IVI LLC EXHIBIT 2008
`XILINX V. IVI LLC
`IPR Case 2013-00029
`
`

`

`Published by
`
`World Scientific Publishing Co. Pte. Ltd.
`
`P O Box 128, Parrot Road, Singapore 9128
`
`USA office: Suite 1B, 1060 Main Street, River Edge, NJ 07661
`UK office: 73 Lynton-Mead, Totteridge, London N20 8DH
`
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`OPTICS AND NONLINEAR OPTICS OF LIQUID CRYSTALS
`
`Copyright © 1993 by World Scientific Publishing Co. Pte. Ltd.
`
`All rights reserved. This book, or parts thereof, may not be reproduced in any form
`orby any means, electronic or mechanical, includingphotocopying, recording orany
`information storage and retrieval system now known or to be invented, without
`written permission from the Publisher.
`
`ISBN 981—02—0934-7
`
`981-02—0935-5 (pbk)
`
`For copying of articles in this volume, please pay :1 copying fee through the
`Copyright Clearance Centre, Inc., 27 Congress Street, Salem, MA 01970.
`
`Printed in Singapore by Utopia Press.
`
`

`

`CONTENTS
`
`Preface
`
`CHAPTER. 1. OPTICAL PROPERTIES OF
`LIQUID CRYSTALS
`
`1.1.
`
`1.2.
`
`1.3.
`
`Introduction
`
`Thermotropic Liquid Crystals
`
`1.2.1. Nematic phase
`
`1.2.2. Cholesteric phase
`
`Smectic phases
`1.2.3.
`Building Blocks of Liquid Crystals
`1.3.1. Basic molecular structures
`
`1.3.2. Phase transition temperatures
`
`1.4.
`
`Eutectic Mixtures
`
`1.4.1.
`
`Schroder—Van Laar equation
`
`1.4.2. Example
`
`1.5.
`
`Electronic Structures
`
`1.5.1.
`
`0' —> (7* transitions
`
`1.5.2.
`
`71 ——-> 7r* transitions
`
`1.5.3.
`
`11' —+ 7r* transitions
`
`1.6.
`
`Experimental Methods for UV Measurement
`1.6.1.
`Solvent method
`
`1.6.2. Guest—host method
`
`1.7.
`
`Polarized Absorption Spectrum
`
`1.7.1.
`
`Single phenyl ring
`
`vii
`
`

`

`viii
`
`Optics and Nonlinear Optics of Liquid Crystals
`
`1.7.2. Biphenyls
`1.7.3. Terphenyls
`1.7.4. Tolanes
`
`'
`
`1.7.5. Diphenyl—diacetylenes
`1.7.6. Other highly conjugated LCs
`Off-Resonance Absorption and Light Scattering
`
`1.8.
`
`Impact of absorption
`1.8.1.
`Principles of measurement
`1.8.2.
`1.8.3. Experimental method
`1.8.4. Results
`
`1.9.
`
`IR Absorption
`1.9.1. Experimental method
`1.9.2. Vibrational absorption spectra
`1.9.3. Order parameter determination '
`1.9.4. Microwave region
`1.10. Refractive Index Dispersions
`1.10.1. Generalized Lorentz—Lorenz formula
`
`1.10.2. Seminempirical models
`1.10.3. Experimental methods for refractive indices
`1.10.4. Comparison of model with experiment
`1.10.5. Temperature dependence
`1.10.6. Birefringence
`
`CHAPTER 2. ELECTRO-OPTICAL PROPERTIES
`
`OF LIQUID CRYSTALS
`
`2.1.
`
`Introduction
`
`2.1.1. Dynamic scattering
`2.1.2. Guest—host effect
`
`2.1.3.
`Field-induced nematic—cholestric phase change
`2.1.4.
`Field-induced director-axis reorientation
`2.1.5. Laser-induced phase change
`2.1.6. Light scattering by micron-sized droplets
`
`Part 1. Electro-Optics of Nematics
`
`2.2.
`
`Liquid Crystal Alignment
`
`28
`31
`36
`
`42
`48
`51
`
`51
`52
`55
`56
`
`60
`61
`62
`66
`70
`72
`72
`
`73
`78
`80
`87
`90
`
`100
`
`100
`101
`
`102
`103
`105
`105
`
`106
`
`

