Numerical Simulation of Optical Wave Propagation with Examples in MATLAB.pdf

Numerical Simulation of Optical Wave Propagation with Examples in MATLAB.pdf

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NumericalSimulationofOpticalWavePropagationWithexamplesinMATLABLibraryofCongressCataloging-in-PublicationDataSchmidt,JasonDaniel,1975-NumericalsimulationofopticalwavepropagationwithexamplesinMATLAB/JasonD.Schmidt.p.cm.-（Pressmonograph;199）Includesbibliographicalreferencesandindex.ISBN978-0-8194-8326-31.Optics-Mathematics.2.Wave-motion,Theoryof-Mathematicalmodels.3.MATLAB.I.Title.QC383.S362010535.42015118-dc222010015089PublishedbySPIEP.O.Box10Bellingham,Washington98227-0010USAPhone:

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/spie.orgCopyright2010SocietyofPhoto-OpticalInstrumentationEngineers（SPIE）Allrightsreserved.Nopartofthispublicationmaybereproducedordistributedinanyformorbyanymeanswithoutwrittenpermissionofthepublisher.Thecontentofthisbookreflectstheworkandthoughtsoftheauthor（s）.Everyefforthasbeenmadetopublishreliableandaccurateinformationherein,butthepublisherisnotresponsibleforthevalidityoftheinformationorforanyoutcomesresultingfromreliancethereon.PrintedintheUnitedStatesofAmerica.Aboutthecover:

50-wattlaserforgeneratingmesosphericsodiumguidestarsover90kmabovetheground.InoperationattheAirForceResearchLaboratorys3.5-mtelescopeattheStarfireOpticalRange,KirtlandAFB,NM.（RobertQ.Fugate,2005,Albuquerque,NM）.Bellingham,WashingtonUSANumericalSimulationofOpticalWavePropagationWithexamplesinMATLABJasonD.SchmidtContentsPreface.ixChapter1FoundationsofScalarDiffractionTheory.11.1BasicsofClassicalElectrodynamics.11.1.1Sourcesofelectricandmagneticfields.21.1.2Electricandmagneticfields.21.2SimpleTraveling-WaveSolutionstoMaxwellsEquations.51.2.1Obtainingawaveequation.51.2.2Simpletraveling-wavefields.71.3ScalarDiffractionTheory.91.4Problems.12Chapter2DigitalFourierTransforms.152.1BasicsofDigitalFourierTransforms.152.1.1Fouriertransforms:

fromanalytictonumerical.152.1.2InverseFouriertransforms:

