatly sheared LC domain; (c) a normal planar LC cell.
120
5.5 Linearity between OPD and Applied Voltage
Another advantage of SLC materials is that they have wide linear range between
OPD and applied voltage, which has significantly simplified the electronics design. The
linear response of SLC materials is defined in Fig. 5.18. In the OPD~V curve, if one
significant part (AB in Fig. 5.18) of the curve can be fitted into a linear function, that part
is defined as the linear response part of the material.
Normally, complicated drivers are utilized to drive liquid crystal devices. For
example, to generate a smooth phase ramp every single pixel on an optical phase array
device has to be driven individually and complicated calculation algorithm has to be used
to control precisely the OPD level. However, if a liquid crystal material has the linear
response between OPD and voltage, simply, a series of resistors can be used to control
the voltage levels for all the pixels by only adjusting the voltage levels on the two ends of
the resistor series. Figure 5.19 demonstrates the concept of simplified driving scheme. A
demo of SLC tip-tilt corrector based on such a driving scheme has been built (Chapter 7).
121
0 40 80 120 160
0
1
2
3
4
46V
Linear fit: Y = 4.47-0.08X
OPD
(μm
)
Applied Voltage (V)
13VA
B
Figure 5.18 Definition of linear response between OPD and voltage in SLC systems. The
linear region is between A and B: fit function is Y=4.47-0.08X. The change of OPD in
AB region is ~2.5 μm.
122
Figure 5.19 Illustration of a driving system using a series of resistors. The voltages
applied on electrodes E1 through E8 are adjusted linearly by simply adjust the voltage at
one end, V0'. If a liquid crystal material has linear response between OPD and voltage,
different linear phase profiles are obtained when V0'=VL,VM, and VS. VL,VM, and VS
represent large, medium, and small voltages respectively.
R R R R R R R
V0 V0'
E1 E2 E3 E4 E5 E6 E7 E8
Phase ProfileVL
VM
VS
123
As shown in Fig. 5.18, a 40-μm-thick 5CB-SLC has OPD of 3.5 μm in which 2.5
μm is in the linear range pointed by the arrows. The linearity percentage is
2.5/3.5=71.4%. As in the proposed model, SLCs are composed of multiple stacks of
submicron liquid crystal domains dispersed in a stretched polymer matrix. They can be
treated as layered structure of which layer thickness is in the submicron range (Fig. 5.20).
Hikmet et al.[79] obtained linear response of liquid crystal birefringence against applied
voltage for the type II gels (Fig. 3.9) and proposed that a liquid crystal/mesogenic-
polymer composite of sheet-like polymer matrix could be modeled as multilayer structure
with a distribution of layer thickness. Considering the ensamble of liquid crystal layers
with different thickness, at a specific voltage, the orientations of the liquid crytals are
different inside each layer: different OPDs are switched for different layers. The OPD~V
curve is normally not linear for one liquid crystal layer or multiple layers with same
thickness; however, combining liquid crystal layers of different thickness, linear response
can be obtained. Close match between the measurement and Hikmet et al.’s calculation
was achieved (Figure 5.21).
SEM micrographs of SLCs (Fig. 3.4) imply that in SLCs liquid crystal domains
exist with a size distribution instead of unidisperse size. Fluorescence confocal
micrographs (Fig. 3.8) also illustrated the various sizes of liquid crystal domains at
different layers inside SLCs. Therefore, SLCs’ multilayer structure with layer thickness
distribution explains the large linear regime between SLCs’ OPD and applied voltage.
124
Figure 5.20 Simplified illustration of multi-layer structures of SLCs. It is assumed that
the layer thickness of each layer is slightly varied.
d1
d2
di
dn
125
Figure 5.21 Birefringence-voltage plot of a 6-μm-thick liquid crystal/polymer gel.
Squares and crosses indicate experimental data for polymer volume fractions of 0.1 and
0.05, respectively. The dotted line is the calculated result for a cell containing 67% of 0.5
μm thick LC layers. Solid lines are calculated from distributions of layer thicknesses
chosen to obtain reasonable fits to the experimental data. From R. A. M. Hikmet and H.
M. J. Boots, Phys. Rev. E 51 (6), 5824-5831 (1995).
126
5.6 Extra-large OPD Achieved by Thick SLCs
A series of thick SLC cells have been fabricated according to the general
fabrication procedure described in the Chapter 2. However, longer cure time is applied to
guarantee complete polymerization, for example, the cure time is increased up to 2 hours
for the 820-μm-thick SLC. In addition, double side UV irradiation was applied. Because
of bulk alignment nature of shear deformation, for all these thick cells, liquid crystals are
still aligned by shear deformation and OPD as large as 55 μm is produced by the 820-
μm-thick SLC (Fig. 5.22). The relaxation time for whole 55 μm is less than 14 ms (Fig.
5.23)
127
0 200 400 600 800
0
20
40
60O
PD (μ
m)
Voltage (V)
Figure 5.22 OPD versus applied voltage for an 820-μm-thick SLC (5CB/NOA65: 90/10)
at 650 μm shear.
128
0 5 10 15
0
20
40
60O
PD (μ
m)
Time (ms)
Figure 5.23 OPD as a function of time of an 820-μm-thick SLC (5CB/NOA65: 90/10) at
650 μm shear after removal of 800 V.
129
Figure 5.24 demonstrates that with the increase of cell thickness OPD increases
approximately in a linear function for 5CB-SLCs. The efficiency of producing OPD for a
SLC is calculated according to formula:
( ) ( %)Measurement Theory Measurement LC Measurement LCOPD OPD OPD n d OPD n d cη = = Δ ⋅ = Δ ⋅ ⋅ (5.6)
Where MeasurementOPD is the measured maximum OPD , nΔ is the birefringence of the
liquid crystal, d is the cell thickness, and the C% is the concentration of the liquid crystal.
For example, assuming liquid crystals switch from θ=90o to θ=0o (θ is the angle between
liquid crystal director and cell normal, i.e. the light incident direction) for the 820-μm-
thick 5CB-SLC, η =55/(0.18*820*90%)=41.4%; for the 40-μm-thick SLC (Fig. 5.2),
η =3.5/(0.18*40*90%)=54.0%. The average efficiency is approximately 50%. However,
inside SLCs, liquid crystal director is not completely perpendicular to the cell normal.
The liquid crystal director depends on the ratio of shear distance/film thickness which
ranges from 1 to 10; thus, the angle between liquid crystal director and cell normal is
from 45o to ~90o. Therefore, in fact, nΔ is 2 2 2 2cos sineff o e o e o on n n n n n nθ θ− = + − ( θ =
45o to ~90o ) which is smaller than e on n− . The efficiency is reduced. The efficiency is
also reduced by non-switchable liquid crystals: liquid crystals dissolved in the polymer
matrix and liquid crystals at the interconnected regions of liquid crystal domains. As
discussed in Chapter 3, up to 30% liquid crystals can be dissolved in NOA65 polymer
matrix for a PDLC system (LC: polymer=1:1) at room temperature. Since SLCs are
fabricated at high temperatures, 30-40 degrees higher than TNI, liquid crystals are
expected to be more easily dissolved in NOA65 polymer matrix. In addition, quenching
130
used in the second cure step inhibits liquid crystals separate out from the polymer matrix
as well. When the amount of switching liquid crystals is decreased, the total OPD is
reduced correspondingly. Figure 5.25 shows the maximum OPD of a 12-μm-thick E7-
SLC decreases in cure temperatures, which is consistent with the assumption.
5.7 Conclusions
SLCs decouple cell thickness and switching speed. SLCs can produce
exceptionally large optical path delay which can be switched in the time scale of
milliseconds. For example, 55 μm OPD of an 820-μm-thick 5CB-SLC can be switched in
less than 14 ms. To obtain 55 μm OPD, a pure 5CB cell has to be ~300 μm thick and the
turn-off time would be a couple of seconds, thousands time slower than the SLC cell.
SLCs have essentially no hysteresis, comparable to regular nematic liquid crystal cells.
They also have a unique electro-optical property: linear response between OPD and
voltage, which can significantly simplify device electronic designs. Therefore, SLCs are
ideal materials for fast, large phase modulation devices. The applications of SLCs are
discussed in the following chapters.
131
0 100 200 300 400 500 600 700 800 9000
10
20
30
40
50
60M
axim
um O
PD (μ
m)
Cell thickness, (μm)
Figure 5.24 Measured maximum OPD of SLC cells of different cell gaps (from 22 μm to
820 μm)
132
80 90 100 1100.8
0.9
1.0
1.1
1.2
1.3O
PD (μ
m)
Cure Temperature (oC)
Figure 5.25 Measured maximum OPD for 12-μm-thick E7-SLCs cured at different
temperatures.
133
CHAPTER 6
Stressed Liquid Crystal Based Optical Phased Arrays for Mid-wave Infrared
(MWIR) Beam-steering Application
6.1 Introduction
Liquid crystal based non-mechanical beam steering devices have been attractive
for many years because liquid crystal devices feature no moving parts, and can achieve
precision steering with full beam agility, compactness, and low power
consumption.[4,96],[97],[98] It is well known that if a prism is inserted into an optical setup
it will introduce an optical path delay which is greater on one side of an aperture than the
other. Due to the difference in the optical path delay, the wavefront passing the prism will
tilt an angle from the original travel direction, thus the optical beam is steered at that
angle. Liquid crystals can behave as prisms with appropriate setup. There are two major
methods of incorporating liquid crystals into beam-steering devices: liquid crystal digital
beam deflector (refraction-based) and liquid crystal tunable blazed phase grating
(diffraction-based).[99]
A digital light deflector (DLD) is generally composed of two optical elements, a
passive birefringent deflector which deflects incident light of two perpendicular linear
polarization orientations by different angles, and an optical switch which selects the
polarization state to be passed on to the deflector. Figure 6.1 shows an example of the
digital beam deflector utilizing liquid crystals. A liquid crystal wedge acts as the
134
birefringent deflector while the twisted nematic (TN) liquid crystal cell functions as the
polarization switch. When the incident light passes the switch and is polarized parallel to
the optic axis of the liquid crystals inside the wedge, it will be steered away; if the light’s
polarization is orthogonal to the optic axis of the liquid crystals inside the wedge, it will
keep its path without being steered away. Thus, the light can travel only in two directions.
Many deflectors can be cascaded to increase the steering angle and to steer to multiple
angles. The disadvantages of refraction-based beam steering are fixed and small steering
angles, and lack of continuous steering.
To achieve continuous beam steering, diffraction-based devices such as tunable
blazed phase gratings have to be used. Liquid crystal based optical phased arrays (OPA)[4]
are one of the most popular blazed gratings. These optical phased arrays are comprised of
liquid crystal materials sandwiched between one patterned indium-tin-oxide (ITO) coated
substrate and one continuous ITO coated substrate. Profiled voltages are applied to
different pixels of the patterned ITO substrate, achieving a blazed phase profile because
of the variation in effective refractive index of liquid crystals (Fig. 6.2). Taking
advantage of the sine wave characteristics of a light wave, at a designed wavelength,
periodic resets are normally applied to the optical phased arrays to form an electrically
tunable blazed phase gratings. Usually over one period a phase difference of 2π is
achieved as shown in Fig. 6.2(b). The phase profile behaves exactly as an optical prism
and steers light in the same manner. The steering angle θ of an OPA is calculated as
follows:
135
sin ndL
θ Δ= (6.1)
where L is the period of the resets of the OPA and Δnd is the optical path delay of the
liquid crystals provide over one period distance. If there is no reset applied, the device
will perform like a tunable prism and steer light by refraction mechanism.
136
Figure 6.1 Operation of a digital light deflector based on LC wedge prism. The incident
light is polarized in the in-plane direction. When the TN cell is not electrically activated,
the incident light rotates its polarization to the parallel direction of the liquid crystal
optical axis inside the LC prism after the switch cell, and then is steered away. When the
TN cell is electrically activated, the incident light keeps its polarization and passes the
LC prism without being steered.
137
(a)
(b)
Figure 6.2 Illustration of liquid crystal optical phased arrays. a) Profiled voltage applied
to patterned electrodes; the distance between v0 electrode and vn electrode is the reset
period L. b) The phase profile formed, assuming the maximum phase retardation
achieved for the liquid crystal film is the designed wavelength.
138
There are two major limitations for liquid crystal optical phase arrays. First, OPAs
are dispersive devices. Generally speaking, OPAs have a 2π phase reset for only one
specific wavelength (the designed one). Although they are suitable for laser
communications which only need to operate at a single wavelength, they are limited for
broadband beam steering applications. For all wavelengths other than the designed one,
the phase profiles have phase resets either smaller or greater than 2π, reducing the beam
steering efficiency.
Another limitation of OPA is the optimization of the steering angle and the
steering efficiency. To increase the steering angle, one can either reduce the reset period
or increase the phase retardation over one reset period according to Eq. (6.1). The
drawback of decreasing period distance is to induce distortion of liquid crystal directors
between adjacent pixels caused by the fringing field effect, which is most significant at
the reset regions. At the reset regions, the phase shift is supposed to drop immediately
from 2π to 0. However, the fringing field leads to the so-called fly-back at the reset
regions of the OPA (Fig. 6.3). When light passes through the fly-back regions, it is
steered to the opposite direction from the designed direction, reducing the steering
efficiency. The fringing field effect depends on the cell gap in proportion to the pixel
width and the gaps between adjacent pixels.[100] The fringing field is more significant
when the pixel width is close to the pixel gap or the cell gap is close to the pixel period.
McMannaman et al.[101] have provided theoretical calculations and experimental
evidence that resets of an integer multiple of the wavelength can produce less dispersion
than reset of one wavelength. They fixed the designed steering angle and varied the reset
139
period and the phase retardation. The results showed that the dispersion of the non-
designed wavelength is reduced while the reset period is increased. Thus liquid crystal
film should be increased to as thick as possible to provide large reset period. In addition,
thicker liquid crystal film can increase steering angle if the reset period is fixed. Because
of the independence of the speed on the thickness of liquid crystal material film and their
fast speed of large phase modulation SLCs are ideal candidates for the broadband beam
steering applications.
Mid wave infrared region (MWIR) is of great interest in many applications
including beam steering. MWIR (2 to 5 micron) is one of the atmospheric windows in
which the atmosphere doesn’t absorb much of the light. In this chapter, a SLC OPA
MWIR beam-steering device was fabricated and characterized. Its steering performance
at wavelength of 3 μm was demonstrated. In addition, IR characteristics of all the
components including substrates, electrodes and SLC films were characterized. Potential
molecular engineering approaches on totally eliminating IR absorption in 2 to 5 micron
region are discussed.
140
Figure 6.3 Illustration of flyback regions in the liquid crystal based optical phased arrays
due to the fringing field effect. Light blue lines represent the ideal phase profile while the
dark black lines represent the real phase profile. The gaps between these two profiles are
called flybacks.
Ideal phase profile
Real phase profile
141
6.2 Fabrication of the SLC-OPA device
The SLC material used is a mixture of 5CB and NOA65 at a weight ratio of 90:10.
Quartz substrates were used. One of the quartz substrates has 100 interdigitally patterned
ITO electrodes with pitch of 100 μm (ITO 97 μm and line gap 3 μm) and the other one
has uniform non-patterned ITO coating. The cell configuration is shown in Fig. 6.4. The
cell thickness is controlled by 22-micron fiber spacers placed outside the active area
(10x10 mm2). The fabrication follows the general steps described in Chapter 2. The shear
direction is perpendicular to the stripes of patterned electrodes. The device is glued at the
sheared state to retain the alignment.
6.3 Beam-steering performance
The electro-optical measurement (EOM) of the SLC-OPA is plotted in Fig.6.5.
The interdigited electrodes on the patterned substrate were connected by a conductive
tape and then behave as a common electrode during the measurement. The
characterization wavelength is 632.8 nm. The total OPD that the OPA can provide is
approximately 2.4 μm in the transmission mode. Thus, 4.8 μm OPD is achieved in the
reflection mode. To demonstrate the SLC-OPA beam steering capability, 3 micron IR
laser was used. The birefringence of liquid crystals has wavelength dispersions. In the
infrared region, the birefringence is reduced to 85% of that at the visible range. Therefore,
the SLC device in the reflection mode has approximately 4 μm maximum OPD, which is
still enough for a 2π phase modulation at wavelength of 3 micron. Jianru Shi from Boslab
at Liquid Crystal Institute in Kent State Univ. performed the beamsteering tests. One
142
wave optical phase shift was encoded onto 8, 12 and 16 electrodes, respectively (Figure
6.6). The corresponding steering angles are determined by OPD/period. The electrode
period is 100 micron, the steering angles were 3.0/800, 3.0/1200, and 3.0/1600 in radian
according to Eq. (6.1), respectively. The measurement setup was illustrated in Figure 6.7.
