Scattering of electromagnetic waves by thin high contrast dielectrics: effects of the object boundary

Abstract

We study the scattered field from thin high contrast dielectrics modeled by the full time-harmonic Maxwell equations while accounting for material boundaries. We derive a formulation of Lippmann-Schwinger type for a dielectric scatterer; this formulation has an additional surface term to account for the material discontinuities. The layer potential operator resulting from this surface term is shown to converge in a weak sense to an explicitly computable limit as the thickness of the domain approaches zero. By properly accounting for the boundary effects, we show two results about the thin high contrast limit: First, the normal component of the electric field’s interior trace on the lateral boundary approaches zero. Second, the perpendicular component of the electric field goes to zero inside the slab. We propose a new two-dimensional limiting equation as a first-order computational technique.