24格林函数和波导介质柱分析

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1、DerivationofGreen’sFunction參Theunitincidentr£10-to-zwaveis£；,=sin^^exp(-y/?1z)exp(-y^z)H卜-豆sin0)/J--cosf—1exp(-y^,z)_卿aa)where如2pe-(7r/a)2=yjk2-(7r/af=-jr}參ThescatteredfieldduetotheinducedcurrentJ(x,z)onthepostisEs=-jcoA-^^/?=丄VxAA•Letg(x,zx,z)representtheGre

2、en’sfunctionforA(x,z),viz.A(%,z)=//JJ(x，,zz)^(x,z

3、/,z)dlfwhichsatisfiesthenthe▽2a+々2a=—//7•Sincetheinducedcurrentonlyhasthey-component,J=yjy(x,z),magneticvectorpotentialbecomesA=yAy(x,z)whichsatisfiesd2Ad2Alz+l^+kA>=~^andA'、(x,z)=//J,Jy(xz，)

4、

5、ewehave/z(Jv(/，z,)

6、++[?(义,zI/，z')d7,=—///、,U，Z)替+¥+k、=l麟—z’)Multiplicationwithsin(z?7rx/67)onbothsidesandintegrationoverthewidesideoftheguideyieldsasindx=-S{x-x)8{z-zz)sinIdxa>JoIaItfollowsfromthepartialintegrationformulathat.njrxa7sindx=-ag(x9zx9z)sin(^-d

7、xa)Jovahencedz2g(x,zx,zz)sinzn7rx、6tr=-sin

8、n7lXS(z-zf)aDefineanauxiliaryfunctionQnasg/zI

9、)O)£dHs-dH1d2AydydzIjcopedxdy=0E【=dHsxdH)O)£dzdx一4jco/^edy2+kA=-jo)AyE：dH:，dHsxJO)£dxdyjjcojnedydzOnthepost，theDirichletboundaryconditionforE;isz=z，+2=2SinceisrelatedtoA=yAy(x,z)byEy=-jo)AythentheDirichletboundaryconditiononthepostforAisA.2=2»+A.2=2’•Itisfound

10、fromAv(x,z)=/zj7v(x,z)g(x,zxz)dl"thattheDirichletboundaryconditiononthepostforgis1(3A,dAy}==—z=zZ=2AL办dz)•TheDirichletboundaryconditiononthepostforQnisobtainedbyusing(z

11、/，/)=£《(％，z

12、/，/)sinn7TXdxgivingC,

13、2=Z=Qnz=^TheNeumannboundaryconditionsonthepostforQcanbe

14、determinedasfollows=_siniZ!££

15、j(z_/12=2dz12=2=-sin二-sinn7rx2=22=2Theboundaryvalueproblem(BVP)forQnissummarizedasS(z-z--sin2=r=-sin參ThesolutiontotheboundaryvalueproblemforQnIssetbelow.Qn(z

16、/，z)=zz

17、rstkindforQngivesrisetoQnz^=aJ2=-an(x,/)exp(-说/)=bn(xz)exp^j/3nz)參TheboundaryconditionofsecondkindforQflgivesdzz=z•十=-sinnjtxa(llTTY“,,(/，Z’)(-j•及)exp(-y及z’)-/?,,(/，z’XjT?