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Iam-Choon Khoo. Liquid Crystals
Table of Contents
List of Tables
List of Illustrations
Guide
Pages
Liquid Crystals
Preface
1 Introduction to Liquid Crystals
1.1. MOLECULAR STRUCTURES AND CHEMICAL COMPOSITIONS
1.2. OPTICAL PROPERTIES
1.2.1. Electronic Optical Transitions and UV Absorption
1.2.2. Visible and Infrared Absorption; Terahertz, Microwave
1.3. LYOTROPIC, POLYMERIC, AND THERMOTROPIC LIQUID CRYSTALS
1.3.1. Lyotropic Liquid Crystals
1.3.2. Polymeric Liquid Crystals
1.3.3. Thermotropic Liquid Crystals: Smectic, Nematic, Cholesteric, and Blue‐phase Liquid Crystals
1.3.4. Functionalized and Discotic Liquid Crystals
1.4. MIXTURES, POLYMER‐DISPERSED, AND DYE‐DOPED LIQUID CRYSTALS
1.4.1. Mixtures
1.4.2. Dye‐doped Liquid Crystals
1.4.3. Polymer‐dispersed and Polymer‐stabilized Liquid Crystals
1.5. LIQUID CRYSTAL CELLS FABRICATION
1.5.1. Nematic LC Cells Assembly
1.5.2. Cholesteric Liquid Crystal Cell Assembly
1.5.3. Blue‐phase Liquid Crystal Cell Assembly
1.5.4. Photosensitive and Tunable Optical Waveguide, Photonic Crystals, and Metamaterial Nanostructures
1.5.5. Isotropic Liquid Crystal Cored Fiber Array
REFERENCES
2 Order Parameter, Phase Transition, and Free Energies. 2.1. BASIC CONCEPTS. 2.1.1. Introduction
2.1.2. Scalar and Tensor Order Parameters
2.1.3. Long‐ and Short‐range Order
2.2. MOLECULAR INTERACTIONS AND PHASE TRANSITIONS
2.3. MOLECULAR THEORIES AND RESULTS FOR THE LIQUID CRYSTALLINE PHASE
2.3.1. Maier–Saupe Theory: Order Parameter Near Tc
2.3.2. Nonequilibrium and Dynamical Dependence of the Order Parameter
2.4. ISOTROPIC PHASE OF LIQUID CRYSTALS
2.4.1. Free Energy and Phase Transition
2.4.2. Free Energy in the Presence of an Applied Field
REFERENCES
3 Nematic Liquid Crystals. 3.1. INTRODUCTION
3.2. ELASTIC CONTINUUM THEORY. 3.2.1. The Vector Field: Director Axis
3.2.2. Elastic Constants, Free Energies, and Molecular Fields
3.3. DIELECTRIC CONSTANTS AND REFRACTIVE INDICES
3.3.1. DC and Low‐frequency Dielectric Permittivity, Conductivities, and Magnetic Susceptibility
3.3.2. Free Energy and Torques by Electric and Magnetic Fields
3.4. OPTICAL DIELECTRIC CONSTANTS AND REFRACTIVE INDICES. 3.4.1. Linear Susceptibility and Local Field Effect
3.4.2. Equilibrium Temperature and Order Parameter Dependences of Refractive Indices
3.5. FLOWS AND HYDRODYNAMICS
3.5.1. Hydrodynamics of Ordinary Isotropic Fluids
3.5.2. General Stress Tensor for Nematic Liquid Crystals
3.5.3. Flows with Fixed Director Axis Orientation
3.5.4. Flows with Director Axis Reorientation
3.6. FIELD‐INDUCED DIRECTOR AXIS REORIENTATION EFFECTS
3.6.1. Field‐induced Reorientation Without Flow Coupling: Freedericksz Transition
3.6.2. Reorientation with Flow Coupling
REFERENCES
4 Cholesteric, Smectic, and Ferroelectric Liquid Crystals. 4.1. CHOLESTERIC LIQUID CRYSTALS
4.1.1. Free Energies
4.1.2. Field‐induced Effects and Dynamics
4.1.2.1. Magnetic Field
4.1.2.2. Electric Field
4.1.3. Twist and Conic Mode Relaxation Times
4.2. OPTICAL PROPERTIES OF CHOLESTERICS
4.2.1. Bragg Regime (Optical Wavelength ~ Pitch)
4.2.2. Reflection and Transmission of Polarized Light: Normal Incidence
4.2.3. Cholesteric Liquid Crystal as a One‐dimensional Photonic Crystal, Photonic Bandgap, and Dispersion
