On the Scattering by a Biperiodic Structure

Consider scattering of electromagnetic waves by a nonmagnetic biperiodic structure. 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 de ned by a bounded measurable dielectric coe cient. Given the structure and a timeharmonic electromagnetic plane wave incident on the structure, the scattering (di raction) problem is to predict the eld distributions away from the structure. In this note, the problem is reduced to a bounded domain and solved by a variational method. The main result establishes existence and uniqueness of the weak solutions in W .