In addition to one dimensional steering, a two-dimensional steering was also performed
for a 632.8 nm laser by connecting two SLC OPAs in tandrum with their shear directions
perpendicular to each other. A 90o twisted-nematic cell was placed between these two
OPAs to switch light polarization.
143
Figure 6.4 Configuration of SLC-OPA. Shear direction is orthogonal to the electrode
direction. Each electrode is 97 μm wide and the gap between adjacent electrodes is 3 μm.
144
0 20 40 60 80 100 120
0.0
0.5
1.0
1.5
2.0
2.5
Δnd
(μm
)
Voltage (V)
0 2 4 6
0.0
0.5
1.0
1.5
2.0
2.5
Δnd
(μm
)
toff (ms)
Figure 6.5 Electro-optical measurements of a 22 μm SLC cell: (a) OPD vs. voltage; (b)
OPD vs. relaxation time. A red laser (λ = 632.8 nm) was used.
145
Figure 6.6 Illustration of the optical path delay profiles encoded on the SLC-OPA. From
top to bottom, 8, 12, and 16 electrodes are chosen as the reset period, respectively. From
Jianru Shi, Dissertation, Kent State University, 2005.
146
Figure 6.7 Experimental setup of the reflective SLC-OPA during a beam steering
operation. The incident light is polarized parallel to the shear direction of the SLC-OPA.
A highly reflective gold mirror is placed behind the SLC-OPA to reflect the light towards
the detector.
147
Figure 6.8 The measured maximum steering angles with varied reset periods. On the top
the non-steered wave was plotted. Plots of steering were also provided when the reset
periods are 16, 12, and 8 electrodes, respectively. The corresponding steering angles (in
degree) are 0.115, 0.144, and 0.215, respectively. From Jianru Shi, Dissertation, Kent
State University, 2005.
148
6.4 IR Transmission of the designed MWIR SLC-OPA
6.4.1 IR transmittance of the substrates
Because UV light is used to fabricate SLCs, an ideal IR substrate for the SLC-
OPA has to be transparent both in UV-Vis and 2 to 5 micron regions. Sapphire was
therefore selected as the designed substrates due to its high transparency from 0.2 to 5
microns and its transmission spectrum is shown in Figure 6.9. Air was used as reference.
Sapphire has refractive indices as high as 1.77. Most of the transmission loss is due to the
reflection, which can be greatly reduced or even eliminated by placing anti-reflection
films on the sapphire-air interfaces.
6.4.2 IR transmittance of the electrode material
The electrode material used in the SLC-OPA was ITO. The film thickness in the
SLC-OPA was approximate 300 Å, and the conductivity was approximately 500
Oh/square. Figure 6.10 shows the ITO’s IR spectrum measured on a sapphire substrate. A
sapphire substrate was used as the reference.
149
0 2 4 60
20
40
60
80
100
T%
Wavelength(μm)
sapphire
Figure 6.9 Transmittance spectra of sapphire in the range of 0.2 to 6 μm. It is measured
with air as the reference.
150
2.0 2.5 3.0 3.5 4.0 4.5 5.040
60
80
100
ITO's IR transmittance
λ (μm)
T%
Figure 6.10 IR transmittance of an ITO film on sapphire substrate in the 2 to 5 micron
region. It is measured with an uncoated sapphire substrate as the reference.
151
6.4.3 IR transmittance of the SLC materials
The IR spectra of 5CB, E7, E44, deuterated 8CB and NOA65 were measured. In
order to be able to predict the IR transmission for all these materials at any thickness,
absorption coefficients in the 2 to 5 μm range are needed. Because pure material was
used, the concentration is constant and assumed to be 1 and no dimension for
simplification. According to Beer’s Law: A = εd, the ε can be calculated directly from the
available absorption spectrum for a cell of a specific thickness. However, in order to
obtain absorbance value through the whole 2 to 5 μm at the linear regime of Beers Law,
two series of samples were needed: thick cells (greater than 40 μm) and thin cells (less
than 10 μm). Thin cells can give accurate absorption ε about the major absorption peaks
(CH and CN), however, not the baseline because thin cells essentially have no absorption
in those regions. Therefore, the thick cells are needed to calculate the coefficients of
absorption in the baseline. Note that thick cells are not appropriate for measuring the
absorption coefficients at the major absorption peaks because these peaks’ absorption
was saturated. Thus, the absorption coefficient ε of a material at the 2 to 5 μm region was
composed of data from a thin cell’s absorption peaks and a thick cell’s baseline. For
instance, to calculate the ε of E7, the mid wave infrared range (2 to 5 μm) is divided into
five regions, AB, BC, CD, DE, and EF in Fig. 6.11. At AB, CD, and EF regions, ε are
calculated from the 50-μm-thick E7 cell. While the absorption coefficients of BC and DE
are obtained from the 6-μm-thick cell. That is, ε is ( , , , ,Thick Thin Thick Thin ThickAB BC CD DE EFε ε ε ε ε ), in which
/Thick ThickAB AB ThickA dε = , /Thin Thin
BC BC ThinA dε = , etc. In Table 6.1, selections of baselines and
152
absorption peaks range are listed for the materials measured. For different materials, the
absorption peaks vary so that the selections of the spectrum branches are different.
153
Figure 6.11 IR spectra of a 6-μm-thick (dashed line) and a 50-μm-thick (solid line) E7
cells. The alignment of the two cells is parallel to the polarizer’s transmission axis. The
absorption peak at 4.49 μm represents the cyano band while the peaks between 3 to 4 μm
represent the carbon-hydrogen vibration bands.
154
Material 5CB Deuterated 8CB NOA65
Thick Cell 2.00-3.10 μm
3.65-4.40 μm
4.55-5.00 μm
2.00-4.20 μm
2.00-2.80 μm
Thin Cell 3.10-3.65 μm
4.40-4.55 μm
4.20-5.00 μm 2.80-5.00 μm
Table 6.1 Spectrum branch selection of different materials for the calculation of IR
absorption coefficients (ε)
155
Figure 6.12 Calculated coefficients of absorbance for 5CB (a) and NOA65 (b).
2 4
0.00
0.05
0.10
0.15
0.20
0.25
λ (μm)
ε (μ
m-1)
2 4
0.00
0.05
0.10
0.15
0.20
ε (μ
m-1)
λ (μm)
(a)
(b)
156
Absorbance coefficients for 5CB and NOA65 for the parallel polarization light in
the 2 to 5 micron region are calculated and plotted in the Fig. 6.13. There are two major
absorption groups for 5CB. Absorption peaks around 3~3.4 microns are the C-H
absorptions, while the sharp 4.49 μm absorption peak is attributed by cyano group.
Regarding the NOA65, the major absorption in the 2 to 5 micron region is the C-H and
residual O-H vibrations.
Second, based on the Beer’s Law, the IR spectrum of a 22-μm-thick 5CB-SLC was
calculated according to Eq. (6.2) and plotted in Fig. 6.13.
, 65, , 65, 65( ) ( ), 65, 10 10LC NOA LC LC NOA NOAA A d d
LC NOAT T T λ λ λ λε ελ λ λ
− + − ⋅ + ⋅= ⋅ = = (6.2)
Where dLC is 19.8 μm and dNOA65 is 2.2 μm for the 22-μm-thick 5CB-SLC film assuming
that the volume ratio is roughly the weight ratio of 5CB and NOA65 (90:10).
157
2.0 2.5 3.0 3.5 4.0 4.5 5.0
0
20
40
60
80
100
22 um SLC
λ (μm)
T%
Figure 6.13 Calculated IR transmittance of a 22-μm-thick 5CB-SLC film.
158
6.4.4 IR transmittance of the SLC-OPA
The reflective spectrum of sapphire based SLC-OPA is measured using the air as
the reference. The setup is arranged as Fig. 6.7 except that the light source is a broad IR
source. The measured result is compared with the calculated IR transmittance. In the
calculation, the reflectivity of a gold mirror RAu is 0.98; the reflection at the back surface
of the OPA is neglected because a negligibly thin layer of liquid crystal film (E7) was put
between the back surface of the OPA and the gold mirror. Therefore, reflection between
sapphire and air (surface 1 in Fig. 6.14) is only calculated twice. Because there is no
absorption below 4 micron for sapphire, the pure absorption loss of a sapphire substrate
can be simply estimated by normalizing the transmission spectrum. Then the reflection
on two sapphire-air surfaces is simplified to the normalizing value used in the
simplification. It is seen from the configuration of the reflective SLC-OPA (Fig. 6.14)
that the incident light pass through sapphire and ITO four times assuming the two
sapphire substrates are identical. The incident light passes the SLC film twice. Thus, the
transmission of the sapphire based SLC OPA device is calculated according to Eq. 6.3.
( ) ( )4 2 4 2Abs reflectionSLC OPA Sapphire Sapphire ITO SLC AuT T T T T R− = ⋅ ⋅ ⋅ ⋅ (6.3)
The compared results are plotted in Fig. 6.15. The calculation is highly consistent with
the measurement.
159
Figure 6.14 Configuration of reflective SLC-OPA.
160
2.0 2.5 3.0 3.5 4.0 4.5 5.0
0
20
40
60
measured reflective sapphire cell calculated reflective sapphire cell
λ (μm)
T%
Figure 6.15 Comparison between experimental measurement and calculation for a SLC-
OPA with a 22 μm SLC film operating in the reflective mode.
161
6.5 Molecular engineering design to optimize SLC’s IR transmission
To increase the depth of phase modulation, SLCs can be built as thick as one
millimeter. However, the IR absorption of a thick liquid crystal film in the 2 to 5 micron
region is significantly strong. Figure 6.16 shows the calculated IR spectrum of an 800-
μm-thick 5CB-SLC. The film is barely transmissive in the 2 to 5 micron IR window.
Therefore, a liquid crystal material with low or essentially no absorption is required for a
large phase retardation modulation in the mid wave infrared region. Molecular
engineering such as changing chemical structures to shift absorption bands out of the
transmission windows is considered to open the 2 to 5 μm atmospheric transmission
window.
Infrared vibration frequency of a chemical bond can be obtained by 12
kc
νπ μ
=
where ν is the frequency of the vibration, k is the force constant, c is the velocity of the
light and the μ is the reduced mass of the atoms involved which can be calculated from
1 2
1 2
m mm m
μ =+
where m1 and m2 are the atomic molecular weights of the two atoms
forming the chemical bond if only two atoms are involved. The vibration wavelength is
2 ckμλ π= . When C-H bond is replaced by C-D bond the reduced mass of C-D is
approximate 2 times of that of C-H bond because the atomic molecular weight of
deuterium atom is twice of the atomic molecular weight of hydrogen atom. Assuming
that force constant k of the bond does not change after deuteration considering the isotope
162
nature of hydrogen and deuterium, one knows that the absorption band wavelength λ (CD)
is approximate 2 times of the absorption peak wavelength of λ (CH). Linli Su et al.[102]
have already demonstrated the shift of absorption peaks using perdeuteration on 8CB for
MWIR beam steering application in 2000. In 2002, Wu et al.[103] obtained perdeuterated
5CB and completely characterized its IR spectrum and other physical properties. Their
illustrated that deuterated cyanobiphenyls keep their original liquid crystalline property
and relevant physical properties such as birefringence, dielectric anisotropy, etc.
Therefore, for the MWIR region, per-deuteration is effective to shift the C-H stretching
absorption bands from 3.3-3.6 μm of to the 4.4-5 μm of C-D stretching. The measured
transmission spectra of the liquid crystals 8CB and deuterated 8CB (D8CB) are plotted in
Fig. 6.17. The deuteration effect is obvious: absorption bands are shifted from 3.3-3.6 μm
to 4.4 to 5 μm and the transmission window of 2 ~ 4.3 μm has been cleared. Figure 6.18
plots the calculated IR spectrum of 820-μm-thick D8CB. Compared with Fig. 6.16, the
thick D8CB does improve the transparency in the 2 to 4.3 μm region. However, the
transmittance is only around 20% to 40% for most wavelengths. It can be seen from Fig.
6.17 that the deuteration is not 100% for the D8CB, which causes the small amount of
residual absorption. When the film thickness is increased to 820 μm, the residual
absorption is magnified and easily observed. Therefore, theoretically if liquid crystal
materials are 100% deuterated the transmittance in the 2 to 4.3 μm region will be much
higher than the calculated results in Fig. 6.18.
163
Figure 6.16 Calculated IR spectrum of an 800-μm-thick SLC.
2 2.5 3 3.5 4 4.5 50
10
20
30
40
50
60
70
80
90
100
SLC-5CB/NOA65 Transmittance Vs Wavelength
Wavelength (um)
%Tr
ansm
ittan
ce
164
2 3 4 5
0
20
40
60
80
100
T%
Wavelength (μm)
8CB D8CB
Figure 6.17 IR transmission in 2 – 5 micron region of approximate 5 μm thick layers of
4’-octyl-4-cyanobiphenyl (8CB) and Deuterated 4’-octyl-4-cyanobiphenyl (D8CB).
165
2 2.5 3 3.5 4 4.5 50
10
20
30
40
50
60
70
80
90
100
D8CB Transmittance Vs Wavelength
Wavelength (um)
%Tr
ansm
ittan
ce
d= 820 um
Figure 6.18 Calculated IR transmittance for 820-μm-thick deuterated 8CB film.
166
Obviously perdeuteration couldn’t clear out the absorption of 4.4 to 5 micron
region. In order to open 2 to 5 μm transmission window bigger reduced mass has to be
induced. It is natural to take into consideration fluorine because fluorine has the similar
volume as hydrogen atom but much bigger atomic weight: 19 compared to 1 of hydrogen,
which favors red-shifting absorption peaks of C-H even more than deuteration. On the
other hand, after per-fluorination, the force constant k could not be assumed unchanged
anymore due to big electronegativity difference between F and H atoms. As a matter of
fact, kCF is much larger than kCH, which to some extent reduces the red-shift effect caused
by larger reduced mass of C-F bond. To test the red-shift due to perfluorination a per-
fluorinated liquid crystal rigid core structure-Pentafluorophenyl-(2,3,5,6-tetrafluoro-4-
trifluoromethoxy-phenyl)-diazene was designed and its IR absorption bands were
calculated by the program GAMESS plugged in ChemOffice software. The spectrum is
shown on the right of Fig. 6.19. Apparently, the total substitution of hydrogen atoms by
fluorine atoms shifts all the absorption bands out of the 2 ~ 5 μm region.
167
Figure 6.19 The structure of pentafluorophenyl-(2,3,5,6-tetrafluoro-4-trifluoromethoxy-
phenyl)-diazene and the calculated IR absorption bands.
N
N
FF
F3CO
F F
F F
F
FF
2 4 6 8 10 12 14
0
5
10
15
20
Abso
rban
ce In
tens
ity(a
.u.)
wavelength( μm)
compound left
Pentafluorophenyl-(2,3,5,6-tetrafluoro-4-trifluoromethoxy-phenyl)-diazene
168
Fluorinated liquid crystals have been extensively investigated and it is shown that
they exhibit optical and chemical stability, wide mesomorphic temperature range, low
melting point, low viscosity and low conductivity. Generally speaking fluorine atoms can
be mainly introduced to two categories of positions: rigid cores and aliphatic chains.
Fluorine atoms introduced to the rigid cores have two opposite effects on the liquid
crystalline properties: one is that fluorine atoms can give rise to more intermolecular
separation which will decrease the stability of liquid crystal phases; the other is that
fluorine atoms will enhance the phase stability due to stronger polarity of C-F bond.[104]
In addition, per-fluorinated rings tend to produce smectic phase rather than nematic phase.
Other experiments showed that highly fluorinated aliphatic chains introduce suppression
of the nematic or cholesteric phases, however, when these phases exist the stability of
these phases are increased.[105] Despite of the uncertainty of the liquid crystalline property
of perfluorinated liquid crystals, it may be possible to synthesize totally per-fluorinated
liquid crystals which will be utilized to completely open the transmission window of 2 ~
5 μm.
An alternative method of opening transmission windows is to use multi-channel
liquid crystal devices. For example deuterated 8CB can shift the C-H absorption bands to
over 4.4 μm region so the 2 ~ 4.3 mm region is opened. 8CB can open the 4.5 ~ 5 micron
region as shown in Fig. 6.18. Therefore, by combining these two liquid crystals one can
fabricate a two-channel device which can modulate the complete 2 ~ 5 μm region. The
CN can be neglected since its absorption is a considerably sharp peak. Or one can just
select a liquid crystal without CN bonds and its deuterated derivative to fabricate a dual-
169
channel device. Similarly, the long infrared window can be open using multiple liquid
crystal materials of which absorption peaks do not overlap with each other. In Fig. 6.20,
the IR spectra of cyclohexane, 5CB, PCH5, and pyridine are plotted. It demonstrates the
concept of materials’ combination for multichannel application. For example, it can be
seen that pyridine’s absorption peaks are completely different from 5CB’s absorption
peaks. Therefore, a device utilizing pyridine based LC in one channel and 5CB in the
other channel would be able to open 8 to 12 μm transmission window.
