Fresnel coefficients of a rough interface

Second-order perturbation theory has been used to compute the optical transfer coefficients of a rough dielectric interface. The derivation proceeds through classical solution of Maxwell’s equations at normal incidence. Reflection and transmission coefficients were first obtained for an interface represented by a sine profile of wave vector G interacting with a planar wave polarized perpendicular to G. Second, the expressions have been generalized to a real rough interface, i.e., the sum of sine profiles, and arbitrary polarization. We discuss the validity of the linear approximation, comparing the reflection calculated by the more general Davies–Bennett formula to that calculated by our formula. It appears that, for most real multilayer systems, this approximation is valid.