Effective dielectric function of mixtures of three or more materials: a numerical procedure for computations

A numerical procedure for solving the mathematical equations that define the effective medium for a mixture of materials is presented. The basic idea is to transform the inherent complex root-finding problem into a minimization task in real space so that the method can be implemented through a standard two-dimensional minimization algorithm. This leads to general, simple and useful procedures for ellipsometric and/or spectrophotometric data analysis in the optical characterization of materials and surfaces.