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1、Chapter2TheoreticalFoundationsLightembracesthemostfascinatingspectrumofelectromagneticradiation.Thisismainlyduetothefactthattheenergyoflightquanta(photons)lieintheenergyrangeofelectronictransitionsinmatter.Thisgivesusthebeautyofcolorandisthereasonwhyoureyesadaptedtosensetheoptic
2、alspectrum.Lightisalsofascinatingbecauseitmanifestsitselfinformsofwavesandparticles.Innootherrangeoftheelectromagneticspectrumwearemoreconfrontedwiththewave-particledualitythanintheopticalregime.Whilelongwavelengthradiation(radiofrequencies,microwaves)iswelldescribedbywavetheory
3、,shortwavelengthradiation(X-rays)exhibitsmostlyparticleproperties.Thetwoworldsmeetintheopticalregime.Todescribeopticalradiationinnano-opticsitismostlysufficienttoadaptthewavepicture.ThisallowsustouseclassicalfieldtheorybasedonMaxwell’sequa-tions.Ofcourse,innano-optics,thesystemswit
4、hwhichthelightfieldsinteractaresmall(singlemolecules,quantumdots)whichnecessitatesaquantumdescriptionofthematerialproperties.Thus,inmostcaseswecanusetheframeworkofsemiclassi-caltheorywhichcombinestheclassicalpictureoffieldsandthequantumpictureofmatter.However,occasionally,wehaveto
5、gobeyondthesemiclassicaldescription.Forexamplethephotonsemittedbyaquantumsystemcanobeynon-classicalphotonstatisticsinformofphoton-antibunching.Thissectionsummarizesthefundamentalsofelectromagnetictheoryformingthenecessarybasisforthiscourse.Onlythebasicpropertiesarediscussedandfo
6、rmoredetailedtreatmentsthereaderisreferredtostandardtextbooksonelectromagnetismsuchasthebooksbyJackson[1],Stratton[2],andothers.ThestartingpointareMaxwell’sequationsestablishedbyJamesC.Maxwellin1873.12CHAPTER2.THEORETICALFOUNDATIONS2.1MacroscopicElectrodynamicsInmacroscopicelect
7、rodynamicsthesingularcharacterofchargesandtheirassociatedcurrentsisavoidedbyconsideringchargedensitiesρandcurrentdensitiesj.IndifferentialformandinSIunitsthemacroscopicMaxwell’sequationshavetheform∂B(r,t)∇×E(r,t)=−,(2.1)∂t∂D(r,t)∇×H(r,t)=+j(r,t),(2.2)∂t∇·D(r,t)=ρ(r,t),(2.3)∇·B(r,
8、t)=0.(2.4)whereEdenotestheelectricfield,Dtheelec
