负介电常数球的镜像理论
Image theory for a sphere with negative permittivity
摘要：
本文提出了一种在相对介电常数为全复值$ε=ε'+iε''$时，介质球外点电荷的成象系统。标准的图像积分解决方案的点电荷外的电介质球涉及的图像点电荷加上线源示出发散为$ε'<-1$，并提出了这种情况下，涉及图像多极的无穷大幅度，正则化发散线积分的校正。对于正整数$n$，这些多极子的数量取决于$ε$相对于谐振值$ε=-1-1/n$的位置。还考虑了内电位源和偶极子源。
英文摘要：
An image system for a point charge outside a dielectric sphere is presented for all complex values of relative permittivity $ε=ε'+iε''$. The standard image integral solution of a point charge outside a dielectric sphere involving an image point charge plus a line source is shown to diverge for $ε'<-1$, and a correction is proposed for this case, involving image multipoles of infinite magnitude that regularise the divergent line integral. The number of these multipoles depends on the position of $ε$ relative to the resonant values $ε=-1-1/n$ for positive integer $n$. The internal potential and dipole sources are also considered.
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