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ID:27418732
大小:495.18 KB
页数:14页
时间:2018-12-03
《24格林函数和波导介质柱分析》由会员上传分享,免费在线阅读,更多相关内容在学术论文-天天文库。
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(^-d7、xa)Jovahencedz2g(x,zx,zz)sinzn7rx、6tr=-sin8、n7lXS(z-zf)aDefineanauxiliaryfunctionQnasg/zI)=J(:《(x,zI/,z’)sin丨dxwhichshouldsatisfywhereW、2-Ja)/H£=-jrnThescatteredH-fieldwillbeHs=—VxAAor丄M//dz1(dAvdAzjUdzdx=0//dxdy1A4V.//dx•AndthescatteredE-fieldisVxHorE:=—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’•Itisfound10、fromAv(x,z)=/zj7v(x,z)g(x,zxz)dl"thattheDirichletboundaryconditiononthepostforgis1(3A,dAy}==—z=zZ=2AL办dz)•TheDirichletboundaryconditiononthepostforQnisobtainedbyusing(z11、/,/)=£《(%,z12、/,/)sinn7TXdxgivingC,13、2=Z=Qnz=^TheNeumannboundaryconditionsonthepostforQcanbe14、determinedasfollows=_siniZ!££15、j(z_/12=2dz12=2=-sin二-sinn7rx2=22=2Theboundaryvalueproblem(BVP)forQnissummarizedasS(z-z--sin2=r=-sin參ThesolutiontotheboundaryvalueproblemforQnIssetbelow.Qn(z16、/,z)=zz17、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?
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(^-d7、xa)Jovahencedz2g(x,zx,zz)sinzn7rx、6tr=-sin8、n7lXS(z-zf)aDefineanauxiliaryfunctionQnasg/zI)=J(:《(x,zI/,z’)sin丨dxwhichshouldsatisfywhereW、2-Ja)/H£=-jrnThescatteredH-fieldwillbeHs=—VxAAor丄M//dz1(dAvdAzjUdzdx=0//dxdy1A4V.//dx•AndthescatteredE-fieldisVxHorE:=—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’•Itisfound10、fromAv(x,z)=/zj7v(x,z)g(x,zxz)dl"thattheDirichletboundaryconditiononthepostforgis1(3A,dAy}==—z=zZ=2AL办dz)•TheDirichletboundaryconditiononthepostforQnisobtainedbyusing(z11、/,/)=£《(%,z12、/,/)sinn7TXdxgivingC,13、2=Z=Qnz=^TheNeumannboundaryconditionsonthepostforQcanbe14、determinedasfollows=_siniZ!££15、j(z_/12=2dz12=2=-sin二-sinn7rx2=22=2Theboundaryvalueproblem(BVP)forQnissummarizedasS(z-z--sin2=r=-sin參ThesolutiontotheboundaryvalueproblemforQnIssetbelow.Qn(z16、/,z)=zz17、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?
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)=J(:《(x,zI/,z’)sin丨dxwhichshouldsatisfywhereW、2-Ja)/H£=-jrnThescatteredH-fieldwillbeHs=—VxAAor丄M//dz1(dAvdAzjUdzdx=0//dxdy1A4V.//dx•AndthescatteredE-fieldisVxHorE:=—
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)=zz17、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?
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?
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