Inverse Electromagnetic Diffraction by Biperiodic Dielectric Gratings

TL;DR

This paper introduces a fast, stable method for reconstructing biperiodic dielectric grating surfaces from electromagnetic diffraction data, achieving super-resolved resolution with only a single incident wave.

Contribution

A novel approach for the inverse electromagnetic diffraction problem that is simple, fast, and stable, utilizing Fourier transform techniques and requiring only one incident field.

Findings

Successfully reconstructs grating surfaces with super-resolution.

Method is computationally efficient and stable.

Requires only a single incident wave for reconstruction.

Abstract

Consider the incidence of a time-harmonic electromagnetic plane wave onto a biperiodic dielectric grating, where the surface is assumed to be a small and smooth perturbation of a plane. The diffraction is modeled as a transmission problem for Maxwell's equations in three dimensions. This paper concerns the inverse diffraction problem which is to reconstruct the grating surface from either the diffracted field or the transmitted field. A novel approach is developed to solve the challenging nonlinear and ill-posed inverse problem. The method requires only a single incident field and is realized via the fast Fourier transform. Numerical results show that it is simple, fast, and stable to reconstruct biperiodic dielectric grating surfaces with super-resolved resolution.