Optical properties of plane and rough interfaces in the electrostatic approximation

The optical properties of an interface with small-scale roughness (i.e. the wavelengths and the amplitudes of the modes of this roughness being smaller than the wavelength of the light) are calculated, without restriction on the local interfacial slope. The ellipticity of the reflected light (which can be measured by ellipsometry) on a rough interface with small slope is rederived; it is proportional to Σqζ12 (where ζq is the amplitude of the mode q). In this case the ellipticity is sensitive to the amplitude and the slope of the roughness. It is shown that when the interfacial slope and the deepness of the roughness increase, the interface becomes equivalent to a flat but diffuse interface, the optical properties of which can be calculated using a generalized Drude equation, taking into account the interfacial optical anisotropy.