170
8 9 10 11 12-0.2
0.0
0.2
4000 3000 2000 1000
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
Cyclohexane 5CB PCH5 Pyridine
Abs
orba
nce
Wavelength (μm)
wavenumber(CM-1)
Figure 6.20 Measured infrared spectra for thin films of cyclohexane, 5CB, PCH5 and
pyridine. Offsets of absorbance are used for easier comparison.
171
6.6 Conclusions
In this chapter, a SLC OPA MWIR beam-steering device was fabricated and
characterized. It can steer a 3 μm IR laser in less than 2 ms. This device potentially is
suitable for the broad band MWIR beam steering since the SLC film can be built as thick
as possible without slowing down the response. Through molecular engineering
approaches novel SLC materials can be fabricated and eventually provide ideal functional
materials, which totally eliminate IR absorption of liquid crystal materials in 2 to 5
micron region.
172
CHAPTER 7
SLC-OPA for the Application of Tip-Tilt Corrector
7.1 Introduction
It is well known that ground-based astronomers’ optical observation has been
limited by the distortion of the Earth’s atmosphere. It is important to smooth out the
millisecond time scale distorting effects of the atmospheric turbulence by using adaptive
optics systems, which are able to adaptively cancel out, or at least minimize atmospheric
distortion in real time. While a wavefront experiences a turbulent atmosphere, the tip-tilt
distortion accounts for about 85% of all the aberrations induced upon the wavefront.
Therefore, it is the primary concern of any adaptive optics system, and it becomes critical
to find a simple and effective way to perform the tip-tilt correction.[106],[107],[108] Although
devices are available to provide this correction, much faster correction speed (>10KHz) is
required in fast moving and aero-optical systems.[109]
It has been more than 17 years since people started to utilize liquid crystal devices
to perform wavefront control.[110],[111] There are many advantages of using liquid crystal
spatial light modulators, such as low cost, low power consumption, no moving parts
involved and device compactness. However, there exist two main drawbacks of nematic
liquid crystal devices: the polarization dependence and the slow response time.[112] The
first drawback can be overcome by incorporating a quarter-wave plate into a device used
173
in reflection mode[113] or using two orthogonal devices of identical LC materials
connected in tandem.[114] In order to achieve large OPD (several wavelengths) for
wavefront corrections, the thickness of the liquid crystals in all these devices has to be
increased.
SLCs are a perfect solution for the second drawback. SLCs decouple the
switching speed and the cell thickness so that the increase of the SLCs’ thickness will not
slow down their response time. The SLCs can provide a large OPD in a fraction of a
millisecond. In addition, the SLCs have linear response between OPD and applied
voltage, which greatly simplifies driving electronics design. Based on the optical phased
array (OPA)[4],[115] technology, a SLC tip-tilt corrector was fabricated, which can provide
3.1 μm OPD in 0.1 ms (10 KHz) in the reflection mode.
This research is done through the collaboration with Boslab in Liquid Crystal
Institute of Kent State Univ. Bin Wang installed the SLC tip-tilt corrector driving device
and performed the optics setup and characterization on the beam profile and steering
efficiency. The fabrication and characterization of the SLC tip-tilt corrector is described
in Sections 7.2 and 7.3. The performance of this tip-tilt corrector is presented in Section
7.4.
7.2 Fabrication of the SLC-OPA
The SLC material used for tip-tilt correctors is a mixture of liquid crystal 5CB,
monomer RM82, and optical adhesive NOA65 at a weight ratio of 90:2:8. The
photoinitiator is 0.2% of the whole mixture. One of the tip-tilt corrector substrates has 24
174
interdigitally patterned ITO electrodes with pitch of 417 μm (ITO 412 μm and line gap 5
μm) and the other one has uniform unpatterned ITO coating as shown in Fig. 7.1. The
cell thickness is controlled by 40-micron fiber spacers placed outside the pixel area. The
mixture of the LC material is sandwiched between two substrates and then the cell is
placed into a UV lamp chamber and undergone the UV polymerization. The temperature
of the chamber is close to 50oC and the UV intensity is 20 mW/cm2. The polymerization
process takes an hour. The cell shows strong scattering after the polymerization. However,
it turns transparent after 80 micron shear distance is applied. The shearing direction is
perpendicular to the stripes of patterned electrodes. Figure 7.2 shows the transmission
spectra before and after the shearing of the liquid crystal device. Fig. 7.2 also indicates
that the transmission of the SLC cell decreases at shorter wavelength region. Because the
interconnected polymer domain sizes are comparable to the wavelength of light,
scattering takes place. The device is glued at the sheared state to retain shearing
alignment.
175
Figure 7.1 The structure of the SLC tip-tilt corrector with a 24 interdigitally patterned
ITO bottom substrate and a non-patterned ITO top substrate. The width of ITO strips is
412 μm, and the line gap is 5 μm.
176
Figure 7.2 The SLC tip-tilt corrector transmittance at the states before and after shear. It
is referenced to transmission of a NOA65-cell to correct the reflection loss.
177
7.3 Electro-optical characterizations of the SLC device
The electro-optical characterization setup of the SLC tip-tilt corrector is the same
as described in Chapter 2. A near IR laser with wavelength of 1.55 μm serves as the light
source. The device shear direction is 45° with respect to the transmission axes of a pair of
crossed polarizer and analyzer. The patterned electrodes are connected, so the SLC acts
as a single pixel device for this measurement.
The measured switching speeds are shown in Fig. 7.3. The switching speeds for
voltage on and off are about 55 μs and 30 μs, respectively, for half wave phase shift in
transmission mode. They are much faster than other nematic liquid crystal devices which
switch the same amount of phase shift. The measured OPD as a function of voltage is
shown in Fig. 7.4. The linear OPD region is roughly from 67.0V to 191.0V, which agrees
with the linear fitting. The linearity of the OPD allows the tip-tilt corrector driving
electronics to be realized by a simple resistor network. Figure 7.5 shows the measured
SLC device transmission spectra when it is switched to “ON” and “OFF” states. These
results are also referenced to transmission of a NOA65 cell. One can clearly see that the
transmission loss of the SLC itself is minimal in NIR region.
178
Figure 7.3 The measured switching times of the SLC tip-tilt corrector. λ = 1.55 μm and V
= 200.0 V.
179
Figure 7.4 The measured OPD of SLC tip-tilt corrector as function of voltage. The linear
range is roughly from 67.0V to191.0V.
180
Figure 7.5 Measured transmission spectra of SLC Tip-Tilt corrector. It is referenced to a
NOA65 cell.
181
7.4 Characterizations of the performances of the tip-tilt corrector
7.4.1. Steering angle and drive methods considerations
The SLC tip-tilt corrector is based on optical phased array beam steering
technology. Fig. 7.6(a) shows that when no voltage is applied to the SLC device (left),
the optical phase profile is a rectangular shape (right), and the incident laser beam will
not change its propagation direction. Fig. 7.6(b) shows that when a linear voltage ramp is
applied (left), the optical phase profile is a triangle or prism (right), and the beam is
steered away from its incident direction. From Fig. 7.6 we know that there is a linear
OPD region between 67.0 V and 191.0 V. Therefore, a serial resistor network connected
to the interdigitally patterned ITO electrodes can easily provide a linear voltage ramp. By
setting two-end voltage VH (high voltage) and VL (low voltage) to 191.0 and 67.0 V,
respectively, the linear voltage ramp is realized. The steering angle is governed by
expression (Eq. 6.1)
sin ndL
θ Δ= (6.1)
where L is the bottom width of the triangle phase profile for the tip-tilt corrector.
Therefore, OPD Δnd and L determine the steering angle θ.
182
Figure 7.6 Schematic drawings of beam steering effect of a liquid crystal cell at different
voltage driving condition. The drawing on the left side is liquid crystal director
configurations, on the right side is the corresponding optical phase profile. ↔ indicates
the beam polarization direction and ↑ indicates the beam propagation direction. (a) No
voltage is applied; (b) Linear voltage ramp is applied, left side has low voltage and right
side has high voltage; (c) Linear voltage ramp is applied, left side has high voltage and
right side has low voltage.
183
For the SLC tip-tilt corrector, L and Δnd are about 10000 μm and 2.0 μm,
respectively. Thus, the steering angle is about 0.0115°. When VL is applied to the left end
and VH applied to the right end, phase profile shown in Fig. 7.6(b) is obtained so that an
incident beam is steered to the left. If VL and VH is flipped, the triangle phase profile has
a different slope as depicted in Fig. 7.6(c). Therefore, the incident beam is steered to the
right. By operating this device between the states of Fig. 7.6(b) and Fig. 7.6(c), the
steering angle is doubled to 2θ. The steering angle can be further doubled by operating
the device in reflection mode, since the Δnd is doubled. These considerations are adopted
in the device design, which is going to be discussed in the next section.
7.4.2. Beam profile and steering efficiency
The experimental setup for measuring the beam profile and steering efficiency is
shown in Fig. 7.7(a). A laser beam (λ =1.55 μm ) passes through a polarizer, which
transmission axis is in z-direction. Then the beam goes through a beam expander (BE)
and reaches the reflective SLC tip-tilt corrector. The reflected beam first passes through a
beam compressor (BC) and is received by a photo-detector. By employing the beam
expander and beam compressor, the steering angle is further increased.
184
Figure 7.7 (a) Schematic drawing of the setup for beam profile and switching speed
measurements, BE and BC stand for beam expender and beam compressor. (b) Three
possible positions the beam can be steered to.
185
Figure 7.7(b) is a side-view simplified version of Fig. 7.7(a), which is only
focused on the three positions of the reflected beam. There are three possible positions in
z-axis for a reflected beam. Position P0 corresponds to the state when no voltage is
applied to the SLC device; P1 and P2 correspond to the states when there are two
different voltage ramps shown in Fig. 7.6(b) and Fig. 7.6(c) applied to the device. A
detector can be moved to any of these three positions by micrometer translation stage.
At first, a reflective cell filled with fully-cured NOA65 replaces the SLC device
shown in Fig. 7.7(a) and Fig. 7.7(b), which is used as a base reference to check the beam
profile and steering efficiency. The detector is placed in the position P0. A 15-micron
pinhole was attached to the detector. By moving the detector in Z- and Y-directions and
recording the readings of the detector cross the whole beam, we obtained the beam
profile from the reflected reference cell. The beam profiles in Z- and Y-directions are
shown in Fig. 7.8 (a) and Fig. 7.8 (b). Then the reference cell is replaced by the SLC tip-
tilt corrector. Repeating the same beam profile measurement done for the reference cell,
the beam profiles with and without voltage ramp applied in Z- and Y- directions are
plotted in Fig. 7.8(c) and Fig. 7.8(d). Fig. 7.8(c) shows the beam profiles in the steering
and non-steering cases in Z-direction. The plot bottom horizontal-axis shows the beam
width and position of the non-steered beam; and its top horizontal-axis shows the beam
width and position of the steered beam in Z-direction. The plotted two peaks are aligned
up to compare their peak intensities. Similarly, Figure 7.8(d) shows the beam profiles for
steered and non-steered cases in Y-direction. For both Fig. 7.8(c) and Fig. 7.8(d), the
186
(a) (b)
(c) (d)
(a) (b)
(c) (d)
Figure 7.8 (a) and (b) are the beam profiles from a reflected reference cell in Z- and Y-
direction. (c) is the SLC steered and non-steered beam profiles in Z-direction. To
compare the beam intensity, the two peaks of the beams are aligned up. The bottom
horizontal axis is for non-steered beam width and position, the top horizontal axis is for
steered beam width and position. (d) is the SLC steered and non-steered beam profiles in
Y-direction.
187
measured intensities of the steered and non-steered peaks are very close. The measured
beam steering efficiency is about 91%.
7.4.3. Switching speed of the SLC tip-tilt corrector
The SLC tip-tilt corrector switching speed at room temperature measured by an
oscilloscope is shown in Fig. 7.9. The waveform on the top is the time response of the
SLC tip-tilt corrector, and here it is called a switching curve; and the waveform on the
bottom is a driving waveform applied to one end of the device. The driving waveform
applied to the other end of the device is opposite to the one shown in Fig. 7.9, which does
not show here. Therefore, the device has low voltage on one end and high voltage on the
other when it steers the beam. The driving waveform base frequency is 10 KHz. The
amplitudes of the waveform are ±67.0 V and ±191.0 V, respectively. The switching curve
is obtained with setup shown in Fig. 7.7. When the switching curve is at low amplitude
level, point A, and from D to E, it indicates that the beam is steered away from the
detector placed at position P1 in Fig. 7.7(b); when the switching curve is at high
amplitude level, from B to C, it indicates that the beam is steered into the detector placed
at position P1 in Fig. 7.7(b). The rise time from point A to B indicates how fast the beam
is steered into the detector, and the fall time from points C to D indicates how fast the
beam is steered away from the detector. The beam size is about 2.8 mm, and the detector
diameter is about 1.5 mm. The measured rise and fall time is about 100 μs, which is
much faster than conventional nematic liquid crystal devices switching the same amount
of OPD.
188
Figure 7.9 Measured response time of the SLC tip-tilt corrector. Waveform on the top is
the time response of the SLC device, waveform on the bottom is the driving waveform.
The base frequency of the driving waveform is 10.0 KHz and amplitudes are ±67.0 V and
±191.0 V, respectively.
189
7.5 Conclusions
A fast switching tip-tilt corrector based on stressed liquid crystal optical phase
arrays is fabricated. It provides a OPD about 3.1 μm in 100 μs (reflection mode) under
the driving voltage less than 200.0V. The linear characteristic of the OPD versus voltage
simplifies the driving electronics design. The optical characterizations show the device
not only has fast switching speed, but also possesses high beam diffraction efficiency
(>90%). Therefore, a real-time tip-tilt corrector with a 10 KHz bandwidth is feasible by
the SLC device.
190
CHAPTER 8
Photo-patterned SLC Prisms
8.1 Introduction
As described in Chapter 6, liquid crystal optical phased array is thus far the most
promising technology for non-mechanical beam steering applications. However, it’s
rather complicated in design and has its intrinsic limitations (i.e., wavelength dispersion).
Simpler design can use either a gradient electric field or a liquid crystal concentration
gradient to build a prismatic device to perform beam steering function. The electric field
gradient can be introduced through many approaches, such as individually addressing
pixelated electrodes,[106] addressing continuous high resistance electrode,[116-118] fringing
field effect of a hole-pattern electrode,[119] or imbedding lens profile electrode inside the
flat substrate.[120] Even simpler, gradient of the liquid crystal concentration can be
imposed in a polymer/liquid crystal composite system during the polymerization by the
UV irradiation through photo masks. Ren et al.[121],[122],[123] have demonstrated the
concept of photo patterned nano-PDLC and PNLC/PSLC which can function as beam
deflectors and lenses. Generally speaking, when a UV light of inhomogeneous intensity is
used, the polymerization is a non-uniform phase separation. Strong UV irradiation
regions consume monomers faster. Therefore, to balance chemical potential among the
system, extra monomers in the weak UV irradiation regions diffuse into the strong UV
irradiation regions. Conversely, liquid crystals diffuse from the high UV intensity regions
191
to the low ones. A concentration variation in liquid crystal is thus formed. In addition, the
speed and monomer concentration determine the morphology of the polymer matrix,
resulting in a variation of liquid crystal domain sizes as well. Those regions with a higher
(lower) level of liquid crystal concentration provide a higher (lower) value of phase
retardation. When a uniform electric field is applied over the entire area of the sample,
different amount of the liquid crystal is reoriented in different places, resulting in
variation of phase retardation. The spatial profile of phase retardation is determined by
the optical density profile of the mask and may be varied in a different manner in
accordance with a particular application: centrosymmetric, cylindrical, saw-tooth profiled,
etc.
In this chapter, the concept of fast SLC prisms is introduced. A gradient photo-
mask is used to achieve gradient UV intensity during the fabrication of SLC prisms,
which feature a large aperture and linearly gradient phase profile. The 18 μm thick SLC
prism has a maximum of 1.6 μm optical path delay difference between the two ends and
switches in 4 miliseconds.
8.2 Experimental setup
The materials used are E7 and NOA65 at a weight ratio of 86:14. Two continuous
ITO glass substrates (1x2") are used. The cell gap is 18 μm controlled by glass fiber
spacers. The photo-mask is a 12x18 mm2 transparency film with a gradient pattern
printed on. The SLC mixture is sandwiched between the two ITO glass substrates and
192
heated up to 80 degree. The UV mask is kept in close contact with the top surface of the
SLC prism during the polymerization. (Fig. 8.1).
Figure 8.1 Illustration of polymerization of SLC prism using a UV photo-mask.
193
8.3 Characterizations and performance
The optical transmittance of the photo-mask at λ=365 nm is plotted in Fig. 8.2.
