Table Of Content(cid:2)
PhotorefractiveMaterialsforDynamicOpticalRecording
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Photorefractive Materials for Dynamic Optical
Recording
Fundamentals,Characterization,andTechnology
JaimeFrejlich†
StateUniversityofCampinas
GlebWataghinInstituteofPhysics(IFGW)
Campinas-SP,Brazil
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Thiseditionfirstpublished2020
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LibraryofCongressCataloging-in-PublicationData
Names:Frejlich,Jaime,1946-author.
Title:Photorefractivematerialsfordynamicopticalrecording:
fundamentals,characterization,andtechnology/JaimeFrejlich
StateUniversityofCampinas,GlebWataghinInstituteofPhysics
(IFGW),Campinas-SPBrazil.
Description:Firstedition.|Hoboken,N.J.:JohnWiley&SonsInc.,2020.
|Includesindex.
Identifiers:LCCN2019032247(print)|LCCN2019032248(ebook)|ISBN
9781119563778(hardback)|ISBN9781119563730(adobepdf)|ISBN
9781119563761(epub)
Subjects:LCSH:Laserrecording–Materials.|Photorefractivematerials.
Classification:LCCTK7882.S3S672020(print)|LCCTK7882.S3(ebook)|
DDC621.382/34–dc23
LCrecordavailableathttps://lccn.loc.gov/2019032247
LCebookrecordavailableathttps://lccn.loc.gov/2019032248
CoverDesign:Wiley
CoverImage:©ArtLightProduction/Shutterstock
Setin10/12ptWarnockProbySPiGlobal,Chennai,India
PrintedintheUnitedStatesofAmerica
10 9 8 7 6 5 4 3 2 1
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v
Contents
ListofFigures xi
ListofTables xxxiii
Preface xxxv
Acknowledgments xxxvii
PartI Fundamentals 1
Introduction 3
1 Electro-OpticEffect 5
1.1 LightPropagationinCrystals 5
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1.1.1 WavePropagationinAnisotropicMedia 5
1.1.2 GeneralWaveEquation 6
1.1.3 IndexEllipsoid 6
1.2 TensorialAnalysis 8
1.3 Electro-OpticEffect 8
1.4 PerovskiteCrystals 11
1.5 SilleniteCrystals 11
1.5.1 IndexEllipsoid 11
1.5.1.1 IndexEllipsoidwithAppliedElectricField 13
1.5.2 OtherCubicNoncentrosymmetricCrystals 15
1.5.3 LithiumNiobate 15
1.5.4 KDP-(KH PO ) 16
2 4
1.5.5 BismuthTelluriumOxide-Bi TeO (BTeO) 17
2 5
1.6 ConcludingRemarks 17
2 PhotoactiveCentersandPhotoconductivity 19
2.1 PhotoactiveCenters:DeepandShallowTraps 20
2.1.1 CadmiumTelluride 21
2.1.2 Sillenite-TypeCrystals 22
2.1.2.1 DopedSillenites 25
2.1.3 LithiumNiobate 28
2.1.4 BismuthTellurideOxide:Bi TeO 28
2 5
2.2 Luminescence 28
2.3 Photoconductivity 29
2.3.1 LocalizedStates:TrapsandRecombinationCenters 29
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vi Contents
2.3.2 TheoreticalModels 32
2.3.2.1 One-CenterModel 35
2.3.2.2 Two-Center/One-ChargeCarrierModel 37
2.3.2.3 DarkConductivityandDopants 40
2.4 PhotovoltaicEffect 40
2.4.1 PhotovoltaicCrystals 41
2.4.1.1 LithiumNiobateandOtherFerroelectricCrystals 41
2.4.1.2 SomePhotovoltaicNonferroelectricMaterials 41
2.4.2 LightPolarization-DependentPhotovoltaicEffect 43
2.5 NonlinearPhotovoltaicEffect 44
