Holey random walks: Optics of heterogeneous turbid composites

Tomas Svensson, Kevin Vynck, Marco Grisi, Romolo Savo, Matteo Burresi, and Diederik S. Wiersma
Phys. Rev. E 87, 022120 – Published 15 February 2013

Abstract

We present a probabilistic theory of random walks in turbid media with nonscattering regions. It is shown that important characteristics such as diffusion constants, average step lengths, crossing statistics, and void spacings can be analytically predicted. The theory is validated using Monte Carlo simulations of light transport in heterogeneous systems in the form of random sphere packings and good agreement is found. The role of step correlations is discussed and differences between unbounded and bounded systems are investigated. Our results are relevant to the optics of heterogeneous systems in general and represent an important step forward in the understanding of media with strong (fractal) heterogeneity in particular.

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  • Received 13 November 2012

DOI:https://doi.org/10.1103/PhysRevE.87.022120

©2013 American Physical Society

Authors & Affiliations

Tomas Svensson1,*, Kevin Vynck1,†, Marco Grisi1,‡, Romolo Savo1, Matteo Burresi1,2, and Diederik S. Wiersma1,2

  • 1European Laboratory for Non-Linear Spectroscopy, University of Florence, Via Nello Carrara 1, 50019 Sesto Fiorentino, Firenze, Italy
  • 2Istituto Nazionale di Ottica, Consiglio Nazionale delle Ricerche, Largo Fermi 6, 50125 Firenze, Firenze, Italy

  • *svensson@lens.unifi.it
  • Present address: Institut Langevin, ESPCI ParisTech, 1 rue Jussieu, 75005 Paris, France.
  • Present address: Swiss Federal Institute of Technology of Lausanne (EPFL), Switzerland.

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Issue

Vol. 87, Iss. 2 — February 2013

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