Light scattering by a two-dimensional, rough penetrable medium: A mean-field theory

The problem of scattering of electromagnetic waves by two-dimensional, rand omly rough surfaces is solved by means of a mean-field theory. The results are compared with available numerical simulations and perturbative solution s. It is found that the new method is accurate for surfaces with a, dielect ric constant lower than 5 and roughness of up to half a wavelength. There a re no limitations on the slopes. The explicit form of the result permits us to analyze in simple terms the polarization and angular scattering pattern of the diffuse intensity. It is shown that the angular scattering pattern depends not only on the correlation length but also on the rms height delta , when delta is greater than one tenth of a wavelength. Finally, the theory is used to analyze the scattering pattern produced by a rough film above a mirror.