Novel Integral Equation Formulation for Scattering on Dielectric Objects Free of Low-Frequency and Oversampling Breakdowns

Abstract

In our recent work [1] we have demonstrated analytic solution of a novel Surface-Volume-Surface Electric Field Integral Equation with magnetic current (SVS-EFIE-M formulation) for the problem of Hertzian dipole radiation in the vicinity of a homogeneous non-magnetic dielectric sphere. The SVS-EFIE-M stated with respect to magnetic current $\hat{n}\times I$ on object’s surface S is shown in (1), where $\overline{\overline{G}}_{m\in}$ is the magnetic field dyadic Green’s function of the homogeneous non-magnetic space with relative permittivity $\epsilon, \overline{\overline{G}}_{e0}$ is the electric field dyadic Green’s function of free-space, and $\hat{n}\times E^{inc}$ is the tangential component of the incident electric field on the surface S. It is obtained through single-source magnetic current based surface integral representation of the electric field inside the dielectric object (see first term in (1) representing $\hat{n}\times E, E$ being the total electric field) constrained by the classical Volume-EFIE (V-EFIE) enforced on the boundary of the object for the tangential component of the electric field.