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A formalism is introduced for the non-perturbative, purely numerical,solution of the reduced Rayleigh equation for the scattering of light fromtwo-dimensional penetrable rough surfaces. As an example, we apply thisformalism to study the scattering of p- or s-polarized light from two-dimensional dielectric or metallic randomly rough surfaces by calculating thefull angular distribution of the co- and cross-polarized intensity of thescattered light. In particular, we present calculations of the meandifferential reflection coefficient for glass and silver surfaces characterizedby (isotropic or anisotropic) Gaussian and cylindrical power spectra. Theproposed method is found, within the validity of the Rayleigh hypothesis, togive reliable results. For a non-absorbing metal surface the conservation ofenergy was explicitly checked, and found to be satisfied to within 0.03%, orbetter, for the parameters assumed. This testifies to the accuracy of theapproach and a satisfactory discretization.

Numerical simulations of scattering of light from two-dimensional surfaces using the Reduced Rayleigh Equation