Preface ...................................................... xiii
Chapter 1. Introduction to Liquid Crystals ...................... 1
1.1. Molecular Structures and Chemical Compositions ............. 1
1.1.1. Chemical Structures ................................. 1
1.2. Electronic Properties ...................................... 3
1.2.1. Electronic Transitions and Ultraviolet Absorption ... 3
1.2.2. Visible and Infrared Absorption ..................... 4
1.3. Lyotropic, Polymeric, and Thermotropic Liquid Crystals ..... 6
1.3.1. Lyotropic Liquid Crystals ........................... 6
1.3.2. Polymeric Liquid Crystals ........................... 6
1.3.3. Thermotropic Liquid Crystals: Nematics,
Choleslerics, and Smectics .......................... 7
1.3.4. Other Liquid Crystalline Phases and Molecular
Engineered Structures .............................. 10
1.4. Mixtures and Composites ................................... 11
1.4.1. Mixtures ........................................... 12
1.4.2. Dye-Doped Liquid Crystals .......................... 13
1.4.3. Polymer-Dispersed Liquid Crystals .................. 14
1.5. Liquid Crystal Cells and Sample Preparation ............... 14
1.5.1. Bulk Thin Film ..................................... 15
1.5.2. Liquid Crystal Optical Slab Waveguide, Fiber, and
Nanostruclured Photonic Crystals ................... 17
References ..................................................... 19
Chapter 2. Order Parameter, Phase Transition, and Free
Energies ............................................ 22
2.1. Basic Concepts ............................................ 22
2.1.1. Introduction ....................................... 22
2.1.2. Scalar and Tensor Order Parameters ................. 23
2.1.3. Long- and Short-Range Order ........................ 25
2.2. Molecular Interactions and Phase Transitions .............. 26
2.3. Molecular Theories and Results for the Liquid
Crystalline Phase ......................................... 26
2.3.1. Maier-Saupe Theory: Order Parameter Near Tc ........ 27
2.3.2. Nonequilibrium and Dynamical Dependence of
the Order Parameter ................................ 29
2.4. Isotropic Phase of Liquid Crystals ........................ 32
2.4.1. Free Energy and Phase Transition ................... 32
2.4.2. Free Energy in the Presence of an Applied Field .... 33
References ..................................................... 35
Chapter 3. Nematic Liquid Crystals ............................. 36
3.1. Introduction .............................................. 36
3.2. Elastic Continuum Theory .................................. 36
3.2.1. The Vector Field: Direct Axis n(r) ................. 36
3.2.2. Elastic Constants, Free Energies, and Molecular
Fields ............................................. 38
3.3. Dielectric Constants and Refractive Indices ............... 41
3.3.1. de and Low-Frequency Dielectric Permittivity,
Conductivities, and Magnetic Susceptibility ........ 41
3.3.2. Free Energy and Torques by Electric and Magnetic
Fields ............................................. 44
3.4. Optical Dielectric Constants and Refractive Indices ....... 45
3.4.1. Linear Susceptibility and Local Field Effect ....... 45
3.4.2. Equilibrium Temperature and Order Parameter
Dependences of Refractive Indices .................. 47
3.5. Flows and Hydrodynamics ................................... 51
3.5.1. Hydrodynamics of Ordinary Isotropic Fluids ......... 52
3.5.2. General Stress Tensor for Nematic Liquid
Crystals ........................................... 55
3.5.3. Flows with Fixed Director Axis Orientation ......... 55
3.5.4. Flows with Director Axis Reorientation ............. 57
3.6. Field-Induced Director Axis Reorientation Effects ......... 58
3.6.1. Field-Induced Reorientation without Flow
Coupling: Freedericksz Transition .................. 58
3.6.2. Reorientation with Flow Coupling ................... 61
References ..................................................... 62
Chapter 4. Cholesteric, Smectic, and Ferroelectric Liquid
Crystals ............................................ 64
4.1. Cholesteric Liquid Crystals ............................... 64
4.1.1. Free Energies ...................................... 64
4.1.2. Field-Induced Effects and Dynamics ................. 66
4.1.3. Twist and Conic Mode Relaxation Times .............. 69
4.2. Light Scattering in Cholesterics .......................... 70
4.2.1. General Optical Propagation and Reflection:
Normal Incidence ................................... 70
