On the scattering by a biperiodic structure
Gang Bao, David C. Dobson · Proceedings of the American Mathematical Society · 2000
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 defined by a bounded measurable dielectric coefficient. Given the structure and a time-harmonic electromagnetic plane wave incident on the structure, the scattering (diffraction) problem is to predict the field 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 $W^{1,2}$.