Scattering of electromagnetic plane waves from rough periodic multilayered films

I use the Rayleigh-Fano theory to calculate the optical response of a stack of N thin films with rough interfaces, defined by arbitrary periodic functions of the same period, bounded by two semi-infinite media. Each medium is assumed to be homogeneous, isotropic, local, and linear and characterized by a frequency-dependent complex dielectric constant. I derive two matrix equations that relate the reflected and the transmitted fields to the incident wave. These matrices can be calculated in a recursive way. The solution involves Fourier coefficients of functions that are dependent on the roughness profiles. This treatment is valid for both TM(p) or TE(s) polarizations. I apply this formulation to some particular cases.