Four locations on the photo-mask were measured. These four locations were
corresponding to the four spots on the SLC prism shown on the top of Fig. 8.2. Adjacent
spots are 5 mm apart from each other.
After polymerization, it was observed that the strong-UV-cure region shows less
light scattering than the weak-UV-cure region. However, when shear alignment was
applied, the weak-UV-cure region was more transparent than the strong-UV-cure region.
The shear was along the gradient direction. The polymer network structures at different
positions of the SLC prism were characterized by SEM. The preparation of SEM samples
has been previously described in detail (see Chapter 2). SEM graphs of A, B, C and D are
demonstrated in Fig. 8.3. The UV intensities in these four spots were 41 mW/cm2, 36
mW/cm2, 27 mW/cm2, and 15 mW/cm2, respectively. As a result of monomer diffusion
upon polymerization, the region exposed to stronger UV irradiation had a higher polymer
concentration than the one exposed to weaker UV irradiation. The polymer matrix at spot
A showed a coarse and thick network structure in the strong UV cured region. In contrast,
the polymer sheet structure was smooth and thin in the low UV irradiation region (at spot
D). The transition between these two structures is observed in the medium UV irradiation
cure regions (spots B and C).
194
0 2 4 6 8 10 12 14 16 18
30
40
50
60
70
80
D
C
B
Tran
smis
sion
(%)
Position (mm)
A
Figure 8.2 UV transmittance measurements of four locations on the photo-mask
corresponding to the four spots, A, B, C, and D, of the SLC prism. The four spots were
round spots of 1 mm diameter, constrained by a pinhole of 1 mm diameter. Adjacent
spots were 5 mm apart from each other. λ=365 nm.
A B C D
Mask
SLC prism
195
Figure 8.3 SEM of A, B, C, and D are shown in this graph. The strong UV irradiation
produced the rough polymer matrix (micrograph a) while the weak UV irridiation
produced thin and smooth polymer matrix (micrograph d). For the medium UV intensity
regions, a transition from a coarse network structure to a thin sheet structure is observed
(micrographs b and c).
a b
c d
196
Spots A and D, 16 mm apart at the two ends of the SLC prism, located in the
strong-UV-cure region and the weak-UV-cure region, respectively, were selected to
evaluate the electro-optical performance of SLC prism. The optical path delay (OPD=Δnd)
at spots A and D were measured at varied shear states. The difference between OPD A
and OPD D (ΔOPD = OPD D - OPD A) is plotted in Fig. 8.4. There are two factors that
cause the optical path delay difference (ΔOPD ): liquid crystal concentration and liquid
crystal alignment efficiency. At the zero shear state when no alignment was applied to
liquid crystals inside the SLC prism, both OPD A and OPD D were small and ΔOPD was
0.12 μm. ΔOPD at the 0 μm shear state is completely caused by the concentration
variation in liquid crystal. When Lshear is greater than 30 μm, ΔOPD was increased to 0.9
μm. The large difference is due to both the liquid crystal concentration difference and the
shear alignment efficiency variation for liquid crystal domains of different sizes.
Compared with spot D, spot A had larger liquid crystal domains; consequently, the shear
alignment was less efficient. In addition, spot A had less liquid crystal. Thus, OPD A <
OPD D.
Figure 8.5 demonstrates the relationship between optical path delay and voltage at
the two ends (spots A and D) of the SLC prism. A linear response of phase retardation to
voltage is observed for both spots. OPDA dropped faster than OPDD in the linear regions
when the voltage increased. Therefore, ΔOPD at different voltage levels varies. Figure
8.6 demonstrates the change of ΔOPD for the SLC prism at different shear states. ΔOPD
197
0 20 40 60 80 1000.0
0.2
0.4
0.6
0.8
1.0
ΔO
PD =
OPD
D-O
PDA (μ
m)
Shearing distance (μm)
Figure 8.4 Optical path delay difference across the gradient SLC prism at the different
shear states.
198
-10 0 10 20 30 40 50 60 70 800.0
0.4
0.8
1.2
1.6
2.0
OPD
(μm
)
Voltage (v)
100 μm shearingDA
Figure 8.5 Variation of optical path delay for spots A and D which were at the two ends
of the SLC prism with the change of the voltage. The SLC prism was at the 100 μm shear
state.
199
experiences an increase at low voltage before it decreases when voltages increase further.
For example, at the 100 μm shear distance, ΔOPD increases to a maximum (ΔOPDmax)
when the applied voltage increases from 0 V to 8 V. Then ΔOPD decreases gradually
when the voltage increases from 8 V to 70 V and becomes zero eventually. The
explanation is as follows. Spot A had larger LC domains and smaller threshold voltage
compared to spot D, thus the liquid crystals were easier to be oriented by the electrical
field when the applied voltage increased from 0 V to 8 V. As a result, OPDA dropped
faster than OPDD, causing the increase of ΔOPD. When the applied voltage increased
from 8 V to 70 V, OPDA did not change because most liquid crystals at spot A had
already been oriented by the electric field; in contrast, OPDD continued to decrease due to
the further orientation of liquid crystals at spot D. Therefore, ΔOPD decreased gradually
in the 8 V to 70 V range. The voltage for ΔOPDmax varies slightly at different shear states.
SLC prisms are fast switching devices. Figure 8.7 illustrates the turn-off time for
spots A and D on the SLC prism at 100 μm shear distance. Spot D has a faster response
than spot A due to its smaller LC domain size. In spite of this, for both spots, most of the
phase shifts can be switched within 4 ms, which indicates that the turn-off time for the
entire SLC prism was less than or equal to 4 ms.
A 2D phase retardation profile (Fig. 8.9) was constructed by Xinghua Wang using
a 2D Birefringence Measurement setup in Boslab of Liquid Crystal Insitute (Fig. 8.8).
The SLC prism was at its 100 μm shear state. Figure 8.9 shows the electronically tunable
phase retardation profile of the gradient SLC prism and the linearity of the gradient phase
200
0 10 20 30 40 50 60 70 80
0.0
0.5
1.0
1.5Δ
OPD
= (O
PDD-O
PDA) (
μm)
Voltage (V)
0 μm shear 30 μm shear 100 μm shear
Figure 8.6 Measured voltage dependent ΔOPD at 0 μm, 30 μm, 100 μm shear states,
respectively.
201
0 2 4 6 8 10 12 14
0.0
0.5
1.0
1.5
2.0O
PD (μ
m)
Time (ms)
Spot D Spot A
Figure 8.7 Measured turn-off times for spots A and D on the SLC prism.
202
shift across the SLC prism under different voltages. Figure 8.9 also verifies that with the
increase of the voltage, ΔOPD rises to a maximum before falling to zero. The maximum
optical path delay difference across the prism (ΔOPD max) is about 1.6 μm (0.633 μm x
2.5) across the distance of 18 mm, giving rise to a steering angle of 0.005 degree
(θ=1.6/18000*180/3.14=0.005).
A set of SLC lenses of large apertures were fabricated with varied photo masks
(Fig. 8.10). The focal length obtained was approximately 30 m according to the formula:
f=πr2/λΔδ=r2/2ΔOPD.[124] The performance of patterned SLCs can be improved if high-
precision photo masks (e.g., chromium ones) are utilized to fabricate micro-prisms or
lenses for wider bream steering angles or a better tunability. Thicker SLC films can also
be used to increase the phase shift.
8.4 Conclusions
The photo-patterned SLCs can be used to make electronically controlled tunable
prisms and gratings, variable focus lenses, microlens arrays, and other possible phase
modulators simply by varying photo-mask patterns. The resulting devices can be
addressed using a single electrode and single applied voltage. This approach is much
simpler than using complicated electrode patterns and complex drive schemes. It can also
overcome the fringing field problem for the wide angle beam steering applications.
203
Figure 8.8 2D birefringence measurement setup.
5 7 6 2 3
14
Birefringence measurement
1. Laser 2. Polarizer 3. 30X Beam expander and special filter set 4. Soleil-Babinet compensator 5. SLC prism 6. Analyzer 7.Camera
204
Figure 8.9 Phase profiles across the gradient SLC sample at different voltages λ = 0.633
μm.
205
Figure 8.10 The photo-mask presented on the top was used to demonstrate the SLC lens
concept. The 2-D birefringence pattern measurements of SLC lenses fabricated with the
mask are provided at the bottom.
206
CHAPTER 9
Mechanically Patterned SLCs
9.1 Introduction
Liquid crystal polarization converting devices can transform a linear polarization
into a radially or azimuthally distributed polarized light. These devices normally require a
micro-fabrication process. Yamaguchi et al.[125] described that a nematic liquid crystal
cell consisting of a unidirectionally rubbed substrate and a circularly rubbed substrate can
change the polarization of the incident light parallel to the unidirection rub direction into
a circularly distributed one. It can also convert the polarization perpendicular to the
unidirection rub direction into a radially distributed one. Furthermore, Stalder and
Schadt[126] explored a nematic liquid crystal cell of two circularly rubbed substrates in
addition to a cell similar to Yamaguchi’s. They generated polarized lights with a higher-
order spacial distribution by cascading these two types of devices. In this chapter, a
twisted stressed liquid crystal (T-SLC) is investigated. A twist-shear is applied to a SLC
sample. An azimuthally aligned liquid crystal distribution along the twist-shear direction
is produced. In addition to the azimuthal spatial distribution of the liquid crystal director,
the T-SLC also has a gradient phase retardation distribution in the radial direction. The T-
SLC can be used as a polarization converter.
207
9.2 Experimentals
5CB, RM82 and NOA65 were mixed at a weight ratio of 90:1:9. The initiator
(Irgacure) for RM82 was 0.1% of the whole mixture in weight. Then the mixture was
sandwiched between two orthogonally positioned indium-tin-oxide (ITO) coated glasses
with 22 μm fiber spacers to control the cell thickness. The fabrication procedure has been
described in detail in Chapter 2. A dye-doped T-SLC was also fabricated to examine the
liquid crystal director configuration. M-483, an anisotropic dye, was used and it has a
maximum absorption at ~630 nm (Fig. 4.7). As shown in Fig. 9.1(a), a counterclockwise
twist-shear on the top substrate was exerted while the bottom substrate was fixed with
two supports. Fig. 9.1(b) demonstrates the view of the T-SLC between crossed polarizers.
Based on the crossed polarizer setup, a 20X beam expander was added to enlarge the red
laser beam to cover a round area of 10 mm radius on the T-SLC. Digital videos were
taken, from which still images were extracted.
The electro-optical measurement setup was the crossed polarizer setup (Fig. 2.4 in
Chapter 2). Crossed polarizers were placed at 45 degrees to the horizontal direction. Then,
the T-SLC was inserted between the two polarizers. The characterizations were taken on
the six marked spots along the horizontal line on the cell, P0 through P5 (2 mm apart for
adjacent spots) and were exhibited in Fig. 9.1(c). With a fully-cured NOA65 cell as a
reference to correct the reflection loss, the transmission of the T-SLC was measured with
unpolarized laser light passing through. The laser wavelength was 632.8 nm for both the
electro-optical measurements and the transmittance measurement.
208
Figure 9.1 (a) Demonstration of twist-shear scheme for the T-SLC; (b) pattern image of
the T-SLC between crossed polarizers; (c) marked six spots along the horizontal line for
measurements of electro-optical properties and transmittance.
(a) (b)(a) (b)(a) (b)(a) (b)
012345 012345
(c)(a) (b)(a) (b)(a) (b)(a) (b)(a) (b)(a) (b)(a) (b)(a) (b)
012345 012345
(c)
209
9.3 Results and discussions
A pattern of crossed dark brushes and dark rings was observed after the T-SLC
was inserted between crossed polarizers. The pattern remained unchanged upon an in-
plane rotation of the T-SLC. The transmittance intensity follows the
equation: 2 20 sin ( ) sin (2 )ndI I π β
λ⋅Δ
= ⋅ ⋅ ,1 where β is the angle between liquid crystal
directors and the polarizer. When nd mλΔ = or 2
k πβ = ⋅ , where m and k are integers,
the transmittance is minimal (shown as the black rings and crossed dark brushes in Fig.
9.1(b)). There are two possible liquid crystal director configurations to explain this
pattern: an azimuthal structure and a radial structure (Table 9.1). Wu et al.[127] described a
radial configuration resulting from the off-axis sheared polymer network liquid crystals.
They proposed that the off-axis shear can cause the polymer network to contract and thus,
a radial director configuration forms. However, more commonly, shear deformation
aligns liquid crystals’ director along the shear direction. Table 9.1 lists the comparison
between the radial and azimuthal configurations: the intensity patterns of T-SLC
observed with crossed polarizers setup and the intensity patterns of dye-doped T-SLC
observed using one analyzer.
To identify the director configuration inside the T-SLC, the M483-doped T-SLC
was put on a white light box and observed with a linearly polarized analyzer. A pattern of
alternating darker regions and lighter regions appeared and it rotated with the rotation of
the analyzer. Figure 9.3 shows pictures of the M483-doped T-SLC taken while the optical 1 The derivation of this formula is presented in Appendix C.
210
transmission axis of the analyzer was along the horizontal and vertical direction. The dye
absorbs more light when the polarization of the transmitting light is parallel to the dye’s
director than when it is perpendicular. It is known that, in an anisotropic-dye-doped
liquid crystal system, the dye molecules align along the liquid crystal director direction.
Therefore, the darker regions in Fig. 9.2 where more light was absorbed suggest that the
dye’s directors (i.e., liquid crystal director) over those areas are aligned along the
transmission axis of the analyzer. The fact that the pattern rotated along with the rotation
of the analyzer indicates that the liquid crystal director configuration inside a T-SLC has
an azimuthal distribution. In other words, liquid crystals align along the twist-shear
direction.
211
Properties Radial structure Azimuthal structure
Liquid crystal director
configuration
Intensity pattern observed
with crossed polarizers
Intensity pattern observed
for dye-doped T-SLC with
one analyzer aligned along
the vertical direction
Table 9.1 Comparison of transmission intensity patterns between radial structure and
azimuthal structure.
2 2
0 sin ( ) sin (2 )ndI I π βλ
⋅ Δ= ⋅ ⋅
212
Figure 9.2 Images of the M483-doped T-SLC taken through a linearly polarized analyzer
horizontally (left) or vertically (right) aligned. Black arrows represent the optical
transmission axis of the analyzer. The pattern rotates when the analyzer rotates. The real
dimension of each area is 20x20 mm2.
Analyzer Analyzer
213
As mentioned earlier, the original twist-shear direction for the T-SLC was
counterclockwise. A further twist along the counterclockwise direction reduced the
spacing between adjacent rings. In contrast, reducing the twist force increased the spacing.
An additional linear shear can shift the ring/brush patterns, resulting in asymmetric
structures in the active area. At first, directions of linear shears and pattern shifts are
represented using αshear/shift = 0o, 90o, 180o, and 270o shown as the coordinate in the Fig.
9.3(a). For example, when a 90o linear shear is applied as shown by Fig. 9.3(b), the ring
pattern was observed to shift to the left (Fig. 9.3(c)). The mechanism is illustrated in Fig.
9.4. Assuming the azimuthal distribution in a T-SLC (Fig. 9.4(a)), the shear force at point
S, fS, is along the 270o shear direction. When the additional linear shear force, f', is in the
90o shear direction and has the same amplitude as fS (i.e. |f'| = |fS|), S is no longer
influenced by any shear force. Consequently, the center of the rings shifts from O to S
(i.e. αshift = 180o ), as shown in Fig. 9.4(b). If an additional linear shear is applied to a
radial configuration, the center of the rings should move along the shear direction.
Therefore, the additional linear shear test results also prove the azimuthal configuration
of T-SLCs. Similarly, 0o, 180o, and 270o linear shears induce 90o, 270o, and 0o shift of the
ring pattern. In general, αshift= αshear +90o for a T-SLC of counterclockwise twist shear.
214
Figure 9.3 Illustration of a pattern shift for T-SLC upon application of a linear shear force.
(a) The angle representation of shear/shift directions; (b) ring pattern obtained before a
linear shear (90o) was applied; (c) the shift of the ring pattern after a 90o linear shear.
0o
90o
180o
270o
Linear shear (b)
(c)
(a)
Pattern shift
215
Figure 9.4 Mechanism of pattern shift of a T-SLC upon a 90o additional linear shear. The
arrows on the outer circle represent the counterclockwise twist direction.
