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

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 ii

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

iii

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 iv

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

v

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 vi

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, neff ≠ n p ; light scatters; (b) with an electric field applied, neff = no ≈ n p ; 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 semiminor 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 ( Δλ = 2Δd sin θ ). 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

ix

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 cyanobiphenyl-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) aftershear 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 x

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-μmthick 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

xi

Fig. 4.5 Measured difference of transmittance at two polarizations. ΔT= T⊥-T‖. (a) 5CBSLCs 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 5CBSLC is 3.0 ms and τon is 0.2 ms………………………………………………….95

xii

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 semiminor 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 xiii

Fig. 5.11 Comparison between measurement and calculations for a 22-μm-thick 5CBSLC. (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 xiv

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

xv

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

xvi

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 xvii

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 SLCOPA 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-trifluoromethoxyphenyl)-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

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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 xix

Fig. 7.8 (a) and (b) are the beam profiles from a reflected reference cell in Z- and Ydirection. (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 xx

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 xxi

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

xxii

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 =

the

rotation

angle

between

the

lab

frame

and

π 2

+ β , where β is

XY

coordinates

(i.e., ∠ POX)…………………………………………………………………….251

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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

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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.

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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, fastswitching 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 = Δn ⋅ d

(1.1)

Δn = ne − no

(1.2)

1

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]

τ off = γ d 2 / π 2 K

γ d 2 ⎛ Δε 2 ⎞ τ on = 2 ⎜ 2 V − 1⎟ π K ⎝π K ⎠

(1.3) −1

(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 ( neff ≠ n p ). The effective refractive index of a droplet is estimated as neff = ne no

ne2 cos 2 θ + no2 sin 2 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 ( neff = no ). 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, neff ≠ n p ; light scatters; (b) with an electric field applied, neff = no ≈ n p ; 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 Δλ = 2Δd ⋅ cos θ ). 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 electrooptical 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 electrooptic 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 voltageholding-ratio are promising for the development of fast displays. Chapter 11 concludes this dissertation.

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 28

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, T1cure , is greater than the clearing temperature of the mixture); and (2) low temperature polymerization (The cure temperature in the second step, T2cure , is room temperature, ~20 oC). Two separate heating stages are used to control T1cure and T2cure , respectively. The metal halide UV lamp, ELC2540, 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.

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,

40

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

Sample

5CB/RM82/NOA65

5CB/RM82/NOA65

94/2/4

90/2/8

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

30-40

10-20

5-8

~2

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.

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.

67

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

N/A

N/A

N/A

NOA65

1.524

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

100

(a)

80

T%

60 40

A2 after-shear A2 before-shear A1 after-shear

20

A1 before-shear

0 500

1000

1500

2000

wavelength (nm)

100

(b)

T%

80 60 40

A5 after-shear A5 before-shear A4 after-shear

20

A4 before-shear A3 after-shear

0

A3 before-shear

500

1000

1500

2000

wavelength (nm)

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.

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

100

(a) 100dg 90dg 80dg 70dg 41dg 60dg 50dg

80

T%

60 40 20 0

500

1000

1500

2000

Wavelength (nm) 100

(b)

80

T%

60 100dg 90dg 80dg 70dg 50dg 41dg

40 20 0 500

1000

1500

2000

Wavelength (nm)

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.

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

Materials Composition (weight ratio)

B3

B4

B5

B6

5CB/RM82/NOA65 90/0/10

90/2/8

90/2/8

90/6/4

B7 E7/NOA65

90/6/4/dye

86/14

86/14

(0.15) 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

100oC to 20oC

70oC to 20oC

submicron

1~3

60oC to 20oC

Quenching DLC (μm)

1~2

submicron

Table 4.2 Fabrication conditions of the series B SLC samples for polarization dependence studies on transmittance.

79

40

(a) B2 (Weak UV)

ΔT,%

30 20

B1

10 B3

0

B4

0

20

40

60

80

100 120

Shear distance (μm) 40

(b)

ΔT,%

30

B7

20 10 0

B6

0

20

40

60

80

100 120

Shear distance (μm)

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).

