Rigorous solution of scattering by randomly rough surfaces: recent contributions to open problems

In this paper, we address some of the most difficult problems encountered in surface scattering. The first part is devoted to our recent work about the rigorous solution for 2D metallic surfaces. An impedance approximation has been implemented to take into account the finite conductivity of the metals, and, to deal with surfaces of arbitrary size, the beam simulation method has been generalized. But still, several problems cannot be rigorously solved in three dimensions. One of them concerns shallow metallic surfaces in optics: how taking accurately into account the propagation of surface polaritons? A second challenge consists in solving a surface scattering problem under grazing incidence. Since the field on the surface spreads out in both problems, the same answer holds. The surface current is described in the Fourier space, while the sampling of the rigorous integral equation is still achieved in the coordinate space. The number of unknowns is drastically reduced, and standard forward solvers can be used. The last problem studied here is a step towards the inverse problem. What kind of geometrical parameter describing the surface can be extracted from intensity measurements in the far field? For multi-scale rough surfaces, we show that the wavelet correlation dimension is a good candidate for such a characterization.