The Nonlinear Problem of the 3d Datum Transformation and the Procrustes Algorithm

620 Pages·2013·4.549 MB·English

by  Erik W Grafarend (Prof. Dr.-Ing.) Affiliation: Geodetic Institute, University of Stuttgart, Geschwister-Scholl-Strasse 24D, Stuttgart, 70174, Germany, Joseph L Awange (Prof. Dr.-Ing.) Affiliation: Environment and Earth Sciences, Maseno University, Maseno, Kenya

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Contents
PrefacetotheThirdEdition xiii
PrefacetotheSecondEdition xv
PrefacetotheFirstEdition xvii
1. TheNonlinearOpticalSusceptibility 1
1.1. IntroductiontoNonlinearOptics 1
1.2. DescriptionsofNonlinearOpticalProcesses 4
1.3. FormalDefinitionoftheNonlinearSusceptibility 17
1.4. NonlinearSusceptibilityofaClassicalAnharmonic
Oscillator 21
1.5. PropertiesoftheNonlinearSusceptibility 33
1.6. Time-DomainDescriptionofOpticalNonlinearities 52
1.7. Kramers–KronigRelationsinLinearandNonlinearOptics 58
Problems 63
References 65
2. Wave-EquationDescriptionofNonlinearOpticalInteractions 69
2.1. TheWaveEquationforNonlinearOpticalMedia 69
2.2. TheCoupled-WaveEquationsforSum-Frequency
Generation 74
2.3. PhaseMatching 79
2.4. Quasi-Phase-Matching 84
2.5. TheManley–RoweRelations 88
2.6. Sum-FrequencyGeneration 91
2.7. Second-HarmonicGeneration 96
vii
viii Contents
2.8. Difference-FrequencyGenerationandParametric
Amplification 105
2.9. OpticalParametricOscillators 108
2.10. NonlinearOpticalInteractionswithFocused
GaussianBeams 116
2.11. NonlinearOpticsatanInterface 122
Problems 128
References 132
3. Quantum-MechanicalTheoryoftheNonlinearOptical
Susceptibility 135
3.1. Introduction 135
3.2. SchrödingerCalculationofNonlinearOpticalSusceptibility 137
3.3. DensityMatrixFormulationofQuantumMechanics 150
3.4. PerturbationSolutionoftheDensityMatrix
EquationofMotion 158
3.5. DensityMatrixCalculationoftheLinearSusceptibility 161
3.6. DensityMatrixCalculationoftheSecond-Order
Susceptibility 170
3.7. DensityMatrixCalculationoftheThird-OrderSusceptibility 180
3.8. ElectromagneticallyInducedTransparency 185
3.9. Local-FieldCorrectionstotheNonlinear
OpticalSusceptibility 194
Problems 201
References 204
4. TheIntensity-DependentRefractiveIndex 207
4.1. DescriptionsoftheIntensity-DependentRefractiveIndex 207
4.2. TensorNatureoftheThird-OrderSusceptibility 211
4.3. NonresonantElectronicNonlinearities 221
4.4. NonlinearitiesDuetoMolecularOrientation 228
4.5. ThermalNonlinearOpticalEffects 235
4.6. SemiconductorNonlinearities 240
4.7. ConcludingRemarks 247
References 251
5. MolecularOriginoftheNonlinearOpticalResponse 253
5.1. NonlinearSusceptibilitiesCalculatedUsing
Time-IndependentPerturbationTheory 253
Contents ix
5.2. SemiempiricalModelsoftheNonlinear
OpticalSusceptibility 259
ModelofBoling,Glass,andOwyoung 260
5.3. NonlinearOpticalPropertiesofConjugatedPolymers 262
5.4. Bond-ChargeModelofNonlinearOpticalProperties 264
5.5. NonlinearOpticsofChiralMedia 268
5.6. NonlinearOpticsofLiquidCrystals 271
Problems 273
References 274
6. NonlinearOpticsintheTwo-LevelApproximation 277
6.1. Introduction 277
6.2. DensityMatrixEquationsofMotionfora
Two-LevelAtom 278
6.3. Steady-StateResponseofaTwo-LevelAtomtoa
MonochromaticField 285
6.4. OpticalBlochEquations 293
6.5. RabiOscillationsandDressedAtomicStates 301
6.6. OpticalWaveMixinginTwo-LevelSystems 313
Problems 326
References 327
7. ProcessesResultingfromtheIntensity-DependentRefractive
Index 329
7.1. Self-FocusingofLightandOtherSelf-ActionEffects 329
7.2. OpticalPhaseConjugation 342
7.3. OpticalBistabilityandOpticalSwitching 359
7.4. Two-BeamCoupling 369
7.5. PulsePropagationandTemporalSolitons 375
Problems 383
References 388
8. SpontaneousLightScatteringandAcoustooptics 391
8.1. FeaturesofSpontaneousLightScattering 391
8.2. MicroscopicTheoryofLightScattering 396
8.3. ThermodynamicTheoryofScalarLightScattering 402
x Contents
8.4. Acoustooptics 413
Problems 427
References 428
9. StimulatedBrillouinandStimulatedRayleighScattering 429
