Table Of ContentMODERN OPTICS
Modern Optics
Second Edition
B. D. Guenther
DukeUniversity,USA
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Preface
The second edition of this textbook is designed for use in a standard physics course on
optics. The book is the result of a one-semester elective course that has been taught to
juniors,seniors,andfirst-yeargraduatestudentsinphysicsandengineeringatDukeUni-
versity for 13 years and has been used as a graduate text in a number of universities.
Studentswhotakethiscourseshouldhavecompletedanintroductoryphysicscourseand
mathematicscoursesthroughdifferentialequations.Electricityandmagnetismcanbetaken
concurrently.
ModernOpticsdiffersfromtheclassicalapproachofmosttextbooksonthissubjectin
thatitstreatmentofopticsincludessomematerialthatisnotfoundinmoreconventional
textbooks.Thesetopicsincludenonlinearoptics,guidedwaves,GaussianandBesselbeams,
photonicstructures,surfaceplasmons,imagingandcomputationalimaging,andlightmod-
ulation. Moreover, a selection of optional material is provided for the instructor so that
thecoursecontentcanreflecttheinterestoftheinstructorandthestudents.Basicderiva-
tionsareincludedtomakethebookappealingtophysicsdepartments,anddesignconcepts
areincludedtomakethebookappealingtoengineeringdepartments.Becauseofthema-
terialcoveredhere,theelectricalengineeringandbiomedicalengineeringdepartmentsat
Dukehavemadethecorrespondingopticscourseaprerequisiteforsomeoftheiradvanced
coursesinopticalcommunicationsandmedicalimaging.
Beforethe1960s,theonlycontactthattheaveragepersonhadwithopticswasacamera
lensoreyeglasses.Geometricalopticswasquiteadequateforthedesignofthesesystems,
anditwasnaturaltoemphasizethisaspectofopticsinacurriculum.Theapproachused
introduced the students to the theory and to examples of the application of the theory,
accomplishedbyadescriptionofalargevarietyofopticalinstruments.Thereasonforthis
approachwasthatlensdesignisfoundtobequitetedious,andtheoptimizationofalens
designismoreeasilydescribedthanaccomplished.
Today,thestudentisexposedtomanymoreopticalsystems.Everyoneencounterssuper-
marketscanners,copyingmachines,compactdiskplayers,holograms,anddiscussionsof
fiber-opticcommunications.Intheresearchenvironment,lasers,opticalmodulators,fiber-
opticinterconnects,andnonlinearopticshavebecomeimportant.Upongraduation,many
studentswillbecalledontoparticipateintheuseordevelopmentofthesemodernoptical
systems.Anelementarydiscussionofgeometricalopticsandareviewofclassicaloptical
instrumentswillnotadequatelypreparethestudentforthesedemands.
Thesecondeditionretainstheemphasisonbothfundamentalprinciplesofopticsand
an exposure to actual optics engineering problems and solutions. A large portion of the
conventionaltreatmentofgeometricalopticsandadiscussionofclassicalopticalsystems
isnotincluded.Intheirplace,ageometricalopticsdiscussionoffiberopticshasbeenin-
cluded and, in this second edition, a discussion of photonic structures with holography
beingconsideredasaspecialcaseofphotonicstructures.Ratherthandescribeahostof
opticalsystems,afewsystems,suchastheFabry–Perotinterferometer,areexaminedusing
avarietyoftheories.Thesecondeditionretainsitsemphasisondiffractionandtheuseof
Fouriertheorytodescribetheoperationofanopticalsystem.
Toallowthedevelopmentofaone-yearcourseinmodernoptics,anumberoftopics
havebeenaddedorexpanded.Theclassicaltheoryoftheinteractionoflightandmaterials
vi Preface
hasbeenexpandedtoincludesurfaceplasmons.Adiscussionofelectro-opticandmagneto-
opticeffectsisusedtointroduceopticalmodulators,andadiscussionofnonlinearoptics
is constructed around second-harmonic generation. Because of the importance of bire-
fringence in optical modulators and nonlinear optics, an expanded discussion of optical
anisotropyhasbeenincluded.Thisisadeparturefrommosttexts,whichignoreanisotropy
because of the need to use tensors. In modern optics, anisotropy is an important design
tool,anditstreatmentallowsadiscussionofthedesignofopticalmodulatorsandphase
matchinginnonlinearmaterials.
Thefirsttwochaptersreviewwavetheoryandelectromagnetictheory.Exceptforthe
sectiononpolarizationinChapter2,thesechapterscouldbeusedasreadingassignments
for well-prepared students. Chapter 3 discusses reflection and refraction and utilizes the
boundary conditions of Maxwell’s equations to obtain the fraction of light reflected and
refractedatasurface.