2.5.1 Light-InducedAbsorptionandNonlinearPhotovoltaicEffects 46
2.5.2 DeepandShallowCenters 47
2.6 Light-InducedAbsorptionorPhotochromicEffect 48
2.6.1 TransmittancewithLight-InducedAbsorption 51
2.7 DemberorLight-InducedSchottkyEffect 51
2.7.1 DemberandPhotovoltaicEffects 54
PartII HolographicRecording 55
Introduction 56
3 RecordingaSpace-ChargeElectricField 57
3.1 Index-of-RefractionModulation 60
3.2 GeneralFormulation 63
(cid:2) 3.2.1 RateEquations 64 (cid:2)
3.2.2 SolutionforSteady-State 64
3.3 FirstSpatialHarmonicApproximation 66
3.3.1 Steady-StateStationaryProcess 68
3.3.1.1 DiffractionEfficiency 69
3.3.1.2 HologramPhaseShift 70
3.3.2 Time-EvolutionProcess:ConstantModulation 70
3.4 Steady-StateNonstationaryProcess:RunningHolograms 72
3.4.1 RunningHologramswithHole-ElectronCompetition 76
3.4.1.1 MathematicalModel 78
3.5 PhotovoltaicMaterials 84
3.5.1 UniformIllumination:𝜕/𝜕x=0 84
3.5.2 InterferencePatternofLight 85
3.5.2.1 InfluenceofDonorDensity 86
4 VolumeHologramwithWaveMixing 89
4.1 CoupledWaveTheory:FixedGrating 89
4.1.1 DiffractionEfficiency 91
4.1.2 OutofBraggCondition 91
4.2 DynamicCoupledWaveTheory 92
4.2.1 CombinedPhase-AmplitudeStationaryGratings 92
4.2.1.1 FundamentalProperties 94
4.2.1.2 Irradiance 95
4.2.2 PurePhaseGrating 96
4.2.2.1 TimeEvolution 96
4.2.2.2 StationaryHologram 100
4.2.2.3 Steady-StateNonstationaryHologramwithWave-MixingandBulkAbsorption 106
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Contents vii
4.2.2.4 GainandStabilityinTwo-WaveMixing 110
4.3 PhaseModulation 115
4.3.1 PhaseModulationinDynamicallyRecordedGratings 116
4.3.1.1 PhaseModulationintheSignalBeam 116
4.3.1.2 OutputPhaseShift 118
4.4 Four-WaveMixing 119
4.5 Conclusions 120
5 AnisotropicDiffraction 121
5.1 Coupled-WavewithAnisotropicDiffraction 121
5.2 AnisotropicDiffractionandOpticalActivity 122
5.2.1 DiffractionEfficiencywithOpticalActivity,𝜌 123
5.2.2 OutputPolarizationDirection 123
6 StabilizedHolographicRecording 125
6.1 Introduction 125
6.2 MathematicalFormulation 127
6.2.1 StabilizedStationaryRecording 129
6.2.1.1 StableEquilibriumCondition 130
6.2.2 StabilizedRecordingofRunning(Nonstationary)Holograms 130
6.2.2.1 StableEquilibriumCondition 132
6.2.2.2 SpeedoftheFringe-LockedRunningHologram 132
6.2.3 Self-StabilizedRecordingwithArbitrarilySelectedPhaseShift 133
6.3 Self-StabilizedRecordinginActualMaterials 135
(cid:2) 6.3.1 Self-StabilizedRecordinginSillenites 136 (cid:2)
6.3.2 Self-StabilizedRecordinginLiNbO 136
3
6.3.2.1 HolographicRecordingwithoutConstraints 137
6.3.2.2 Self-StabilizedRecording 142
PartIII MaterialsCharacterization 151
Introduction 152
7 GeneralElectricalandOpticalTechniques 155
7.1 Electro-OpticCoefficient 155
7.2 Light-InducedAbsorption 157
7.3 DarkConductivity 161
7.4 Photoconductivity 162
7.4.1 PhotoconductivityinBulkMaterial 163
7.4.2 AlternatingCurrentTechnique 164
7.4.3 Wavelength-ResolvedPhotoconductivity 166
7.4.3.1 TransverseConfiguration 166
