On the relation between the coefficients and solutions for a diffraction problem

Abstract

Consider the diffraction of a time harmonic wave incident on a grating (periodic) structure. An inverse diffraction problem is to determine the grating surface from measured reflected and transmitted waves away from the structure. The surface is characterized completely by the dielectric coefficient of the medium and thus by the coefficients of the model equation. The goal of this paper is to examine regularity properties for the forward map which maps the coefficients to the solutions of the model, where no restrictions on the smoothness of the grating (interface) surfaces are assumed. The results are crucial in the study of the inverse problem via optimization methods.