Theoretical and computational aspects of scattering from periodic surfaces: two-dimensional transmission surfaces using the spectral-coordinate method

We consider the scattering from and transmission through a two-dimensional periodic surface. We use the spectral-coordinate (SC) method for all the computations. It was the fastest method for one-dimensional problems and proved optimal for scattering from two-dimensional surfaces where computation time can prove to be excessive. In particular, we can avoid approximation methods and solve the exact equations. The SC equations are derived for an infinite surface and reduced to coupled equations for a periodic surface which are solved numerically for the two boundary unknowns. Solutions of the SC equations for various periodic sinusoidal surface examples are studied. The surfaces vary in roughness and period. Extensive computations are included in terms of the maximum roughness slope which can be computed using the method with a fixed maximum error as a function of azimuthal angle of incidence, polar angle of incidence, wavelength-to-period ratio, density ratio and wavenumber ratio. Examples of refl...