Fundamentals of Liquid Crystal Devices

Series Editor s Foreword xiii Preface to the First Edition xv Preface to the Second Edition xvii 1 Liquid Crystal Physics 1 1.1 Introduction 1 1.2 Thermodynamics and Statistical Physics 5 1.2.1 Thermodynamic laws 5 1.2.2 Boltzmann Distribution 6 1.2.3 Thermodynamic quantities 7 1.2.4 Criteria for thermodynamical equilibrium 9 1.3 Orientational Order 10 1.3.1 Orientational order parameter 11 1.3.2 Landau de Gennes theory of orientational order in nematic phase 13 1.3.3 Maier Saupe theory 18 1.4 Elastic Properties of Liquid Crystals 21 1.4.1 Elastic properties of nematic liquid crystals 21 1.4.2 Elastic properties of cholesteric liquid crystals 24 1.4.3 Elastic properties of smectic liquid crystals 26 1.5 Response of Liquid Crystals to Electromagnetic Fields 27 1.5.1 Magnetic susceptibility 27 1.5.2 Dielectric permittivity and refractive index 29 1.6 Anchoring Effects of Nematic Liquid Crystal at Surfaces 38 1.6.1 Anchoring energy 38 1.6.2 Alignment layers 39 1.7 Liquid crystal director elastic deformation 40 1.7.1 Elastic deformation and disclination 40 1.7.2 Escape of liquid crystal director in disclinations 42 Homework Problems 48 References 49 2 Propagation of Light in Anisotropic Optical Media 51 2.1 Electromagnetic Wave 51 2.2 Polarization 54 2.2.1 Monochromatic plane waves and their polarization states 54 2.2.2 Linear polarization state 55 2.2.3 Circular polarization states 55 2.2.4 Elliptical polarization state 56 2.3 Propagation of Light in Uniform Anisotropic Optical Media 59 2.3.1 Eigenmodes 60 2.3.2 Orthogonality of eigenmodes 65 2.3.3 Energy flux 66 2.3.4 Special cases 67 2.3.5 Polarizers 69 2.4 Propagation of Light in Cholesteric Liquid Crystals 72 2.4.1 Eigenmodes 72 2.4.2 Reflection of cholesteric liquid crystals 81 2.4.3 Lasing in cholesteric liquid crystals 84 Homework Problems 85 References 86 3 Optical Modeling Methods 87 3.1 Jones Matrix Method 87 3.1.1 Jones vector 87 3.1.2 Jones matrix 88 3.1.3 Jones matrix of non-uniform birefringent film 91 3.1.4 Optical properties of twisted nematic 92 3.2 Mueller Matrix Method 98 3.2.1 Partially polarized and unpolarized light 98 3.2.2 Measurement of the Stokes parameters 100 3.2.3 The Mueller matrix 102 3.2.4 Poincare sphere 104 3.2.5 Evolution of the polarization states on the Poincare sphere 106 3.2.6 Mueller matrix of twisted nematic liquid crystals 110 3.2.7 Mueller matrix of non-uniform birefringence film 112 3.3 Berreman 4 x 4 Method 113 Homework Problems 124 References 125 4 Effects of Electric Field on Liquid Crystals 127 4.1 Dielectric Interaction 127 4.1.1 Reorientation under dielectric interaction 128 4.1.2 Field-induced orientational order 129 4.2 Flexoelectric Effect 132 4.2.1 Flexoelectric effect in nematic liquid crystals 132 4.2.2 Flexoelectric effect in cholesteric liquid crystals 136 4.3 Ferroelectric Liquid Crystal 138 4.3.1 Symmetry and polarization 138 4.3.2 Tilt angle and polarization 140 4.3.3 Surface stabilized ferroelectric liquid crystals 141 4.3.4 Electroclinic effect in chiral smectic liquid crystal 144 Homework Problems 146 References 147 5 Freedericksz Transition 149 5.1 Calculus of Variation 149 5.1.1 One dimension and one variable 150 5.1.2 One dimension and multiple variables 153 5.1.3 Three dimensions 153 5.2 Freedericksz Transition: Statics 153 5.2.1 Splay geometry 154 5.2.2 Bend geometry 158 5.2.3 Twist geometry 160 5.2.4 Twisted nematic cell 161 5.2.5 Splay geometry with weak anchoring 164 5.2.6 Splay geometry with pretilt angle 165 5.3 Measurement of Anchoring Strength 166 5.3.1 Polar anchoring strength 167 5.3.2 Azimuthal anchoring strength 169 5.4 Measurement of Pretilt Angle 171 5.5 Freedericksz Transition: Dynamics 175 5.5.1 Dynamics of Freedericksz transition in twist geometry 175 5.5.2 Hydrodynamics 176 5.5.3 Backflow 182 Homework Problems 187 References 188 6 Liquid Crystal Materials 191 6.1 