Optical properties of semi continuous films on a substrate. Does an effective dielectric constant exist?

We present recent results on the optical properties of semi continuous metal films, and discuss the limits of validity of effective medium approaches. The optical reflectance and transmittance of percolating gold films, close to the metal-insulator transition, were measured over an extended wavelength range: 2.5–500 μm. Comparing the measured data with the predictions of the scaling model for the optical properties yields excellent agreement, while effective medium approach is shown to be non-valid close to the percolation threshold. In particular, the short length scale determined by the anomalous diffusion relation is shown to be the relevant length scale. Determination of the optical response of the films on the substrate, and of the (hypothetical) free standing films, suggests that the optical properties cannot be described by any effective dielectric constant.