Transport properties of random arrays of dielectric cylinders

We apply a recently developed approach for calculating the transport properties of random media to the case of disordered arrays of parallel oriented and normally illuminated cylinders. Within this effective-medium theory resonant scattering of the individual scatterer is treated exactly, and by using a coated cylinder as the basic scattering unit, multiple scattering contributions are incorporated in a mean-field sense. In the long-wavelength limit we are able to calculate the effective dielectric constant analytically. We compare our findings with results for periodic systems. For both “scalar” and “vector” polarization, we reliably calculate the mean-free path, the transport velocity, and the diffusion coefficient for finite frequencies for all densities of scatterers and dielectric contrasts. Furthermore, within this effective-medium approach, we present our results for the localization parameter $\overline{k}{\mathcal{l}}_{\mathrm{t}}$ for both two- and three-dimensional systems, thereby identifying the optimal parameters for observing localization.