fromanalytictonumerical.172.1.3PerformingdiscreteFouriertransformsinsoftware.182.2SamplingPure-FrequencyFunctions.212.3DiscretevsContinuousFourierTransforms.232.4AlleviatingEffectsofDiscretization.262.5ThreeCaseStudiesinTransformingSignals.302.5.1Sincsignals.302.5.2Gaussiansignals.312.5.3Gaussiansignalswithquadraticphase.332.6Two-DimensionalDiscreteFourierTransforms.352.7Problems.37Chapter3SimpleComputationsUsingFourierTransforms.393.1Convolution.393.2Correlation.433.3StructureFunctions.473.4Derivatives.503.5Problems.53Chapter4FraunhoferDiffractionandLenses.554.1FraunhoferDiffraction.554.2Fourier-TransformingPropertiesofLenses.584.2.1Objectagainstthelens.594.2.2Objectbeforethelens.594.2.3Objectbehindthelens.614.3Problems.64Chapter5ImagingSystemsandAberrations.655.1Aberrations.655.1.1Seidelaberrations.665.1.2Zernikecirclepolynomials.665.1.2.1Decompositionandmoderemoval.735.1.2.2RMSwavefrontaberration.755.2ImpulseResponseandTransferFunctionofImagingSystems.775.2.1Coherentimaging.775.2.2Incoherentimaging.795.2.3Strehlratio.825.3Problems.84Chapter6FresnelDiffractioninVacuum.876.1DifferentFormsoftheFresnelDiffractionIntegral.886.2OperatorNotation.896.3Fresnel-IntegralComputation.906.3.1One-steppropagation.906.3.2Two-steppropagation.926.4Angular-SpectrumPropagation.956.5SimpleOpticalSystems.1026.6PointSources.1076.7Problems.113Chapter7SamplingRequirementsforFresnelDiffraction.1157.1ImposingaBandLimit.1157.2PropagationGeometry.1177.3ValidityofPropagationMethods.1207.3.1Fresnel-integralpropagation.1207.3.1.1Onestep,fixedobservation-planegridspacing.1207.3.1.2Avoidingaliasing.1217.3.2Angular-spectrumpropagation.1247.3.3Generalguidelines.1287.4Problems.130Chapter8RelaxedSamplingConstraintswithPartialPropagations.1338.1AbsorbingBoundaries.1348.2TwoPartialPropagations.1358.3ArbitraryNumberofPartialPropagations.1388.4SamplingforMultiplePartialPropagations.1398.5Problems.146Chapter9PropagationthroughAtmosphericTurbulence.1499.1Split-StepBeamPropagationMethod.1499.2RefractivePropertiesofAtmosphericTurbulence.1509.2.1KolmogorovTheoryofturbulence.1529.2.2Opticalpropagationthroughturbulence.1569.2.3Opticalparametersoftheatmosphere.1579.2.4Layeredatmospheremodel.1649.2.5Theory.1649.3Monte-CarloPhaseScreens.1669.4SamplingConstraints.1729.5ExecutingProperlySampledSimulation.1749.5.1Determinepropagationgeometryandturbulenceconditions.1749.5.2Analyzethesamplingconstraints.1769.5.3Performavacuumsimulation.1789.5.4Performtheturbulentsimulations.1799.5.5Verifytheoutput.1809.6Conclusion.1829.7Problems.183AppendixAFunctionDefinitions.185AppendixBMATLABCodeListings.187References.189Index.195PrefaceDiffractionisaveryinterestingandactiveareaofopticalresearch.Unfortunately,analyticsolutionsarerareinmanypracticalproblems,particularlywhenopticalwavespropagatethroughrandomlyfluctuatingmedia.Formanyoftheseproblems,researchersmustresorttonumericalsolutions.Still,simulationsinopticaldiffrac-tionarechallenging.Usually,thesesimulationstakeadvantageofdiscreteFouriertransforms,whichmeansusingdiscretelyspacedsamplesonafinite-sizedgrid.Thisleadstoafewtradeoffsinspeedandmemoryversusaccuracy.Thus,thepa-rametersofthesamplinggridsmustbechosenverycarefully.Somepeopleseektofullyautomatethosechoices,butthiscannotbedoneautomaticallyineverycase.Todeterminegridproperties,onemustcarefullyconsidercomputationalspeed,availablecomputermemory,theNyquistsamplingcriterion,geometry,accuraterepresentationofsourceapertures,andimpactonthepropagatedfieldsquantitiesofinterest.ThisbookgrewoutofanindependentstudyIdidwhileIwasadoctoralstudentatUniversityofDayton.ThestudywasdirectedbyLtColMatthewGoda,thenaprofessorattheAirForceInstituteofTechnology（AFIT）.Aftertheindependentstudywasover,GodathencreatedacourseatAFITonwave-opticssimulations.WhenIgraduated,IbecameaprofessoratAFITwhileGodamovedontoanewmilitaryassignment.WhenIbeganteachingthewave-opticssimulationcourse,therewasnobookwrittentothelevelofdetailrequiredforagraduatecoursefo-cusedonwave-opticssimulationsandsamplingrequirements.Thecoursewasal-waystaughtoutoftheprofessorsnotes,originallycompiledbyGoda.Compilingthesenoteswasnosmallfeat,andGodadidatremendousjobcombiningmaterialfrombooksondiscreteFouriertransforms,opticsjournalarticlesandconferenceproceedings,technicalreportsfromcompaniesliketheOpticalSciencesCompanyandMZAAssociatesCorporation,andprivatecommunicationwithresearchers.Untilthisbook,simulationshavealwaysbeenanafterthoughtinjustafewbooksonimageprocessingandnonlinearoptics.Clearlytherewasagapbetweenthepracticalknowledgerequiredtoperformwave-opticssimulationsandthethe-oreticalmaterialcoveredingreatFourier-opticstextbookslikethosebyJosephGoodmanandJackGaskill.IhaveheardprofessorsacrosstheU.S.talkabouthowtheyincludematerialonsimulationsintheirgraduateFourier-opticscourses.Iap-plaudthemforthateffortbecauseitischallengingtoteachstudentsboththethe-oryandpracticalsimulationofFourieropticsinonecourse.However,ifthestu-ixdentsaretobecomecapableenoughtowritewave-opticssimulationsforthesisordissertationresearchandbeyond,theycannotgetenoughdetailinaone-termFourier-opticscourse.ThisiswhyAFIThasseparatecoursesonFourieropticsandwave-opticssimulations.Thisbookisintendedforgraduatestudentsinprogramslikephysics,electricalengineering,electro-optics,oropticalscience.ThebookgivesalloftherelevantequationsfromFourieroptics,buttofullyunderstandandappreciatethematerial,itisimportanttohaveathoroughunderstandingofFourieropticsbeforereadingthisbook.Ibelievethatpartofthebenefitofthisbookistheuseofspecificcodeexamples,ratherthanjustpseudo-code.However,theprogrammingorscriptinglanguagefortheexamplesneedstobeonethatiswidelyusedandeasytounderstandbythosewhodonotalreadyuseit.Forthosereasons,IhaveusedMATLABinalloftheexamplesthroughoutthisbook.Itisheavilyusedinengineeringbothatuniversitiesandresearchinstitutions.Further,itiseasytoreadbecauseofitssimplelanguageandbecausemanynumericalalgorithms,suchasdiscreteFouriertransformsandconvolution,arepartofitsbasiclibrary.IfIusedotherlanguageslikeC,C+,FORTRAN,Java,andPython,Iwouldneedtopickaparticularexternallibraryofnumericalroutinesorwritemyownalgorithmsandincludetheminthebook.IbelievethatusingMATLABinthisbookallowsreaderstofocusonthewavepropagation,ratherthanthemostbasicnumericalalgorithmslikediscreteFouriertransforms.Further,anyuserwithaccesstotheMATLABinterpretercanexecutethecodeexamplesasshown.Noadditionallibrariesneedtobeacquiredandinstalled.Moreover,myexamplesrarelyuseMATLABstoolboxes,relyingheavilyonitsbasicfunctionality.Readersshouldnotethatthecodeexamplesusedthroughoutthebookaredesignedforconceptualsimplicity,ratherthanoptimizedforspeedormemoryusage.IencouragereaderstoreworkmyMATLABexamplestoachievegreaterperformanceorevenimplementtheminotherlanguages.Ioffermythanksandappreciationtoallthosewhohavepavedthewayforthiswork,particularlyGlennTyler,DavidFried,andPhillipRobertsattheOpticalSciencesCompanyandSteveCoyatMZAAssociatesCorporation.In1982,FriedandTylerwroteatechnicalreportdescribingmethodsofsimulatingopticalwa