`

`2.3.
`
`2.4.
`
`2.5.
`
`2.6.
`
`2.7.
`
`Contents
`
`2.2.1.
`
`2.2.2.
`
`Parallel alignment
`Perpendicular (or homeotropic) alignment
`Twist alignment
`2.2.3.
`Optical Transmission of Liquid Crystal Cells
`Generalized geometricalaoptics approximation
`2.3.1.
`(GGOA)
`4 x 4 matrix method
`Extended Jones matrix
`2.3.3.
`Phase Compensation Methods for Widening
`Viewing Angle
`Double parallel-aligned cells
`Double perpendicular-aligned (or ECB) cells
`Double TN cells
`
`2.3.2.
`
`2.4.1.
`
`2.4.2.
`
`2.4.3.
`
`2.5.2.
`
`Dynamic Response
`Directors distribution
`2.5.1.
`Ericksorr—Leslie equation
`Measurement of response times
`2.5.3.
`Material Parameters for Electro-Optics
`Dielectric constant
`
`2.6.1.
`
`2.6.2.
`
`Elastic constant
`
`Viscosities
`2.6.3.
`Methods for Improving Response Times
`Dual frequency effect
`Crossed electric field effect
`
`2.7.1.
`
`2.7.2.
`
`2.7.3.
`
`2.7.4.
`
`2.7.5.
`
`2.7.6.
`
`2.7.7.
`
`Bias voltage effect
`Transient nematic effect (undershoot effect)
`Fabrerérot effect
`Temperature effect
`Molecular engineering
`
`ix
`
`106
`
`113
`
`116
`
`125
`
`125
`
`128
`
`131
`
`138
`
`139
`
`145
`
`146
`
`148
`
`149
`
`159
`
`163
`
`168
`
`168
`
`176
`
`179
`
`193
`
`194
`
`197
`
`197
`
`201
`
`207
`
`208
`
`210
`
`2.8.
`
`Part 2. Electro-Optics of Polymer—Dispersed Liquid Crystals
`Polymer-Dispersed LC (PD’LC)
`Material preparation
`2.8.1.
`Theories on light scattering
`Optical transmission
`Dynamic response
`Reverse—mode PDLC
`
`2.8.2.
`
`2.8.3.
`
`2.8.4.
`
`2.8.5.
`
`212
`
`213
`
`214
`
`219
`
`226
`
`229
`
`

`

`x
`
`2.9.
`
`Optics and Nonlinear Optics of Liquid Crystals
`
`Polymer-Dispersed Chiral Liquid Crystal
`(PDCLC)
`
`-
`
`231
`
`Part 3. Electro-Optics of Ferroelectric 1.05
`
`2.10.
`
`Surface-Stabilized Ferroelectric LCs
`
`2.10.1. Free energy
`2.10.2. 'One elastic constant approximation
`Soft-Mode FLCs
`
`2.11.
`
`2.11.1. Dynamic response
`2.12. Deformed Helix Ferroelectric Effect
`
`2.13.
`
`Twisted Smectic—C* Cell
`
`Part 4. Selected Applications
`
`2.14.
`
`Liquid Crystal Spatial Light Modulators
`2.14.1. High—definition television (HDTV) projector
`2.14.2. Visible-to—IR dynamic image converter
`
`CHAPTER 3. NONLINEAR OPTICAL PROPERTIES
`
`OF LIQUID CRYSTALS
`
`3.1.
`
`Introduction
`
`3.1.1. General remarks
`
`3.2.
`
`3.3.
`
`3.4.
`
`3.1.2. Mechanisms for laser induced index changes in
`liquid crystals
`Isotropic Phase
`3.2.1. Molecular reorientation-induced ordering
`
`3.2.2.
`3.2.3.
`
`Isotropic phase molecular reorientation dynamics
`Influence of molecular structure on isotropic
`
`phase orientational nonlinearities
`Nematic Phase
`
`3.3.1. Nematic phase molecular reorientations
`3.3.2. Nematic phase reorientation dynamics
`Thermal and. Density Effects in Liquid Crystals
`3.4.1.
`Interplay between temperature, density and
`order parameter-nematic phase
`
`233
`
`234
`238
`241
`
`"241
`244
`
`247
`
`250
`253
`258
`
`269
`
`269
`
`270
`274
`274
`
`276
`
`280
`282
`
`282
`286
`291
`
`291
`
`

