OPTICAL-RESPONSE OF A THIN-FILM WITH ARBITRARY DETERMINISTIC ROUGHNESS OF THE INTERFACES

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