Eigenvalue problems in inverse electromagnetic scattering theory

TL;DR

This paper explores the use of eigenvalues as target signatures in inverse electromagnetic scattering for anisotropic media, aiming to address non-uniqueness issues by analyzing three different eigenvalue sets.

Contribution

It introduces and compares three types of eigenvalues—electric far field, transmission, and Stekloff—as novel target signatures for inverse scattering problems.

Findings

Eigenvalues can serve as effective target signatures.

Comparison of three eigenvalue sets for inverse problems.

Potential for improved uniqueness in scattering solutions.

Abstract

The inverse electromagnetic scattering problem for anisotropic media in general does not have a unique solution. A possible approach to this problem is through the use of appropriate "target signatures," i.e. eigenvalues associated with the direct scattering problem that are accessible to measurement from a knowledge of the scattering data. In this paper we shall consider three different sets of eigenvalues that can be used as target signatures: 1) eigenvalues of the electric far field operator, 2) transmission eigenvalues and 3) Stekloff eigenvalues.