`

`Contents
`
`3.4.2. Coupled hydrodynamical equations for
`temperature and density changes
`
`-—— general formalism
`3.4.3. Dynamics of laser induced thermal, density
`and order~parameter changes in nematic
`
`liquid crystals
`Visible-Infrared Thermal and Density Optical
`
`3.5.
`
`Nonlinearities
`3.5.1. Thermal and density optical nonlinearities of
`nematic liquid crystals in the visible~infrared
`
`3.5.3.
`
`spectrum
`3.5.2. Thermal and density optical nonlinearities of
`isotropic liquid crystals
`Summary of optical nonlinearities of nematic
`and isotropic liquid crystals
`Coupled Nonlinear Optics Effects in Nematic
`Liquid Crystals
`3.6.1. Thermal-orientational coupling in nematic
`
`liquid crystals
`
`Flow—orientational effect
`3.6.2
`Nonresonant Nonlinear Optical Effects in
`
`Smectic and Cholesteric Phases
`
`3.7.1.
`
`Smectic phase
`
`3.7.2. Cholesteric phase
`Electronic Optical Nonlinearities
`3.8.1. Density matrix formalism for optically induced
`electronic polarizations of a molecule
`3.8.2.. Linear optical polarizahilities of a molecule
`3.8.3.
`Second— and third—order electronic
`I
`polarizabilities of a molecule
`3.8.4. Electronic nonlinear polarizations of liquid
`
`crystals
`
`3.6.
`
`3.7.
`
`3.8.
`
`xi
`
`293
`
`299
`
`303
`
`303
`
`309
`
`314
`
`315
`
`316
`
`319
`
`325
`
`325
`
`326
`
`328
`
`328
`
`332
`
`337
`
`341
`
`

`

`xii
`
`Optics and Nonlinear Optics of Liquid Crystals
`
`3.8.5. Effect of orientational orders
`
`345
`
`CHAPTER 4. NONLINEAR OPTICS
`
`4.1.
`
`4.2.
`
`Introduction
`.
`Susceptibility and Refractive Index
`4.2.1. Linear polarization, susceptibility and
`refractive index
`
`4.2.2. Nonlinear susceptibility and intensity—dependent
`
`refractive index
`
`4.3.
`
`General Nonlinear Polarization
`
`4.3.1. General nonlinear polarization and susceptibility
`
`4.3.2. Convention, degeneracy factor, symmetry,
`microscopic and macroscopic parameters
`Coupled Maxwell Wave Equations
`Degenerate Optical Wave Mixing
`‘ 4.5.1. Stationary degenerate four-wave mixing process
`4.5.2. Optical phase conjugation (by degenerate
`four-wave mixing)
`4.5.3. Nonlocal nonlinearity and beam amplification
`Nondegenerate Optical Wave Mixings; Harmonic
`Generations
`
`Self-Focusing and Self-Phase Modulation
`Nonlinear Optical Processes Observed in Liquid
`
`Crystals
`4.8.1. Summary of observed nonlinear effects
`4.8.2.
`Self-focusing, -defocusing, a (1 -phase modulation
`4.8.3. Beam amplification and phase conjugation via
`
`coherent optical wave mixing
`
`4.8.4. Harmonic generations
`
`4.8.5. All—optical switching
`
`4.4.
`
`4.5.
`
`4.6.
`
`4.7.
`
`4.8.
`
`Index
`
`'351
`
`354
`
`354
`
`360
`
`363
`
`363
`
`366
`
`370
`
`373
`
`373
`
`378
`
`382
`
`385
`
`388
`
`393
`
`393
`
`395
`
`401
`
`408
`
`410
`
`419
`
`

