Scattering of scalar waves by two-dimensional gratings of arbitrary shape: application to rough surfaces at near-grazing incidence

Abstract

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.

<title>Study of backscatter scattering cross section from ocean-like surfaces near grazing angle</title>

“…where n ao+2irn/L (5) _yn =/k2-a (6) The parameter a0 = k sin 9, a = k sin 9 and -y,, = k cos 9, where O is the scattering angle of the nth order diffracted wave. For specular reflection 0n0 6 (for V1).…”

“…The work has been further extended to the case of general media{5J and for the case of two dimensional surface, albeit for the case of scalar wave [6]. z Figure 1: Scattering geometry the same kind of surface as that used in the DeSanto method, but instead of solving the scattering problem in Fourier space, we do it in real space.…”

Statistical moments for rough surface scatter from two-way parabolic integral equation at low grazing angles

“…Wave scattering from irregular surfaces continues to present formidable theoretical and computational challenges [1][2][3][4][5][6][7], especially with regard to analytical treatment of statistics, and numerical solution for wave incidence at low grazing angles [8][9][10][11][12][13], where the insonified/illuminated region may become very large. Computationally, the cost of the necessary matrix inversion scales badly with wavelength and domain size and can rapidly become prohibitive; this is compounded by the large number of Green's function evaluations, whose overall cost is therefore sensitive to the form which this function takes.…”