Scaling and renormalization in transmittance of thin metal films near the percolation threshold

Recent transmittance measurements of thin metal films near the percolation threshold Pc [Y. Yagil and G. Deutscher, Thin Solid Films 152, 456 (1987)] are interpreted by scaling arguments reflecting the special structure of the film near Pc. Based on the claim that the relevant length scale over which the optical properties are measured is the optical wave number 1/k=λ/2π, we present an argument showing how the optical transmittance scales with this quantity. Our interpretation, based on real-space renormalization, yields a power law wavelength dependence near the percolation threshold, with a coefficient that vanishes at Pc.