Dielectric and optical properties close to the percolation threshold

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 τ, 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 ${\mathit{p}}^{\mathrm{*}}$.