4.2.2. Cholesterie Liquid Crystal as a One-Dimensional
Photonic Crystal ................................... 74
4.2.3. Cholesterie Liquid Crystals with Magneto-Optic
Activity: Negative Refraction Effect ............... 78
4.3. Smectic and Ferroelectric Liquid Crystals: A Quick
Survey .................................................... 80
4.4. Smectic-A Liquid Crystals ................................. 82
4.4.1. Free Energy ........................................ 82
4.4.2. Light Scattering in SmA Liquid Crystals ............ 84
4.5. Smectic-C Liquid Crystals ................................. 86
4.5.1. Free Energy ........................................ 86
4.5.2. Field-Induced Director Axis Rotation in SmC
Liquid Crystals .................................... 87
4.6. Smectic-C* and Ferroelectric Liquid Crystals .............. 88
4.6.1. Free Energy of Ferroelectric Liquid Crystals ....... 89
4.6.2. Smectic-C*-Smectic-A Phase Transition .............. 93
References ..................................................... 95
Chapter 5. Light Scatterings ................................... 97
5.1. Introduction .............................................. 97
5.2. General Electromagnetic Formalism of Light Scattering
in Liquid Crystals ........................................ 98
5.3. Scattering from Director Axis Fluctuations in Nematic
Liquid Crystals .......................................... 100
5.4. Light Scattering in the Isotropic Phase of Liquid
Crystals ................................................. 104
5.5. Temperature, Wavelength, and Cell Geometry Effects on
Scattering ............................................... 107
5.6. Spectrum of Light and Orientation Fluctuation Dynamics ... 109
5.7. Raman Scatterings ........................................ 111
5.7.1. Introduction ...................................... 111
5.7.2. Quantum Theory of Raman Scattering: Scattering
Cross Section ..................................... 112
5.8. Brillouin and Rayleigh Scatterings ....................... 115
5.8.1. Brillouin Scattering .............................. 117
5.8.2. Rayleigh Scattering ............................... 119
5.9. Nonlinear Light Scattering: Supraoptical Nonlinearity
of Liquid Crystals ....................................... 120
References .................................................... 122
Chapter 6. Liquid Crystal Optics and Electro-Optics ........... 124
6.1. Introduction ............................................. 124
6.2. Review of Electro-Optics of Anisotropic and
Birefringent Crystals .................................... 125
6.2.1. Anisotropic, Uniaxial, and Biaxial Optical
Crystals .......................................... 125
6.2.2. Index Ellipsoid in the Presence of an Electric
Field: Linear Electro-Optics Effect ............... 127
6.2.3. Polarizers and Retardation Plate .................. 128
6.2.4. Basic Electro-Optics Modulation ................... 130
6.3. Electro-Optics of Nematic Liquid Crystals ................ 131
6.3.1. Director Axis Reorientation in Homeotropic and
Planar Cells: Dual-Frequency Liquid Crystals ...... 131
6.3.2. Freedericksz Transition Revisited ................. 133
6.3.3. Field-Induced Refractive Index Change and Phase
Shift ............................................. 136
6.4. Nematic Liquid Crystal Switches and Displays ............. 138
6.4.1. Liquid Crystal Switch: On-Axis Consideration for
Twist, Planar, and Homeotropic Aligned Cells ...... 139
6.4.2. Off-Axis Transmission, Viewing Angle, and
Birefringence Compensation ........................ 139
6.4.3. Liquid Crystal Display Electronics ................ 141
6.5. Electro-Optical Effects in Other Phases of Liquid
Crystals ................................................. 142
6.5.1. Surface Stabilized FLC ............................ 142
6.5.2. Soft-Mode FLCs .................................... 144
6.6. Nondisplay Applications of Liquid Crystals ............... 146
6.6.1. Liquid Crystal Spatial Light Modulator ............ 146
6.6.2. Tunable Photonic Crystals with Liquid Crystal
Infiltrated Nanostructures ........................ 148
6.6.3. Tunable Frequency Selective Planar Structures ..... 148
6.6.4. Liquid Crystals for Molecular Sensing and
Detection ......................................... 150
6.6.5. Beam Steering, Routing, and Optical Switching
and Laser Hardened Optics ......................... 152
References .................................................... 153
Chapter 7. Electromagnetic Formalisms for Optical
