Scattering from rough surfaces at low-grazing angles: Rigorous solution for local perturbation of a plane interface

We address here the numerical solution of the rigorous problem of the scattering of time-harmonic electromagnetic waves from a rough surface separating two homogeneous media at low-grazing incidence and scattering angles. In general, based on a boundary integral formalism, the scattering problem is reduced to the search of fictitious surface currents, which radiate the scattered field in the upper medium. The statistical properties of the scattered field are derived from a Monte-Carlo process which requires solving a large number of deterministic problems. The area of the illuminated surface samples is obviously limited by numerical requirements. To restrict the size of the scattering problem, one may either bound the support of the surface roughness or that of the incident field. The latter is very difficult under low-grazing incidence, since even a collimated beam illuminates a large area. This is why we have considered the model of the local rough perturbation of a plane enlightened by a plane wave.