Fundamentals of Liquid Crystal Devices

Deng-Ke Yang Liquid Crystal Institute, Kent State University, USA Shin-Tson Wu College of Optics and Photonics, University of Central Florida, USA

• Series Editor’s Foreword xiiiPreface to the First Edition xvPreface to the Second Edition xvii1 Liquid Crystal Physics 11.1 Introduction 11.2 Thermodynamics and Statistical Physics 51.2.1 Thermodynamic laws 51.2.2 Boltzmann distribution 61.2.3 Thermodynamic quantities 71.2.4 Criteria for thermodynamical equilibrium 91.3 Orientational Order 101.3.1 Orientational order parameter 111.3.2 Landau–de Gennes theory of orientational order in nematic phase 131.3.3 Maier–Saupe theory 181.4 Elastic Properties of Liquid Crystals 211.4.1 Elastic properties of nematic liquid crystals 211.4.2 Elastic properties of cholesteric liquid crystals 241.4.3 Elastic properties of smectic liquid crystals 261.5 Response of Liquid Crystals to Electromagnetic Fields 271.5.1 Magnetic susceptibility 271.5.2 Dielectric permittivity and refractive index 291.6 Anchoring Effects of Nematic Liquid Crystal at Surfaces 381.6.1 Anchoring energy 381.6.2 Alignment layers 391.7 Liquid crystal director elastic deformation 401.7.1 Elastic deformation and disclination 401.7.2 Escape of liquid crystal director in disclinations 42Homework Problems 48References 492 Propagation of Light in Anisotropic Optical Media 512.1 Electromagnetic Wave 512.2 Polarization 542.2.1 Monochromatic plane waves and their polarization states 542.2.2 Linear polarization state 552.2.3 Circular polarization states 552.2.4 Elliptical polarization state 562.3 Propagation of Light in Uniform Anisotropic Optical Media 592.3.1 Eigenmodes 602.3.2 Orthogonality of eigenmodes 652.3.3 Energy flux 662.3.4 Special cases 672.3.5 Polarizers 692.4 Propagation of Light in Cholesteric Liquid Crystals 722.4.1 Eigenmodes 722.4.2 Reflection of cholesteric liquid crystals 812.4.3 Lasing in cholesteric liquid crystals 84Homework Problems 85References 863 Optical Modeling Methods 873.1 Jones Matrix Method 873.1.1 Jones vector 873.1.2 Jones matrix 883.1.3 Jones matrix of non-uniform birefringent film 913.1.4 Optical properties of twisted nematic 923.2 Mueller Matrix Method 983.2.1 Partially polarized and unpolarized light 983.2.2 Measurement of the Stokes parameters 1003.2.3 The Mueller matrix 1023.2.4 Poincaré sphere 1043.2.5 Evolution of the polarization states on the Poincaré sphere 1063.2.6 Mueller matrix of twisted nematic liquid crystals 1103.2.7 Mueller matrix of non-uniform birefringence film 1123.3 Berreman 4 × 4 Method 113Homework Problems 124References 1254 Effects of Electric Field on Liquid Crystals 1274.1 Dielectric Interaction 1274.1.1 Reorientation under dielectric interaction 1284.1.2 Field-induced orientational order 1294.2 Flexoelectric Effect 1324.2.1 Flexoelectric effect in nematic liquid crystals 1324.2.2 Flexoelectric effect in cholesteric liquid crystals 1364.3 Ferroelectric Liquid Crystal 1384.3.1 Symmetry and polarization 1384.3.2 Tilt angle and polarization 1404.3.3 Surface stabilized ferroelectric liquid crystals 1414.3.4 Electroclinic effect in chiral smectic liquid crystal 144Homework Problems 146References 1475 Fréedericksz Transition 1495.1 Calculus of Variation 1495.1.1 One dimension and one variable 1505.1.2 One dimension and multiple variables 1535.1.3 Three dimensions 1535.2 Fréedericksz Transition: Statics 1535.2.1 Splay geometry 1545.2.2 Bend geometry 1585.2.3 Twist geometry 1605.2.4 Twisted nematic cell 1615.2.5 Splay geometry with weak anchoring 1645.2.6 Splay geometry with pretilt angle 1655.3 Measurement of Anchoring Strength 1665.3.1 Polar anchoring strength 1675.3.2 Azimuthal anchoring strength 1695.4 Measurement of Pretilt Angle 1715.5 Fréedericksz Transition: Dynamics 1755.5.1 Dynamics of Fréedericksz transition in twist