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1、Chapter10DipoleemissionnearplanarinterfacesTheproblemofdipoleradiationinornearplanarlylayeredmediaisofsignificancetomanyfieldsofstudy.Itisencounteredinantennatheory,singlemoleculespectroscopy,cavityquantumelectrodynamics,integratedoptics,circuitdesign(microstrips),andsurfacecontamina
2、tioncontrol.Thetheorywasalsoappliedtoexplainthestronglyz
Eprr
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µ1ε1δx
y
µnεnFigure10.1:Configurationofthedipoleproblem.Thedipoleislocatedatro=(xo,yo,zo)andtheplanarinterfacesarecharacterizedbyz=const..Thesurfaceofthetopmostlayercoincideswiththecoordinateorigin.Thepropertiesoftheupp
3、erandlowerhalf-spacesaredesignatedbytheindex1andn,respectively.12CHAPTER10.DIPOLEEMISSIONNEARPLANARINTERFACESenhancedRamaneffectofadsorbedmoleculesonnoblemetalsurfaces,andinsurfacescienceandelectrochemistryforthestudyofopticalpropertiesofmolecularsystemsadsorbedonsolidsurfaces.Detai
4、ledliteratureonthelattertopicisgiveninRef.[1].Inthecontextofnear-fieldoptics,dipolesclosetoaplanarinterfacehavebeenconsid-eredbyvariousauthorstosimulatetinylightsourcesandsmallscatteringparticles[2].Theacousticanalogueisalsoappliedtoanumberofproblemssuchasseismicinves-tigationsorult
5、rasonicdetectionofdefectsinmaterials[3].Inhisoriginalpaper[4],in1909,Sommerfelddevelopedatheoryforaradiatingdipoleorientedverticallyaboveaplanarandlossyground.Hefoundtwodifferentasymptoticsolutions:spacewaves(sphericalwaves)andsurfacewaves.ThelatterhadalreadybeeninvestigatedbyZennec
6、k[5].Sommerfeldconcludedthatsurfacewavesaccountforlong-distanceradiowavetransmissionbecauseoftheirslowerradialdecayalongtheEarth’ssurfacecomparedwithspace-waves.Later,whenspacewaveswerefoundtoreflectattheionosphere,thecontrarywasconfirmed.Nevertheless,Sommer-feld’stheoryformedthebasi
7、sforallsubsequentinvestigations.In1911H¨orschelmann[6,7],astudentofSommerfeld,analyzedthehorizontaldipoleinhisdoctoraldisser-tationandusedlikewiseexpansionsincylindricalcoordinates.Later,in1919,Weyl[8]expandedtheproblembyasuperpositionofplaneandevanescentwaves(angularspectrumrepres
8、entation),andsimilarapproa