`

` 7KLVPDWHULDOPD\EHSURWHFWHGE\&RS\ULJKWODZ7LWOH86&RGH
`
`This material may be protected by Copyright law (Title 17 US. Code)
`
`CHAPTER 2
`
`ELECTRO-OPTICAL PROPERTIES OF LIQUID CRYSTALS
`
`2.1.
`
`Introduction
`
`Liquid crystals flow as fluids in its mesogenic phase. Thus, they have
`to be either confined in two substrates with a proper surface alignment to
`form an uniaxial crystal, or dispersed in a polymer matrix to form droplets.
`An important feature of liquid crystals is that their directors can be reori—
`ented by a reasonably low external electric, magnetic or optical field, giving
`rise to a variety of electro—optic, magneto—optic and opto—optic modulation
`effects.1 The applied external field deforms the liquid crystal directors from
`their initial states and, thus, alter the. phase or amplitude of the impinging
`light. Once the external field vanishes, the directors may relax to their
`initial states or stay in their final states, depending on the type of liquid
`crystal and the physical mechanism involved.
`
`Several electro-optical effects in liquid crystals have been observed.
`These include:
`(i) dynamic scattering,
`(ii) guest-host effect,
`(iii) field-
`induced nematic—cholesteric phase change, (iv) field-induced director-axis
`reorientation, (v) laser-addressed thermal effect, and (vi) light scattering
`by micron-sized droplets.
`
`2.1.1. Dynamic scattering
`
`When a dc or low frequency ac field is applied to a nematic liquid
`crystal cell,2 the ionic motion due to the conductivity anisotropy induces
`electro-hydrodynamic flow which is coupled to the molecular alignment via
`viscous friction. The liquid crystal becomes turbulent and scatters light
`strongly. Usually a dc field of the order of 104 V/ cm is required to generate
`
`100
`
`

`

`Electra-Optical Properties of Liquid Crystals
`
`101
`
`such effects. The contrast ratio of the maximum and minimum transmitted
`
`light intensities is about 2021 and the response time is about 200 ms.
`
`For pure liquid crystal compounds, the conductivity should be very
`
`low. The observed non—negligible conductivity of liquid crystals may orig—
`
`inate from the impurities or dopants. Because of the finite current flow
`
`involved, the dynamic scattering mode encounters problems such as large
`
`power consumption, instability and short lifetime. The dc field also tends
`
`to trigger undesirable electrochemical reactions amongst the liquid crystal
`molecules, thus generating more impurities and degrading their chemical
`
`stability. The dynamic scattering mode does have the advantage that it
`
`It has been used in
`does not require a polarizer to modulate the light.
`watches and photoaddressed light valves3 in the early stage of liquid crys-
`
`tal device development, but has since been replaced by the field effect owing
`
`to the problems mentioned above.
`
`2.1.2. Guest-host efiect
`
`Guest-host systems4 are formed by dissolving a few percent (1m5%,
`limited by the solubility) of dichroic dye in the liquid crystal. The host ma-
`terial should be highly transparent in the spectral region of interest. The
`dichroic dye molecules should have a strong absorption for one polarization
`and weak in another in order to enhance the contrast ratio. A schematic di—
`agram illustrating the electro—optic effect of the guest-hoSt system is shown
`in Fig. 2.1. In the field-off state, the dye molecules are nearly parallel to
`the incident light polarization so that high absorption is obtained. When
`the liquid crystal directors are reoriented by the field, the dye molecules
`
`will also be reoriented and the absorption is reduced.
`
`Contrast ratio of the device employing the guest—host system is af—
`
`fected by the dichroic ratio and concentration of the dye molecules, and the
`
`cell thickness. For a given cell thickness, a higher dye concentration leads
`to a higher contrast ratio, but the corresponding transmission is reduced
`and the response times are lengthened. Many dichroic dyes are available
`in the visible region. Due to the long conjugation of dye molecules, their
`rotational viscosity is usually very large. The mixture containing merely
`5% dyes is enough to result in a significantly larger viscosity. A typical con-
`
`trast ratio of the guest—host system is about 50:1. The guest—host effects
`
`in ferroelectric liquid crystals have also been investigated where a response
`time of less than 100 us has been observed.5
`
`

