On the direct and inverse electromagnetic scattering in a parallel-plate waveguide

TL;DR

This paper provides a rigorous theoretical framework for electromagnetic scattering in a parallel-plate waveguide, establishing well-posedness of the direct problem and uniqueness of the inverse problem using advanced mathematical tools.

Contribution

It introduces an exact transparent boundary condition and proves the well-posedness and uniqueness results for the direct and inverse scattering problems in the waveguide.

Findings

Well-posedness of the direct scattering problem established.

Uniqueness of the inverse obstacle problem demonstrated.

Explicit series expansion of the Calderón operator provided.

Abstract

This paper devotes to providing rigorous theoretical analysis of the wellposedness of the direct problem and the uniqueness of the inverse problem of electromagnetic scattering in a parallel-plate waveguide. The direct problem is reduced to an equivalent boundary value problem on a bounded domain by introducing an exact transparent boundary condition in terms of the electric-to-magnetic Calder\'on operator which can be explicitly represented as a series expansion. Then the wellopsedness of the reduced problem in appropriate Sobolev spaces is proved via the variational approach provided by some necessary properties of the Calder\'on operator and Helmholtz decomposition. Relying on the Green's representation formula and a reciprocity relation, the probe method, finally, is utilized to show the uniqueness of the inverse obstacle problem.