Scalar wave scattering from two-dimensional, randomly rough surfaces

We study scalar waves scattered from self-affine and Gaussian correlated surfaces. The simulations are performed using rigorous simulation of the integral equations derived from the Helmholtz equation, describing a scalar wave above a non-penetrable surface with a hard wall or free surface boundary condition.An incident, Gaussian shaped beam is scattered from the surface, and the full angular distribution of the scattered intensity is obtained. Self-affine and Gaussian correlated random surfaces are generated, and the resulting scattered intensity is averaged over a large number of surfaces (in the order $N_s=3000$), using the ergodicity of the surface.Compared with analytical calculation of the scattered intensity in the Kirchhoff approximation, our approach gives similar results for less rough surfaces. Compared with simulations of electromagnetic waves scattered from a perfect conductor, without recording the polarisation of the scattered light, our simulations give similar results when using a hard wall boundary condition.We observe phenomena such as specular scattering for less rough surfaces, diffuse forward scattering for more rough surfaces and enhanced backscattering for surfaces where waves scattered multiple times by the surface roughness gives a large contribution to the scattered intensity