The inverse electromagnetic scattering problem in a piecewise homogeneous medium

TL;DR

This paper addresses the electromagnetic scattering problem in a piecewise homogeneous medium, establishing well-posedness and proving unique determination of interfaces and obstacles using far field data, generalizing previous results.

Contribution

It introduces new methods to uniquely identify interfaces and obstacles in layered media from electromagnetic far field patterns, extending prior work to more general settings.

Findings

Proved well-posedness of the direct scattering problem.

Established unique determination of interfaces from far field data.

Demonstrated the recovery of obstacles and their properties.

Abstract

This paper is concerned with the problem of scattering of time-harmonic electromagnetic waves from an impenetrable obstacle in a piecewise homogeneous medium. The well-posedness of the direct problem is established, employing the integral equation method. Inspired by a novel idea developed by Hahner [11], we prove that the penetrable interface between layers can be uniquely determined from a knowledge of the electric far field pattern for incident plane waves. Then, using the idea developed by Liu and Zhang [21], a new mixed reciprocity relation is obtained and used to show that the impenetrable obstacle with its physical property can also be recovered. Note that the wave numbers in the corresponding medium may be different and therefore this work can be considered as a generalization of the uniqueness result of [20].