Cluster plasmon resonances close to the percolation threshold: simulation versus EMA

We present the results of a 2D and 3D electrical conductivity simulation of a metal-insulator composite in the range of cluster plasmon frequencies. For the 3D simulations we use an extension of the matrix transfer method that was first introduced to calculate the percolation critical exponents in the d.c. limit. We compare these results with 2D simulations already published and the Effective Medium Approximation (EMA). In 2D, it appears that the Ping Sheng approximation is very close to the results of the simulation. In 3D, we confirm that if the EMA describe badly the wings and tails of the curve representing the enhancement of the cluster “surface plasmon” absorption. By contrast, exactly at the percolation threshold pc and in its immediate vicinity, the EMA scaling function seems to be appropriate to describe the optical quantities. The maximum of the absorption occurs at p∗ > pc. For that concentration, the optical properties are practically independent of the frequency.