Fundamentals of Liquid Crystal Devices

Liquid Crystal Devices are crucial and ubiquitous components of an ever-increasing number of technologies. They are used in everything from cellular phones, eBook readers, GPS devices, computer monitors and automotive displays to projectors and TVs, to name but a few. This second edition continues to serve as an introductory guide to the fundamental properties of liquid crystals and their technical application, while explicating the recent advancements within LCD technology. This edition includes important new chapters on blue-phase display technology, advancements in LCD research significantly contributed to by the authors themselves.

This title is of particular interest to engineers and researchers involved in display technology and graduate students involved in display technology research.

• Key features:
  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 the properties of blue-phase liquid crystal displays and 3D liquid crystal displays;
• Explains the link between the fundamental scientific principles behind liquid crystal technology and their application to photonic devices and displays, providing a thorough understanding of the physics, optics, electro-optics and material aspects of Liquid Crystal Devices;
• Revised material reflecting developments in LCD technology, including updates on optical modelling methods, transmissive LCDs and tunable liquid crystal photonic devices;
• Chapters conclude with detailed homework problems to further cement an understanding of the topic.

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 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

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