(a)
(b)
Counterclockwise twist
216
The T-SLC had a twist angle of 0.5o. The variation in optical path delay due to
different shear distances gives rise to the dark rings in the pattern. The shear distance (i.e.,
the arc of twist rotation in the T-SLC) is calculated as = .L r θ⋅ For example, the shear
distance at P5, 5p = 10000 0.5/180 3.1416= 87.3L r m mθ μ μ⋅ = ⋅ ⋅ . Similarly, LP0, LP1, LP2,
LP3, and LP4 are obtained as 0, 17.5, 34.9, 52.4, and 69.7 μm, respectively. At the origin
(P0) of the T-SLC, where no shear force is applied, the phase shift is close to zero
because liquid crystal domains are randomly oriented. From P1 to P5, the extent to which
liquid crystal domains are aligned along the shear direction increases. Therefore, optical
path delay of T-SLCs is at its minimum in the center and increases when radius increases
as plotted in Fig. 9.5, exhibiting a negative-lens-like phase profile.
As shown in Fig. 9.6, the center of the T-SLC (P0) had the lowest transmission
because it was not sheared. However, from P1 to P5, the shear distance increases as the
radius increases. This gradually reduces the refractive index mismatch between adjacent
liquid crystal domains, and hence transparency is improved.
The phase profile of the T-SLC is electrically tunable. With the ring pattern
viewing setup, a series of T-SLC images between crossed polarizers were taken when a
voltage ramp from 0V to 120V was applied (Fig. 9.7). As the voltage increased, the rings
of the pattern became less and less and finally disappear. The whole sample turned black
eventually and the negative-lens-like phase profile became completely flat.
217
0 2 4 6 8 10 12
0.0
0.5
1.0
1.5
2.0
P0
P4P3
P2
P5
Radius (mm)
Opt
ical
Pat
h D
elay
(μm
)
P1
Figure 9.5 Optical path delay on the different spots of the T-SLC.
218
0 2 4 6 8 10 1220
40
60
80
T%
Radius (mm)
P5P4P3
P2P1
P0
Figure 9.6 Position-dependent transmittance of the T-SLC. The laser’s wavelength is
632.8 nm.
219
Figure 9.7 With the crossed polarizers viewing setup, T-SLC images were recorded in a
voltage ramp: (a) 0 V, (b) 30 V, (c) 50 V, (d) 80 V, (e) 110 V, and (f) 120 V.
220
T-SLCs can be used as polarization converters due to the azimuthal variation of
liquid crystal directors and its radial variation of the phase retardation. A rather
complicated polarization pattern can be produced. For example, Fig. 9.8 demonstrates the
polarization distribution after a linearly polarized light passes through a T-SLC. As
derived in Appendix C, the Jones vector of the light passing through the T-SLC follows:
cos sin cos2' 2 2'
sin 2 sin2
iVxVy
i
δ δ β
δβ
⎛ ⎞⎛ ⎞ ⎛ ⎞+ ⋅⎜ ⎟ ⎜ ⎟⎜ ⎟⎛ ⎞ ⎝ ⎠ ⎝ ⎠⎜ ⎟=⎜ ⎟ ⎜ ⎟⎛ ⎞⎝ ⎠⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
(9.1)
Where phase retardation 2 ndπδλΔ
= , and β is the angle between liquid crystal
directors and the polarizer, defined in Fig. C.1 of Appendix C. When 2 2ndπδ πλΔ
= = ,
i.e., nd λΔ = , cos sin cos2
' 12 2' 0
sin 2 sin2
iVxVy
i
δ δ β
δβ
⎛ ⎞⎛ ⎞ ⎛ ⎞+ ⋅⎜ ⎟ ⎜ ⎟⎜ ⎟ −⎛ ⎞ ⎛ ⎞⎝ ⎠ ⎝ ⎠⎜ ⎟= =⎜ ⎟ ⎜ ⎟⎜ ⎟⎛ ⎞⎝ ⎠ ⎝ ⎠⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
, which indicates that the
emerging light is linearly polarized along the X axis on that ring. When
2 ndπδ πλΔ
= = , 2' cos2 cos2' sin 2 sin 2
iVxi e
Vy
πβ ββ β
⎛ ⎞ ⎛ ⎞ ⎛ ⎞= =⎜ ⎟ ⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠ ⎝ ⎠, which is a distribution of linearly
polarized light. On the other hand, when 22
ndπ πδλΔ
= = ,' 1 cos2' sin 2
Vx iVy i
ββ
+⎛ ⎞ ⎛ ⎞=⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠, which is
a distribution of more general elliptically polarized light. For simplification, only the
polarization states are concerned while the amplitudes are neglected in the drawing of Fig.
9.8.
221
Figure 9.8 Simplified illustration of distribution of polarization states after a linearly
polarized light (along the X axis) passes through a T-SLC. The large rings are phase
retardation rings; Δnd=λ/4, λ/2, and λ, respectively. Τhe short lines, circles and ellipses
represent linear, circular and elliptical polarizations of light, respectively.
X
Y
Δnd=λ
Δnd=λ/2
Δnd=λ/4
β
222
9.4 Conclusions
In summary, a twisted stressed liquid crystal (T-SLC) has an azimuthal liquid
crystals director configuration. The variation of the extent of shear on a T-SLC gives rise
to an electrically-tunable negative-lens-like phase profile. The T-SLC can convert
uniformly polarized light into a spatially varied polarized light field due to its position-
dependent phase retardation and liquid crystal director direction.
223
CHAPTER 10
SLCs for Fast Display Application
10.1 Introduction
Liquid crystal displays have been applied to many applications such as PC
monitors, TVs, and projectors. In terms of video applications, the response speed of a
liquid crystal material becomes critical in order to reduce motion blur. Many methods
have been developed for fast liquid crystal devices including thin cell gap,[12] overdrive
schemes,[16] and optimization of liquid crystal materials[128] and switching modes.[14]
Another approach to increase response speed is to incorporate liquid crystals into
polymer matrices.[38,40,85] However, the light scattering and relatively high operation
voltages limit the application of conventional liquid crystal polymer composites in
displays.
In this chapter, SLCs’ potential for fast display applications is explored. Thin SLC
films had total response times of 5 ms with switching voltages below 5 V. By adjusting
the shear distance, the response time was reduced to 2 ms while the switching voltage
was increased up to 9 V. The operation temperature range, voltage holding ratio, and
thermal stability of SLCs are then discussed.
224
10.2 Performance of SLC displays
A 5-μm-thick SLC cell was fabricated using a mixture of 5CB and NOA65 at a
90:10 weight ratio. Figure 10.1 deomonstrates its high transparency at the sheared state.
The thin SLC’s electro-optical properties are shown in Fig. 10.2(a). At the 30 μm shear
distance, only 4.7 V was required to switch half wave phase retardation at 633 nm. T10
and T90 were used to estimate the switching time. The turn-on time is 2 ms while turn-off
time is approximately 3 ms. Therefore, the total response time is 5 ms. This is an order of
magnitude improvement compared with cells built with pure liquid crystal 5CB using the
same cell gap. Even when the cell gap of pure 5CB was reduce to less than 2 μm; it had a
6.5 ms response time as shown in Fig. 10.2(b), still slower than the 5-μm-thick SLC cell.
225
Figure 10.1 Transparency of a 5 μm thick 5CB-SLC: (a) before shear; (b) after shear. The
paper with ‘westlab’ written on was placed 1 cm away from the SLC cell.
(a)
(b)
226
0 2 4 6 8
0.0
0.2
0.4
0.6
0.8
1.0N
orm
aliz
ed in
tens
ity
Time (ms)
5μm thick cell 4.7 volt driven τoff
τon
0 2 4 6 8
0.0
0.2
0.4
0.6
0.8
1.0
Nor
mal
ized
Inte
nsity
Time (ms)
Pure 5CB τon
τoff
(a)
(b)
0 2 4 6 8
0.0
0.2
0.4
0.6
0.8
1.0N
orm
aliz
ed in
tens
ity
Time (ms)
5μm thick cell 4.7 volt driven τoff
τon
0 2 4 6 8
0.0
0.2
0.4
0.6
0.8
1.0
Nor
mal
ized
Inte
nsity
Time (ms)
Pure 5CB τon
τoff
(a)
(b)
Figure 10.2 Response time (τon and τoff): (a) a 5-μm-thick SLC cell switching with 4.7 V;
(b) a 1.7-μm-thick 5CB cell switching with 5 V.
227
10 20 30 40 50 602
4
6
8
10
12
4
6
8
10R
espo
nse
time
(ms)
Shear Distance (μm)
Vswitch
Switc
hing
Vol
tage
(V)
τtotal
Figure 10.3 The influence of shear distance on switching voltage and total response time
(τon + τoff). The solid round circles represent the switching voltage (axis on the right). The
solid squares are the response time (axis on the left).
228
The amount of shear affects the electro-optical performance of SLCs, varying the
response time and switching voltage. Figure 10.3 illustrates that when the shear distance
increases from 10 μm to 60 μm, the voltage required to switch a half wave phase shift
increases from 4 V to 9 V and the total response time decreases from 12 ms to 2 ms. This
demonstrates that optimization of SLCs is easy but still balances fast speed with
operation.
For most display applications, a wide nematic temperature range is required. 5CB
based SLC shows excellent electro-optical performance; however, it has a narrow
nematic range (i.e. less than 40 degrees) and low nematic-isostropic transition
temperature, which limit its practical application. SLCs based on wide temperature range
cyanobiphenyls (E7 and E44) were fabricated. The ranges of the nematic phase of E7 and
E44 are from -20 oC to 61 oC and -6 oC to 100 oC, respectively. Similar to 5CB-SLC, E7-
SLC and E44-SLC are much faster than corresponding pure liquid crystal samples.
One drawback of cyanobiphenyls is that their voltage holding ratios (VHRs) are
too low for active matrix display applications. Therefore, liquid crystals with high VHRs
were introduced into SLC systems. TL205 (from Merck) and ZSM5386XX (from Chisso)
have VHRs of greater than 0.9. PN393 was selected as the prepolymer to mix with these
two liquid crystals because of its high solubility with them. The maximum mixing weight
ratio of the two liquid crystals to PN393 is approximately 82:18 at room temperature.
With 6 V operation voltage, the response time of these systems ranged from 14 ms to 18
ms. Further exploration is needed to find more soluble prepolymers with the liquid
crystals and to optimize fabrication conditions which will speed up these SLCs.
229
The VHRs of these two SLC systems were tested. Figure 10.4 shows that the
systems retained high VHR values (i.e. only 3% drop) after PN393 was introduced into
these two liquid crystals (only 3% drop). The high VHRs of these SLC systems make
them suitable for fast display application.
Thermal stability of the thin SLCs was tested at different temperatures (25oC,
60oC, and 100oC). The turn-off time is used to monitor the relaxation of SLC samples.
The relaxation graph is plotted in Fig. 10.5. At room temperature, the SLC’s stability is
well beyond six months. At 100oC, the turn-off time increased over 100% after 300 hrs’
heating while the turn-off time of the sample heated at 60oC increased only 20%. The
SLC samples still can switch in less than 10 ms seconds even after the 300 hrs’ 100 oC
baking. According to Bahadur[129], each 8oC rise in temperature is supposed to accelerate
the deterioration by a factor of two, demonstrating reasonable lifetime for these materials.
However, it is not clear at this point if the decay in switching speed is a result of
relaxation of the edge sealant or of the polymer network. In future research, more sealants
should be studied to optimize the sealing conditions of SLCs for higher thermal stability.
10.3 Conclusions
Stressed liquid crystals do not scatter light, and do not require and alignment layer.
The shear stress significantly increases switching speed. Fast displays based on SLC
material demonstrate 2 ms response time, an order of magnitude faster than traditional
liquid crystal materials. SLCs have great potential for the display application and
particular for LCoS devices.
230
0.0
0.2
0.4
0.6
0.8
1.0
Vol
tage
Hol
ding
Rat
io (V
HR
) pure TL-205 TL-205/PN393 Pure ZSM-5386 ZSM/PN393 5CB-SLC
Figure 10.4 Voltage Holding Ratio measurements for liquid crystals TL205 and
ZSM5386 comparing with SLCs based on the corresponding liquid crystals.
231
0 100 200 300-40
0
40
80
120
160
200
25oC
60oC
Cha
nge
of re
spon
se ti
me
(%)
Time (hr)
100oC60oC25oC
100oC
Figure 10.5 Thermal stability test of SLC at three different temperatures: 25 oC, 60 oC,
and 100oC.
232
CHAPTER 11
Conclusions
Many non-display liquid crystal devices require fast-switching large phase
retardation materials such as spatial light modulators, optical phase arrays. Especially for
infrared applications, of which the operation wavelength is large, the capability of fast-
switching and large phase modulation is crucial.
The only feasible way to achieve large optical path delay (Δnd) is to use thick
liquid crystal films. However, for devices using pure liquid crystals, when liquid crystal
film thickness is large, the response time becomes extremely long (for example, τoff is
over 400 ms for a 20 μm thick pure 5CB cell). Incorporating polymer into liquid crystal
systems can produce fast-switching, large phase modulating materials because of the
significantly increased surface to volume ratio, essentially creating an ensemble of thin
cells. Various types of liquid crystal/polymer composites have been made based on
different liquid crystal/polymers and fabrication conditions during the past twenty years.
The most popular two are polymer dispersed liquid crystal[31] (PDLC) and polymer
network liquid crystal[38] (PNLC). They can switch fast due to the assistance of polymer
matrix during the liquid crystals’ relaxation process, and it’s possible for them to provide
large phase retardation modulation because thick samples are producible. However, these
233
liquid crystal/polymer composites are limited either by their intrinsic light scattering or
the inhibitively high operation electric field for fast large-phase modulation.
Stressed liquid crystals, a unique sheared liquid crystal/polymer composite, on the other
hand, eliminate light scattering and operate with reasonable field (1 V/μm). SLCs
decouple the cell thickness and the switching speeds; therefore, SLCs can be built as
thick as needed to provide large optical path delay while maintaining fast speed. So far an
820-μm-thick SLC film capable of switching 55 μm OPD has been demonstrated. The
relaxation time is less than 14 ms. A comparison of the various systems to achieve 55 μm
OPD is made in Table 11.1. Only pure LC and SLC devices of the thickness specified
have been built; other devices are just assumed to work. Δn of the LC among these
systems is assumed to be 0.19. All the cells compared are assumed to be of planar
alignment and operating at the mode of electrically controlled birefringence. The
effective birefringence of PDLC/Nano-PDLC is calculated as niso-no=(ne-no)/3, and the
concentration of LC in PDLC is assumed to be 50%. Concentration of LCs in PNLC is
assumed to be 95%. It can be seen that to achieve fast and large OPD SLC materials are
the only option: fast, low field operation, high transparency, no hysteresis and having
linear response between OPD and voltage.
234
Pure LC PDLC (normal mode)
Nano-PDLC PNLC (reverse mode)
SLC
Cell gap ~290 μm >1000 μm >1000 μm ~310 μm 820 μm Speed Thousands
of ms Dozens of ms
ms Dozens of ms
Less than 14 ms
Transmittance Field on
H H H L H
Field off H L H H H
Hysteresis N Y Y Y/N N Linear Response
N N N Y/N Y
Field Small <~0.5V/μm
>1V/mm >5V/mm >1V/μm Good:1V/μm
Table 11.1 Comparison between all systems which can switch 55 μm OPD.
The performance of SLCs depends greatly on their morphologies which rely on
fabrication conditions, such as composition, UV intensity, and cure temperature. It is
shown that only a narrow range of composition (84 ~94 wt% of liquid crystals) produces
SLCs. In addition, strong UV intensity (greater than 40 mW/cm2) and high cure
temperatures (30oC higher than the TNI of a liquid crystal used in SLC) are necessary to
create small interconnected liquid crystal domains dispersed in ultra-thin polymer sheets,
which favor fast response and the elimination of light scattering after shear deformation.
SLCs can be treated as films consisting of multiple stacks of close-packed and shaped
liquid crystal domains inside stressed polymer matrices.
Shear deformation inside SLCs not only speeds up the response but also provides
liquid crystal alignment, thereby, eliminating light scattering. Upon shearing, it is
235
observed that polymer matrix is stretched along the shear direction and liquid crystal
domains wrapped by the sheets adopted elliptical shape. During this process, liquid
crystals orient along the shear direction due to the shape anisotropy of liquid crystal
domains. The shear alignment is a bulk effect unlike the surface alignment on traditional
liquid crystal devices, which makes it possible to fabricate films as thick as necessary.
Light scattering of SLCs decreases dramatically upon shearing. Before the shear, each
liquid crystal domain is surrounded by other randomly-oriented liquid crystal domains,
which causes major light scattering. When liquid crystal domains are aligned in the same
direction because of the shear deformation, the light scattering of the film decreases
dramatically as the mismatch of refractive index between adjacent liquid crystal domains
disappears. On the other hand, the light scattering resulting from refractive index
mismatch between liquid crystal and polymer matrix is less significant since the
polymer’s dimension is much smaller than the wavelengths of incident light.
