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1、Incident,transmitted,andreflectedbeamsatinterfacesReflectionandtransmissioncoefficientsThe"FresnelEquations"Brewster'sAngleTotalinternalreflectionPowerreflectanceandtransmittancePhaseshiftsinreflectionThemysteriousevanescentwave第三章波动光学(续)菲涅尔反射和折射公式Fresnel‘sEquationsforReflectiona
2、ndRefraction参照书上第三章内容DefinitionsplaneofincidenceinterfaceMoredefinitionsPerpendicular(“S”)polarizationsticksout oforintotheplaneofincidence.Planeoftheinterface(heretheyzplane)(perpendiculartopage)nintqiqrqtEiErEtInterfacexyzParallel(“P”)polarizationliesparalleltotheplaneofinciden
3、ce.IncidentmediumTransmittingmediumFresnelEquations费涅尔方程Wewouldliketocomputethefractionofalightwavereflectedandtransmittedbyaflatinterfacebetweentwomediawithdifferentrefrac-tiveindices.Fresnelwasthefirsttodothiscalculation.nintqiqrqtEiBiErBrEtBtInterfacexyzBeamgeometryforlightwit
4、hitselectricfieldper-pendiculartotheplaneofincidence(i.e.,outofthepage)Itproceedsbyconsideringtheboundaryconditionsattheinterfacefortheelectricandmagneticfieldsofthelightwaves.We’lldotheperpendicularpolarizationfirst.yxTheTangentialElectricFieldisContinuous切向分量连续！Inotherwords,The
5、totalE-fieldintheplaneoftheinterfaceis continuous.Here,allE-fieldsareinthez-direction,whichisintheplaneoftheinterface(xz), so:Ei(x,y=0,z,t)+Er(x,y=0,z,t)=Et(x,y=0,z,t)nintqiqrqtEiBiErBrEtBtInterfaceBoundaryConditionfortheElectric FieldatanInterface电场的边界条件：xyzxyTheTangentialMagnet
6、icField*isContinuous切向分量连续！Inotherwords,ThetotalB-fieldintheplaneoftheinterfaceis continuous.Here,allB-fieldsareinthexy-plane,so wetakethe x-components:–Bi(x,y=0,z,t)cos(qi)+Br(x,y=0,z,t)cos(qr)=–Bt(x,y=0,z,t)cos(qt)*It'sreallythetangentialB/m,butwe'reusingm=m0BoundaryConditionfo
7、rtheMagnetic FieldatanInterface磁场的边界条件nintqiqrqtEiBiErBrEtBtInterfacexyzqiqiReflectionandTransmissionforPerpendicularly(S)PolarizedLight:S分量的反射和透射Ignoringtherapidlyvaryingpartsofthelightwaveandkeepingonlythecomplexamplitudes:忽略快变部分，只考虑复振幅,我们有方程组利用B和E的振幅关系Reflection&TransmissionCo
8、efficientsforPerpendicularly(s)Polarized