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. SLC + dye A⊥dye, = − log10 (T⊥dye I ⊥SLC , ) = − log 10 ( I ⊥ , , )

(4.1)

D = Adye A⊥dye = log10 (T SLC + dye T SLC ) log10 (T⊥SLC + dye T⊥SLC )

(4.2)

S=

D −1 D+2

(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

Liquid Crystal Director Ordering

0.6

0.4

0.2

0.0 0

20

40

60

80

Shear distance (μm) Figure 4.8 Calculated liquid crystal director orderings in a SLC (B5).

100

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.

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.

88

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: ⎛ πΔnd ⎞ I = I max ⋅ sin 2 ⎜ ⎟ ⎝ λ ⎠

(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:

OPD = Δnd = mλ ±

⎛ I ⎞ λ ⋅ a sin ⎜ ⎟ π ⎝ I max ⎠

m = 0,1, 2 ⋅⋅⋅

(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= AB

branch,

the

value

⎛ I λ a sin ⎜ π ⎝ I max

of

OPD

is

⎞ ⎟ , which is a value between 0 and λ/2. On ⎠ from

λ/2

to

λ,

and

calculated

as

90

OPDAB = λ −

⎛ I λ ⋅ a sin ⎜ π ⎝ I max

⎞ ⎟ . 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-μmthick SLC had a total OPD approximately two and a half waves. The calculated results are plotted in Fig. 5.2.

91

Normalized Intensity

A (IMax)

C

1.0 0.8 E 0.6 0.4 0.2 0.0 0

D 20

B 40

(IMin)

60

80

100 120 140

Voltage (V)

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 OA

AB

BC

CD

DE

Optical Path Delay Formula OPDOA =

⎛ I ⎞ λ ⋅ a sin ⎜ ⎟ π ⎝ I max ⎠

OPDAB = λ −

⎛ I ⎞ λ ⋅ a sin ⎜ ⎟ π ⎝ I max ⎠

OPDBC = λ +

⎛ I ⎞ λ ⋅ a sin ⎜ ⎟ π ⎝ I max ⎠

OPDCD = 2λ −

⎛ I ⎞ λ ⋅ a sin ⎜ ⎟ π ⎝ I max ⎠

OPDCD = 2λ +

⎛ I ⎞ λ ⋅ a sin ⎜ ⎟ π ⎝ I max ⎠

Table 5.1 Formulas for the optical path delay calculation from the T-V curve (Fig. 5.1).

93

4

OPD (μm)

3 2 1 Vs 0

10%

0

40

80

120

160

Applied Voltage (V)

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

(a)

4

100%

OPD (μm)

3

(b)

90%

τoff

2 1 10%

τon

0 0

0%

1

2

3

4

5

Time (ms)

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.

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

VOPD=λ/2

Normalized Intensity

1.0 10 μm 20 μm 40 μm 60 μm

0.8 0.6 0.4 0.2 0.0 0

2

4

6

8

10

Voltage (V)

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 turnoff 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 12μm-thick E7-SLC cured at 100oC increases in shear distance.

102

1.2

OPD (μm)

0.8

0.4

0.0 0

50

100

150

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 electrooptical 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 L a = R ⋅ ( ) 2 + 1 = R ⋅ ( L1 ) 2 + 1 d

where L1 = L d . It is assumed that the volume of liquid crystal

droplets does not change during a shear process so that abc = R 3 . 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 b = R 2 a = R ( L1 ) 2 + 1 . Then the aspect ratio (l) is as follows: l=

a = ( L1 ) 2 + 1 . 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

τ off =

γ a2 K (l − 1) 2

=

γ R 2l

(5.3)

K (l 2 − 1)

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): τ on =

(5.4)

γ ⎛ K 33 ( l 2 − 1) ⎞ ⎛ K33 ( l 2 − 1) ⎞ 4 2 ⎜ ⎟ ⎟ ⋅ ( Δε E 2 ) ⋅ ⎜⎛ − 4 ⎟⎞ E + Δ ε +⎜ 2 2 ⎜ ⎟ ⎜ ⎟ Rl Rl ⎝l ⎠ ⎝ ⎠ ⎝ ⎠ 2

where Δε is the dielectric anisotropy of a liquid crystal, E is the strength of an applied electric field. Switching field (Eswitch): 1

