S. Wang et P. Halevi, OPTICAL-RESPONSE OF A THIN-FILM WITH ARBITRARY DETERMINISTIC ROUGHNESS OF THE INTERFACES, Physical review. B, Condensed matter, 47(16), 1993, pp. 10815-10822
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.