4.2.4. Cholesteric Liquid Crystals with Magneto‐optic Activity: Negative Index of Refraction
4.2.5. Polarization Rotation and Switching by High Period Number CLC – Adiabatic Rotation and Circular Bragg Resonance
4.3. CHOLESTERIC BLUE PHASE LIQUID CRYSTALS. 4.3.1. Free Energies and Equation of Motion under an Applied Field
4.3.2. Field‐induced Lattice Distortion and New Crystalline Structures
4.3.3. Polymer‐stabilization and Electro‐optical Properties of Non‐cubic BPLC
4.4. SMECTIC AND FERROELECTRIC LIQUID CRYSTALS: A BRIEF SURVEY
4.4.1. Smectic‐A Liquid Crystals. 4.4.1.1. Free Energies
4.4.1.2. Light Scattering in SmA Liquid Crystals
4.4.2. Smectic‐C Liquid Crystals. 4.4.2.1. Free Energy
4.4.2.2. Field‐induced Director Axis Rotation in SmC Liquid Crystals
4.4.3. Smectic‐C* and Ferroelectric Liquid Crystals
4.4.3.1. Free Energy of Ferroelectric Liquid Crystals
4.4.4. Smectic‐C* – Smectic‐A Phase Transition
References
5 Light Scattering. 5.1. INTRODUCTION
5.2. ELECTROMAGNETIC FORMALISM OF LIGHT SCATTERING IN LIQUID CRYSTALS
5.3. SCATTERING FROM DIRECTOR AXIS FLUCTUATIONS IN NEMATIC LIQUID CRYSTALS
5.4. LIGHT SCATTERING IN THE ISOTROPIC PHASE OF LIQUID CRYSTALS
5.5. TEMPERATURE, WAVELENGTH, AND CELL GEOMETRY EFFECTS ON SCATTERING
5.6. SPECTRUM OF LIGHT AND ORIENTATION FLUCTUATION DYNAMICS
5.7. RAMAN SCATTERINGS. 5.7.1. Introduction
5.7.2. Quantum Theory of Spontaneous and Stimulated Raman Scattering: Scattering Cross‐section
5.7.3. Spontaneous Raman Scattering
5.7.4. Stimulated Raman Scattering
5.8. BRILLOUIN AND RAYLEIGH SCATTERINGS
5.8.1. Brillouin Scattering
5.8.2. Rayleigh Scattering
5.9. A BRIEF INTRODUCTION TO NONLINEAR LIGHT SCATTERING
REFERENCES
6 Liquid Crystals Optics and Electro‐optics. 6.1. INTRODUCTION
6.2. REVIEW OF ELECTRO‐OPTICS OF ANISOTROPIC AND BIREFRINGENT CRYSTALS. 6.2.1. Anisotropic, Uniaxial and Biaxial Optical Crystals
6.2.2. Index Ellipsoid in the Presence of an Electric Field–Electro‐optics Effect
6.2.3. Polarizers and Retardation Plate
6.2.4. Basic Electro‐optics Modulation
6.3. ELECTRO‐OPTICS OF NEMATIC LIQUID CRYSTALS
6.3.1. Director Axis Reorientation in Homeotropic and Planar Cell; Dual Frequency Liquid Crystals
6.3.2. Freedericksz Transition Revisited
6.3.2.1. Case 1: One Elastic Constant Approximation
6.3.2.2. Case 2: Freedericksz Transition Voltage – Including Elastic Anisotropies
6.3.2.3. Case 3: Freedericksz Transition Voltage – Including Conductivity
6.3.3. Field‐induced Refractive Index Change and Phase Shift
6.4. NEMATIC LIQUID CRYSTAL SWITCHES FOR DISPLAY APPLICATION
6.4.1. Liquid Crystal Switch – on Axis Consideration for Twist, Planar, and Homeotropic Aligned Cells
6.4.2. Off‐axis Transmission, Viewing Angle, and Birefringence Compensation
6.4.3. Liquid Crystal Display Electronics
6.5. ELECTRO‐OPTICAL EFFECTS IN OTHER PHASES OF LIQUID CRYSTALS
6.5.1. Surface Stabilized FLC
6.5.2. Soft‐mode FLCs
6.6. NON‐DISPLAY APPLICATIONS OF LIQUID CRYSTALS
6.6.1. Liquid Crystal Spatial Light Modulator
6.6.2. Tunable Photonic Crystals with Liquid Crystal Infiltrated Nanostructures
6.6.3. Tunable Frequency Selective Structures, Metamaterial, and Metasurfaces
6.6.4. Liquid Crystals for Molecular Sensing and Detection
6.6.5. Beam Steering, Routing, and Tunable Micro‐ring Resonator, and High‐power Laser Optics
References