7.4.3.2 LongitudinalConfiguration 170
7.5 Photo-ElectricConversion 173
7.5.1 Wavelength-ResolvedPhoto-ElectricConversion(WRPC) 173
7.5.1.1 UndopedBTO 174
7.6 ModulatedPhotoconductivity 175
7.6.1 QuantumEfficiencyandMobility-LifetimeProduct 176
7.7 Photo-Electromotive-ForceTechniques(PEMF) 178
7.7.1 Speckle-Photo-Electromotive-Force(SPEMF)Techniques 178
7.7.1.1 SpecklePatternontoaPhotorefractiveMaterial:StationaryState 179
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viii Contents
8 HolographicTechniques 189
8.1 HolographicRecordingandErasing 189
8.2 DirectHolographicTechniques 189
8.2.1 EnergyCoupling 190
8.2.2 DiffractionEfficiency 192
8.2.2.1 DebyeLengthDependenceonLightIntensity 193
8.2.3 HolographicSensitivity 193
8.2.3.1 Computing 195
8.3 HologramRecording 195
8.4 HologramErasure 195
8.4.1 OneSinglePhotoactiveCenterInvolved 196
8.4.1.1 BulkAbsorption 196
8.4.2 Two(orMore)PhotoactiveCenters(LocalizedStates)Involved 197
8.4.2.1 SameChargeCarriers 197
8.4.2.2 HolesandElectronsonDifferentPhotoactiveCenters 197
8.5 Materials 197
8.5.1 Fe-dopedLiNbO :HologramErasureunderWhiteLightIllumination 197
3
8.5.2 Bi TiO (BTO) 199
12 20
8.5.2.1 UndopedBTOunder𝜆=780nmIllumination 199
8.5.2.2 Bi TiO :Pb(BTO:Pb) 200
12 20
8.5.2.3 Bi TiO :V(BTO:V) 202
12 20
8.5.2.4 HolographicRelaxationintheDark:DarkConductivity 203
8.6 PhaseModulationTechniques 205
8.6.1 HolographicSensitivity 205
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8.6.2 HolographicPhase-ShiftMeasurement 206
8.6.2.1 Wave-MixingEffects 207
8.6.3 PhotorefractiveResponseTime 207
8.6.4 SelectiveTwo-WaveMixing 210
8.6.4.1 AmplitudeandPhaseEffectsinGaAs 212
8.6.5 RunningHolograms 214
8.7 HolographicPhoto-Electromotive-Force(HPEMF)Techniques 218
9 Self-StabilizedHolographicTechniques 229
9.1 HolographicPhaseShift 229
9.2 Fringe-LockedRunningHolograms 232
9.2.1 AbsorbingMaterials 232
9.2.1.1 LowAbsorptionApproximation 234
9.2.2 CharacterizationofMaterials 234
9.2.2.1 Measurements 235
9.2.2.2 TheoreticalFitting 236
9.3 CharacterizationofLiNbO :Fe 239
3
PartIV Applications 243
Introduction 244
10 VibrationsandDeformations 245
10.1 MeasurementofVibrationandDeformation 245
10.2 ExperimentalSetup 246
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Contents ix
10.2.1 ReadingofDynamicHolograms 247
10.2.2 OptimizationofIllumination 247
10.2.2.1 TargetIllumination 247
10.2.2.2 DistributionofLightamongReferenceandObjectBeams 247
10.2.3 Self-StabilizationFeedbackLoop 249
10.2.4 Vibrations 251
10.2.5 DeformationandTilting 252
10.2.5.1 ApplicationsofPEMFtoMechanicalVibrationMeasurements 256
11 FixedHolograms 257
11.1 Introduction 257
11.2 FixedHologramsinLiNbO 257
3
11.2.1 SimultaneousRecordingandCompensation 258
11.2.1.1 Theory 258
11.2.1.2 Experiment:SimultaneousRecordingandCompensating 260
12 PhotoelectricConversion 263
12.1 PhotoelectricConversionEfficiency:DemberandPhotovoltaicEffects 263
PartV Appendix 265
Introduction 266
