Holey Random Walks: Optics of Heterogeneous Turbid Composites

Abstract

We present a probabilistic theory of random walks in turbid media with non-scattering 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.

References in corpus (9)

• Multiple scattering of classical waves: from microscopy to mesoscopy and diffusion
• Lévy walks and scaling in quenched disordered media
• Determination of the diffusion constant using phase-sensitive measurements
• Weak localization of light in superdiffusive random systems
• Transport and Scaling in Quenched 2D and 3D Lévy Quasicrystals
• Transmission probability through a Lévy glass and comparison with a Lévy walk
• Photon Channelling in Foams
• Observation of anisotropic diffusion of light in compacted granular porous materials
• Diffusive transport of light in two-dimensional granular materials

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• Superdiffusion and Transport in 2d-systems with Lévy Like Quenched Disorder
• Transport in quenched disorder: light diffusion in strongly heterogeneous turbid media
• Steering random walks with kicked ultracold atoms
• A Reciprocal Formulation of Nonexponential Radiative Transfer. 2: Monte Carlo Estimation and Diffusion Approximation
• Walk dimension for light in complex disordered media
• Lévy flights of photons with infinite mean free path
• Universal properties of branching random walks in confined geometries
• Diffusion of light in semitransparent media
• Probability density functions for photon propagation in a binary (isotropic-Poisson) statistical mixture with unmatched positives/negatives refractive indexes
• Quasiannealed Monte Carlo method for light transport in strongly heterogeneous media