The European Physical Journal E

, Volume 18, Issue 1, pp 123–131

Photon channelling in foams

Authors

    • Fachbereich PhysikUniversität Konstanz
  • MF Miri
    • Institute for Advanced Studies in Basic Sciences
  • H. Stark
    • Fachbereich PhysikUniversität Konstanz
Original Article

DOI: 10.1140/epje/i2005-10034-6

Cite this article as:
Schmiedeberg, M., Miri, M. & Stark, H. Eur. Phys. J. E (2005) 18: 123. doi:10.1140/epje/i2005-10034-6

Abstract.

Experiments by Gittings, Bandyopadhyay and Durian (Europhys. Lett. 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 et al. without any free parameters. It links the photon's path-length fraction f in the liquid phase to the liquid fraction ɛ. 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 ɛ.

PACS.

05.40.Fb Random walks and Levy flights82.70.Rr Aerosols and foams42.68.Ay Propagation, transmission, attenuation, and radiative transfer05.60.-k Transport processes

Copyright information

© EDP Sciences, Società Italiana di Fisica and Springer-Verlag 2005