9.1. StimulatedScatteringProcesses 429
9.2. Electrostriction 431
9.3. StimulatedBrillouinScattering(InducedbyElectrostriction) 436
9.4. PhaseConjugationbyStimulatedBrillouinScattering 448
9.5. StimulatedBrillouinScatteringinGases 453
9.6. StimulatedBrillouinandStimulatedRayleighScattering 455
Problems 468
References 470
10. StimulatedRamanScatteringandStimulatedRayleigh-Wing
Scattering 473
10.1. TheSpontaneousRamanEffect 473
10.2. SpontaneousversusStimulatedRamanScattering 474
10.3. StimulatedRamanScatteringDescribedbythe
NonlinearPolarization 479
10.4. Stokes–Anti-StokesCouplinginStimulated
RamanScattering 488
10.5. CoherentAnti-StokesRamanScattering 499
10.6. StimulatedRayleigh-WingScattering 501
Problems 508
References 508
11. TheElectroopticandPhotorefractiveEffects 511
11.1. IntroductiontotheElectroopticEffect 511
11.2. LinearElectroopticEffect 512
11.3. ElectroopticModulators 516
11.4. IntroductiontothePhotorefractiveEffect 523
11.5. PhotorefractiveEquationsofKukhtarevetal. 526
11.6. Two-BeamCouplinginPhotorefractiveMaterials 528
11.7. Four-WaveMixinginPhotorefractiveMaterials 536
Problems 540
References 540
Contents xi
12. OpticallyInducedDamageandMultiphotonAbsorption 543
12.1. IntroductiontoOpticalDamage 543
12.2. Avalanche-BreakdownModel 544
12.3. InfluenceofLaserPulseDuration 546
12.4. DirectPhotoionization 548
12.5. MultiphotonAbsorptionandMultiphotonIonization 549
Problems 559
References 559
13. UltrafastandIntense-FieldNonlinearOptics 561
13.1. Introduction 561
13.2. UltrashortPulsePropagationEquation 561
13.3. InterpretationoftheUltrashort-Pulse
PropagationEquation 567
13.4. Intense-FieldNonlinearOptics 571
13.5. MotionofaFreeElectroninaLaserField 572
13.6. High-HarmonicGeneration 575
13.7. NonlinearOpticsofPlasmasandRelativistic
NonlinearOptics 579
13.8. NonlinearQuantumElectrodynamics 583
Problem 586
References 586
Appendices 589
A. TheSISystemofUnits 589
Furtherreading 596
B. TheGaussianSystemofUnits 596
Furtherreading 600
C. SystemsofUnitsinNonlinearOptics 600
D. RelationshipbetweenIntensityandFieldStrength 602
E. PhysicalConstants 603
Index 605
Preface to the Third Edition
It has been a great pleasure for me to have prepared the latest edition of my
bookonnonlinearoptics.Myintrigueinthesubjectmatterofthisbookisas
strongasitwaswhenthefirsteditionwaspublishedin1992.
The principal changes present in the third edition are as follows: (1) The
book has been entirely rewritten using the SI system of units. I personally
prefertheeleganceofthegaussiansystemofunits,whichwasusedinthefirst
two editions, but I realize that most readers would prefer the SI system, and
thechangewasmadeforthisreason.(2)Inaddition,alargenumberofminor
changeshavebeenmadethroughoutthetexttoclarifytheintendedmeaning
and to make the arguments easier to follow. I am indebted to the countless
commentsreceivedfromstudentsandcolleaguesbothinRochesterandfrom
around the world that have allowed me to improve the writing in this man-
ner.(3)Moreover,severalsectionsthattreatentirelynewmaterialhavebeen
added.Applicationsofharmonicgeneration,includingapplicationswithinthe
fieldsofmicroscopyandbiophotonics,are treatedinSubsection2.7.1.Elec-
tromagneticallyinducedtransparencyistreatedinSection3.8.Somebriefbut
crucialcommentsregardinglimitationstothemaximumsizeoftheintensity-
inducedrefractive-indexchangearemadeinSection4.7.Theuseofnonlinear
opticalmethodsforinducingunusualvaluesofthegroupvelocityoflightare
discussedbrieflyinSection3.8andinSubsection6.6.2. Spectroscopybased
on coherent anti–Stokes Raman scattering (CARS) is discussed in Section
10.5. In addition, the appendix has been expanded to include brief descrip-
tionsofboththeSIandgaussiansystemsofunitsandproceduresforconver-
sionbetweenthem.
xiii
xiv PrefacetotheThirdEdition
The bookinitspresentformcontainsfartoomuchmaterialtobe covered
withinaconventionalone-semestercourse.Forthisreason,Iamoftenasked
foradviceonhowtostructureacoursebasedonthecontentofmytextbook.