Eswitch

1

2 2 2 2 ⎞ ⎛ K 33 ( l − 1) ⎞ ⎞ ⎛ K 33 ( l − 1) ⎞ V 1 ⎛σ 1 ⎛ σ2 ⎟ = ⎟ = switch = ⎜ 2 + 2 ⎟ ⎜ + 2⎟⎜ ⎜ ⎟ ⎟ d 3a ⎝ σ 1 3Rl ⎝ σ 1 Δε Δε ⎠ ⎜⎝ ⎠ ⎜⎝ ⎠ ⎠

(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

L

After shearing

R

a D

D

b

c

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 semimajor 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

0.2, 0.5, 1, 2

12

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 22μm-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

(a)

Eswitch (V/μm)

15 R= 0.2 μm R= 0.5 μm Eswitch-measured

10

5

0 0

20

40

60

80

Shear distance (μm)

3

(b)

τon (ms)

2

1

0 0

20 40 60 Shear distance (μm)

80

30 R=0.2 μm R=0.5 μm toff-measured

(c)

τoff (ms)

20

10

0 0

40 80 Shear distance (μm)

120

Figure 5.11 Comparison between measurement and calculations for a 22-μm-thick 5CBSLC. (a) Switching field; (b) turn-on time; (c) turn-off time.

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

Intensity (a.u.)

3

2 ΔV

1

0 0

20

40

60

80

Voltage (V) 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

1.2

150 μm shear, decreasing voltage 150 μm shear, increasing voltage

OPD (μm)

1.0 0.8 0.6 0.4 0.2 0.0 0

10

20

30

40

50

60

Voltage (V) Figure 5.13 Hysteresis of a 12-μm-thick E7-SLC cured at 100oC. Shear distance was 150 μm.

114

OPD (μm)

0.6

0.4

0.2 0V to 10V 10V to 0V

0.0 0

2

4

6

8

10

Voltage (V)

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 E7SLC 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

4

ΔVhysteresis (V)

3 2

B7

1

B6 0 0

20

40

60

80

100

Lshear (μm)

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

4

OPD (μm)

3

13V

A

2

Linear fit: Y = 4.47-0.08X

1

B

46V

0 0

40

80

120

160

Applied Voltage (V) 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

VS VM Phase Profile

E1 R

E2

E3

R

R

VL

E4 R

E5

E6

E7

R

R

R

V0

E8

V0 '

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.

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/mesogenicpolymer 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

d1

d2 di dn

Figure 5.20 Simplified illustration of multi-layer structures of SLCs. It is assumed that the layer thickness of each layer is slightly varied.

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 820μm-thick SLC (Fig. 5.22). The relaxation time for whole 55 μm is less than 14 ms (Fig. 5.23)

127

60

OPD (μm)

40

20

0 0

200

400

600

800

Voltage (V) Figure 5.22 OPD versus applied voltage for an 820-μm-thick SLC (5CB/NOA65: 90/10) at 650 μm shear.

128

60

OPD (μm)

40

20

0 0

5

10

15

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:

η = OPDMeasurement OPDTheory = OPDMeasurement ( Δn ⋅ d LC ) = OPDMeasurement ( Δn ⋅ d ⋅ cLC %) (5.6) Where OPDMeasurement is the measured maximum OPD , Δn 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-μmthick 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, Δn is neff − no = ne no

ne2 cos2 θ + no2 sin 2 θ − no ( θ =

45o to ~90o ) which is smaller than ne − no . 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 E7SLC 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

60

Maximum OPD (μm)

50 40 30 20 10 0

0

100 200 300 400 500 600 700 800 900

Cell thickness, (μm)

Figure 5.24 Measured maximum OPD of SLC cells of different cell gaps (from 22 μm to 820 μm)

132

1.3

OPD (μm)

1.2 1.1 1.0 0.9 0.8

80

90

100

110 o

Cure Temperature ( C) Figure 5.25 Measured maximum OPD for 12-μm-thick E7-SLCs cured at different temperatures.

