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Electrostatic T-matrix for a torus on bases of toroidal and spherical harmonics. (arXiv:1904.10807v1 [physics.comp-ph])
来源于:arXiv
Semi-analytic expressions for the static limit of the $T$-matrix for
electromagnetic scattering are derived for a circular torus, expressed in both
a basis of toroidal harmonics and spherical harmonics. The scattering problem
for an arbitrary static excitation is solved using toroidal harmonics, and
these are then compared to the extended boundary condition method to obtain
analytic expressions for auxiliary $Q$ and $P$-matrices, from which
$\mathbf{T}=\mathbf{P}\mathbf{Q}^{-1}$ (in a toroidal basis). By applying the
basis transformations between toroidal and spherical harmonics, the
quasi-static limit of the $T$-matrix block $\mathbf{T}^{22}$ for
electric-electric multipole coupling is obtained. For the toroidal geometry
there are two similar $T$-matrices on a spherical basis, for computing the
scattered field both near the origin and in the far field. Static limits of the
optical cross-sections are computed, and analytic expressions for the limit of
a thin ring are derived. 查看全文>>