電磁場(chǎng)與電磁波第22講電解質(zhì)邊界與多層垂直入射

11.NormalIncidenceataPlaneConductingBoundary⊙⊙⊙xzyanraniErEiHrHiReflectedwaveIncidentwavePerfectconductorMedium2(2=)Medium1(1=0)z=0Review22.ObliqueIncidenceataPlaneConductingBoundaryirPerfectconductorE

iE

rH

iH

rzxMedium1(1=0)z=0anianrReflectedwaveIncidentwaveyirPerfectconductorE

iE

rH

iH

rzxMedium1(1=0)z=0anianrReflectedwaveIncidentwavey3MaintopicPlaneElectromagneticWaves2.NormalIncidenceatMultipleDielectricInterfaces1.NormalIncidenceataPlaneDielectricBoundary4ConsiderthesituationinFigurewheretheincidentuniformplanewavetravelsinthe+z-direction,andtheboundarysurfaceistheplanez=0.Theincidentelectricandmagneticfieldintensityphasorsare1.NormalIncidenceataPlaneDielectricBoundary⊙⊙xzyanraniErEiHrHiReflectedwaveIncidentwaveMedium1(1,1)z=0⊙EtHtantTransmittedwaveMedium2(2,2)5a)Forthereflectedwave(Er,Hr):b)Forthetransmittedwave(Et,Ht):Atthedielectricinterfacez=0thetangentialcomponents(thex-components)oftheelectricandmagneticfieldintensitiesmustbecontinuous.Wehave⊙⊙xzyanraniErEiHrHiReflectedwaveIncidentwaveMedium1(1,1)z=0⊙EtHtantTransmittedwaveMedium2(2,2)6WeobtainTheratiosEr0/Ei0andEt0/Ei0arecalledreflectioncoefficient反射系數(shù)

andtransmissioncofficient透射系數(shù),respectively.IntermsoftheintrinsicimpedancestheyareNotethatthereflectioncoefficientcanbepositiveornegative可正可負(fù),dependingonwhether2

isgreaterorlessthan1.Thetransmissioncoefficient

,however,isalwayspositive正.Thedefinitionsfor

andapplyevenwhenthemediaaredissipative有耗-thatisevenwhen1,and/or2

arecomplex復(fù)數(shù).Thus

and

maysimplythemselvesbecomplexinthegeneralcase.Acomplex(or)simplymeansthataphaseshiftisintroducedattheinterfaceuponreflection(ortransmission).可以為復(fù)數(shù)，引入一個(gè)相位7Reflectionandtransmissioncoefficientsarerelatedbythefollowingequation:Ifmedium2isaperfectconductor理想導(dǎo)體,2=0,equationsyield=-1,and=0.consequently,Er0=-Ei0,andEt0=0.Theincidentwavewillbetotallyreflected全反射,andastandingwave駐波

willbeproducedinmedium1,asdiscussedinSection8-6.Ifmedium2isnotaperfectconductor,partialreflection部分反射

willresult.Thetotalelectricfieldinmedium1canbewrittenasor8WeseethatE1(z)iscomposedoftwoparts:atravelingwave行波

withanamplitudeEi0andstandingwave駐波

withanamplitude2Ei0.Becauseoftheexistenceofthetravelingwave,E1(z)doesnotgotozeroatfixeddistancesfromtheinterface界面上不為零;itmerelyhaslocationsofmaximumandminimumvalues.ThelocationsofmaximumandminmumE1(z)areconvenientlyfoundbyrewritingE1(z)asFordissipationless無(wú)損耗

media,1and2arereal,makingbothandalsoreal實(shí)數(shù).However,canbepositiveornegative.Considerthefollowingtwocases.1.0(2>1).92.<0(2<1).Theratioofthemaximumvaluetotheminimumvalueoftheelectricfieldintensityofastandingwaveiscalledthestanding-waveratio(SWR),S.駐波比AninverserelationisWhilethevalueofrangesfrom-1to+1,thevalueofSrangesfrom1to.ItiscustomarytoexpressSonalogarithmicscale對(duì)數(shù)坐標(biāo).Thestanding-waveratioindecibelsis20log10S.01z10Themagneticfieldintensityinmedium1isobtainedbycombingHi(z)andHr(z),respectively:Inadissipationless無(wú)損耗

medium,isreal;andH1(z)willbeaminimumatlocationswhereE1(z)isamaximum,andviceversa.Inmedium2,(Et,Ht)constitutethetransmittedwavepropagatingin+z-direction.Wehave112.NormalIncidenceatMultipleDielectricInterfaces⊙⊙xzyanraniErEiHrHiReflectedwaveIncidentwaveMedium1(1,1)z=0⊙E3H3an3TransmittedwaveMedium2(2,2)Medium3(3,3)⊙a(bǔ)ni+E2+H2+an2-E2-H2-z=dAssuminganx-polarizedincidentfield,thetotalelectricfieldintensityinmedium1canbealwaysbewrittenasthesumoftheincidentcomponentaxEi0e-j1zandareflectedaxEr0ej1z

component:TheH1(z)inregion1thatcorrespondstotheE1(z)is12Theelectricandmagneticfieldsinregion2canalsoberepresentedbycombinationsofforwardandbackwardwaves:Inregion3,onlyaforwardwavetravelingin+z-directionexists.ThusThereareatotaloffourunknownamplitudes:Er0,E2+

,E2-

,andE3+

.Theycanbedeterminedbysolvingthefourboundary-conditionequationsrequiredbythecontinuityofthetangentialcomponentsoftheelectricandmagneticfields.132.1waveimpedanceofthetotalfieldWedefinethewaveimpedanceofthetotalfieldatanyplaneparalleltotheplaneboundaryastheratioofthetotalelectricfieldintensitytothetotalmagneticfieldintensity.Withaz-dependentuniformplanewave,aswasshowninfigure,wewrite,ingeneral,Forasinglewavepropagatinginthe+z-directioninanunboundedmedium,thewaveimpedanceequalstheintrinsicimpedance,,ofthemedium;forasinglewavetravelinginthe–z-direction,itis–forallz.14Theirratiodefinesthewaveimpedanceofthetotalfieldinmedium1atadistancezfromtheboundaryplane:Whichisobviouslyafunctionofz.Adistancez=-ltotheleftoftheboundaryplane,Usingthedefinitionof=(2-1)/(2+1),weobtainWhichcorrectlyreducesto1when2=1.152.1impedancetransformationwithmultipledielectrics⊙⊙xzyanraniErEiHrHiReflectedwaveIncidentwaveMedium1(1,1)z=0⊙E3H3an3TransmittedwaveMedium2(2,2)Medium3(3,3)⊙a(bǔ)ni+E2+H2+an2-E2-H2-z=dThewaveimpedanceofthetotalfieldinmedium2attheleft-handinterfacez=0canbefoundfromtherightsideofEq.(8-117)byreplacing2by3,1by2,1by2,andl

byd.thus,Asfarasthewaveinmedium1isconcerned,itencountersadiscontinuityatz=0andthediscontinuitycanbecharacterizedbyaninfinitemediumwithanintrinsicimpedanceZ2(0).16Theeffectivereflectioncoefficientatz=0fortheincidentwaveinmedium1isWenotethat0differsfromonlyinthat2hasbeenreplacedbyZ2(0).Hencetheinsertionofadielectriclayerofthicknessdandintrinsicimpedance2infrontofmedium3,whichhasintrinsicimpedance3,hastheeffectoftransforming3toZ2(0).Given1and3,0canbea