Uniqueness in determining binary grating profiles and refractive indices with a single incoming wave

TL;DR

This paper proves that the shape and refractive index of a binary grating can be uniquely identified using data from a single incident wave, advancing inverse diffraction problem theory.

Contribution

It introduces a novel proof of uniqueness for determining binary grating profiles and refractive indices from limited near-field data in TE polarization.

Findings

Unique determination of binary grating and refractive index from one wave.

Application of corner singularity analysis to inverse diffraction problems.

Advances in corner scattering theory for non-convex domains.

Abstract

We investigate inverse diffraction problems for penetrable gratings in a piecewise constant medium. In the TE polarization case, it is proved that a binary grating profile together with the refractive index beneath it can be uniquely determined by the near-field observation data incited by a single plane wave and measured on a line segment above the grating. Our approach relies on the expansion of solutions to the Helmholtz equation and the corner singularity analysis of solutions to the inhomogeneous Laplace equation with a piecewise continuous source term in a sector. This paper also contributes to corner scattering theory for the Helmholtz equation in a special non-convex domain.