7 Optical Propagation in Anisotropic Materials. 7.1. ELECTROMAGNETIC FORMALISMS FOR OPTICAL PROPAGATION
7.1.1. Maxwell Equations and Wave Equations in Anisotropic Media
7.1.2. Complex Refractive Index – Real and Imaginary Components
7.1.3. Negative Index Material
7.1.4. Normal Modes, Power Flow and Propagation Vectors in a Lossless Isotropic Medium
7.1.5. Normal Modes and Propagation Vectors in a Lossless Anisotropic Medium
7.2. POLARIZED LIGHT PROPAGATION IN LIQUID CRYSTAL DISPLAY PANEL
7.2.1. Pane Polarized Wave and Jones Vectors
7.2.2. Jones Matrix Method
7.2.3. Oblique Incidence – 4 × 4 Matrix Methods
7.3. EXTENDED JONES MATRIX METHOD
7.4. FINITE‐DIFFERENCE TIME‐DOMAIN TECHNIQUE
7.5. NONLINEAR LIGHT PROPAGATION IN LIQUID CRYSTALS – A FIRST LOOK
7.6. SYSTEMS OF UNITS
References
8 Laser‐induced Reorientation Nonlinear Optical Effects. 8.1. INTRODUCTION
8.2. LASER‐INDUCED MOLECULAR REORIENTATIONS IN THE ISOTROPIC PHASE. 8.2.1. Individual Molecular Reorientations in Anisotropic Liquids
8.2.2. Correlated Molecular Reorientation Dynamics
8.2.3. Influence of Molecular Structure on Isotropic Phase Reorientation Nonlinearities
8.3. MOLECULAR REORIENTATIONS IN THE NEMATIC PHASE
8.3.1. Simplified Treatment of Optical Field‐induced Director Axis Reorientation
8.3.2. More Exact Treatment of Optical Field‐induced Director Axis Reorientation
8.3.3. Nonlocal Director Axis Reorientation and Nonlocal Optical Nonlinearity
8.4. NEMATIC PHASE REORIENTATION DYNAMICS
8.4.1. Plane Wave Optical Field
8.4.2. Sinusoidal Optical Intensity
8.4.3. Polarization Grating with Uniform Optical Intensity
8.5. LASER‐INDUCED DIRECTOR AXIS REALIGNMENT IN DYE‐DOPED LIQUID CRYSTALS
8.5.1. Reorientation Caused by Inter‐Molecular Torque
8.5.2. Laser‐induced Trans–Cis Isomerism in Dye‐doped Liquid Crystals
8.6. DC FIELD AIDED OPTICALLY INDUCED NONLINEAR OPTICAL EFFECTS IN LIQUID CRYSTALS – PHOTOREFRACTIVITY
8.6.1. Orientation Photorefractivity – Bulk Effects
8.6.2. Experimental Results and Surface Charge/Field Contribution
8.7. REORIENTATION IN OTHER PHASES OF PRISTINE (UNDOPED) LIQUID CRYSTALS
8.7.1. Smectic Phase
8.7.2. Cholesteric and Blue‐phase Liquid Crystals
REFERENCES
9 Thermal, Density, Lattice Distortion Optical Nonlinearities in Nematic, Cholesteric, and Blue‐phase Liquid Crystals. 9.1. INTRODUCTION
9.2. ELECTROSTRICTION AND FLOWS IN NON‐ABSORBING LIQUID CRYSTALS – A GENERAL OVERVIEW
9.3. LASER‐INDUCED DENSITY AND TEMPERATURE MODULATIONS IN LIQUID CRYSTALS
9.3.1. Modulations by Sinusoidal Optical Intensity
9.3.2. Refractive Index Changes: Temperature and Density Effects
9.4. OPTICAL NONLINEARITIES OF NEMATIC LIQUID CRYSTALS
9.4.1. Steady‐State Thermal Nonlinearity of Nematic Liquid Crystals
9.4.2. Short Laser Pulse‐induced Thermal Index Change in Nematics and Near‐Tc Effect
9.4.3. Optical Nonlinearities of Isotropic Liquid Crystals
9.5. COUPLED NONLINEAR OPTICAL EFFECTS IN NEMATIC LIQUID CRYSTALS
9.5.1. Thermal Orientation Coupling Effect
9.5.2. Flow‐reorientation Effect
9.6. NONLINEAR OPTICAL RESPONSES OF CHOLESTERIC BLUE‐PHASE LIQUID CRYSTALS. 9.6.1. General Overview
9.6.2. Non‐electronics Optical Nonlinearities of BPLC
REFERENCES
10 Electronic Optical Nonlinearities. 10.1. INTRODUCTION TO QUANTUM MECHANICAL TREATMENT OF MOLECULES
