On the scattering by a biperiodic structure

Consider scattering of electromagnetic waves by a nonmagnetic biperiodic st ructure. The structure separates the whole space into three regions: above and below the structure the medium is assumed to be homogeneous. Inside the structure, the medium is assumed to be defined by a bounded measurable die lectric coefficient. Given the structure and a time-harmonic electromagneti c plane wave incident on the structure, the scattering (diffraction) proble m is to predict the field distributions away from the structure. In this no te, the problem is reduced to a bounded domain and solved by a variational method. The main result establishes existence and uniqueness of the weak so lutions in W-1,W-2.