SCATTERING OF SCALAR WAVES BY 2-DIMENSIONAL GRATINGS OF ARBITRARY SHAPE - APPLICATION TO ROUGH SURFACES AT NEAR-GRAZING INCIDENCE

We present the numerical study of scattering of scalar waves from impenetrable two-dimensional periodic surfaces of arbitrary shape. Nearly all numerical simulations of scattering of waves from rough surfaces in the past have been limited to one-dimensional surfaces and moderate angles of incidence. By making the surface infinite and bi-periodic, it becomes possible to simulate numerically scattering from two-dimensional surfaces, even down to grazing angle. Only impenetrable surfaces are considered. Some calculations are presented, and are used to compare with the small perturbation, or Rayleigh-Rice theory. It is found that for near grazing incidence, Neumann boundary condition, the small perturbation theory gives inaccurate values, especially near the backscatter direction.