Table Of ContentreD bOx ruleS Are FOr PrOOF StAGe Only. Delete beFOre FinAl PrintinG. 30.3MM PPC FinAl ArtwOrk
Modeling and Optimization of
SID
LCD Optical Performance
yAkOvlev
ChiGrinOv
Dmitry A. Yakovlev Saratov State University, Russia
kwOk
Vladimir G. Chigrinov Hong Kong University of Science & Technology, Hong Kong
Hoi-Sing Kwok Hong Kong University of Science & Technology, Hong Kong
LM
Focussing on polarization matrix optics in many forms, this book includes coverage of a wide range of
methods which have been applied to lCD modeling, ranging from the simple Jones matrix method to Co
elaborate and high accuracy algorithms suitable for off-axis optics. researchers and scientists are constantly d
D
striving for improved performance, faster response times, wide viewing angles, improved colour in liquid e
crystal display development, and with this comes the need to model lCD devices effectively. the authors l
i
have significant experience in dealing with the problems related to the practical application of liquid crystals, On
in particular their optical performance. g
key features: pa
n
explores analytical solutions and approximations to important cases in the matrix treatment of different
t
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lC layer configurations, and the application of these results to improve the computational method
i
Provides the analysis of accuracies of the different approaches discussed in the book cO
explains the development of the eigenwave Jones matrix method which offers a path to improved ap
accuracy compared to Jones matrix and extended Jones matrix formalisms, while achieving significant t DMitry A. yAkOvlev
li
improvement in computational speed and versatility compared to full 4x4 matrix methods m
includes a companion website hosting the authors’ program library lMOPtiCS (FOrtrAn 90), a collection Pi vlADiMir G. ChiGrinOv
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of routines for calculating the optical characteristics of stratified media, the use of which allows for the
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easy implementation of the methods described in this book. the website also contains a set of sample
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programs (source codes) using lMOPtiCS, which exemplify the application of these methods in different rio
situations.
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SID Series in Display Technology rf Modeling and Optimization of
m
Series editors: Anthony C. Lowe, The Lambent Consultancy, Braishfield, UK
Ian Sage, Abelian Services, Malvern, UK
The Society for Information Display (SID) is an international society which has the aim of a LCD Optical
encouraging the development of all aspects of the field of information display. Complementary
n
to the aims of the society, the Wiley–SID series is intended to explain the latest developments
in information display technology at a professional level. The broad scope of the series c
addresses all facets of information displays from technical aspects through systems
e
and prototypes to standards and ergonomics.
Per formance
www.wiley.com/go/modelinglcd
Cover design: Cylinder
SID Series in Display Technology
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MODELING AND
OPTIMIZATION OF
LCD OPTICAL
PERFORMANCE
i
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Wiley-SIDSeriesinDisplayTechnology
SeriesEditors:
AnthonyC.LoweandIanSage
DisplaySystems:DesignandApplications
LindsayW.MacDonaldandAnthonyC.Lowe(Eds.)
ElectronicDisplayMeasurement:Concepts,Techniques,andInstrumentation
PeterA.Keller
ReflectiveLiquidCrystalDisplays
Shin-TsonWuandDeng-KeYang
ColourEngineering:AchievingDeviceIndependentColour
PhilGreenandLindsayMacDonald(Eds.)
DisplayInterfaces:FundamentalsandStandards
RobertL.Myers
DigitalImageDisplay:AlgorithmsandImplementation
GheorgheBerbecel
FlexibleFlatPanelDisplays
GregoryCrawford(Ed.)
PolarizationEngineeringforLCDProjection
MichaelG.Robinson,JianminChen,andGaryD.Sharp
IntroductiontoMicrodisplays
DavidArmitage,IanUnderwood,andShin-TsonWu
MobileDisplays:TechnologyandApplications
AchintyaK.Bhowmik,ZiliLi,andPhilipBos(Eds.)
PhotoalignmentofLiquidCrystallineMaterials:PhysicsandApplications
VladimirG.Chigrinov,VladimirM.Kozenkov,andHoi-SingKwok
ProjectionDisplays,SecondEdition
MatthewS.BrennesholtzandEdwardH.Stupp
IntroductiontoFlatPanelDisplays
Jiun-HawLee,DavidN.Liu,andShin-TsonWu
LCDBacklights
ShunsukeKobayashi,ShigeoMikoshiba,andSungkyooLim(Eds.)
LiquidCrystalDisplays:AddressingSchemesandElectro-OpticalEffects,SecondEdition
ErnstLueder
TransflectiveLiquidCrystalDisplays
ZhibingGeandShin-TsonWu
LiquidCrystalDisplays:FundamentalPhysicsandTechnology
RobertH.Chen
3DDisplays
ErnstLueder
OLEDDisplayFundamentalsandApplications
TakatoshiTsujimura
Illumination,ColorandImaging:EvaluationandOptimizationofVisualDisplays
PeterBodrogiandTranQuocKhanh
InteractiveDisplays:NaturalHuman-InterfaceTechnologies
AchintyaK.Bhowmik(Ed.)
AddressingTechniquesofLiquidCrystalDisplays
TemkarN.Ruckmongathan
FundamentalsofLiquidCrystalDevices,SecondEdition
Deng-KeYangandShin-TsonWu
ModelingandOptimizationofLCDOpticalPerformance
DmitryA.Yakovlev,VladimirG.Chigrinov,andHoi-SingKwok
ii
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MODELING AND
OPTIMIZATION OF
LCD OPTICAL
PERFORMANCE
DmitryA.Yakovlev
SaratovStateUniversity,Russia
VladimirG. Chigrinov
HongKongUniversityofScience&Technology,HongKong
Hoi-SingKwok
HongKongUniversityofScience&Technology,HongKong
iii
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Thiseditionfirstpublished2015
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LibraryofCongressCataloging-in-PublicationData
Yakovlev,DmitryA.
