Diffusion of Light in Two-dimensional Granular Materials

We study diffusive light transport in a two dimensional packing of monodisperse disks. Ray optics approximation is employed to follow a light beam or photon as it is transmitted or reflected by the grains. We present an analytic expression for the transport-mean-free path based on persistent random walk of photons in a packing of disks and express the diffusion constant of photons in terms of the refractive indices of grains and host medium, grain diameter, and packing fraction. Our analytical results are examined with numerical simulations. The derived results are beneficial for better understanding of the dynamics of granular systems.