Liquid Crystals IAM-CHOON 1(1100 .,4 WILEY 2007 WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION. 'i; Second Edition. n z

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1 Liquid Crystals Second Edition IAM-CHOON 1(1100.,4 z 'i; BICENTCNNIAL WILEY 2007 DICENTENNIAL n z z r WILEY-INTERSCIENCE A JOHN WILEY & SONS, INC., PUBLICATION

2 Contents Preface xiii Chapter 1. Introduction to Liquid Crystals Molecular Structures and Chemical Compositions Chemical Structures Electronic Properties Electronic Transitions and Ultraviolet Absorption Visible and Infrared Absorption Lyotropic, Polymeric, and Thermotropic Liquid Crystals Lyotropic Liquid Crystals Polymeric Liquid Crystals Thermotropic Liquid Crystals: Nematics, Cholesterics, and Smectics Other Liquid Crystalline Phases and Molecular Engineered Structures Mixtures and Composites Mixtures Dye-Doped Liquid Crystals Polymer-Dispersed Liquid Crystals Liquid Crystal Cells and Sample Preparation Bulle Thin Film Liquid Crystal Optical Slab Waveguide, Fiber, and Nanostructured Photonic Crystals 17 References 19 Chapter 2. Order Parameter, Phase Transition, and Free Energies Basic Concepts Introduction Scalar and Tensor Order Parameters Long- and Short-Range Order Molecular Interactions and Phase Transitions Molecular Theories and Results for the Liquid Crystalline Phase Maier-Saupe Theory: Order Parameter Near 7', Nonequilibrium and Dynamical Dependence of the Order Parameter 29 v

3 vi CONTENTS 2.4. Isotropic Phase of Liquid Crystals Free Energy and Phase Transition Free Energy in the Presence of an Applied Field 33 References 35 Chapter 3. Nematic Liquid Crystals Introduction Elastic Continuum Theory The Vector Field: Direct Axis n (r) Elastic Constants, Free Energies, and Molecular Fields Dielectric Constants and Refractive Indices dc and Low-Frequency Dielectric Permittivity, Conductivities, and Magnetic Susceptibility Free Energy and Torques by Electric and Magnetic Fields Optical Dielectric Constants and Refractive Indices Linear Susceptibility and Local Field Effect Equilibrium Temperature and Order Parameter Dependences of Refractive Indices Flows and Hydrodynamics Hydrodynamics of Ordinary Isotropic Fluids General Stress Tensor for Nematic Liquid Crystals Flows with Fixed Director Axis Orientation Flows with Director Axis Reorientation Field-Induced Director Axis Reorientation Effects Field-Induced Reorientation without Flow Coupling: Freedericksz Transition Reorientation with Flow Coupling 61 References 62 Chapter 4. Cholesteric, Smectic, and Ferroelectric Liquid Crystals Cholesteric Liquid Crystals Free Energies Field-Induced Effects and Dynamics Twist and Conic Mode Relaxation Times Light Scattering in Cholesterics General Optical Propagation and Reflection: Normal Incidence Cholesteric Liquid Crystal as a One-Dimensional Photonic Crystal Cholesteric Liquid Crystals with Magneto-Optic Activity: Negative Refraction Effect 78

4 CONTENTS vii 4.3. Smectic and Ferroelectric Liquid Crystals: A Quick Survey Smectic-A Liquid Crystals Free Energy Light Scattering in SmA Liquid Crystals Smectic-C Liquid Crystals Free Energy Field-Induced Director Axis Rotation in SmC Liquid Crystals Smectic-C* and Ferroelectric Liquid Crystals Free Energy of Ferroelectric Liquid Crystals Smectic-C* Smectic-A Phase Transition 93 References 95 Chapter 5. Light Scatterings Introduction General Electromagnetic Formalism of Light Scattering in Liquid Crystals Scattering from Director Axis Fluctuations in Nematic Liquid Crystals Light Scattering in the Isotropic Phase of Liquid Crystals Temperature, Wavelength, and Cell Geometry Effects an Scattering Spectrum of Light and Orientation Fluctuation Dynamics Raman Scatterings Introduction Quantum Theory of Raman Scattering: Scattering Cross Section Brillouin and Rayleigh Scatterings Brillouin Scattering Rayleigh Scattering Nonlinear Light Scattering: Supraoptical Nonlinearity of Liquid Crystals 120 References 122 Chapter 6. Liquid Crystal Optics and Electro-Optics Introduction Review of Electro-Optics of Anisotropic and Birefringent Crystals Anisotropic, Uniaxial, and Biaxial Optical Crystals Index Ellipsoid in the Presence of an Electric Field: Linear Electro-Optics Effect Polarizers and Retardation Plate Basic Electro-Optics Modulation 130

5 viii CONTENTS 6.3. Electro-Optics of Nematic Liquid Crystals Director Axis Reorientation in Homeotropic and Planar Cells: Dual-Frequency Liquid Crystals Freedericksz Transition Revisited Field-Induced Refractive Index Change and Phase Shift Nematic Liquid Crystal Switches and Displays Liquid Crystal Switch: On-Axis Consideration for Twist, Planar, and Homeotropic Aligned Cells Off-Axis Transmission, Viewing Angle, and Birefringence Compensation Liquid Crystal Display Electronics Electro-Optical Effects in Other Phases of Liquid Crystals Surface Stabilized FLC Soft-Mode FLCs Nondisplay Applications of Liquid Crystals Liquid Crystal Spatial Light Modulator Tunable Photonic Crystals with Liquid Crystal Infiltrated Nanostructures Tunable Frequency Selective Planar Structures Liquid Crystals for Molecular Sensing and Detection Beam Steering, Routing, and Optical Switching and Laser Hardened Optics 152 References 153 Chapter 7. Electromagnetic Formalisms for Optical Propagation Introduction Electromagnetism of Anisotropic Media Revisited Maxwell Equations and Wave Equations Complex Refractive Index Negative Index Material Normal Modes, Power Flow, and Propagation Vectors in a Lossless Isotropic Medium Normal Modes and Propagation Vectors in a Lossless Anisotropic Medium General Formalisms for Polarized Light Propagation Through Liquid Crystal Devices Plane-Polarized Wave and Jones Vectors Jones Matrix Method for Propagation Through a Nematic Liquid Crystal Cell Oblique Incidence: 4X4 Matrix Methods Extended Jones Matrix Method 177