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 133

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 θ =

Δnd L

(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 nondesigned 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

Real phase profile

Ideal phase profile

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.

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

2.5

Δnd (μm)

2.0 1.5 1.0 0.5 0.0 0

20

40

60

80

100

120

Voltage (V)

2.5

Δnd (μm)

2.0 1.5 1.0 0.5 0.0 0

2

4

6

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 SLCOPA 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

100

sapphire

80

T%

60 40 20 0 0

2

4

6

Wavelength(μm)

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

100

T%

80

60 ITO's IR transmittance

40 2.0

2.5

3.0

3.5

4.0

4.5

5.0

λ (μm)

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 Thick Thin Thick Thin Thick are obtained from the 6-μm-thick cell. That is, ε is ( ε AB ), in which , ε BC , ε CD , ε DE , ε EF Thick Thick Thin Thin ε AB = AAB / d Thick , ε BC = ABC / d Thin , 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

Thick Cell

2.00-3.10 μm 3.65-4.40 μm

Deuterated 8CB

NOA65

2.00-4.20 μm

2.00-2.80 μm

4.20-5.00 μm

2.80-5.00 μm

4.55-5.00 μm Thin Cell

3.10-3.65 μm 4.40-4.55 μm

Table 6.1 Spectrum branch selection of different materials for the calculation of IR absorption coefficients (ε)

155

0.20

-1

(a)

ε (μm )

0.15 0.10 0.05 0.00 2

4

λ (μm) 0.25

-1

ε (μm )

0.20

(b)

0.15 0.10 0.05 0.00 2

4

λ (μm)

Figure 6.12 Calculated coefficients of absorbance for 5CB (a) and NOA65 (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. Tλ = TLC ,λ ⋅ TNOA65,λ = 10

− ( ALC ,λ + ANOA 65,λ )

= 10

− ( ε LC ,λ ⋅d LC +ε NOA 65,λ ⋅d NOA 65 )

(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

100

T%

80 60

22 um SLC

40 20 0 2.0

2.5

3.0

3.5

4.0

4.5

λ (μm)

Figure 6.13 Calculated IR transmittance of a 22-μm-thick 5CB-SLC film.

5.0

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.

Abs reflection 2 TSLC −OPA = (TSapphire ⋅ RAu ) ⋅ (TSapphire ) ⋅ TITO4 ⋅ TSLC 4

2

(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

measured reflective sapphire cell calculated reflective sapphire cell

60

T%

40

20

0 2.0

2.5

3.0

3.5

4.0

4.5

5.0

λ (μm)

Figure 6.15 Comparison between experimental measurement and calculation for a SLCOPA 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 800μm-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 ν =

1

k

2π c 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

μ=

m1 m2 m1 + m2

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

λ = 2π c

μ k

approximate

. When C-H bond is replaced by C-D bond the reduced mass of C-D is 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

SLC-5CB/NOA65 Transmittance Vs Wavelength 100 90 80

%Transmittance

70 60 50 40 30 20 10 0 2

2.5

3

3.5 Wavelength (um)

4

Figure 6.16 Calculated IR spectrum of an 800-μm-thick SLC.

4.5

5

164

100

T%

80 8CB D8CB

60 40 20 0 2

3

4

5

Wavelength (μm) 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

D8CB Transmittance Vs Wavelength 100 d= 820 um

90 80

%Transmittance

70 60 50 40 30 20 10 0

2

2.5

3

3.5 Wavelength (um)

4

4.5

Figure 6.18 Calculated IR transmittance for 820-μm-thick deuterated 8CB film.

5

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 perfluorinated liquid crystal rigid core structure-Pentafluorophenyl-(2,3,5,6-tetrafluoro-4trifluoromethoxy-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.

F

F F

F3CO

F

N N F

F

F F

F

Pentafluorophenyl-(2,3,5,6-tetrafluoro-4trifluoromethoxy-phenyl)-diazene

Absorbance Intensity(a.u.)

