Scaling theory for the optical properties of semicontinuous metal films

Abstract

The optical properties of thin semicontinuous metal films are calculated within the framework of the scaling theory of percolation. The effective ac conductivity is calculated over a length scale determined by the optical frequency. The relevant length scale depends on the frequency through the anomalous diffusion relation. At finite frequencies the ac conductivity fluctuates over the surface of the film, resulting in fluctuations of the local optical response. These fluctuations are described by a broad bimodal distribution. The optical response of the whole film is then calculated by averaging the local contributions, using the above distribution function. We find that the intercluster capacitance is essential in understanding the optical response of a percolating film. Numerical calculations based on this model show excellent agreement with experimental data over the entire range of surface coverages.