Persistent random walk on a site-disordered one-dimensional lattice: Photon subdiffusion

TL;DR

This paper investigates photon transport on a disordered one-dimensional lattice, revealing conditions for diffusive and subdiffusive behavior, supported by simulations and proposing an experimental setup for observing photon subdiffusion.

Contribution

It introduces a model for photon random walks on disordered lattices with specific transmittance distributions, analyzing diffusive and subdiffusive regimes, and suggests an experimental realization.

Findings

Photon subdiffusion occurs depending on the transmittance distribution near zero.

Monte Carlo simulations confirm the predicted anomalous diffusion behaviors.

A dielectric film stack is proposed for experimental observation of photon subdiffusion.

Abstract

We study the persistent random walk of photons on a one-dimensional lattice of random transmittances. Transmittances at different sites are assumed independent, distributed according to a given probability density $f(t)$. Depending on the behavior of $f(t)$ near $t=0$, diffusive and subdiffusive transports are predicted by the disorder expansion of the mean square-displacement and the effective medium approximation. Monte Carlo simulations confirm the anomalous diffusion of photons. To observe photon subdiffusion experimentally, we suggest a dielectric film stack for realization of a distribution $f(t)$.