An extended charge-current formulation of the electromagnetic transmission problem

TL;DR

This paper introduces a boundary integral equation approach for electromagnetic transmission problems that guarantees unique solutions across various wavenumber scenarios, facilitating accurate numerical simulations.

Contribution

It presents a novel extended charge-current formulation that ensures unique solutions for all relevant wavenumber combinations in electromagnetic scattering problems.

Findings

Provides a boundary integral formulation with guaranteed uniqueness.

Applicable to both smooth and non-smooth objects.

Validated through numerical examples.

Abstract

A boundary integral equation formulation is presented for the electromagnetic transmission problem where an incident electromagnetic wave is scattered from a bounded dielectric object. The formulation provides unique solutions for all combinations of wavenumbers in the closed upper half-plane for which Maxwell's equations have a unique solution. This includes the challenging combination of a real positive wavenumber in the outer region and an imaginary wavenumber inside the object. The formulation, or variants thereof, is particularly suitable for numerical field evaluations as confirmed by examples involving both smooth and non-smooth objects.