geometry 1755.5.2 Hydrodynamics 1765.5.3 Backflow 182Homework Problems 187References 1886 Liquid Crystal Materials 1916.1 Introduction 1916.2 Refractive Indices 1926.2.1 Extended Cauchy equations 1926.2.2 Three-band model 1936.2.3 Temperature effect 1956.2.4 Temperature gradient 1986.2.5 Molecular polarizabilities 1996.3 Dielectric Constants 2016.3.1 Positive Δε liquid crystals for AMLCD 2026.3.2 Negative Δε liquid crystals 2026.3.3 Dual-frequency liquid crystals 2036.4 Rotational Viscosity 2046.5 Elastic Constants 2046.6 Figure-of-Merit (FoM) 2056.7 Index Matching between Liquid Crystals and Polymers 2066.7.1 Refractive index of polymers 2066.7.2 Matching refractive index 208Homework problems 210References 2107 Modeling Liquid Crystal Director Configuration 2137.1 Electric Energy of Liquid Crystals 2137.1.1 Constant charge 2147.1.2 Constant voltage 2157.1.3 Constant electric field 2187.2 Modeling Electric Field 2187.3 Simulation of Liquid Crystal Director Configuration 2217.3.1 Angle representation 2217.3.2 Vector representation 2257.3.3 Tensor representation 228Homework Problems 232References 2328 Transmissive Liquid Crystal Displays 2358.1 Introduction 2358.2 Twisted Nematic (TN) Cells 2368.2.1 Voltage-dependent transmittance 2378.2.2 Film-compensated TN cells 2388.2.3 Viewing angle 2418.3 In-Plane Switching Mode 2418.3.1 Voltage-dependent transmittance 2428.3.2 Response time 2438.3.3 Viewing angle 2468.3.4 Classification of compensation films 2468.3.5 Phase retardation of uniaxial media at oblique angles 2468.3.6 Poincaré sphere representation 2498.3.7 Light leakage of crossed polarizers at oblique view 2508.3.8 IPS with a positive a film and a positive c film 2548.3.9 IPS with positive and negative a films 2598.3.10 Color shift 2638.4 Vertical Alignment Mode 2638.4.1 Voltage-dependent transmittance 2638.4.2 Optical response time 2648.4.3 Overdrive and undershoot voltage method 2658.5 Multi-Domain Vertical Alignment Cells 2668.5.1 MVA with a positive a film and a negative c film 2698.5.2 MVA with a positive a, a negative a, and a negative c film 2738.6 Optically Compensated Bend Cell 2778.6.1 Voltage-dependent transmittance 2788.6.2 Compensation films for OCB 279Homework Problems 281References 2839 Reflective and Transflective Liquid Crystal Displays 2859.1 Introduction 2859.2 Reflective Liquid Crystal Displays 2869.2.1 Film-compensated homogeneous cell 2879.2.2 Mixed-mode twisted nematic (MTN) cells 2899.3 Transflector 2909.3.1 Openings-on-metal transflector 2909.3.2 Half-mirror metal transflector 2919.3.3 Multilayer dielectric film transflector 2929.3.4 Orthogonal polarization transflectors 2929.4 Classification of Transflective LCDs 2939.4.1 Absorption-type transflective LCDs 2949.4.2 Scattering-type transflective LCDs 2969.4.3 Scattering and absorption type transflective LCDs 2989.4.4 Reflection-type transflective LCDs 3009.4.5 Phase retardation type 3029.5 Dual-Cell-Gap Transflective LCDs 3129.6 Single-Cell-Gap Transflective LCDs 3149.7 Performance of Transflective LCDs 3149.7.1 Color balance 3149.7.2 Image brightness 3159.7.3 Viewing angle 315Homework Problems 316References 31610 Liquid Crystal Display Matrices, Drive Schemes and Bistable Displays 32110.1 Segmented Displays 32110.2 Passive Matrix Displays and Drive Scheme 32210.3 Active Matrix Displays 32610.3.1 TFT structure 32810.3.2 TFT operation principles 32910.4 Bistable Ferroelectric LCD and Drive Scheme 33010.5 Bistable Nematic Displays 33210.5.1 Introduction 33210.5.2 Twisted-untwisted bistable nematic LCDs 33310.5.3 Surface-stabilized nematic liquid crystals 33910.6 Bistable Cholesteric Reflective Display 34210.6.1 Introduction 34210.6.2 Optical properties of bistable Ch reflective displays 34410.6.3 Encapsulated cholesteric liquid crystal displays 34710.6.4 Transition between cholesteric