Vector scattering from one dimensional periodic perfectly conducting surface: TE polarization

•An efficient approach to study the vector electromagnetic scattering by a 1D grating structures is proposed.•The proposed approach has much higher computational efficiency than IM and T-matrix formulations.•The proposed approach has the ability to account for the cross-polarized and anisotropic characteristic of the scattering by gratings.•The approach can be applied to solve not only the scalar scattering but also the vector electromagnetic scattering from periodic surface.•We numerically confirmed interesting behaviors of the vector wave scattering by periodic surfaces.

Based on the Rayleigh hypothesis and the Floquet's theorem, we propose a vector method for the problem of TE electromagnetic wave scattering by one-dimensional periodic conducting surface. The numerical results are consistent with the integral method and the T-matrix method in the particular case where the incidence plane is perpendicular to the row direction of the periodic surface. For the general case where the incidence plane is not perpendicular to the row direction of the surface, the proposed method obtains significant results which reveal cross-polarized and anisotropic characteristics in the scattering while the energy balance is kept satisfactory. This straight forward approach is much more efficient than the integral technique, thus suitable to be extended to other more involved periodic scattering problems.