With modification of B-G Wu et al.’s model of elliptical droplets inside PDLC,
formulas are derived for switching electrical fields and response times of SLC systems at
different shear distances based on the layered structure of close-packed and shaped liquid
crystal domains inside a stressed polymer matrix. The calculated electro-optic responses
of the SLC samples are consistent with experimental results. The electro-optical
performance of SLCs depends on not only the liquid crystal domain size but also the
aspect ratio of the liquid crystal domains. Small liquid crystal domains require high
switching fields and they produce fast speed. In addition, the switching field rises with
the increase of shear distances and both the relaxation time and the rise time declines
236
with the increase of the shear distance because the aspect ratio of the elliptical domains
increases. As such, this model provides a tool for understanding electro-optical
performance of SLCs.
The novelty of SLCs on electro-optical performance is that they are not only fast,
capable of large phase modulation, they also have unique linear response between OPD
and applied voltage and essentially hysteresis-free. The linear response is mainly due to
the size distribution of liquid crystal domains inside SLCs and it can significantly
simplify the driving scheme. Hysteresis-free makes the control of OPD as precisely as
possible, independent of the switching scheme.
Based on these advantages, SLCs are utilized in many applications including Mid-
Wave IR beam-steering and tip-tilt wavefront correction because they are capable of
switching large OPD at fast speeds. SLC beam-steering devices which switch 4.5 μm in 2
ms have demonstrated continuous beam steering for an IR laser of (λ=3 μm) as well as
visible and NIR laser wavelengths. A design of using a series of resistors to control phase
ramp was utilized to operate a SLC based tip-tilt corrector according to SLC’s linear
response between OPD and voltage. This SLC tip-tilt corrector can switch 1.55 μm OPD
as fast as 100 μs. SLCs are also patternable, either through photo-mask or by mechanical
approach. For instance, SLC prisms and lenses were made by polymerizing SLC films
through photo-masks of various intensity patterns. The profile of the difference of the
phase retardation value in different areas is determined by the optical density profile of
the mask and may be varied in a different manner in accordance with a particular
application: centrosymmetric, cylindrical, saw-tooth profiled, etc. These devices have
237
great potential for tunable lenses of large aperture because the OPD of SLCs can be
increase as large as needed without sacrificing switching speed. Mechanically patterned
SLCs can serve as light polarization converter. A twist-SLC (T-SLC) was made when a
twist shear was applied to a SLC film. It has large phase retardation at the edges and
small phase retardation in the center, resulting in a negative lens. This lens is not only
electrically tunable but also mechanically adjustable. In addition to the twist shear, an
extra linear shear can shift the lens structure, creating asymmetric phase profile in the
active area of the device. Due to the distribution of OPD, the T-SLC can convert a
uniform polarization into a complicated polarization distribution. In addition, the concept
of fast displays based on SLCs is also demonstrated. All in all, SLCs are unique and
versatile fast-switching, large-phase light modulating materials, and they exhibit great
potential for non mechanical beam-steering applications, spatial light modulators, large
aperture liquid crystal lenses and prisms, and fast displays.
238
APPENDIX A
Components/Chemical Structures of the Materials Used in SLCs
Name Detailed components/Chemical structures
5CB 4-pentyl-4'-cyanobiphenyl
N
E7 51 wt% of 4-cyano-4`-pentylbiphenyl;
25 wt% of 4-cyano-4’-heptylbiphenyal;
16 wt% of 4-cyano-4’-octyloxybiphenyl;
8 wt% of 4-cyano-4’’-pentyl-p-terphenyl.
[From Ulrich Maschke et al., Macromolecular Rapid Communications 23 (3), 159 - 170 (2002).]
E44 Major components are cyano-biphenyls and terphenyls
RM82
O
O
O
O
O
O
O
O
O
O
Irgcure
651 2,2-Dimethoxy-1,2-diphenylethan-1-one
NOA65 consisting of trimethylol-propane diallyl ether, trimethylol-propane tris thiol, and isophorone diisocyanate ester, benzophenone photoinitiator [From George W. Smith, Mol. Cryst. Liq. Cryst. 196, 89-102 (1991)]
239
APPENDIX B
Calculations of Electro-optical Responses for SLCs
This calculation is based on the model proposed by Wu et al.[45] At first, a liquid
crystal’s director can be expressed as ( ) ( ): (sin , ,0,cos , )n r z r zθ θr , shown in Fig. B.1
using cylindrical coordinates. Then, the divergence, curl of nr and ( )n n× ∇ ×r r
are
calculated in Equation B.1, B.2, and B.3, respectively.
Figure B.1 Illustration of liquid crystal director in the cylindrical coordinates.
r
Z
X
Yφ
θ
n̂
240
( ) ( ) ( )
( ) ( )
( )
1 1
sin cossin 0
sin cos sin
sin cos sin
r z
r z
rn n nn
r r r z
r r z
r r z
r
φφ
θ θθ
θ θ θθ θ
θ θ θ θ θ
∂ ∂ ∂∇ • = + +
∂ ∂ ∂
∂ ∂= + + +
∂ ∂∂ ∂
= + • + − •∂ ∂
= + • − •
r
(B.1)
where θr = rθ∂
∂ and θz =
zθ∂
∂
( )
( )1 1( ) ( ) ( )
1 cos (0) sin cos 1 ( 0) sin( ) ( ) ( )
cos sin
z z r z r
z r
r nn n n n nn r zr z z r r dr d
rr zr z z r r dr d
φφφ φ
θ θ θ θφφ φ
θ θ θ θ φ
∧
∧
∧
∂ •∂ ∂ ∂ ∂ ∂∇ × = ⋅ − • + − • + ⋅ − •
∂ ∂ ∂ ∂∂ ∂ ∂ ∂ ∂ • ∂
= ⋅ − • + − • + ⋅ − •∂ ∂ ∂ ∂
= • + • •
r$ $
$ $ (B.2)
( )$
( ) $
[ ] [ ]
sin 0 cos
0 cos sin 0
cos (cos sin ) sin (cos sin )
z r
z r z r
r zn n
r z
φθ θ
θ θ θ θ φ
θ θ θ θ θ θ θ θ θ θ
× ∇× =
⋅ + ⋅
= − ⋅ + ⋅ + ⋅ + ⋅
$ $r r
$ $
(B.3)
The elastic energy can be expressed as follows:
241
( ) ( )
( )
( )11 33
2 211 33
2211 33
2 233 33
2 233 33
233
( )2 2
sin cos sin cos sin2 2
0 0 ( 0)2 2
2 2
2
elastic
r z z r
K Kr z
is verysmall
r z
independent on rz
K Kf n n n
K Kr
K K
K K
K
θ
θ
θ θ θ θ θ θ θ θ θ
θ θ
θ θ
θ
=
− − −
= ⋅ ∇ • + ⋅ × ∇ ×
⎛ ⎞= ⋅ + ⋅ − ⋅ + ⋅ ⋅ + ⋅⎜ ⎟⎝ ⎠
= ⎯⎯⎯⎯⎯→ + − + +
= +
= ⎯⎯⎯⎯⎯⎯→
r r r
(B.4)
because sincos
r
z
nn
θθ
= , then r tgz
θ= , so 1tan zcr
θ − ⎛ ⎞= ⎜ ⎟⎝ ⎠
2 2 2
1 1
1z
rr r zz
r
θ −= − ⋅ =
+⎛ ⎞+ ⎜ ⎟⎝ ⎠
at the equator of a spherical droplet, z=0
22
1z r
θ =
generalize it to elongated droplet
233 3322 2elastic z
K Kfr
θ= = , where 2 2
22 2 2 2cos sin
a brb aα α
=⋅ + ⋅
so
2 2 2 2 2 2 233 33 332 2 2 2
cos sin cos sin2 2 2elasticK K Kb a lfr a b a
α α α α⋅ + ⋅ + ⋅= = ⋅ = ⋅ (B.5)
242
E
a
N
nb
λ1
λ
λ2
a,b: semi-major and semi-minor axisE: electric fieldN: director orientation of LC after field appliedn: LC director orientation in the droplet
E
a
N
nb
λ1
λ
λ2
a,b: semi-major and semi-minor axisE: electric fieldN: director orientation of LC after field appliedn: LC director orientation in the droplet
a
N
nb
λ1
λ
λ2
a
N
nb
λ1
λ
λ2
a,b: semi-major and semi-minor axisE: electric fieldN: director orientation of LC after field appliedn: LC director orientation in the droplet
Figure B.2 Illustration of liquid crystal director direction in a liquid crystal droplet before
and after electrical field.
notice: EOn λ∠ =ur r
; 2EOa λ∠ =ur r
; 2α λ λ= −
( ) ( )
2 2 233
2
2 2 22 233
2
cos sin2
cos sin2
elasticK lf
alK
a
α α
λ λ λ λ
+ ⋅= ⋅
− + ⋅ −= ⋅
(B.6)
B.1 Relaxation time: τoff
The elastic torque is elasticd
dfd
τλ
=
243
( ) ( ) ( )
( ) [ ]
2332 2 2 22
2332 22
23322
2 sin( ) cos( ) 1 2sin( ) cos( ) 12
sin 2( ) sin 2( )2
1 sin 2( )2
elasticdf K ld a
K la
K la
λ λ λ λ λ λ λ λλ
λ λ λ λ
λ λ
⎡ ⎤= ⋅ − − ⋅ − ⋅ − + ⋅ − − ⋅ −⎣ ⎦
⎡ ⎤= ⋅ − − −⎣ ⎦
= ⋅ − −
Viscosity torque:
ddtγλτ γ= ⋅ (B.7)
in order to get relaxation time ( offτ )
If make 0d γτ τ+ =
( ) [ ]23322 1 sin 2( )
2K dla dt
λλ λ γ⋅ − − = ⋅
set 2α λ λ= − , so
( ) [ ]2332 1 sin 2
2K dla dt
αα γ⋅ − = ⋅
try solution:
( )2
233
tan exp
1
taa
K l
αγ
⎛ ⎞⎡ ⎤⎜ ⎟⎢ ⎥
−⎜ ⎟⎢ ⎥= ⎜ ⎟⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟⋅ −⎢ ⎥⎣ ⎦⎝ ⎠
Left side: ( ) [ ] ( ) ( ) ( )( )
2 2 233 33 332 2 2 2 2
22 tan1 sin 2 1 12 2 1 tan 2 1
EXPK K Kl l la a a EXP
ααα
⋅ − = ⋅ − ⋅ = ⋅ − ⋅+ +
244
Right side: ( )( ) ( )2
332 2 2
1tan 11 1
K ld a EXPd dEXP EXPdt dt EXP dt EXP aαγ γ
γ
⎛ ⎞− ⋅ −⎜ ⎟= = =⎜ ⎟+ + ⎝ ⎠
So Left ==Right
General solution is
( )2
233
tan exp
1
ta Ba
K l
αγ
⎛ ⎞⎡ ⎤⎜ ⎟⎢ ⎥
−⎜ ⎟⎢ ⎥= ⎜ ⎟⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟⋅ −⎢ ⎥⎣ ⎦⎝ ⎠
where B is a constant.
So
( )2 2
233
tan exp
1
ta Ba
K l
λ λγ
⎛ ⎞⎡ ⎤⎜ ⎟⎢ ⎥
−⎜ ⎟⎢ ⎥= + ⎜ ⎟⎢ ⎥⎜ ⎟⎢ ⎥⎜ ⎟⋅ −⎢ ⎥⎣ ⎦⎝ ⎠
In this equation, the characteristic time offτ is obtained as:
( )2
233 1off
aK l
γτ =⋅ −
(B.8)
B.2 Turn-on time: τon
( ) [ ]
( ) ( )
( ) ( )
2 23322
233 2
2 22
2 233 332
2 22 2
0
1 sin 2( ) sin 2 02 2
1sin 2 cos 2 cos 2 sin 2 sin 2 0
2 21 1
cos 2 sin 2 sin 2 cos 22 2 2
e d
K dl Ea dt
K l dEa dt
K l K l dEa a dt
γτ τ τ
ε λλ λ λ γ
ε λλ λ λ λ λ γ
ε λλ λ λ λ γ
+ + =
Δ⇒ ⋅ − − + + =
− Δ⇒ − + + =
⎡ ⎤− −Δ⎢ ⎥⇒ ⋅ + ⋅ − ⋅ ⋅ = −⎢ ⎥⎣ ⎦
set
245
( )
( )
233 2
22
233
22
1cos 2
2 21
sin 22
K lA E
aK l
Ba
ελ
λ
⎧ − Δ⎪ = ⋅ +⎪⎨
−⎪= ⋅⎪⎩
the torque equation will change into
2 2
2 2 2 2
2 2
sin 2 cos 2
sin 2 cos 2
sin(2 )
dA Bdt
A B dA BdtA B A B
dA Bdt
λλ λ γ
λλ λ γ
λλ β γ
− = −
⎛ ⎞⇒ + ⋅ ⋅ − ⋅ = −⎜ ⎟
+ +⎝ ⎠
⇒ + ⋅ − = −
set 22
u λ β−= then
2 2
2 2
sin(2 )
sin(2 )
dA Bdt
A B duudt
λλ β γ
γ
+ ⋅ − = −
+⇒ ⋅ = −
similar as what we’ve done with the relaxation time τoff
try the solution
2 2
tan exp
2
tu a C
A Bγ
⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟−⎢ ⎥⎜ ⎟= − ⋅⎢ ⎥⎜ ⎟
⎜ ⎟⎢ ⎥+⎝ ⎠⎣ ⎦
then we obtained the solution for λ
2 2
tan exp2 2
2
tu a C
A B
β βλ γ
⎡ ⎤⎛ ⎞⎢ ⎥⎜ ⎟−⎢ ⎥⎜ ⎟= + = − ⋅⎢ ⎥⎜ ⎟
⎜ ⎟⎢ ⎥+⎝ ⎠⎣ ⎦
246
so the characteristic time τon is
( ) ( )
( ) ( )
( ) ( ) ( )
2 2 2 22 233 332
2 22 2
22 2233 332 2
22 2
22 233 332 2
2 2
2 1 12 cos 2 sin 2
2 2 2
1 12 2 cos 2
2 2 2 2
1 12cos
onA B K l K l
Ea a
K l K lE E
a a
K l K lE E
a a
γ γτελ λ
γ
ε ε λ
γ
ε ε
= =+ ⎛ ⎞ ⎛ ⎞− −Δ⎜ ⎟ ⎜ ⎟⋅ + + ⋅
⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
=⎛ ⎞ ⎛ ⎞− −Δ Δ⎛ ⎞ ⎛ ⎞⎜ ⎟ ⎜ ⎟+ + ⋅ ⋅⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠⎝ ⎠ ⎝ ⎠
=⎛ ⎞ ⎛ ⎞− −⎜ ⎟ ⎜ ⎟+ Δ + ⋅ Δ ⋅⎜ ⎟ ⎜ ⎟⎝ ⎠ ⎝ ⎠
( )22 2λ −
(B.9)
22 2cos 2 2cos 1λ λ= − and 2 2 2 2 2
1
1 1cos1
1
dd L LL
d
λ = = =+ +⎛ ⎞+ ⎜ ⎟
⎝ ⎠
as shown in the
program.
B.3 Switching voltage: Vswitch
0e dτ τ+ = ;
2
2
2 2e
n EEfε
∧
⊥
⎛ ⎞Δ •⎜ ⎟ε ⎝ ⎠= − −
ur
; 2 sin 22
ee
df Ed
ετ λλ
Δ= = ;
( ) [ ]23322 1 sin 2( )
2dK la
τ λ λ= ⋅ − −
so
( ) [ ]2 23322 1 sin 2( ) sin 2 0
2 2K l Ea
ελ λ λΔ⋅ − − + =
247
( )[ ]
( ) ( )
( )
( )( )
2 2332 22
2 2 233 332 22 2
23322
22
2 23322 2
2332
1 sin 2 cos 2 cos 2 sin 2 sin 2 02 2
1 cos 2 sin 2 1 sin 2 cos 22 2 2
1 sin 2 sin 22tan 21 cos 2 cos 22 2 1
sin1 tan2
K l EaK Kl E la a
K la
K El EKa la
a
ελ λ λ λ λ
ελ λ λ λ
λ λλε ελ λ
λ
Δ⇒ − ⋅ − ⋅ − ⋅ + =
Δ⎡ ⎤⇒ − ⋅ − + ⋅ = ⋅ − ⋅⎢ ⎥⎣ ⎦
⋅ − ⋅⇒ = =
Δ Δ⋅ − + +⋅ −
⇒ =
( )
22
2233
2
2
cos 21
EK la
λελ
⎛ ⎞⎜ ⎟⎜ ⎟⎜ ⎟⎜ ⎟Δ
+⎜ ⎟⋅ −⎜ ⎟
⎝ ⎠
noticing that λ is λ1 ( the angle between liquid crystal director and the E field) and when
λ1 is 0 and λ2 is 90o, we obtain switching field.