167

20

compound left

15 10 5 0 2

4

6

8

10

12

14

wavelength( μm)

Figure 6.19 The structure of pentafluorophenyl-(2,3,5,6-tetrafluoro-4-trifluoromethoxyphenyl)-diazene and the calculated IR absorption bands.

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

wavenumber(CM-1) 4000 3000

2000

1000 1.0

Cyclohexane 5CB PCH5 Pyridine

Absorbance

0.2

0.8

0.6

0.4

0.0 0.2

0.0

-0.2

-0.2

8

9

10

11

12

Wavelength (μm) 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.

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

172

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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

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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.

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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.

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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.

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Figure 7.3 The measured switching times of the SLC tip-tilt corrector. λ = 1.55 μm and V = 200.0 V.

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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.

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Figure 7.5 Measured transmission spectra of SLC Tip-Tilt corrector. It is referenced to a NOA65 cell.

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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 θ =

Δnd L

(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.

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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.

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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.

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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.

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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 tiptilt 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)

Figure 7.8 (a) and (b) are the beam profiles from a reflected reference cell in Z- and Ydirection. (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.

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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.

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 190

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 photomask 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.

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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

Mask A

80

B

D

SLC prism

A

70 Transmission (%)

C

B

60

C

50 40

D

30

0

2

4

6

8 10 12 14 16 18 Position (mm)

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.

195

a

b

c

d

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).

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

ΔOPD = OPDD-OPDA (μm)

1.0 0.8 0.6 0.4 0.2 0.0 0

20

40

60

80

100

Shearing distance (μm)

Figure 8.4 Optical path delay difference across the gradient SLC prism at the different shear states.

198

2.0

OPD (μm)

1.6 100 μm shearing D A

1.2 0.8 0.4 0.0 -10

0

10

20

30

40

50

60

70

80

Voltage (v)

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

ΔOPD= (OPDD-OPDA) (μm)

200

1.5 0 μm shear 30 μm shear 100 μm shear

1.0

0.5

0.0 0

10

20

30

40

50

60

70

80

Voltage (V) Figure 8.6 Measured voltage dependent ΔOPD at 0 μm, 30 μm, 100 μm shear states, respectively.

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2.0

OPD (μm)

1.5 1.0

Spot D Spot A

0.5 0.0 0

2

4

6

8

10

12

Time (ms) Figure 8.7 Measured turn-off times for spots A and D on the SLC prism.

14

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 highprecision 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.

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Birefringence measurement

1

2

3

4

5

6

1. Laser 2. Polarizer 3. 30X Beam expander and special filter set 4. Soleil-Babinet compensator 5. SLC prism 6. Analyzer 7.Camera

Figure 8.8 2D birefringence measurement setup.

7

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.

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 higherorder 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 TSLC can be used as a polarization converter.

206

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

543210

(a)

(b)

(c)

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.

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 inplane

rotation

of

equation: I = I 0 ⋅ sin 2 (

the

T-SLC.

The

transmittance

intensity

follows

the

π ⋅ Δnd ) ⋅ sin 2 (2β ) , 1 where β is the angle between liquid crystal λ

directors and the polarizer. When Δnd = mλ or β = k ⋅

π 2

, 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

I = I 0 ⋅ sin 2 (

π ⋅ Δnd ) ⋅ sin 2 (2 β ) λ

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.

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Analyzer

Analyzer

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.

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

Linear shear

(a) 180

90

(b)

o

0

o

o

(c) 270

o

Pattern shift

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.

215

Counterclockwise twist

(a)

(b)

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.

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, Lp5 =r ⋅ θ = 10000μ m ⋅ 0.5/180 ⋅ 3.1416= 87.3μ m . 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

Optical Path Delay (μm)

2.0 P4

1.5

P3 P2

1.0 0.5

P5

P1 P0

0.0 0

2

4

6

8

Radius (mm) Figure 9.5 Optical path delay on the different spots of the T-SLC.

