Optical properties of thin films on rough surfaces

A general theory, of second order in the film thickness and surface roughness over the wavelength, is developed of the optical properties of a thin film. These properties are described by a small number of electromagnetic constitutive coefficients. Formulae for these coefficients are derived in terms of the height-height correlation functions of the upper and lower surfaces of the film, and its average thickness. The reflectance, transmittance and ellipsometric coefficient are expressed in terms of the constitutive coefficients, for arbituary angles of incidence.