Modified electromagnetic transmission eigenvalues in inverse scattering theory

TL;DR

This paper introduces a new eigenvalue problem in inverse scattering theory derived from Maxwell's equations, enabling the determination of eigenvalues from scattering data for nondestructive testing.

Contribution

It proposes a novel eigenvalue problem related to Maxwell's equations that allows eigenvalues to be identified from scattering measurements, expanding inverse scattering methods.

Findings

Eigenvalues are shown to be discrete.

Eigenvalues can be determined from measured scattering data.

The auxiliary problem facilitates regularity and Fredholm properties.

Abstract

A recent problem of interest in inverse problems has been the study of eigenvalue problems arising from scattering theory and their potential use as target signatures in nondestructive testing of materials. Towards this pursuit we introduce a new eigenvalue problem related to Maxwell's equations that is generated from a comparison of measured scattering data to that of a non-standard auxiliary scattering problem. This choice of auxiliary problem permits the application of regularity results for Maxwell's equations in order to show that a related interior transmission problem possesses the Fredholm property, which is used to establish that the eigenvalues are discrete. We investigate the properties of this new class of eigenvalues and show that the eigenvalues may be determined from measured scattering data, concluding with a simple demonstration of this fact.