`

`102
`
`Optics and Nonlinear Optics of Liquid Crystals
`
`POLARIZER
`
`A
`
`ABS
`
`ABS
`
`NEMATIC DOMAINS
`(HOST)
`
`PLEOCHROIC DYE
`(GUEST)
`
`TRANSPARENT
`CONDUCTOR
`
`‘3
`g
`/
`3
`9'
`g
`
`?4
`
`hu ml»
`
`
`
`(a) GUEST-HOST SYSTEM — NO FIELD
`
`by M4
`
`
` m\\\\\\\\\\\\\\\\
`
`(b) GUEST-HOS! SYSTEM WITH FIELD
`
`Fig. 2.1. Electro—optic modulation of light using the guest-host liquid crystal system.
`(a) field-off state, (b) field-on state. (After Ref. 4.)
`
`2.1.3. Field-induced nematic-cholesteric phase change
`
`Electric field-induced nematic-cholest-eric phase change has been
`observed experimentally“'7 and used for displays.8 The liquid crystal is
`initially at the cholesteric phase (represented by F in Fig. 2.2), where it
`has a helical structure whose axis is parallel to the glass substrates. The
`incident light is scattered and the cell appears milky white. When the ap—
`plied electric field exceeds 105 V/cm, it will unwind the helix to give an
`aligned nematic phase H. The cell then becomes transparent.
`
`When the voltage is decreased, it has been observed that an inter—
`mediate metastable nematic phase H’ can appear.9 In the phase H’ , the
`directors near the surfaces remain homeotropic but those in the bulk are
`
`slightly tilted. The optical output will therefore exhibit a hysteresis loop
`
`as shown in Fig. 2.2. This hysteresis effect can be used for optical storage.
`
`

`

`Electra-Optical Properties of Liquid Crystals
`
`103
`
`1:1
`
`CE
`
`N EMATIC
`
`100
`
`
`
`TRANSMITTANCE(%)
`
`CHOLESTERIC
`1:3 ‘
`“mull".....nlllillllv- F
`"Illlllll||""'|||!||lll="-
`I:
`
`01o
`
`APPLIED VOLTAGE
`
`Fig. 2.2. Electric field-induced cholesteric—nematic phase change. At low voltages, the cell
`is in the cholesteric phase F. As the voltage increases, the cell is driven to homeotropic
`nematic phase H. When the voltage is reduced, an intermediate metastable state
`(nematic phase H ’) exists. (Redraw after Ref. 8.)
`
`Once the voltage is removed completely, the liquid crystal directors return
`
`to their initial scattering states within a few milliseconds.
`
`2.1.4. Field-induced director-act's reorientation
`
`Field—induced director—axis reorientation on aligned nematic and fer-
`roelectric liquid crystals is one of the most common electro—optic effects
`employed for modulating light. Many alignment methods have been devel-
`oped for various applications employing nematic liquid crystals. For ex-
`amples, 90° twist,10 homeotropic (also called perpendicular) alignment,11
`45° twist,12 7r—cell,13 and a variety of supertwist cells.14‘18 Each alignment
`exhibits its own unique features and also drawbacks. For ferroelectric liquid
`crystals, the surface—stabilization alignment method for smectic—C phase,19
`and the electroclinic effect for smectic-A phase” are both fundamentally
`interesting and practically important.
`
`(i) Nematics
`
`In nematics, the electric field—induced polarization of a LG molecule
`
`follows the field up to a few MHZ of frequency before the dielectric relaxation
`
`