Calculation of the optical dielectric function of 2D and 3D inhomogeneous media by real space renormalization

We propose a position space renormalization group approach based on Kadanoff's block method, for the calculation of an effective dielectric function of cermet type films (3D) or island films (2D). The results obtained on simulated lattices account for both the resonant absorption and the optical cross-over corresponding to the metal-nonmetal transition. The effective dielectric function is found to obey scaling laws with critical exponents s3D = 0.75 and s2D = 1.35 for polarization terms and t3D = 2.2, t2D = 1.52 for the conduction, very close to the theoretical estimates. These models have also been applied to digitized transmission electron micrographs of 2D and 3D systems, and we obtain a very good agreement with most of the experimental data.