Optical response of a thin film with arbitrary deterministic roughness of the interfaces

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Abstract
We present a theoretical study of the optical response of a thin film with arbitrary, deterministic roughness of the interfaces (in one dimension). The three layers of the film are characterized each by a spatially nondispersive dielectric constant and magnetic permeability. The incident light may have TE(s) or TM(p) polarization. Using the Rayleigh hypothesis, we derive an integral matrix equation which relates the reflected fields, the transmitted fields, and the fields inside the thin film to the incident wave. This equation is applied to the special case of periodic corrugation, leading to a solution in terms of an infinite set of linear equations for the amplitudes of the diffracted partial waves in the three media. For aperiodic roughness the numerical solution is still given by a similar set of equations. For periodic (aperiodic) films the solution involves Fourier coefficients (Fourier integrals) of functions related to the roughness profiles. We also derive the secular equations for the polariton eigenmodes of periodic and aperiodic films.