Someofmythoughtsalongtheselinesareasfollows:(1)Ihaveendeavored
as much as possible to make each part of the book self-contained. Thus, the
sophisticatedreadercanreadthebookinanydesiredorderandcanreadonly
sectionsofpersonalinterest.(2)Nonetheless,whenusingthebookasacourse
text,IsuggeststartingwithChapters1and2,whichpresentthebasicformal-
ism of the subject material. At that point, topics of interest can be taught in
nearly any order. (3) Special mention should be made regarding Chapters 3
and 6, which deal with quantum mechanical treatments of nonlinear optical
phenomena.Thesechaptersareamongthemostchallengingofanywithinthe
book.Thesechapterscanbeskippedentirelyifoneiscomfortablewithestab-
lishingonlyaphenomenologicaldescriptionofnonlinearopticalphenomena.
Alternatively,thesechapterscanformthebasisofaformaltreatmentofhow
the laws of quantum mechanics can be applied to provide detailed descrip-
tionsofavarietyofopticalphenomena.(4)Fromadifferentperspective,Iam
sometimesasked formy adviceonextractingtheessentialmaterialfromthe
book—that is, in determining which are topics that everyone should know.
This question often arises in the context of determining what material stu-
dentsshouldstudywhenpreparingforqualifyingexams.Mybestresponseto
questionsofthissortisthattheessentialmaterialisasfollows:Chapter1in
itsentirety;Sections2.1–2.3,2.4,and2.10ofChapter2;Subsection3.5.1of
Chapter 3; Sections 4.1, 4.6, and 4.7 of Chapter 4; Chapter 7 in its entirety;
Section8.1ofChapter8;andSection9.1ofChapter9.(5)Finally,Ioftentell
my classroom students that my course is in some ways as much a course on
opticalphysicsasitisacourseonnonlinearoptics.Isimplyusetheconcept
of nonlinear optics as a unifying theme for presenting conceptual issues and
practical applications of optical physics. Recognizing that this is part of my
perspectiveinwriting,thisbookcouldbeusefultoitsreaders.
Iwanttoexpressmythanksonceagaintothemanystudentsandcolleagues
whohavegivenmeusefuladviceandcommentsregardingthisbookoverthe
past fifteen years. I am especially indebted to my own graduate students for
theassistanceandencouragementtheyhavegiventome.
RobertBoyd
Rochester,NewYork
October,2007
Preface to the Second Edition
Inthetenyearssincethepublicationofthefirsteditionofthisbook,thefield
ofnonlinearopticshascontinuedtoachievenewadvancesbothinfundamen-
tal physics and in practical applications. Moreover, the author’s fascination
with this subject has held firm over this time interval. The present work ex-
tends the treatment of the first edition by including a considerable body of
additionalmaterialandbymakingnumeroussmallimprovementsinthepre-
sentationofthematerialincludedinthefirstedition.
The primary differences between the first and second editions are as fol-
lows.
TwoadditionalsectionshavebeenaddedtoChapter1,whichdealswiththe
nonlinear optical susceptibility. Section 1.6 deals with time-domain descrip-
tions of optical nonlinearities, and Section 1.7 deals with Kramers–Kronig
relationsinnonlinearoptics.Inaddition,adescriptionofthesymmetryprop-
ertiesofgalliumarsenidehasbeenaddedtoSection1.5.
Three sections have been added to Chapter 2, which treats wave-equation
descriptionsofnonlinearopticalinteractions.Section2.8treatsopticalpara-
metricoscillators,Section2.9 treatsquasi-phase-matching,andSection2.11
treatsnonlinearopticalsurfaceinteractions.
TwosectionshavebeenaddedtoChapter4,whichdealswiththeintensity-
dependentrefractiveindex.Section4.5treatsthermalnonlinearities,andSec-
tion4.6treatssemiconductornonlinearities.
Chapter 5 is an entirely new chapter dealing with the molecular origin of
the nonlinearopticalresponse. (Consequentlythe chapter numbersof all the
followingchaptersareonegreaterthanthoseofthefirstedition.)Thischap-
ter treats electronic nonlinearities in the static approximation, semiempirical
xv