Introduction 191 6.2 Refractive Indices 192 6.2.1 Extended Cauchy equations 192 6.2.2 Three-band model 193 6.2.3 Temperature effect 195 6.2.4 Temperature gradient 198 6.2.5 Molecular polarizabilities 199 6.3 Dielectric Constants 201 6.3.1 Positive liquid crystals for AMLCD 202 6.3.2 Negative liquid crystals 202 6.3.3 Dual-frequency liquid crystals 203 6.4 Rotational Viscosity 204 6.5 Elastic Constants 204 6.6 Figure-of-Merit (FoM) 205 6.7 Index Matching between Liquid Crystals and Polymers 206 6.7.1 Refractive index of polymers 206 6.7.2 Matching refractive index 208 Homework problems 210 References 210 7 Modeling Liquid Crystal Director Configuration 213 7.1 Electric Energy of Liquid Crystals 213 7.1.1 Constant charge 214 7.1.2 Constant voltage 215 7.1.3 Constant electric field 218 7.2 Modeling Electric Field 218 7.3 Simulation of Liquid Crystal Director Configuration 221 7.3.1 Angle representation 221 7.3.2 Vector representation 225 7.3.3 Tensor representation 228 Homework Problems 232 References 232 8 Transmissive Liquid Crystal Displays 235 8.1 Introduction 235 8.2 Twisted Nematic (TN) Cells 236 8.2.1 Voltage-dependent transmittance 237 8.2.2 Film-compensated TN cells 238 8.2.3 Viewing angle 241 8.3 In-Plane Switching Mode 241 8.3.1 Voltage-dependent transmittance 242 8.3.2 Response time 243 8.3.3 Viewing angle 246 8.3.4 Classification of compensation films 246 8.3.5 Phase retardation of uniaxial media at oblique angles 246 8.3.6 Poincare sphere representation 249 8.3.7 Light leakage of crossed polarizers at oblique view 250 8.3.8 IPS with a positive a film and a positive c film 254 8.3.9 IPS with positive and negative a films 259 8.3.10 Color shift 263 8.4 Vertical Alignment Mode 263 8.4.1 Voltage-dependent transmittance 263 8.4.2 Optical response time 264 8.4.3 Overdrive and undershoot voltage method 265 8.5 Multi-Domain Vertical Alignment Cells 266 8.5.1 MVA with a positive a film and a negative c film 269 8.5.2 MVA with a positive a, a negative a, and a negative c film 273 8.6 Optically Compensated Bend Cell 277 8.6.1 Voltage-dependent transmittance 278 8.6.2 Compensation films for OCB 279 Homework Problems 281 References 283 9 Reflective and Transflective Liquid Crystal Displays 285 9.1 Introduction 285 9.2 Reflective Liquid Crystal Displays 286 9.2.1 Film-compensated homogeneous cell 287 9.2.2 Mixed-mode twisted nematic (MTN) cells 289 9.3 Transflector 290 9.3.1 Openings-on-metal transflector 290 9.3.2 Half-mirror metal transflector 291 9.3.3 Multilayer dielectric film transflector 292 9.3.4 Orthogonal polarization transflectors 292 9.4 Classification of Transflective LCDs 293 9.4.1 Absorption-type transflective LCDs 294 9.4.2 Scattering-type transflective LCDs 296 9.4.3 Scattering and absorption type transflective LCDs 298 9.4.4 Reflection-type transflective LCDs 300 9.4.5 Phase retardation type 302 9.5 Dual-Cell-Gap Transflective LCDs 312 9.6 Single-Cell-Gap Transflective LCDs 314 9.7 Performance of Transflective LCDs 314 9.7.1 Color balance 314 9.7.2 Image brightness 315 9.7.3 Viewing angle 315 Homework Problems 316 References 316 10 Liquid Crystal Display Matrices, Drive Schemes and Bistable Displays 321 10.1 Segmented Displays 321 10.2 Passive Matrix Displays and Drive Scheme 322 10.3 Active Matrix Displays 326 10.3.1 TFT structure 328 10.3.2 TFT operation principles 329 10.4 Bistable Ferroelectric LCD and Drive Scheme 330 10.5 Bistable Nematic Displays 332 10.5.1 Introduction 332 10.5.2 Twisted-untwisted bistable nematic LCDs 333 10.5.3 Surface-stabilized nematic liquid crystals 339 10.6 Bistable Cholesteric Reflective Display 342 10.6.1 Introduction 342 10.6.2 Optical properties of bistable Ch reflective displays 344 10.6.3 Encapsulated cholesteric liquid crystal displays 347 10.6.4 Transition between cholesteric states 347 10.6.5 Drive schemes for bistable Ch displays 355 Homework Problems 358 References 359 11 