6 CONTENTS ix 7.5. Finite-Difference Time-Domain Technique The Implementation of FDTD Methods Example: FDTD Computations of the Twisted Nematic Cell in One Dimension 186 References 188 Chapter 8. Laser-Induced Orientational Optical Nonlinearities in Liquid Crystals General Overview of Liquid Crystal Nonlinearities Laser-Induced Molecular Reorientations in the Isotropic Phase Individual Molecular Reorientations in Anisotropic Liquids Correlated Molecular Reorientation Dynamics Influence of Molecular Structure an Isotropic Phase Reorientational Nonlinearities Molecular Reorientations in the Nematic Phase Simplified Treatment of Optical Field-Induced Director Axis Reorientation More Exact Treatment of Optical Field-Induced Director Axis Reorientation Nonlocal Effect and Transverse Dependence Nematic Phase Reorientation Dynamics Plane Wave Optical Field Sinusoidal Optical Intensity Laser-Induced Dopant-Assisted Molecular Reorientation and Trans-Cis Isomerism DC Field Aided Optically Induced Nonlinear Optical Effects in Liquid Crystals: Photorefractivity Orientational Photorefractivity: Bulk Effects Some Experimental Results and Surface Charge/Field Contribution Reorientation and Nonelectronic Nonlinear Optical Effects in Smectic and Cholesteric Phases Smectic Phase Cholesteric Phase 222 References 223 Chapter 9. Thermal, Density, and Other Nonelectronic Nonlinear Mechanisms Introduction Density and Temperature Changes Induced by Sinusoidal Optical Intensity Refractive Index Changes: Temperature and Density Effects 233

7 CONTENTS 9.4. Thermal and Density Optical Nonlinearities of Nematic Liquid Crystals in the Visible-Infrared Spectrum Steady-State Thermal Nonlinearity of Nematic Liquid Crystals Short Laser Pulse Induced Thermal Index Change in Nematics and Near-T, Effect Thermal and Density Optical Nonlinearities of Isotropic Liquid Crystals Coupled Nonlinear Optical Effects in Nematic Liquid Crystals Thermal-Orientational Coupling in Nematic Liquid Crystals Flow-Orientational Effect 247 References 251 Chapter 10. Electronic Optical Nonlinearities Introduction Density Matrix Formalism for Optically Induced Molecular Electronic Polarizabilities Induced Polarizations Multiphoton Absorptions Electronic Susceptibilities of Liquid Crystals Linear Optical Polarizabilities of a Molecule with No Permanent Dipole Second-Order Electronic Polarizabilities Third-Order Electronic Polarizabilities Electronic Nonlinear Polarizations of Liquid Crystals Local Field Effects and Symmetry Symmetry Considerations Permanent Dipole and Molecular Ordering Quadrupole Contribution and Field-Induced Symmetry Breaking Molecular Structural Dependence of Nonlinear Susceptibilities 269 References 271 Chapter 11. Introduction to Nonlinear Optics Nonlinear Susceptibility and Intensity-Dependent Refractive Index Nonlinear Polarization and Refractive Index Nonlinear Coefficient and Units General Nonlinear Polarization and Susceptibility Convention and Symmetry Coupled Maxwell Wave Equations 282

8 CONTENTS xi Nonlinear Optical Phenomena Stationary Degenerate Four-Wave Mixing Optical Phase Conjugation Nearly Degenerate and Transient Wave Mixing Nondegenerate Optical Wave Mixing: Harmonic Generations Self-Focusing and Self-Phase Modulation Stimulated Scatterings Stimulated Raman Scatterings Stimulated Brillouin Scatterings Stimulated Orientational Scattering in Liquid Crystals Stimulated Thermal Scattering (STS) 316 References 317 Chapter 12. Nonlinear Optical Phenomena Observed in Liquid Crystals Self-Focusing, Self-Phase Modulation, and Self-Guiding Self-Focusing and Self-Phase Modulation and cw Optical Limiting with Nematic Liquid Crystals Self-Guiding, Spatial Soliton, and Pattern Formation Optical Wave Mixing Stimulated Orientational Scattering and Polarization Self-Switching: Steady State Stimulated Orientational Scattering: Nonlinear Dynamics Optical Phase Conjugation with Orientation and Thermal Gratings Self-Starting Optical Phase Conjugation Liquid Crystals for All-Optical Image Processing Liquid Crystals as All-Optical Information Processing Materials All-Optical Image Processing Intelligent Optical Processing Harmonic Generations and Sum-Frequency Spectroscopy Optical Switching Nonlinear Absorption and Optical Limiting of Short Laser Pulses in Isotropic Phase Liquid Crystals and Liquids Introduction Nonlinear Fiber Array RSA Materials (C60 Doped ILC) Optical Limiting by TPA Materials (L34 Fiber Core Liquid) Conclusion 358 References 358 Index 365

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