ModelingandoptimizationofLCDopticalperformance/DmitryA.Yakovlev,VladimirG.Chigrinov,
Hoi-SingKwok.
pagescm
Includesbibliographicalreferencesandindex.
ISBN978-0-470-68914-1(hardback)
1.Liquidcrystaldisplays. I.Chigrinov,V.G.(VladimirG.) II.Kwok,Hoi-Sing. III.Title.
TK7872.L56Y352014
621.3815′422–dc23
2014001761
AcataloguerecordforthisbookisavailablefromtheBritishLibrary.
ISBN:9780470689141
Setin9/11ptTimesbyAptaraInc.,NewDelhi,India
1 2015
iv
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Toourbelovedwives:Larisa,Larisa,andYing-Hung
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Contents
SeriesEditor’sForeword xiii
Preface xv
Acknowledgments xix
ListofAbbreviations xxi
AbouttheCompanionWebsite xxiii
1 PolarizationofMonochromaticWaves.BackgroundoftheJonesMatrix
Methods.TheJonesCalculus 1
1.1 HomogeneousWavesinIsotropicMedia 1
1.1.1 PlaneWaves 1
1.1.2 Polarization.JonesVectors 3
1.1.3 CoordinateTransformationRulesforJonesVectors.Orthogonal
Polarizations.DecompositionofaWaveintoTwoOrthogonally
PolarizedWaves 9
1.2 InterfaceOpticsforIsotropicMedia 14
1.2.1 Fresnel’sFormulas.Snell’sLaw 14
1.2.2 ReflectionandTransmissionJonesMatricesforaPlaneInterfacebetween
IsotropicMedia 20
1.3 WavePropagationinAnisotropicMedia 23
1.3.1 WaveEquations 23
1.3.2 WavesinaUniaxialLayer 25
1.3.3 ASimpleBirefringentLayerandItsPrincipalAxes 30
1.3.4 TransmissionJonesMatricesofaSimpleBirefringentLayerat
NormalIncidence 32
1.3.5 LinearRetarders 36
1.3.6 JonesMatricesofAbsorptivePolarizers.IdealPolarizer 38
1.4 JonesCalculus 41
1.4.1 BasicPrinciplesoftheJonesCalculus 42
1.4.2 ThreeUsefulTheoremsforTransmissiveSystems 46
1.4.3 ReciprocityRelations.Jones’sReversibilityTheorem 50
1.4.4 TheoremofPolarizationReversibilityforSystemsWithoutDiattenuation 53
1.4.5 ParticularVariantsofApplicationoftheJonesCalculus.CartesianJones
VectorsforWaveFieldsinAnisotropicMedia 55
References 57
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viii Contents
2 TheJonesCalculus:SolutionsforIdealTwistedStructuresandTheir
ApplicationsinLCDOptics 59
2.1 JonesMatrixandEigenmodesofaLiquidCrystalLayerwithanIdeal
TwistedStructure 59
2.2 LCDOpticsandtheGooch–TarryFormulas 64
2.3 InteractiveSimulation 67
2.4 ParameterSpace 69
References 73
3 OpticalEquivalenceTheorem 75
3.1 GeneralOpticalEquivalenceTheorem 75
3.2 OpticalEquivalencefortheTwistedNematicLiquidCrystalCell 77
3.3 PolarizationConservingModes 77
3.3.1 LP1Modes 78
3.3.2 LP2Modes 79
3.3.3 LP3Modes 80
3.3.4 CPModes 81
3.4 ApplicationtoNematicBistableLCDs 82
3.4.1 2𝜋BistableTNDisplays 82
3.4.2 𝜋BistableTNDisplays 83
3.5 ApplicationtoReflectiveDisplays 84
3.6 MeasurementofCharacteristicParametersofanLCCell 86
3.6.1 CharacteristicAngleΩ 86
3.6.2 CharacteristicPhaseΓ 87
References 87
4 Electro-opticalModes:PracticalExamplesofLCDModelingandOptimization 91
4.1 OptimizationofLCDPerformanceinVariousElectro-opticalModes 91
4.1.1 ElectricallyControlledBirefringence 91
4.1.2 TwistEffect 101
4.1.3 SupertwistEffect 109
4.1.4 OptimizationofOpticalPerformanceofReflectiveLCDs 116
4.2 TransflectiveLCDs 119
4.2.1 Dual-ModeSingle-Cell-GapApproach 119
4.2.2 Single-ModeSingle-Cell-GapApproach 122
4.3 TotalInternalReflectionMode 124
4.4 FerroelectricLCDs 131
4.4.1 BasicPhysicalProperties 131
4.4.2 Electro-opticalEffectsinFLCCells 135
4.5 BirefringentColorGenerationinDichromaticReflectiveFLCDs 145
References 149
5 NecessaryMathematics.RadiometricTerms.Conventions.VariousStokesand
JonesVectors 153
5.1 SomeDefinitionsandRelationsfromMatrixAlgebra 153
5.1.1 GeneralDefinitions 153
5.1.2 SomeImportantPropertiesofMatrixProducts 160
5.1.3 UnitaryMatrices.UnimodularUnitary2×2Matrices.STUMatrices 160
5.1.4 NormsofVectorsandMatrices 163
5.1.5 KroneckerProductofMatrices 166
5.1.6 Approximations 167
