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SCATTERING OF ELECTROMAGNETIC WAVES BY THIN HIGH CONTRAST DIELECTRICS: EFFECTS OF THE OBJECT BOUNDARY
Journal article   Open access

SCATTERING OF ELECTROMAGNETIC WAVES BY THIN HIGH CONTRAST DIELECTRICS: EFFECTS OF THE OBJECT BOUNDARY

David M. Ambrose and Shari Moskow
Communications in mathematical sciences, v 11(1), pp 293-314
01 Mar 2013
DOI: https://doi.org/10.4310/CMS.2013.v11.n1.a9
url
https://doi.org/10.4310/cms.2013.v11.n1.a9View
Published, Version of Record (VoR)Maybe Open Access (Publisher Bronze),  Open
url
https://doi.org/10.4310/CMS.2013.v11.n1.a9View
Published, Version of Record (VoR) Open

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
We study the scattered field from a thin high contrast dielectric volume of finite extent. The waves are modeled by the full three dimensional 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 third component of the electric field (which corresponds to the direction perpendicular to the slab) goes to zero inside the slab. We propose a new two-dimensional limiting equation as a first-order computational technique.

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Mathematics, Applied
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