Inverse Electromagnetic Diffraction by Biperiodic Dielectric Gratings
It provides a simple, fast, and stable solution to an ill-posed inverse problem in electromagnetics, enabling high-resolution surface reconstruction for applications like optics and nanophotonics.
The paper develops a novel method to reconstruct biperiodic dielectric grating surfaces from a single incident field, achieving super-resolved resolution with fast Fourier transform-based computation.
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.