Liquid Crystal/Polymer Composites 363 11.1 Introduction 363 11.2 Phase Separation 365 11.2.1 Binary mixture 365 11.2.2 Phase diagram and thermal induced phase separation 369 11.2.3 Polymerization induced phase separation 371 11.2.4 Solvent-induced phase separation 374 11.2.5 Encapsulation 376 11.3 Scattering Properties of LCPCs 377 11.4 Polymer Dispersed Liquid Crystals 383 11.4.1 Liquid crystal droplet configurations in PDLCs 383 11.4.2 Switching PDLCs 385 11.4.3 Scattering PDLC devices 387 11.4.4 Dichroic dye-doped PDLC 391 11.4.5 Holographic PDLCs 393 11.5 PSLCs 395 11.5.1 Preparation of PSLCs 395 11.5.2 Working modes of scattering PSLCs 396 11.6 Scattering-Based Displays from LCPCs 400 11.6.1 Reflective displays 400 11.6.2 Projection displays 402 11.6.3 Transmissive direct-view displays 403 11.7 Polymer-Stabilized LCDs 403 Homework Problems 407 References 409 12 Tunable Liquid Crystal Photonic Devices 413 12.1 Introduction 413 12.2 Laser Beam Steering 414 12.2.1 Optical phased array 415 12.2.2 Prism-based beam steering 417 12.3 Variable Optical Attenuators 419 12.4 Tunable-Focus Lens 423 12.4.1 Tunable-focus spherical lens 423 12.4.2 Tunable-focus cylindrical lens 426 12.4.3 Switchable positive and negative microlens 428 12.4.4 Hermaphroditic LC microlens 434 12.5 Polarization-Independent LC Devices 435 12.5.1 Double-layered homogeneous LC cells 436 12.5.2 Double-layered LC gels 438 Homework Problems 441 References 442 13 Blue Phases of Chiral Liquid Crystals 445 13.1 Introduction 445 13.2 Phase Diagram of Blue Phases 446 13.3 Reflection of Blue Phases 447 13.3.1 Basics of crystal structure and X-ray diffraction 447 13.3.2 Bragg reflection of blue phases 449 13.4 Structure of Blue Phase 451 13.4.1 Defect theory 452 13.4.2 Landau theory 459 13.5 Optical Properties of Blue Phase 471 13.5.1 Reflection 471 13.5.2 Transmission 472 Homework Problems 475 References 475 14 Polymer-Stabilized Blue Phase Liquid Crystals 477 14.1 Introduction 477 14.2 Polymer-Stabilized Blue Phases 480 14.2.1 Nematic LC host 482 14.2.2 Chiral dopants 483 14.2.3 Monomers 483 14.3 Kerr Effect 484 14.3.1 Extended Kerr effect 486 14.3.2 Wavelength effect 489 14.3.3 Frequency effect 490 14.3.4 Temperature effects 491 14.4 Device Configurations 496 14.4.1 In-plane-switching BPLCD 497 14.4.2 Protruded electrodes 501 14.4.3 Etched electrodes 504 14.4.4 Single gamma curve 504 14.5 Vertical Field Switching 507 14.5.1 Device structure 507 14.5.2 Experiments and simulations 508 14.6 Phase Modulation 510 References 510 15 Liquid Crystal Display Components 513 15.1 Introduction 513 15.2 Light Source 513 15.3 Light-guide 516 15.4 Diffuser 516 15.5 Collimation Film 518 15.6 Polarizer 519 15.6.1 Dichroic absorbing polarizer 520 15.6.2 Dichroic reflective polarizer 521 15.7 Compensation Film 530 15.7.1 Form birefringence compensation film 531 15.7.2 Discotic liquid crystal compensation film 531 15.7.3 Compensation film from rigid polymer chains 532 15.7.4 Drawn polymer compensation film 533 15.8 Color Filter 535 References 536 16 Three-Dimensional Displays 539 16.1 Introduction 539 16.2 Depth Cues 539 16.2.1 Binocular disparity 539 16.2.2 Convergence 540 16.2.3 Motion parallax 540 16.2.4 Accommodation 541 16.3 Stereoscopic Displays 541 16.3.1 Head-mounted displays 542 16.3.2 Anaglyph 542 16.3.3 Time sequential stereoscopic displays with shutter glasses 542 16.3.4 Stereoscopic displays with polarizing glasses 544 16.4 Autostereoscopic Displays 546 16.4.1 Autostereoscopic displays based on parallax barriers 546 16.4.2 Autostereoscopic displays based on lenticular lens array 550 16.4.3 Directional backlight 552 16.5 Integral imaging 553 16.6 Holography 554 16.7 Volumetric displays 556 16.7.1 Swept volumetric displays 556 16.7.2 Multi-planar volumetric displays 557 16.7.3 Points volumetric displays 560 References 560 Index 565

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