Effective medium theory for embedded obstacles in electromagnetic scattering with applications

TL;DR

This paper introduces a new theoretical framework for approximating embedded obstacles in electromagnetic scattering by effective isotropic media, aiding inverse problem analysis in complex materials.

Contribution

It develops a novel method to model embedded obstacles as effective isotropic media with verified estimates, advancing inverse EM scattering theory.

Findings

Embedded obstacles can be effectively approximated by isotropic media.

Derived sharp estimates for the approximation accuracy.

Implications for inverse scattering problems with complex media.

Abstract

This paper focuses on the time-harmonic electromagnetic (EM) scattering problem in a general medium which may possess a nontrivial topological structure. We model this by an inhomogeneous and possibly anisotropic medium with embedded obstacles and the EM waves cannot penetrate inside the obstacles. Such a situation naturally arises in studying inverse EM scattering problems from complex mediums with partial boundary measurements, or inverse problems from EM mediums with metal inclusions. We develop a novel theoretical framework by showing that the embedded obstacles can be effectively approximated by a certain isotropic medium with a specific choice of material parameters. We derive sharp estimates to verify this effective approximation and also discuss the practical implications of our results to the inverse problems mentioned above, which are longstanding topics in inverse scattering theory.