Unusual Brownian motion of photons in open absorbing media

TL;DR

This paper develops a first-principles theory describing how photons diffuse in open absorbing media, revealing unusual Brownian motion and spatially resolved diffusion coefficients that depend on the returning probability, confirmed by simulations and experiments.

Contribution

It introduces a novel theoretical framework for photon diffusion in absorbing media, showing spatially resolved diffusion coefficients and single parameter scaling.

Findings

Photons exhibit unusual Brownian motion in absorbing media.

The diffusion coefficient depends on space via the returning probability.

The theory agrees with numerical simulations and experimental results.

Abstract

Very recent experiments have discovered that localized light in strongly absorbing media displays intriguing diffusive phenomena. Here we develop a first-principles theory of light propagation in open media with arbitrary absorption strength and sample length. We show analytically that photons in localized open absorbing media exhibit unusual Brownian motion. Specifically, wave transport follows the diffusion equation with the diffusion coefficient exhibiting spatial resolution. Most strikingly, despite that the system is controlled by two parameters -- the ratio of the localization (absorption) length to the sample length -- the spatially resolved diffusion coefficient displays novel single parameter scaling: it depends on the space via the returning probability. Our analytic predictions for this diffusion coefficient are confirmed by numerical simulations. In the strong absorption limit they agree well with the experimental results.