Factorization Method for Electromagnetic Inverse Scattering from Biperiodic Structures

We investigate the Factorization method as an analytical as well as a numerical tool to solve inverse electromagnetic wave scattering problems from penetrable biperiodic structures in three dimensions. This method constructs a simple criterion whether a given point in space lies inside or outside the penetrable biperiodic structure, yielding a fast imaging algorithm. The required data consists of tangential components of Rayleigh sequences corresponding to (measured) scattered electromagnetic fields. In our setting, the incident electromagnetic fields causing these scattered waves are plane incident electromagnetic waves. We propose on the one hand a rigorous analysis for the Factorization method in this electromagnetic plane wave setting, building upon existing results for the method in the context of inverse electromagnetic scattering from bounded objects and of scalar periodic inverse scattering problems. On the other hand, we provide, to the best of our knowledge, the first three-dimensional numerical examples for electromagnetic inverse scattering from biperiodic structures in three dimensions and consider the dependence of the method on the noise level and on the number of Rayleigh coefficients involved in the imaging process.