( )
( )
( )
2
2332
233
2
233
1 01
1
1
EK la
K lE
a
K ldV E da
ε
ε
ε
Δ− =
⋅ −
−⇒ =
Δ ⋅
−⇒ = ⋅ =
Δ
considering dielectric effect
( )1
2 2332
1
12
3switch
K ldVa
σσ ε
⎛ ⎞−⎛ ⎞⎜ ⎟= +⎜ ⎟⎜ ⎟Δ⎝ ⎠⎝ ⎠
(B.10)
248
APPENDIX C
Jones Matrix Derivation of Light Polarization State for T-SLC
Based on Jones matrix method,[130] the polarization of the outgoing light passing
through the T-SLC can be formulated. Vector V' can be obtained from:
0
'( ) ( )
'Vx Vx
R W RVy Vy
ψ ψ⎛ ⎞ ⎛ ⎞= − ⋅ ⋅⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠ (C.1)
where, ( )R ψ is the coordination rotation matrix, ψ is the angle between the slow axis and
X axis.
cos sin( )
sin cosR
ψ ψψ
ψ ψ⎛ ⎞
= ⎜ ⎟−⎝ ⎠ (C.2)
W0 is the Jones matrix for the retardation plate, e.g. the T-SLC. ie φ− represents the
initial phase information and it is normally neglected during the polarization state
calculation.
2
0
2
0
0
i
i
i
eW e
e
δ
φδ
−
−
⎛ ⎞⎜ ⎟= ⎜ ⎟⎜ ⎟⎝ ⎠
(C.3)
Generally speaking, a retardation plate is characterized by its phase retardation
δ ( 2 ndπδλΔ
= ) and the azimuth angle ψ and presented as
249
2
0
2
cos sin 0 cos sin( ) ( )
sin cos sin cos0
i
i
i
eW R W R e
e
δ
φδ
ψ ψ ψ ψψ ψ
ψ ψ ψ ψ
−
−
⎛ ⎞−⎛ ⎞ ⎛ ⎞⎜ ⎟= − ⋅ ⋅ = ⋅ ⋅⎜ ⎟ ⎜ ⎟⎜ ⎟ −⎝ ⎠ ⎝ ⎠⎜ ⎟
⎝ ⎠ (C.4)
W is obtained after neglecting ie φ− :
2 22 2 2 2
2 22 2 2 2
cos sin sin cos
sin cos sin cos
i i i i
i i i i
e e e eW
e e e e
δ δ δ δ
δ δ δ δ
ψ ψ ψ ψ
ψ ψ ψ ψ
− −
− −
⎛ ⎞⎛ ⎞⋅ + ⋅ −⎜ ⎟⎜ ⎟
⎝ ⎠⎜ ⎟= ⎜ ⎟⎛ ⎞⎜ ⎟− ⋅ + ⋅⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
(C.5)
Assuming the incident light is linearly polarized along the X axis, the polarization
of the light passing through the T-SLC can be obtained using the Jones vector:
2 22 2 2 2
2 22 2 2 2
2 22 2
2 2
''
cos sin sin cos10
sin cos sin cos
cos sin
sin cos
i i i i
i i i i
i i
i i
Vx VxW
Vy Vy
e e e e
e e e e
e e
e e
δ δ δ δ
δ δ δ δ
δ δ
δ δ
ψ ψ ψ ψ
ψ ψ ψ ψ
ψ ψ
ψ ψ
− −
− −
−
−
⎛ ⎞ ⎛ ⎞= ⋅⎜ ⎟ ⎜ ⎟
⎝ ⎠ ⎝ ⎠⎛ ⎞⎛ ⎞
⋅ + ⋅ −⎜ ⎟⎜ ⎟⎛ ⎞⎝ ⎠⎜ ⎟= ⋅ ⎜ ⎟⎜ ⎟⎛ ⎞ ⎝ ⎠⎜ ⎟− ⋅ + ⋅⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
⎛ ⎞⋅ + ⋅⎜ ⎟
⎜ ⎟= ⎛ ⎞⎜ ⎟−⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
(C.6)
As seen from Fig. C-1, 2πψ β= + . Therefore, the polarization of the light passing
through the T-SLC can be expressed as
250
2 22 2
2 2
cos cos2 sinsin cos' 2 2' sin cos sin 2 sin
2
i i
i i
ie eVxVy e e i
δ δ
δ δ
δ δββ β
δβ β β
−
−
⎛ ⎞ ⎛ ⎞+⋅ + ⋅⎜ ⎟ ⎜ ⎟⎛ ⎞⎜ ⎟= = ⎜ ⎟⎜ ⎟ ⎛ ⎞⎜ ⎟⎝ ⎠ ⎜ ⎟− −⎜ ⎟ ⎜ ⎟⎜ ⎟ ⎝ ⎠⎝ ⎠⎝ ⎠
(C.7)
When an analyzer linearly polarized along the Y axis is used to observe the T-
SLC, the Jones vector for the polarization of the light passing through the analyzer is
calculated as follows:
2 22 2
2 2
2 2
sin cos'' 0 0'' 0 1 sin cos
0
sin cos
0
1 sin 2 cos sin cos sin2 2 2 2 2
i i
i i
i i
e eVxVy e e
e e
i i
δ δ
δ δ
δ δ
β β
β β
β β
δ δ δ δβ
−
−
−
⎛ ⎞⋅ + ⋅⎜ ⎟⎛ ⎞ ⎛ ⎞
⎜ ⎟= ⋅⎜ ⎟ ⎜ ⎟ ⎛ ⎞⎜ ⎟⎝ ⎠ ⎝ ⎠ − −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠⎛ ⎞⎜ ⎟= ⎛ ⎞⎜ ⎟− −⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠
⎛ ⎞⎜ ⎟= − ⎛ ⎞⎛ ⎞ ⎛ ⎞ ⎛ ⎞ ⎛ ⎞⎜ ⎟− + − − −⎜ ⎟ ⎜ ⎟ ⎜ ⎟ ⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠ ⎝ ⎠ ⎝ ⎠ ⎝ ⎠⎝ ⎠⎝ ⎠
=0
1 sin 2 2sin2 2
0
sin 2 sin2
i
i
δβ
δβ
⎛ ⎞⎜ ⎟− ⎛ ⎞⎛ ⎞⎜ ⎟− ⎜ ⎟⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠⎝ ⎠⎛ ⎞⎜ ⎟= ⋅ ⎛ ⎞⎜ ⎟⋅ ⎜ ⎟⎜ ⎟⎝ ⎠⎝ ⎠ (C.8)
0 00 1
⎛ ⎞⎜ ⎟⎝ ⎠
is the Jones matrix of the Y axis analyzer. The intensity of the output
light is calculated as:
2 2sin 2 sin2
I δβ ⎛ ⎞= ⋅ ⎜ ⎟⎝ ⎠
(C.9)
251
Figure C.1 Illustration of the lab frame coordinates (regular slow and fast axis
coordinates) and the angles used in the Jones Matrix representation. For Point P on the T-
SLC, the angle between the liquid crystal director and X axis, ψ = 2π β+ , where β is the
rotation angle between the lab frame and XY coordinates (i.e., ∠ POX).
β
P
X
Y
Ψ
O
252
Reference
[1] U. Efron, S.T. Wu, P.O. Braatz et al., "The Liquid Crystal-Based Visible to IR
Dynamic Image Converter (VIDIC)," Proc. SPIE 465, 181-191 (1984).
[2] R.A. Forber, A. Au, U. Efron et al., "Dynamic IR scene projection using the
Hughes liquid crystal light valve," SPIE Proceedings 1665, 259-273 (1992).
[3] Guoqiang Li, Pouria Valley, M. S. Giridhar et al., "Large-aperture switchable thin
diffractive lens with interleaved electrode patterns," Appl. Phys. Lett. 89 (14),
141120 (2006).
[4] Paul F. McManamon, Terry A. Dorschner, David L. Corkum et al., "Optical
Phased Array Technology," Proc. IEEE 84 (2), 268-298 (1996).
[5] E. Jakeman and E. P. Raynes, "Electro-optic response times in liquid crystals,"
Physics Letter A 39 (1), 69-70 (1972).
[6] E. Lueder, Liquid Crystal Displays: Addressing Schemes and Electro-optical
Effect. (Wiley, Chichester, 2001).
[7] Shin-Tson Wu and Robert J. Cox, "Optical and electro-optic properties of
cyanotolanes and cyanostilbenes: Potential infrared liquid crystals," J. Appl. Phys.
64 (2), 821-826 (1988).
[8] Shin-Tson Wu, Anna M. Lackner, and Uzi Efron, "Optimal operation temperature
of liquid crystal modulators," (1987).
253
[9] Shin-Tson Wu, M. E. Neubert, S. S. Keast et al., "Wide nematic range alkenyl
diphenyldiacetylene liquid crystals," Appl. Phys. Lett. 77 (7), 957-959 (2000).
[10] Sebastian GAUZA, Chien-Hui WEN, Bijun TAN et al., "UV Stable High
Birefringence Liquid Crystals," Japanese Journal of Applied Physics 43 (10),
7176–7180 (2004).
[11] Minhua Lu, "Nematic liquid-crystal technology for Si wafer-based reflective
spatial light modulators," Journal of the Society for Information Display 10 (1),
37-47 (2002).
[12] Qingbing Wang and Satyendra Kumar, "Submillisecond switching of nematic
liquid crystal in cells fabricated by anisotropic phase-separation of liquid crystal
and polymer mixture," Appl. Phys. Lett. 86 (7), 071119 (2005).
[13] Valery Vorflusev and Satyendra Kumar, "Phase-Separated Composite Films for
Liquid Crystal Displays," Science 283 (5409), 1903-1905 (1999).
[14] Philip J. Bos and K. Rickey Koehler/Beran, "The Pi-cell: A Fast Liquid-Crystal
Optical Switching Device," Mol. Cryst. Liq. Cryst. 113, 329-339 (1984).
[15] K. Kawabe and T. Furuhashi, "New TFT-LCD Driving Method For Improved
Moving Picture Quality," SID Tech Digest, 998-1001 (2001).
[16] Richard I. McCartney, "A Liquid Crystal Display Response Time Compensation
Feature Integrated into an LCD Panel Timing Controller," SID Tech Digest,
1350-1353 (2003).
254
[17] W. J. De Jeu, C. J. Gerritsma, P. Van Zanten et al., "Relaxation of the dielectric
constant and electrohydro-dynamic instabilities in a liquid crystal," Physics Letter
A 39 (5), 355-356 (1972).
[18] M. Schadt, "Low-Frequency Dielectric Relaxations in Nematics and Dual-
Frequency Addressing of Field Effects," Mol. Cryst. Liq. Cryst. 89, 77-92 (1982).
[19] Andrew K. Kirby and Gordon D. Love, "Fast, large and controllable phase
modulation using dual frequency liquid crystals," Opt. Express. 12 (7), 1470-1475
(2004).
[20] Yan-Qing Lu, Xiao Liang, Yung-Hsun Wu et al., "Dual-frequency addressed
hybrid-aligned nematic liquid crystal," Appl. Phys. Lett. 85 (16), 3354-3356
(2004).
[21] C. H. Wen, Y. H. Fan, Shin-Tson Wu et al., "Side chain effects on high-
birefringence liquid crystals," Proc. SPIE 4658, 28-33 (2002).
[22] Hong Sun, Wing Shun Cheung, and B. M. Fung, "Diazo liquid crystals for
potential infrared applications," Liq. Cryst. 27 (11), 1473-1479 (2000).
[23] Hong Sun, Frederick Roussel, Wing Shun Cheung et al., "Liquid crystal mixtures
for potential infrared applications," Liq. Cryst. 28 (10), 1483-1486 (2001).
[24] Chibing Tan and B. M. Fung, "A practical liquid crystal mixture for IR
applications," Liq. Cryst. 30 (5), 623-626 (2003).
[25] Shin-Tson Wu, "Infrared properties of nematic liquid crystals: an overview,"
Optical Engineering 26 (2), 120-128 (1987).
255
[26] Gregory P. Crawford and Slobodan Zumer, Liquid Crystals in Complex
Geometries: Formed by Polymer and Porous Networks. (Taylor & Francis Inc.,
1996), p.584.
[27] Paul S. Drzaic, "Liquid crystal dispersions," (1995).
[28] H. G. Craighead, Julian Cheng, and S. Hackwood, "New display based on
electrically induced index-matching in an inhomogeneous medium," Applied
Physics Letters 40 (1), 22-24 (1982).
[29] I. C. Khoo, J. Ding, Y. Zhang et al., "Supra-nonlinear photorefractive response of
single-walled carbon nanotube- and C[sub 60]-doped nematic liquid crystal,"
Appl. Phys. Lett. 82 (21), 3587-3589 (2003).
[30] M. Mucha, "Polymer as an important component of blends and composites
with liquid crystals," Prog. Polym. Sci. 28 (2003) 837–873 (2003).
[31] J. W. Doane, A. Golemme, John L. West et al., "Polymer Dispersed Liquid
Crystals for Display Application," Mol. Cryst. Liq. Cryst. 165, 511-532 (1988).
[32] John L. West, "Phase Separation of liquid crystals in polymers," Mol. Cryst. Liq.
Cryst. 157, 427-441 (1988).
[33] J.L. Fergason, SID Tech Digest 16, 68 (1985).
[34] Paul S. Drzaic, "Polymer dispersed nematic liquid crystal for large area displays
and light valves," J. Appl. Phys. 60 (6), 2142-2148 (1986).
[35] Timothy J. Bunning, Lalgudi V. Natarajan, Vincent P. Tondiglia et al.,
"Holographic Polymer-Dispersed Liquid Crystals (H-PDLCs)," Annu. Rev. Mater.
Sci. 30, 83-115 (2000).
256
[36] S. Matsumoto, M. Houlbert, T. Hayashi et al., "Nanosized fine droplets of liquid
crystals for optical application," Materials Research Society Symp. Proc. 457, 89-
92 (1997).
[37] Hongwen Ren, Yun-Hsing Fan, Yi-Hsin Lin et al., "Tunable-focus microlens
arrays using nanosized polymer-dispersed liquid crystal droplets," Opt. Commun.
247, 101–106 (2005).
[38] Ingo Dierking, "Polymer Network-Stablized Liquid Crystals," Advanced
Materials 12 (3), 167-181 (2000).
[39] R. A. M. Hikmet, "Electrically induced light scattering from anisotropic gels," J.
Appl. Phys. 68 (9), 4406-4412 (1990).
[40] D. K. Yang, L. C. Chien, and J. W. Doane, "Cholesteric liquid crystal/polymer
dispersion for haze-free light shutters," Appl. Phys. Lett. 60 (25), 3102-3104
(1992).
[41] Yun-Hsing Fan, Hongwen Ren, Xiao Liang et al., "Dual-frequency liquid crystal
gels with submillisecond response time," Appl. Phys. Lett. 85 (13), 2451-2453
(2004).
[42] O. A. Aphonin, Yu. V. Panina, A. B. Pravdin et al., "Optical properties of
stretched polymer dispersed liquid crystal films," Liq. Cryst. 15 (3), 395-407
(1993).
[43] Julien Brazeau, Yanick Chenard, and Yue Zhao, "Orientated Polymer-Dispersed
Liquid Crystals," Mol. Cryst. Liq. Cryst. 329, 137-144 (1999).
257
[44] Karl Amundson, Alfons van Blaaderen, and Pierre Wiltzius, "Morphology and
electro-optic properties of polymer-dispersed liquid-crystal films," Phys. Rev. E
55 (2), 1646 (1997).
[45] Bao-Gang Wu, John H. Erdmann, and J. William Doane, "Response times and
voltages for PDLC light shutters," Mol. Cryst. Liq. Cryst. 5 (5), 1453-1465 (1989).
[46] P. Sixou, C. Gautier, and H. Villanova, "Nematic and Cholesteric PDLC
Elaborated under Shear Stress," Mol. Cryst. Liq. Cryst. 364, 679-690 (2001).
[47] S. Pajeda, S. Pajediene, R. Vaidnoras et al., "Shear deformation and electrooptical
switch "on" and "off" in PDLC film," Proc. SPIE 3318, 418 (1998).
[48] Michael E. De Rosa, Vincent P. Tondiglia, and Lalgudi V. Natarajan,
"Mechanical deformation of a liquid crystal diffraction grating in an elastic
polymer," J. Appl. Polym. Sci. 68 (4), 523 - 526 (1998).
[49] Heinz-S. Kitzerow, Henning Molsen, and Gerd Heppke, "Linear electro-optic
effects in polymer-dispersed ferroelectric liquid crystals," Appl. Phys. Lett. 60
(25), 3093-3095 (1992).
[50] Henning Molsen and Heinz- S. Kitzerow, "Bistability in polymer-dispersed
ferroelectric liquid crystals," J. Appl. Phys. 75 (2), 710-716 (1994).
[51] Oleg A. Aphonin, "Optical properties of stretched polymer dispersed liquid
crystal films: angle-dependent polarized light scattering," Liq. Cryst. 19 (4), 469-
480 (1995).