10

12

218

80 P3 T%

60 P1

P4

P5

P2

40 P0 20 0

2

4 6 8 Radius (mm)

10

12

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: ⎛ ⎞ ⎛δ ⎞ ⎛δ ⎞ cos ⎜ ⎟ + i sin ⎜ ⎟ ⋅ cos 2 β ⎟ ⎜ ⎛ Vx ' ⎞ ⎜ ⎝2⎠ ⎝2⎠ ⎟ ⎜Vy ' ⎟ = ⎜ ⎟ δ ⎛ ⎞ ⎝ ⎠ i sin 2 β sin ⎜ ⎟ ⎜ ⎟ ⎝2⎠ ⎝ ⎠ Where phase retardation δ =

2πΔnd

λ

(9.1)

, and β is the angle between liquid crystal

directors and the polarizer, defined in Fig. C.1 of Appendix C. When δ =

2πΔnd

λ

= 2π ,

⎛ ⎞ ⎛δ ⎞ ⎛δ ⎞ cos ⎜ ⎟ + i sin ⎜ ⎟ ⋅ cos 2 β ⎟ ⎜ −1 ⎛ Vx ' ⎞ ⎜ ⎝2⎠ ⎝2⎠ ⎟ = ⎛⎜ ⎞⎟ , which indicates that the i.e., Δnd = λ , ⎜ = ⎟ ⎟ ⎝0⎠ ⎛δ ⎞ ⎝Vy ' ⎠ ⎜ i sin 2 β sin ⎜ ⎟ ⎜ ⎟ ⎝2⎠ ⎝ ⎠ emerging light is linearly polarized along the X axis on that ring. When

δ=

2πΔnd

λ

⎛ Vx ' ⎞ ⎛ cos 2 β ⎞ i π2 ⎛ cos 2 β ⎞ =π , ⎜ ⎟ = i⎜ ⎟ = e ⎜ sin 2 β ⎟ , which is a distribution of linearly ⎝Vy ' ⎠ ⎝ sin 2 β ⎠ ⎝ ⎠

polarized light. On the other hand, when δ =

2πΔnd

λ

=

π ⎛Vx ' ⎞ ⎛ 1 + i cos 2 β ⎞ = , which is , 2 ⎜⎝Vy ' ⎟⎠ ⎜⎝ i sin 2 β ⎟⎠

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

Y Δnd=λ/4 Δnd=λ/2 Δnd=λ

β

X

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.

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 positiondependent phase retardation and liquid crystal director direction.

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.

223

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

(a)

(b)

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.

226

Normalized intensity

1.0 0.8

5μm thick cell 4.7 volt driven τoff

0.6

τon

0.4

(a)

0.2 0.0 0

2

4

6

8

Normalized Intensity

Time (ms)

1.0 0.8 Pure 5CB

0.6

τon τoff

0.4

(b)

0.2 0.0 0

2

4

6

8

Time (ms) 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

τtotal

Vswitch

10

8

8 6

6 4

4

Switching Voltage (V)

Response time (ms)

12

2 10

20

30

40

50

60

Shear Distance (μm) 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, E7SLC 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

Voltage Holding Ratio (VHR)

1.0 0.8

pure TL-205 TL-205/PN393 Pure ZSM-5386 ZSM/PN393 5CB-SLC

0.6 0.4 0.2 0.0

Figure 10.4 Voltage Holding Ratio measurements for liquid crystals TL205 and ZSM5386 comparing with SLCs based on the corresponding liquid crystals.

Change of response time (%)

231

200

o

100 C o

100 C o 60 C o 25 C

160 120 80

o

60 C

40 0

o

-40

25 C

0

100

200

300

Time (hr) Figure 10.5 Thermal stability test of SLC at three different temperatures: 25 oC, 60 oC, and 100oC.

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 fastswitching 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

232

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 ~290 μm Thousands of ms Transmittance H Field on Cell gap Speed

PDLC (normal mode) >1000 μm Dozens of ms H

Nano-PDLC

H

PNLC (reverse mode) ~310 μm Dozens of ms L

820 μm Less than 14 ms H

>1000 μm ms

SLC

Field off

H

L

H

H

H

Hysteresis Linear Response Field

N N

Y N

Y N

Y/N Y/N

N Y

>5V/mm

>1V/μm

Good:1V/μm

Small >1V/mm