Photon Channelling in Foams

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 $\epsilon$.

9 pages, minor changes

Cited by in corpus (8)

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• Holey Random Walks: Optics of Heterogeneous Turbid Composites
• Gaussian and non-Gaussian speckle fluctuations in the diffusing-wave spectroscopy signal of a coarsening foam
• Superdiffusion in a Honeycomb Billiard
• Persistent random walk on a site-disordered one-dimensional lattice: Photon subdiffusion
• Diffusive transport of light in two-dimensional granular materials
• Persistent random walk on a one-dimensional lattice with random asymmetric transmittances
• Diffusive transport of light in three-dimensional disordered Voronoi structures