Propagation ........................................ 157
7.1. Introduction ............................................. 157
7.2. Electromagnet!sm of Anisotropic Media Revisited .......... 158
7.2.1. Maxwell Equations and Wave Equations .............. 158
7.2.2. Complex Refractive Index .......................... 159
7.2.3. Negative Index Material ........................... 160
7.2.4. Normal Modes, Power Flow, and Propagation
Vectors in a Lossless Isotropic Medium ............ 163
7.2.5. Normal Modes and Propagation Vectors in
a Lossless Anisotropic Medium ..................... 164
7.3. General Formalisms for Polarized Light Propagation
Through Liquid Crystal Devices ........................... 168
7.3.1. Plane-Polarized Wave and Jones Vectors ............ 169
7.3.2. Jones Matrix Method for Propagation Through
a Nematic Liquid Crystal Cell ..................... 173
7.3.3. Oblique Incidence: 4×4 Matrix Methods ............. 175
7.4. Extended Jones Matrix Method ............................. 177
7.5. Finite-Difference Time-Domain Technique .................. 181
7.5.1. The Implementation of FDTD Methods ................ 181
7.5.2. Example: FDTD Computations of the Twisted
Nematic Cell in One Dimension ..................... 186
References .................................................... 188
Chapter 8. Laser-Induced Orientational Optical
Nonlinearities in Liquid Crystals .................. 190
8.1. General Overview of Liquid Crystal Nonlinearities ........ 190
8.2. Laser-Induced Molecular Reorientations in the Isotropic
Phase .................................................... 193
8.2.1. Individual Molecular Reorientations in
Anisotropic Liquids ............................... 193
8.2.2. Correlated Molecular Reorientation Dynamics ....... 196
8.2.3. Influence of Molecular Structure on Isotropic
Phase Reorienlational Nonlinearities .............. 198
8.3. Molecular Reorientations in the Nematic Phase ............ 200
8.3.1. Simplified Treatment of Optical Field-Induced
Director Axis Reorientation ....................... 201
8.3.2. More Exact Treatment of Optical Field-Induced
Director Axis Reorientation ....................... 204
8.3.3. Nonlocal Effect and Transverse Dependence ......... 205
8.4. Nematic Phase Reorientation Dynamics ..................... 206
8.4.1. Plane Wave Optical Field .......................... 206
8.4.2. Sinusoidal Optical Intensity ...................... 210
8.5. Laser-Induced Dopant-Assisted Molecular Reorientation
and Trans-Cis Isomerism .................................. 211
8.6. DC Field Aided Optically Induced Nonlinear Optical
Effects in Liquid Crystals: Photorefractivity ............ 213
8.6.1. Orientational Photorefractivity: Bulk Effects ..... 215
8.6.2. Some Experimental Results and Surface Charge/
Field Contribution ................................ 220
8.7. Reorientation and Nonelectronic Nonlinear Optical
Effects in Smectic and Cholesteric Phases ................ 221
8.7.1. Smectic Phase ..................................... 221
8.7.2. Cholesteric Phase ................................. 222
References .................................................... 223
Chapter 9. Thermal, Density, and Other Nonelectronic
Nonlinear Mechanisms ............................... 227
9.1. Introduction ............................................. 227
9.2. Density and Temperature Changes Induced by Sinusoidal
Optical Intensity ........................................ 230
9.3. Refractive Index Changes: Temperature and Density
Effects .................................................. 233
9.4. Thermal and Density Optical Nonlinearities of Nematic
Liquid Crystals in the Visible-Infrared Spectrum ......... 238
9.4.1. Steady-State Thermal Nonlinearity of Nematic
Liquid Crystals ................................... 240
9.4.2. Short Laser Pulse Induced Thermal Index Change
in Nematics and Near-Tc Effect .................... 241
9.5. Thermal and Density Optical Nonlinearities of Isotropic
Liquid Crystals .......................................... 243
9.6. Coupled Nonlinear Optical Effects in Nematic Liquid
Crystals ................................................. 245
9.6.1. Thermal-Orientational Coupling in Nematic Liquid
Crystals .......................................... 246
9.6.2. Flow-Orientational Effect ......................... 247
References .................................................... 251
Chapter 10. Electronic Optical Nonlinearities ................ 253
