Dielectric and optical properties close to the percolation threshold.

Abstract

We have analyzed the dielectric and conductivity properties of a metal-insulator composite, using the Bruggemann approximation. We have concluded that it is possible to predict the existence of an optical threshold at a concentration ${\mathit{p}}^{\mathrm{*}}$ slightly higher than the percolation threshold ${\mathit{p}}_{\mathit{c}}$. At that concentration, which is defined by the vanishing of the real part of the dielectric constant and which depends on the dimensionality and on the relaxation time \ensuremath{\tau}, the composite optical conductivity (or the optical absorption) is constant up to near-infrared frequencies. This result can be related to the percolation scaling laws of a mixture of resistors, self-inductors, and capacitors. We discuss recent experimental data, which indicate that the transition to a metallic regime occurs at ${\mathit{p}}^{\mathrm{*}}$.