258
[52] Oleg. A. Aphonin and V. F. NAZVANOV, "Light transmission, linear dichroism
and birefringence of nematic/polymer dispersions," Liq. Cryst. 23 (6), 845-859
(1997).
[53] Ichiro Amimori, Nikolai V. Priezjev, Robert A. Pelcovits et al., "Optomechanical
properties of stretched polymer dispersed liquid crystal films for scattering
polarizer applications," J. Appl. Phys. 93 (6), 3248-3252 (2003).
[54] Darran R. Cairns, Guy M. Genin, Amy J. Wagoner et al., "Amplified stain-rate
dependence of deformation in polymer-dispersed liquid-crystal materials," Appl.
Phys. Lett. 75 (13), 1872-1874 (1999).
[55] Scott A. Holmstrom, Lalgudi V. Natarajan, Vincent P. Tondiglia et al.,
"Mechanical tuning of holographic polymer-dispersed liquid crystal reflection
gratings," Appl. Phys. Lett. 85 (11), 1949-1951 (2004).
[56] John L. West and Anatoliy Glushchenko, "Polymer Dispersed Liquid Crystals for
Fast Electrically Controlled Phase Retarder," Polymer Preprints 43 (2), 532-533
(2002).
[57] John L. West, Guoqiang Zhang, and Anatoliy Glushchenko, "Stressed Liquid
Crystals for Electrically Controlled Fast Shift of Phase Retardation," SID Tech
Digest, 1469-1471 (2003).
[58] John L. West, Guoqiang Zhang, Anatoliy Glushchenko et al., "Fast birefringent
mode stressed liquid crystal," Appl. Phys. Lett. 86 (3), 031111 (2005).
259
[59] I Dierking, L. L. KOSBAR, A. C. LOWE et al., "Polymer network structure and
electro-optic performance of polymer stabilized cholesteric textures I. The
influence of curing temperature," Liq. Cryst. 24 (3), 387-395 (1998).
[60] I Dierking, L. L. KOSBAR, A. C. LOWE et al., "Polymer network structure and
electro-optic performance of polymer stabilized cholesteric textures. II. The effect
of UV curing conditions," Liq. Cryst. 24 (3), 397- (1998).
[61] J. D. LeGrange, S. A. Carter, M. Fuentes et al., "Dependence of the electro-
optical properties of polymer dispersed liquid crystals on the photopolymerization
process," J. Appl. Phys. 81 (9), 5984-5991 (1997).
[62] S. A. Carter, J. D. LeGrange, W. White et al., "Dependence of the morphology of
polymer dispersed liquid crystals on the UV polymerization process," J. Appl.
Phys. 81 (9), 5992-5999 (1997).
[63] Andrew J. Lovinger, Karl R. Amundson, and Don D. Davis, "Morphological
Investigation of UV-Curable Polymer-Dispersed Liquid-Crystal (PDLC)
Materials," Chem. Mater. 6, 1726 (1994).
[64] George W. Smith, "Cure Parameters and Phase Behavior of An Ultraviolet-Cured
Polymer-Dispersed Liquid Crystal," Mol. Cryst. Liq. Cryst. 196, 89-102 (1991).
[65] D. Nwabunma and T. Kyu, "Phase behavior, photopolymerization, and
morphology development in mixtures of eutectic nematic liquid crystal and
photocurable monomer," Polymer 42 (2), 801-806 (2001).
260
[66] Ulrich Maschke, Xavier Coqueret, and Mustapha Benmouna, "Electro-Optical
Properties of Polymer-Dispersed Liquid Crystals," Macromolecular Rapid
Communications 23 (3), 159 - 170 (2002).
[67] Fang Du, Sebastian Gauza, and Shin-Tson Wu, "Influence of curing temperature
and high birefringence on the properties of polymerstabilized liquid crystals," Opt.
Express. 11 (22), 2891-2896 (2003).
[68] Takeshi Murashige, Hideo Fujikake, Seiichiro Ikehata et al., "Relationship of
Polymer Molecular Weight and Cure Temperature in Photopolymerization-
Induced Phase Separation of Liquid Crystal and Polymer Fiber Networks," Jpn. J.
Appl. Phys. 41, L1152-L1154 (2002).
[69] No-hyung Park, Seong-a Cho, Ju-young Kim et al., "Preparation of polymer
dispersed liquid crystal films containing a small amount of liquid crystalline
polymer and their properties," J. Appl. Polym. Sci. 77 (14), 3178 - 3188 (2000).
[70] Domasius Nwabunma and Thein Kyu, "Phase Behavior of Mixtures of Low
Molar Mass Nematic Liquid Crystal and in Situ Photo-Cross-Linked Polymer
Network," Macromolecules 32 (3), 664-674 (1999).
[71] Rohit Bhargava, Shi-Qing Wang, and Jack L. Koenig, "FTIR Imaging Studies of
a New Two-Step Process To Produce Polymer Dispersed Liquid Crystals,"
Macromolecules 32 (8), 2748-2760 (1999).
[72] Rohit Bhargava, Shi-Qing Wang, and Jack L. Koenig, "Studying Polymer-
Dispersed Liquid-Crystal Formation by FTIR Spectroscopy. 1. Monitoring Curing
Reactions," Macromolecules 32 (26), 8982-8988 (1999).
261
[73] Rohit Bhargava, Shi-Qing Wang, and Jack L. Koenig, "Studying Polymer-
Dispersed Liquid-Crystal Formation by FTIR Spectroscopy. 2. Phase Separation
and Ordering," Macromolecules 32 (26), 8989-8995 (1999).
[74] George W. Smith, "Mixing and phase separation in liquid crystal /matrix
systems," Int. J. Mod. Phys. B 7 (25), 4187-4213 (1993).
[75] John L. West, Anatoliy Glushchenko, Guangxun Liao et al., "Drag on particles in
a nematic suspension by a moving nematic-isotropic interface," Phys. Rev. E 66
(1), 012702-012702-012704 (2002).
[76] C. M. Leader, W. Zheng, J. Tipping et al., "Shear aligned polymer dispersed
ferroelectric liquid crystal devices," Liq. Cryst. 19 (4), 415-419 (1995).
[77] Yue Zhao, Shuying Bai, Thanh-Nha Banh et al., "Orientation and anchoring
effects in stretched polymer dispersed nematic liquid crystals," Liq. Cryst. 27 (9),
1183-1187 (2000).
[78] George W. Smith, "A calorimetric Study of Phase Separation in Liquid
Crystal/Matrix Systems: Determination of the Excess Specific Heat of Mixing,"
Mol. Cryst. Liq. Cryst. 239, 63-85 (1994).
[79] R. A. M. Hikmet and H. M. J. Boots, "Domain structure and switching behavior
of anisotropic gels," Phys. Rev. E 51 (6), 5824-5831 (1995).
[80] J.William Doane, Polymer Dispersed Liquid Crystal Displays in Liquid Crystals
Applications and Uses. (World Scientific, 1990), p.579.
262
[81] Stanislaw J. Klosowicz and Jozef Zmija, "Optics and electro-optics of polymer-
dispersed liquid crystals: physics, technology, and application," Opt. Eng. 34 (12),
3440-3450 (1995).
[82] G. Paul Montgomery, John L. West, and Winifred Tamura-Lis, "Light scattering
from polymer-dispersed liquid crystal films: Droplet size effects," J. Appl. Phys.
69 (3), 1605-1612 (1991).
[83] Paul S Drzaic, "Droplet density, droplet size, and wavelength effects in PDLC
light scattering," Mol. Cryst. Liq. Cryst. 261, 383-392 (1995).
[84] Paul S. Drzaic and Anne M. Gonzales, "Refractive index gradients and light
scattering in polymer-dispersed liquid crystal films," Appl. Phys. Lett. 62 (12),
1332-1334 (1993).
[85] J. W. Doane, N. A. Vaz, B. G. Wu et al., "Field controlled light scattering from
nematic microdroplets," Appl. Phys. Lett. 48 (4), 269-271 (1986).
[86] Paul S Drzaic, "Electro-Optics of Polymer-Dispersed Liquid Crystal Materials,"
Mat. Res. Soc. Symp. Proc. 425, 259-268 (1996).
[87] Renate Ondris-Crawford, Evan P. Boyko, Brian G. Wagner et al., "Microscope
textures of nematic droplets in polymer dispersed liquid crystals," J. Appl. Phys.
69 (9), 6380-6386 (1991).
[88] G. H. Heilmeier and L. A. Zanoni, "GUEST-HOST INTERACTIONS IN
NEMATIC LIQUID CRYSTALS. A NEW ELECTRO-OPTIC EFFECT," Appl.
Phys. Lett. 13 (3), 91-92 (1968).
263
[89] Chin-Chun Chen, Jier-Fu Lyuu, and Jiunn-Yih Lee, "The Electro-optical Property
of Guest-host PDFLC Film Containing Anthraquinone Dye," Mol. Cryst. Liq.
Cryst. 433, 129-141 (2005).
[90] P. Gautier, M. Brunet, J. Grupp et al., "Switching behavior and electro-optical
properties of liquid crystals in nematic gels," Phys. Rev. E 62 (5), 7528-7531
(2000).
[91] P. Gautier, M. Brunet, J. Grupp et al., "Structure and texture of anisotropic
nematic gels," Phys. Rev. E 68 (1), 011709-011709-011712 (2003).
[92] John L. West, Keith Jewell, James Francl et al., "Surface anchoring , polymer
glass transistion and polymer dispersed liquid crystal electro-optics," SPIE
Proceedings 1665, 8-12 (1992).
[93] Zili Li, J. R. Kelly, P. Palffy-Muhoray et al., "Comparison of magnetic and
electric field induced switching in polymer dispersed liquid crystal films," Appl.
Phys. Lett. 60 (25), 3132-3134 (1992).
[94] Paul S Drzaic, "Reorientation dynamics of polymer dispersed nematic liquid
crystal films," Liq. Cryst. 3 (11), 1543-1559 (1988).
[95] S. Niiyama, Y. Hirai, Y. Ooi et al., "Hysteresis and Dynamic Response Effects on
the Image Quality in a LCPC Projection Display," SID tech Digest, 869-872
(1993).
[96] Steven Serati and Jay Stockley, "Advanced Liquid Crystal on Silicon Optical
Phased Arrays," IEEE 3, 3-1395- 1393-1402 (2002).
264
[97] Xu Wang, Daniel Wilson, Richard Muller et al., "Liquid-Crystal Blazed-Grating
Beam Deflector," Appl. Opt. 39 (35), 6545 (2000).
[98] Edward. A. Watson, Donald T. Miller, and Paul F. McManamon, "Applications
and requirements for nonmechanical beam steering in active electro-optic
sensors," Proc. SPIE 3633, 216-225 (1999).
[99] Charles Titus, Doctor, Kent State University, 2000.
[100] Jay E. Stockley, Darius Subacius, and Steven A. Serati, "Influence of the
interpixel region in liquid crystal diffraction gratings," Proc. SPIE 3635, 127-136
(1999).
[101] Paul F. McManamon, Jianru Shi, and Phil Bos, "Broadband optical phased-array
beam steering," Optical Engineering 44 (12), 128004 (2005).
[102] Linli Su and John L. West, "Infrared Electro-Optic Properties of Liquid Crystals,"
Proceedings of the Optical Beam Steering Symposium, Kent State Univ., OH,
205-210 (2000).
[103] Shin-Tson Wu, Qiong-Hua Wang, Michael D. Kempe et al., "Perdeuterated
cyanobiphenyl liquid crystals for infrared applications," J. Appl. Phys. 92 (12),
7146-7148 (2002).
[104] George W. Gray, "Advances in Synthesis and the Role of Molecular Geometry in
Liquid Crystallinity," Molecular Crystals and Liquid Crystals 7, 127-151 (1969).
[105] Frederic Guittard, Elisabeth Taffin de Givenchy, Serge Geribaldi et al., "Highly
fluorinated thermotropic liquid crystals: an update," Journal of Fluorine
Chemistry 100 (1-2), 85-96 (1999).
265
[106] Gordon D. Love, John V. Major, and Alan Purvis, "Liquid Crystal prisms for tip-
tilt adaptive optics," Opt. Lett. 19 (15), 1170-1172 (1994).
[107] M.S. Zakynthinaki and Y.G. Saridakis, "Stochastic optimization for a tip-tilt
adaptive correcting system," Comput. Phys. Commun. 150, 274-292 (2003).
[108] Laird A. Thompson, "Adaptive Optics in Astronomy," Phys. Today 47 (12), 24-
31 (1994).
[109] John P. Siegenthaler, Stanislav Gordeyev, and Eric J. Jumper, "Mapping the
Optically-Aberrating Environment in a Partially-Quieted Mach 0.6 Free Shear
Layer," 34th AIAA Plasmadynamics and Lasers Conference (AIAA Paper), 3607
(2003).
[110] V. A. Dorezyuk, A. F. Naumov, and V. I. Shmal'gauzen, "Control of liquid-
crystal correctors in adaptive optical systems," Soviet Physics - Technical Physics
34 (12), 1389-1393 (1989).
[111] Gordon D. Love, Thomas J. D. Oag, and Andrew K. Kirby, "Common path
interferometric wavefront sensor for extreme adaptive optics," Opt. Express. 13
(9), 3491-3499 (2005).
[112] A.V. Kudryashov, J. Gonglewski, S. Browne et al., "Liquid crystal phase
modulator for adaptive optics. Temporal performance characterization," Opt.
Commun. 141, 247-253 (1997).
[113] Gordon D. Love, "Liquid-crystal phase modulator for unpolarized light," Appl.
Opt. 32 (13), 2222-2223 (1993).
266
[114] Stephen T. Kowel, Philipp Kornreich, and Akbar Nouhi, "Adaptive spherical
lens," Appl. Opt. 23 (16), 2774-2777 (1984).
[115] Paul F. McManamon, Edward A. Watson, Terry A. Dorschner et al.,
"Applications look at the use of liquid crytal writable gratings for steering passive
radiation," Opt. Eng. 32 (11), 2657-2664 (1993).
[116] Andrii B. Golovin, Sergij V. Shiyanovskii, and Oleg D. Lavrentovich, "Gradient
beam steering device based on nematic cell with continuous ramp of the phase
retardation," Proc. SPIE 5741, 146-153 (2005).
[117] A.F. Naumov, G.D. Love, M.Y. Loktev et al., "Control optimization of spherical
modal liquid crystal lenses," Opt. Express 4 (9), 344-352 (1999).
[118] G.D. Love, J.V. Major, and A. Purvis, "Liquid-crystal prisms for tip-tilt adaptive
optics," Opt. Lett. 19 (15), 1170-1172 (1994).
[119] Susumu Sato, "Applications of liquid crystals to variable-focusing lenses,"
Optical Review 6 (6), 471-485 (1999).
[120] H. Ren, Y.H. Fan, S. Gauza et al., "Tunabl-focus flat liquid crystal spherical
lens," Appl. Phys. Lett. 84 (23), 4789-4791 (2004).
[121] Hongwen Ren and Shin-Tson Wu, "Inhomogeneous nanoscale polymer-dispersed
liquid crystals with gradient refractive index," Applied Physics Letters 81 (19),
3537-3539 (2002).
[122] Hongwen Ren, Yun-Hsing Fan, and Shin-Tson Wu, "Prism grating using polymer
stabilized nematic liquid crystal," Applied Physics Letters 82 (19), 3168-3170
(2003).
267
[123] Hongwen Ren and Shin-Tson Wu, "Tunable electronic lens using a gradient
polymer network liquid crystal," Applied Physics Letters 82 (1), 22-24 (2003).
[124] M. Born and E. Wolf, Principles of Optics, 7th ed. (Cambridge Univ. Press,
Cambridge, UK, 1999).
[125] Rumiko Yamaguchi, Toshiaki Nose, and Susumu Sato, "Liquid crystal polarizers
with axially symmetrical properties," Jpn. J. Appl. Phys. 28, 1730-1731 (1989).
[126] M. Stalder and M. Schadt, "Linearly polarized light with axial symmetry
generated by liquid-crystal polarization converters," Opt. Lett. 21 (23), 1948-1950
(1996).
[127] Yung-Hsun Wu, Yi-Hsin Lin, Hongwen Ren et al., "Axially-symmetric sheared
polymer network liquid crystals," Opt. Express. 13 (12), 4638-4644 (2005).
[128] I. C. Khoo and S.T. Wu, Optics and Nonlinear Optics of Liquid Crystals. (World
Scientific, Singapore, 1993).
[129] Birendra Bahadur, Dichroic Liquid Crystal Displays. (World Scientific,
Singapore, 1992), pp.65-208.
[130] Pochi Yeh and Claire Gu, Optics of Liquid Crystal Displays, 1st ed. (John Wiley
& Sons, 1999), p.438.