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1、Chap.5.Interactionbetweenradiationandmatter§5.1Electromagnetismofradiationandmatter5.1.1DielectricconstantandopticalconstantMaxwell’sequation∂B∂DrotE=−,rotH=+j,divD=ρ,divB=0∂t∂tE(r,t)andH(r,t):electricandmagneticfields,respectivelyD(r,t)andB(r,t):electricandmagneticf
2、luxdensities,respectivelyjandρ:currentandrealchargedensities,respectivelyIncontinuousandisotropicmatter,D=εεE,B=μμH,j=σE,00whereε0isdielectricconstantofvacuum,ε,thatofmatterrelativetoε0,μ0,permeabilityofvacuum,μ,permeabilityofmatterrelativetoμ0andσ,electricconductivi
3、ty.Waveequationsinthecaseinwhichnorealchargeexists(ρ=0)are222∂E∂E2∂H∂H∇E=εμεμ+μμσ,∇H=εμεμ+μμσ.00200020∂t∂t∂t∂ta.Innon-absorbingmatter(σ=0)222∂E2∂H∇E=εμεμ,∇H=εμεμ.002002∂t∂tE=Eexp{−i(ωt−k⋅r)},H=Hexp{−i(ωt−k⋅r)},00wherekiswavevectorwithdirectionofpropagation,andωisangu
4、larfrequency(ω=2πν,ν:frequency).22k=εμεμω00Phasevelocityoflightinmatter:v=νλ=1εμεμ00−12−68ε＝8.854×10C/Vm，μ＝1.257×10Wb/Am,c=1εμ＝2.998×10ｍ/s0000Intheregionofopticalfrequency,22μ=1.Therefore,(cω)k=ε.Refractionindexnisdefinedas,n≡cv=ε.Thelightistransversewaveask⋅E=k⋅H=0.
5、Electricfieldisperpendiculartomagneticfieldask×E=ωB.b.Inabsorbingmatter(σ>0)~k→k=k′+ik′′(k′,k′′:realvector)~~E=Eexp{−i(ωt−k⋅r)},H=Hexp{−i(ωt−k⋅r)}00E=Eexp{}−i()ωt−k′⋅rexp(−k′′⋅r),H=Hexp{}−i(ωt−k′⋅r)exp(−k′′⋅r),00wherethefirstandsecondexponentialsareoscillatinganddamp
6、ingterms,respectively.Forarbitraryr,k′⋅r=constant:equi-phasesurface,k′′⋅r=constant:equi-amplitudesurface.~2222Inthecaseofk′∥k′′,k=k′−k′′+2ik′⋅k′′=εμεμω+iμμσω,μ=1.000~~~σ()22~cωk=ε,ε=ε+iε,ε=ε,ε=.(Hereafterε→ε.)1212εω0~~2Usingcomplexrefractionindexn=n+iκ,n=εand22n−κ=ε,
7、2nκ=ε,12herenisrefractionindexandκisextinctioncoefficient.k′′=ωκc.−μzAbsorptionoflightgoingtoｚdirection:intensityatzisI(z)=Ie.02SinceI∝E,μ=2ωκc=4πκλ:linearabsorptioncoefficient.22Energylossfunction:Im(−1ε)=ε(ε+ε)1125.1.2Fresnel’sformulasIncidentlight:E=Eexp{−i(ωt−k⋅r
8、)}n1011Reflectedlight:E=Eexp{−i(ωt−k⋅r)}rr0r~Refractedlight:E=Eexp{−i(ωt−k⋅r)}2022ThesimilarexpressionsareobtainedasforH.a.Snell’sl
