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Updated throughout to reflect the latest technical state-of-the-art in LCD research and development, including new chapters and material on topics such as
Table of Contents
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 Poincaré sphere 104
3.2.5 Evolution of the polarization states on the Poincaré 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 × 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 Fréedericksz 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 Fréedericksz 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 Fréedericksz Transition: Dynamics 175
5.5.1 Dynamics of Fréedericksz 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 Δε liquid crystals for AMLCD 202
6.3.2 Negative Δε 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 Poincaré 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
