Vector scattering from one-dimensional periodic perfectly conducting surface: transverse magnetic polarization

Based on the Rayleigh hypothesis and Floquet's theorem, a vector method for studying electromagnetic wave scattering from a one-dimensional periodic conducting surface with tapered transverse magnetic (TM) wave incidence is presented. The fields are represented by vectors instead of scalars so that the vector behavior of scattering (such as cross polarization) can be naturally explored. The new formulation opens a wide range of applications of the method, concerning not only gratings used in TM polarization but also conical diffraction, crossed gratings, two-dimensional problems, photonic band gaps, nonlinear optics, etc. The numerical results are consistent with the T-matrix method in the particular case in which the plane of incidence is perpendicular to the generators of the surface. For the general case in which the plane of incidence is not perpendicular to generators of the surface, the proposed method obtains significant results that reveal cross-polarized and anisotropic characteristics in the scattering while the energy balance is kept satisfactory. This straightforward approach is much more efficient than the T-matrix; thus it is suitable to extend to other more involved periodic scattering problems.