Communications in Mathematical Sciences

Volume 15 (2017)

Number 4

Scattering of electromagnetic waves by thin high contrast dielectrics II: Asymptotics of the electric field and a method for inversion

Pages: 1041 – 1053

DOI: https://dx.doi.org/10.4310/CMS.2017.v15.n4.a6

Authors

David M. Ambrose (Department of Mathematics, Drexel University, Philadelphia, Pennsylvania, U.S.A.)

Jay Gopalakrishnan (Portland State University, Portland, Oregon, U.S.A.)

Shari Moskow (Department of Mathematics, Drexel University, Philadelphia, Pennsylvania, U.S.A.)

Scott Rome (Department of Mathematics, Drexel University, Philadelphia, Pennsylvania, U.S.A.)

Abstract

We consider the full time-harmonic Maxwell equations in the presence of a thin, highcontrast dielectric object. As an extension of previous work by two of the authors, we continue to study limits of the electric field as the thickness of the scatterer goes to zero simultaneously as the contrast goes to infinity. We present both analytical and computational results, including simulations which demonstrate that the interior transverse component of the electric field has limit zero, and a rigorous asymptotic approximation accurate outside of the scatterer. Finally, we propose an inversion method to recover the geometry of the scatterer given its two-dimensional plane and we present numerical simulations using this method.

Keywords

scattering, Maxwell’s equations, asymptotics, thin dielectric, inverse problem, perfectly matched layer

2010 Mathematics Subject Classification

35C20, 45E99, 78A45, 78A46

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Published 16 May 2017