Chapter 15_ Theoretical methods .pdf

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1、Chapter15TheoreticalMethodsinNano-OpticsAmajorprobleminnano-opticsisthedeterminationofelectromagneticfielddistri-butionsnearnanoscalestructuresandtheassociatedradiationproperties.Asolidtheoreticalunderstandingoffielddistributionsholdspromisefornew,optimizedde-signsofnear-fieldopticaldevi

2、ces,inparticularbyexploitationoffield-enhancementeffectsandfavorabledetectionschemes.Calculationsoffielddistributionsarealsonecessaryforimagereconstructionpurposes.Fieldsnearnanoscalestructureshaveoftentobereconstructedfromexperimentallyaccessiblefarfielddata.However,mostcommonlytheinvers

3、escatteringproblemcannotbesolvedinauniquewayandcalcu-lationsoffield-distributionsareneededtoprovidepriorknowledgeaboutsourceandscatteringobjectsandtorestrictthesetofpossiblesolutions.AnalyticalsolutionsofMaxwell’sequationsprovideagoodtheoreticalunderstand-ingbutcanbeobtainedforsimplepr

4、oblemsonly.Otherproblemshavetobestronglysimplified.Ontheotherhand,apurenumericalanalysisallowstohandlecomplexproblemsbydiscretizationofspaceandtimebutcomputationalrequirements(usu-allygivenbycputimeandmemory)limitthesizeoftheproblemandtheaccuracyofresultsisoftenunknown.Theadvantageofpu

5、renumericalmethods,suchasthefinite-differencetime-domain(FDTD)methodorthefinite-element(FE)method,istheeaseofimplementation.Wewillnotreviewthesepurenumericaltechniquessincetheyarewelldocumentedintheliterature.Insteadwewillreviewtwocommonlyusedsemi-analyticalmethodsinnano-optics:themultip

6、le-multipolemethod(MMP)andthevolumeintegralmethod.Thelatterexistsindifferentimplementationssuchasthecoupled-dipolemethod,thedipole-dipoleapproximation,orthemethodofmo-ments.BothMMPandthevolumeintegralmethodaresemiclassicalmethodssincetheyrenderananalyticalexpansionfortheelectromagnetic

7、fieldbynumericalmeans.12CHAPTER15.THEORETICALMETHODSINNANO-OPTICS15.1TheMultipleMultipoleMethodThemultiplemultipolemethod(MMP)isacompromisebetweenapureanalyticalandapurenumericalapproach.Itisawell-establishedtechniqueforsolvingMaxwell’sequationsinarbitrarilyshaped,isotropic,linearandpi

8、ecewi