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# Communications in Mathematical Sciences

## Volume 11 (2013)

### Number 1

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

Pages: 293 – 314

DOI: http://dx.doi.org/10.4310/CMS.2013.v11.n1.a9

#### Authors

#### Abstract

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.

#### Keywords

scattering, Maxwell’s equation, asymptotics, thin dielectric

#### 2010 Mathematics Subject Classification

34E05, 45Exx, 78A45