Chapter4discussesinterferenceofwavesanddescribesseveralinstrumentsthatareused
tomeasureinterference.Twooftheinterferometers—Young’stwo-slitexperimentandthe
Fabry–Perotinterferometer—shouldreceiveemphasisindiscussionsofthischapterbecause
oftheroletheyplayinlaterdiscussions.Anappendixtothischapterprovidesabriefintro-
ductiontosomeofthedesigntechniquesthatareusedtoproducemultilayerinterference
filters.Alloftheappendicesinthebookareincludedtofillingapsinstudents’knowledge
andtoprovidesomeflexibilityfortheinstructor.Theappendicesmaythereforebeignored
orusedasthesubjectmatterforspecialassignments.
Thetreatmentofgeometricaloptics,presentedinChapter5,isnottraditional.Itwas
throughthereductionoftraditionalsubjectmatterthatspacehasbeenfreedtoallowthe
introduction of more modern topics. A brief introduction to the matrix formalism used
in lens design is presented, and its use is demonstrated by analyzing a confocal Fabry–
Perotresonator.Geometricalopticsandtheconceptofinterferenceareusedtoanalyzethe
propagationoflightinafiber.Thisintroductiontofiberopticsisthenextendedthrough
theuseoftheLagrangianformulationtopropagationinagraded-indexopticalfiber.The
connectionbetweenthematrixequationsandthemorefamiliarlensequationsisestablished
inAppendix5A.BecauseoftheirimportanceintheGraduateRecordsExam,aberrations
aretreatedinAppendix5B.
AformalconnectionbetweengeometricalandwaveopticswaspresentedinChapter5
inthefirstedition.Ithasbeenremovedfromthiseditionbecauseitwasnotfoundusefulin
theclassroom.
TheFouriertheoryinChapter6ispresentedasareviewofandrefresheronthesubject.
ItisanimportantelementinthediscussionsoftheconceptofcoherenceinChapter8and
ofFraunhoferdiffractioninChapter10.ThediscussionsofopticalsignalprocessinginAp-
pendix10AandofimaginginAppendix10BdrawheavilyonFouriertheory.Thetreatment
ofimaginghasbeenexpandedtoincludecomputationalimagingandcodedapertures.
ThediscussionofdispersiongiveninChapter7couldbedelayedandcombinedwiththe
otherchaptersonmaterialinteractions(Chapters13and15).Itisincludedheretojustify
thediscussionofcoherenceinChapter8.Thediscussionofdispersioninmaterialshadas
itsobjectivethedevelopmentbythestudentofaunifyingviewoftheinteractionoflight
andmatter.Ithasbeenexpandedtoincludesurfaceplasmons.
ThedevelopmentofcoherencetheoryinChapter8isbuiltaroundapplicationsofthe
theorytospectroscopyandastronomy.Itisaverydifficultsubject,butbuildingthetheory
aroundthemethodsusedtomeasurecoherenceshouldmakethesubjectmoreintelligible.
Both the Fresnel and Gaussian wave formalisms of diffraction are introduced in
Chapter 9. The Gaussian wave formalism is used to analyze a Fabry–Perot cavity and
Preface vii
thinlens.Thischaptercanbeskipped,andthematerialintroducingtheFresnel–Huygens
integralcanbecoveredinasinglelecture.
TheFresnelformalismisexpandedanddiscussedinChapters10and11.Fraunhofer
diffractionistreatedfromalinearsystemviewpointinChapter10,andapplicationsofthe
theorytosignalprocessingandimagingarepresentedinAppendices10Aand10B.These
two appendices are the most important in the book. Fresnel diffraction is introduced in
Chapter 11, where it is used to interpret Fermat’s principle and analyze zone plates and
pinholecameras.
In this second edition, Chapter 12 is constructed around a presentation of photonic
structures. Guided by the presentation found in the book Photonic Crystals: Molding the
Flow of Light by Joannopoulos, Johnson, Winn, and Meade (Princeton University Press,
SecondEdition,2008),anoverviewofdiffractivestructuresandtheirapplicationsisgiven.
Multidimensionalperiodicmodulationoftheindexofrefractionisshowntoproducelight
propagation properties similar to the behavior of electrons in crystals. The similarity to
holograms is discussed. A simple theory of holography is presented, and Fresnel theory
is used to discuss the operation of a hologram. To generate the space needed to discuss
photonicstructures,muchofthematerialonholographyfoundinthefirsteditionhasbeen
removed.
Chapter 13 uses the introduction of polarizers and retarders as a basis for the devel-
opmentofthetheoryofthepropagation oflightinanisotropicmaterials. Thetreatment
of anisotropic materials is expanded over the conventional presentation to allow an easy
transition into the discussion of light modulation in Chapter 14. The many geometrical
constructions used in the discussion of anisotropy are confusing to everyone. To try to
makethematerialunderstandable,onlyoneconstructionisusedinChapter13.Topro-
videthestudentwithreferencematerialtoaidinreadingotherbooksandpapers,theother
constructionsarediscussedintheappendices.
