An inverse electromagnetic scattering problem for a bi-periodic inhomogeneous layer on a perfectly conducting plate

TL;DR

This paper addresses the unique reconstruction of a periodic inhomogeneous medium on a conducting plate using electromagnetic scattering data, employing eigenvalue analysis of a Sturm-Liouville problem without relying on TE or TM polarization assumptions.

Contribution

It introduces a novel approach to identify the refractive index through eigenvalues and eigenfunctions, extending inverse scattering theory for periodic media.

Findings

Established an orthogonal relation for refractive indices.

Proposed a method to determine the refractive index using eigenvalues.

Demonstrated uniqueness in reconstructing the inhomogeneous layer.

Abstract

This paper is concerned with uniqueness for reconstructing a periodic inhomogeneous medium covered on a perfectly conducting plate. We deal with the problem in the frame of time-harmonic Maxwell systems without TE or TM polarization. An orthogonal relation for two refractive indices is obtained, and then inspired by Kirsch's idea, the refractive index can be identified by utilizing the eigenvalues and eigenfunctions of a quasi-periodic Sturm-Liouville eigenvalue problem.