10.2. DENSITY MATRIX FORMALISM FOR OPTICAL INDUCED MOLECULAR ELECTRONIC POLARIZABILITIES
10.2.1. Field‐induced Polarizations – First and Higher Orders
10.2.2. Linear and Nonlinear Absorptions
10.3. LINEAR AND NONLINEAR ELECTRONIC SUSCEPTIBILITIES. 10.3.1. Linear Optical Polarizabilities of a Molecule
10.3.2. Complex Susceptibilities and Index of Refraction – Dispersion, Absorption, and Amplification of Light, Lasers
10.3.3. Second‐order Electronic Polarizabilities
10.3.4. Third‐order Electronic Polarizabilities
10.3.5. Local Field Effects and Symmetry
10.3.6. Symmetry Considerations
10.3.7. Permanent Dipole and Molecular Ordering
10.3.8. Quadrupole Contribution and Field‐induced Symmetry Breaking
10.3.9. Influence of Molecular Structures
10.4. INTENSITY‐DEPENDENT REFRACTIVE INDEX CHANGE AND NONLINEAR ABSORPTION
10.4.1. Nonlinear Absorption
REFERENCES
11 Nonlinear Optics. 11.1. INTRODUCTION
11.1.1. General Nonlinear Polarization and Susceptibility
11.1.2. Convention and Symmetry
11.2. COUPLED MAXWELL WAVE EQUATIONS
11.3. NONLINEAR OPTICAL PHENOMENA
11.3.1. Stationary Degenerate Optical Wave Mixing
11.3.2. Optical Phase Conjugation
11.3.3. Transient and Nearly Degenerate Wave Mixing
11.3.4. Nondegenerate Optical Wave Mixing; Harmonic Generations
11.3.5. Stationary Self‐phase Modulation and Self‐action
11.4. STIMULATED SCATTERINGS
11.4.1. Stimulated Raman Scatterings
11.4.2. Stimulated Brillouin Scatterings
11.4.3. Stimulated Orientation Scattering in Liquid Crystals
11.4.3.1. Steady‐state Small Signal Regime
11.4.3.2. Steady‐state Pump‐depletion Limit
11.4.4. Stimulated Thermal Scattering
11.5. ULTRAFAST LASER PULSE SELF‐ACTION EFFECTS IN CHOLESTERIC LIQUID CRYSTALS
11.5.1. Coupled Wave Equations for Forward and Backward Propagating Waves
11.5.2. Ultrafast Pulse Modulations – Compression, Stretching, and Recompression with Cholesteric Liquid Crystals
REFERENCES
12 Nonlinear Optical Processes Observed in Liquid Crystals
12.1. SELF‐ACTION NONLINEAR OPTICAL PROCESSES. 12.1.1. Self‐induced Spatial and Temporal Phase Shift
12.1.2. Self‐phase Modulation, Self‐focusing, ‐defocusing of Continuous‐Wave (CW) or Pulsed Laser
12.1.3. Self‐guiding, Spatial Soliton and Pattern Formation
12.1.4. Pulse Modulations, Polarization Rotation of and Switching by Ultrafast (Picosecond–Femtoseconds) Laser
12.2. OPTICAL WAVE MIXINGS
12.2.1. Stimulated Orientational Scattering and Polarization Self‐switching–Steady State
12.2.2. Stimulated Orientational Scattering – Nonlinear Dynamics
12.2.3. Optical Phase Conjugation with Orientation and Thermal Gratings
12.2.4. Self‐starting Optical Phase Conjugation
12.3. LIQUID CRYSTALS FOR ALL‐OPTICAL IMAGE PROCESSING. 12.3.1. Liquid Crystals as All‐optical Information Processing Materials
12.3.2. All‐optical Image Processing
12.3.3. Intelligent Optical Processing
12.4. HARMONIC GENERATIONS AND SUM‐FREQUENCY SPECTROSCOPY
12.5. OPTICAL SWITCHING
12.6. NONLINEAR ABSORPTION AND OPTICAL LIMITING OF LASERS FOR EYE/SENSOR PROTECTION. 12.6.1. Introduction
12.6.2. Nonlinear Fiber Array – An Intensity Dependent Spatial Frequency Filter
12.6.3. Optical Limiting Action of Fiber Array Containing RSA Materials
12.6.4. Optical Limiting Action of Fiber Array Containing TPA Materials
References
Index
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