AppendixA ReversibleReal-TimeHolograms 267
A.1 Naked-EyeDetection 267
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A.1.1 Diffraction 267
A.1.2 Interference 268
A.2 InstrumentalDetection 268
AppendixB DiffractionEfficiencyMeasurement 271
B.1 AngularBraggSelectivity 271
B.1.1 In-BraggRecordingBeams 272
B.1.2 ProbeBeam 272
B.2 ReversibleHolograms 274
B.3 HighIndex-of-RefractionMaterial 275
AppendixC EffectivelyAppliedElectricField 279
AppendixD PhysicalMeaningofSomeParameters 281
D.1 Temperature 281
D.1.1 DebyeScreeningLength 282
D.1.1.1 DebyeLengthinPhotorefractives 283
D.2 DiffusionandMobility 284
AppendixE Photodiodes 287
E.1 PhotovoltaicRegime 288
E.2 PhotoconductiveRegime 289
E.3 OperationalAmplifier 290
Bibliography 291
Index 305
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xi
ListofFigures
Figure1 Naturallybirefringentuniaxiallithiumniobatecrystalviewunderconverging
whitelightbetweencrossedpolarizerswithitsc-axis(opticalaxis)laying
perpendiculartotheplane(upper)andontheplane(lower). 2
Figure1.1 Refractiveindexellipsoid. 7
Figure1.2 Refractiveindicesforaplanewavepropagatinginananisotropicmedium. 7
Figure1.3 Crystallographicaxesofasilleniteandanapplied3Delectricfield. 9
Figure1.4 Structureofanundistortedcubicperovskitestructurewithgeneralchemical
formulaABX .ThedifferentlyshadedspheresrepresentXatoms(usually
3
oxygens),Batoms(asmallermetalcation,suchasTi4+)andAatoms(alarger
metalcation,suchasCa2+). 10
(cid:2) Figure1.5 Three-dimensionalsillenitestructure:darkerspheresrepresentBi3+ionsand (cid:2)
palergrayonesareO2−.AcknowledgmentstoProf.JesielF.Carvalho,
IF/UFG-Goiânia-GO,Brazil. 10
Figure1.6 SchematicrepresentationofarawBTOcrystalboulewithitsstriations,
indicatingthewayitwillbesliced(topleft);alreadyslicedcrystalwithstriations
notperpendiculartothe(011)-face(topright)andready-to-usecrystalwith
renamedaxes(bottom). 11
Figure1.7 Bi TiO crystalbouleasgrownalongits[001]-axis. 12
12 20
Figure1.8 Actualundopedsillenitecrystals:rawBi TiO crystalboulegrownalongits
12 20
[001]-axis,showingstriationsonthelateralsurfaceswithbothopposite
(001)-facescutandpolished(left);Bi SiO crystalshowingits(110)-surface
12 20
cutandpolished(center)andBi TiO crystalwithitslarger(110)-facecutand
12 20
polishedwithits[001]-axisdirectionalongitslongerdimension(right). 12
Figure1.9 Index-of-refractionofBTOthatisformulatedby
n=0.00863∕𝜆4+0.0199∕𝜆2+2.46[6]. 14
Figure1.10 Bi SiO -typecubiccrystalanditscrystallographicaxesX ,X andX withan
12 20 1 2 3
externallyelectricfieldEappliedalongthe“x”-direction. 14
Figure1.11 Principalcoordinateaxessystem𝜂−𝜁 arisingbytheeffectofanelectricfieldE
appliedalongthe“x”-axis,asshowninFig.1.10. 14
Figure1.12 Sillenitecrystalcutalongitsprincipalcrystallographicaxes,withanelectric
fieldalongthe[001]-axis. 15
Figure1.13 Lithiumniobatecrystalwithanappliedelectricfieldalongthephotovoltaic
c-axis. 16
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