10.1. Introduction ............................................ 253
10.2. Density Matrix Formalism for Optically Induced
Molecular Electronic Polarizabilities ................... 253
10.2.1. Induced Polarizations ........................... 256
10.2.2. Multiphoton Absorptions ......................... 256
10.3. Electronic Susceptibilities of Liquid Crystals .......... 259
10.3.1. Linear Optical Polarizabilities of a Molecule
with No Permanent Dipole ........................ 259
10.3.2. Second-Order Electronic Polarizabilities ........ 262
10.3.3. Third-Order Electronic Polarizabilities ......... 264
10.4. Electronic Nonlinear Polarizations of Liquid Crystals ... 266
10.4.1. Local Field Effects and Symmetry ................ 267
10.4.2. Symmetry Considerations ......................... 268
10.4.3. Permanent Dipole and Molecular Ordering ......... 268
10.4.4. Quadrupole Contribution and Field-Induced
Symmetry Breaking ............................... 269
10.4.5. Molecular Structural Dependence of Nonlinear
Susceptibilities ................................ 269
References .................................................... 271
Chapter 11. Introduction to Nonlinear Optics .................. 273
11.1. Nonlinear Susceptibility and Intensity-Dependent
Refractive Index ........................................ 273
11.1.1. Nonlinear Polarization and Refractive Index ..... 273
11.1.2. Nonlinear Coefficient and Units ................. 276
11.2. General Nonlinear Polarization and Susceptibility ....... 277
11.3. Convention and Symmetry ................................. 278
11.4. Coupled Maxwell Wave Equations .......................... 282
11.5. Nonlinear Optical Phenomena ............................. 284
11.5.1. Stationary Degenerate Four-Wave Mixing .......... 284
11.5.2. Optical Phase Conjugation ....................... 288
11.5.3. Nearly Degenerate and Transient Wave Mixing ..... 291
11.5.4. Nondegenerate Optical Wave Mixing: Harmonic
Generations ..................................... 294
11.5.5. Self-Focusing and Self-Phase Modulation ......... 297
11.6. Stimulated Scatterings .................................. 303
11.6.1. Stimulated Raman Scatterings .................... 303
11.6.2. Stimulated Brillouin Scatterings ................ 306
11.6.3. Stimulated Orientational Scattering in Liquid
Crystals ........................................ 311
11.6.4. Stimulated Thermal Scattering (STS) ............. 316
References .................................................... 317
Chapter 12. Nonlinear Optical Phenomena Observed in Liquid
Crystals .......................................... 319
12.1. Self-Focusing, Self-Phase Modulation, and
Self-Guiding ............................................ 319
12.1.1. Self-Focusing and Self-Phase Modulation and cw
Optical Limiting with Nematic Liquid Crystals ... 319
12.1.2. Self-Guiding, Spatial Soliton, and Pattern
Formation ....................................... 324
12.2. Optical Wave Mixing ..................................... 326
12.2.1. Stimulated Orientational Scattering and
Polarization Self-Switching: Steady State ....... 326
12.2.2. Stimulated Orientational Scattering: Nonlinear
Dynamics ........................................ 329
12.2.3. Optical Phase Conjugation with Orientation and
Thermal Gratings ................................ 332
12.2.4. Self-Starting Optical Phase Conjugation ......... 333
12.3. Liquid Crystals for All-Optical Image Processing ........ 337
12.3.1. Liquid Crystals as All-Optical Information
Processing Materials ............................ 337
12.3.2. All-Optical Image Processing .................... 339
12.3.3. Intelligent Optical Processing .................. 341
12.4. Harmonic Generations and Sum-Frequency Spectroscopy ..... 343
12.5. Optical Switching ....................................... 344
12.6. Nonlinear Absorption and Optical Limiting of Short
Laser Pulses in Isotropic Phase Liquid Crystals and
Liquids ................................................. 348
12.6.1. Introduction .................................... 348
12.6.2. Nonlinear Fiber Array ........................... 350
12.6.3. RSA Materials (C60 Doped ILC) ................... 351
12.6.4. Optical Limiting by TPA Materials
(L34 Fiber Core Liquid) ......................... 355
12.7. Conclusion .............................................. 358
References .................................................... 358
Index ......................................................... 365
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