Recovery of an embedded obstacle and the surrounding medium for Maxwell's system

TL;DR

This paper proves that an embedded obstacle and surrounding medium can be uniquely reconstructed from electromagnetic far-field data across frequencies, advancing inverse scattering theory for complex media.

Contribution

It introduces new unique recovery results for embedded obstacles and media using low-frequency expansions and harmonic analysis techniques.

Findings

Embedded obstacle can be uniquely recovered independently of the surrounding medium.

Surrounding medium can be recovered if it is piecewise homogeneous.

Results are novel in the context of inverse electromagnetic scattering.

Abstract

In this paper, we are concerned with the inverse electromagnetic scattering problem of recovering a complex scatterer by the corresponding electric far-field data. The complex scatterer consists of an inhomogeneous medium and a possibly embedded perfectly electric conducting (PEC) obstacle. The far-field data are collected corresponding to incident plane waves with a fixed incident direction and a fixed polarisation, but frequencies from an open interval. It is shown that the embedded obstacle can be uniquely recovered by the aforementioned far-field data, independent of the surrounding medium. Furthermore, if the surrounding medium is piecewise homogeneous, then the medium can be recovered as well. Those unique recovery results are new to the literature. Our argument is based on low-frequency expansions of the electromagnetic fields and certain harmonic analysis techniques.