Optical properties of the fluid-fluid interface

In this paper we derive formulae for the optical properties (reflection, transmission and ellipsometric coefficients) of a fluid-fluid interface. An expansion to the second order in the interfacial thickness is used. Deviations of the above-mentioned coefficients from the value found using a step function profile for the refractive index (Fresnel) are found to be the sum of three terms. The first follows from the so-called intrinsic profile using the standard theory for stratified media. The second is due to capillary waves and was already analyzed in two earlier papers [B.J.A. Zielinska, D. Bedeaux and J. Vlieger, Physica A 107 (1981) 91; 117 (1983) 28]. The third is due to the modification of the relevant correlation functions in the neigbourhood of the interface due to fluctuations with a wavelength comparable to or smaller than the bulk correlation length. A comparison is made with experimental results close to the critical point. We discuss how the introduction of the rigidity of the interface as suggested by Meunier [J. Phys. (Paris) 48 (1987) 1819] may reduce the contributions due to capillary waves to the reflection and the ellipsometric coefficients. Expressions for these coefficients are given explicitly contain both the rigidity as well as the large wavevector cutoff used by Sengers and van Leeuwen [Phys. Rev. A 39 (1989) 6346] in their analysis of the behaviour of the surface tension. The rigidity is found not to affect the scaling behaviour of these coefficients near the critical point. For zero rigidity the expressions for the capillary wave contributions reduce to those given in the two earlier papers while for an infinite cutoff wavevector they reduce to those given by Meunier.