Unique determination of a penetrable scatterer of rectangular type for inverse Maxwell equations by a single incoming wave

TL;DR

This paper proves that in 2D electromagnetic scattering, a single incoming wave's far-field pattern uniquely determines a rectangular-shaped penetrable scatterer, advancing inverse problem solutions.

Contribution

It establishes uniqueness results for shape identification of rectangular penetrable scatterers using only one incident wave in Maxwell equations.

Findings

Unique shape determination from a single wave in TE polarization

Extension to inverse transmission problems with Helmholtz equations

Confirmation of uniqueness for scatterers with right-angled corners

Abstract

This work is concerned with an inverse electromagnetic scattering problem in two dimensions. We prove that in the TE polarization case, the knowledge of the electric far-field pattern incited by a single incoming wave is sufficient to uniquely determine the shape of a penetrable scatterer of rectangular type. As a by-product, the uniqueness is also confirmed to inverse transmission problems modelled by scalar Helmholtz equations with discontinuous normal derivatives at the scattering interface. Keywords: Uniqueness, inverse medium scattering, Maxwell equations, one incoming wave, shape identification, right corners