states 34710.6.5 Drive schemes for bistable Ch displays 355Homework Problems 358References 35911 Liquid Crystal/Polymer Composites 36311.1 Introduction 36311.2 Phase Separation 36511.2.1 Binary mixture 36511.2.2 Phase diagram and thermal induced phase separation 36911.2.3 Polymerization induced phase separation 37111.2.4 Solvent-induced phase separation 37411.2.5 Encapsulation 37611.3 Scattering Properties of LCPCs 37711.4 Polymer Dispersed Liquid Crystals 38311.4.1 Liquid crystal droplet configurations in PDLCs 38311.4.2 Switching PDLCs 38511.4.3 Scattering PDLC devices 38711.4.4 Dichroic dye-doped PDLC 39111.4.5 Holographic PDLCs 39311.5 PSLCs 39511.5.1 Preparation of PSLCs 39511.5.2 Working modes of scattering PSLCs 39611.6 Scattering-Based Displays from LCPCs 40011.6.1 Reflective displays 40011.6.2 Projection displays 40211.6.3 Transmissive direct-view displays 40311.7 Polymer-Stabilized LCDs 403Homework Problems 407References 40912 Tunable Liquid Crystal Photonic Devices 41312.1 Introduction 41312.2 Laser Beam Steering 41412.2.1 Optical phased array 41512.2.2 Prism-based beam steering 41712.3 Variable Optical Attenuators 41912.4 Tunable-Focus Lens 42312.4.1 Tunable-focus spherical lens 42312.4.2 Tunable-focus cylindrical lens 42612.4.3 Switchable positive and negative microlens 42812.4.4 Hermaphroditic LC microlens 43412.5 Polarization-Independent LC Devices 43512.5.1 Double-layered homogeneous LC cells 43612.5.2 Double-layered LC gels 438Homework Problems 441References 44213 Blue Phases of Chiral Liquid Crystals 44513.1 Introduction 44513.2 Phase Diagram of Blue Phases 44613.3 Reflection of Blue Phases 44713.3.1 Basics of crystal structure and X-ray diffraction 44713.3.2 Bragg reflection of blue phases 44913.4 Structure of Blue Phase 45113.4.1 Defect theory 45213.4.2 Landau theory 45913.5 Optical Properties of Blue Phase 47113.5.1 Reflection 47113.5.2 Transmission 472Homework Problems 475References 47514 Polymer-Stabilized Blue Phase Liquid Crystals 47714.1 Introduction 47714.2 Polymer-Stabilized Blue Phases 48014.2.1 Nematic LC host 48214.2.2 Chiral dopants 48314.2.3 Monomers 48314.3 Kerr Effect 48414.3.1 Extended Kerr effect 48614.3.2 Wavelength effect 48914.3.3 Frequency effect 49014.3.4 Temperature effects 49114.4 Device Configurations 49614.4.1 In-plane-switching BPLCD 49714.4.2 Protruded electrodes 50114.4.3 Etched electrodes 50414.4.4 Single gamma curve 50414.5 Vertical Field Switching 50714.5.1 Device structure 50714.5.2 Experiments and simulations 50814.6 Phase Modulation 510References 51015 Liquid Crystal Display Components 51315.1 Introduction 51315.2 Light Source 51315.3 Light-guide 51615.4 Diffuser 51615.5 Collimation Film 51815.6 Polarizer 51915.6.1 Dichroic absorbing polarizer 52015.6.2 Dichroic reflective polarizer 52115.7 Compensation Film 53015.7.1 Form birefringence compensation film 53115.7.2 Discotic liquid crystal compensation film 53115.7.3 Compensation film from rigid polymer chains 53215.7.4 Drawn polymer compensation film 53315.8 Color Filter 535References 53616 Three-Dimensional Displays 53916.1 Introduction 53916.2 Depth Cues 53916.2.1 Binocular disparity 53916.2.2 Convergence 54016.2.3 Motion parallax 54016.2.4 Accommodation 54116.3 Stereoscopic Displays 54116.3.1 Head-mounted displays 54216.3.2 Anaglyph 54216.3.3 Time sequential stereoscopic displays with shutter glasses 54216.3.4 Stereoscopic displays with polarizing glasses 54416.4 Autostereoscopic Displays 54616.4.1 Autostereoscopic displays based on parallax barriers 54616.4.2 Autostereoscopic displays based on lenticular lens array 55016.4.3 Directional backlight 55216.5 Integral imaging 55316.6 Holography 55416.7 Volumetric displays 55616.7.1 Swept volumetric displays 55616.7.2 Multi-planar volumetric displays 55716.7.3 Points volumetric displays 560References 560Index 565