Generalized Maxwell Garnett equations for rough surfaces

An optical model of a rough surface is made up of a layer of metal particles of sizes much smaller than a wavelength, dispersed in a dielectric medium. The metal particles are approximated by a layer of dipoles of identical dipole moment arranged in square or hexagonal planar array. The two-dimensional dipole-dipole interaction results in surface anisotropy represented by a pair of Maxwell Garnett-type equations. This surface anisotropy due to surface geometry may be a good indication of the degree of roughness of a given surface.