Photon Channelling in Foams

TL;DR

This paper investigates photon channelling in foams, demonstrating how total internal reflection causes light to preferentially propagate in the liquid phase, and models this behavior through simulations and theoretical relations.

Contribution

It derives a parameter-free relation linking photon path-length fraction to liquid fraction and models photon transport in disordered foams using ray optics and a random-walk approach.

Findings

Photon channelling causes superdiffusive light propagation in ordered foams.

Disorder induces a transition to diffusive behavior.

The diffusion constant depends on channel width and refractive index.

Abstract

Experiments by Gittings, Bandyopadhyay, and Durian [Europhys. Lett.\ \textbf{65}, 414 (2004)] demonstrate that light possesses a higher probability to propagate in the liquid phase of a foam due to total reflection. The authors term this observation photon channelling which we investigate in this article theoretically. We first derive a central relation in the work of Gitting {\em et al.} without any free parameters. It links the photon's path-length fraction $f$ in the liquid phase to the liquid fraction $\epsilon$. We then construct two-dimensional Voronoi foams, replace the cell edges by channels to represent the liquid films and simulate photon paths according to the laws of ray optics using transmission and reflection coefficients from Fresnel's formulas. In an exact honeycomb foam, the photons show superdiffusive behavior. It becomes diffusive as soon as disorder is introduced into the foams. The dependence of the diffusion constant on channel width and refractive index is explained by a one-dimensional random-walk model. It contains a photon channelling state that is crucial for the understanding of the numerical results. At the end, we shortly comment on the observation that photon channelling only occurs in a finite range of $\epsilon$.