ThediscussionofmodulatorsinChapter14providesanapplication-basedintroduction
toelectro-andmagneto-opticinteractions.Thedesignofanelectro-opticmodulatorpro-
videsthestudentwithanexampleoftheuseoftensors.Thematerialinteractionspresented
inChapters14and15requiretheuseoftensors,asubjectnormallyavoidedinanunder-
graduatecurriculum.Tensornotationhasbeenusedinthisbookbecauseitiskeyinthe
understandingofmanyopticaldevices.Somefamiliaritywithtensorsremovesmuchofthe
“magic”associatedwiththedesignofmodulatorsandtheapplicationsofphasematching
discussedinChapter15.
ThesubjectofnonlinearopticsinChapter15isdevelopedbyusingexamplesbasedon
frequencydoubling.Onlyafewbriefcommentsaremadeaboutthird-ordernonlinearities.
Theadditionaldiscussionofthird-orderprocessesisbestpresentedfromaquantumme-
chanicalviewpoint.Itwasthoughtthatthiswouldbebestdoneinaseparatecourse.The
materialpresentedinthischaptershouldpreparethestudenttoimmediatelyundertakea
courseinnonlinearoptics.
Enoughmaterialhasbeenincludedforaone-yearcourseinoptics.Chapters2–4,6,9
(excludingGaussianwaves),and10containthecorematerialandcouldbeusedinaone-
quartercourse.ByaddingChapters7and8alongwithAppendices10Aand10B,aone-
semestercoursecanbecreated.Theinstructorcanalterthesubjectsdiscussedfromyear
toyearbyaddingtopicssuchasAppendix4A,theguidedwavediscussionofChapter5,
or the discussion of holography in Chapter 12 in place of Appendices 10A and 10B. A
lessdemandingone-semestercoursecanbecreatedbyignoringChapter8andsubstituting
Chapter5,Appendix4A,orpossiblyChapter12.Inanticipationofdevelopingskilland
knowledge, the subject matter and problems increase in difficulty as the student moves
throughthebook.
viii Preface
Anumberofpeopleprovidedhelpinthepreparationofthisbook.Thosewhoprovided
photographsordrawingsareidentifiedinthefigurecaptions.Theirgenerosityismostap-
preciated.Dr.FrankDeLuciaprovidedtheinitialmotivationforwritingthebook.Many
ideasandconceptsaretheresultofbreakfastdiscussionswithA.VanderLugt.Thebook
wouldneverhavegonepastthenotestagewithouttheequationwriterwrittenbyDennis
Venable.DuncanSteelreviewedsomeoftheadditionstothesecondedition,andIwantto
thankhimforthateffort.ThomasStoneprovidedideas,photographicskills,andencour-
agementduringthepreparationofmostofthephotographsinthisbook.Hisenthusiasm
keptmeworking.
Very special thanks must go to Nicholas George. He loaned me equipment and lab-
oratory space to prepare many of the photographs. His encouragement prevented me
from shelving the project, and his technical discussions provided me with an improved
understandingofoptics.
ROBERTD.GUENTHER
Contents
1 WaveTheory 1
1.1 Introduction 1
1.2 TravelingWaves 1
1.3 WaveEquation 4
1.4 TransmissionofEnergy 5
1.5 ThreeDimensions 6
1.6 AttenuationofWaves 10
1.7 Summary 11
1.8 Problems 12
2 ElectromagneticTheory 15
2.1 Introduction 15
2.2 Maxwell’sEquations 16
2.2.1 Gauss’sLaw 16
2.2.1.1 Gauss’s(Coulomb’s)LawfortheElectricField 16
2.2.1.2 Gauss’sLawfortheMagneticField 17
2.2.2 Faraday’sLaw 17
2.2.3 Ampére’sLaw(LawofBiotandSavart) 17
2.2.4 ConstitutiveRelations 18
2.3 FreeSpace 19
2.4 WaveEquation 19
2.5 TransverseWaves 21
2.6 Interdependenceof EandB 22
2.7 EnergyDensityandFlow 24
2.8 Polarization 28
2.8.1 PolarizationEllipse 29
2.8.1.1 LinearPolarization 32
2.8.1.2 CircularPolarization 33
2.8.2 StokesParameters 36
2.8.3 JonesVector 39
2.9 PropagationinaConductingMedium 40
2.10 Summary 44
2.11 Problems 45
References 47
Appendix2A:Vectors 47
2A.1 Products 48
2A.2 Derivatives 48
Appendix2B:ElectromagneticUnits 50
3 ReflectionandRefraction 52
3.1 Introduction 52
3.2 ReflectionandTransmissionataDiscontinuity 53
