Diffraction from anisotropic random rough surfaces

The diffraction beam from an anisotropic, random, rough surface is investigated. Two kinds of anisotropic surfaces with either a correlation-length anisotropy or a scaling anisotropy are considered. For the correlation-length anisotropic surface with an isotropic scaling, the shape of the diffraction beam directly reflects the surface anisotropy under any diffraction condition. However, for the correlation-length anisotropic surface with an anisotropic scaling, the anisotropic scaling exponents may alter the anisotropy in the diffraction beam shape, sometimes even rotating the direction of anisotropy as the diffraction condition q_⊥w changes. Here q_⊥ and w are the momentum transfer perpendicular to the surface and the interface width, respectively. This result demonstrates that one must be cautious when analyzing anisotropic diffraction beams. These results also provide a way to differentiate experimentally the correlation length anisotropy from the scaling anisotropy in anisotropic rough surfaces.