Diffusive transport of light in two-dimensional granular materials

TL;DR

This paper models photon diffusion in a 2D granular material using ray optics, deriving an analytical expression for the transport-mean-free path and validating it through numerical simulations.

Contribution

It introduces a novel analytical formula for photon transport in granular media considering angle-dependent reflectance and polarization effects.

Findings

Analytical expression for transport-mean-free path derived.

Numerical simulations confirm the analytical model.

Dependence of photon diffusion on material parameters established.

Abstract

We study photon diffusion in a two-dimensional random packing of monodisperse disks as a simple model of granular material. We apply ray optics approximation to set up a persistent random walk for the photons. We employ Fresnel's intensity reflectance with its rich dependence on the incidence angle and polarization state of the light. We present an analytic expression for the transport-mean-free path in terms of the refractive indices of grains and host medium, grain radius, and packing fraction. We perform numerical simulations to examine our analytical result.