Transport in quenched disorder: light diffusion in strongly heterogeneous turbid media

We present a theoretical and experimental study of light transport in disordered media with strongly heterogeneous distribution of scatterers formed via non-scattering regions. Step correlations induced by quenched disorder are found to prevent diffusivity from diverging with increasing heterogeneity scale, contrary to expectations from annealed models. Spectral diffusivity is measured for a porous ceramic where nanopores act as scatterers and macropores render their distribution heterogeneous. Results agree well with Monte Carlo simulations and a proposed analytical model.Comment: 12 pages, 9 figures (significant amount of supplemental information

Diffusing-wave spectroscopy in a standard dynamic light scattering setup

Diffusing-wave spectroscopy (DWS) extends dynamic light scattering measurements to samples with strong multiple scattering. DWS treats the transport of photons through turbid samples as a diffusion process, thereby making it possible to extract the dynamics of scatterers from measured correlation functions. The analysis of DWS data requires knowledge of the path length distribution of photons traveling through the sample. While for flat sample cells this path length distribution can be readily calculated and expressed in analytical form; no such expression is available for cylindrical sample cells. DWS measurements have therefore typically relied on dedicated setups that use flat sample cells. Here we show how DWS measurements, in particular DWS-based microrheology measurements, can be performed in standard dynamic light scattering setups that use cylindrical sample cells. To do so we perform simple random-walk simulations that yield numerical predictions of the path length distribution as a function of both the transport mean free path and the detection angle. This information is used in experiments to extract the mean-square displacement of tracer particles in the material, as well as the corresponding frequency-dependent viscoelastic response. An important advantage of our approach is that by performing measurements at different detection angles, the average path length through the sample can be varied. For measurements performed on a single sample cell, this gives access to a wider range of length and time scales than obtained in a conventional DWS setup. Such angle-dependent measurements also offer an important consistency check, as for all detection angles the DWS analysis should yield the same tracer dynamics, even though the respective path length distributions are very different. We validate our approach by performing measurements both on aqueous suspensions of tracer particles and on solidlike gelatin samples, for which we find our DWS-based microrheology data to be in good agreement with rheological measurements performed on the same samples

L\'evy flights of photons in hot atomic vapours

Properties of random and fluctuating systems are often studied through the use of Gaussian distributions. However, in a number of situations, rare events have drastic consequences, which can not be explained by Gaussian statistics. Considerable efforts have thus been devoted to the study of non Gaussian fluctuations such as L\'evy statistics, generalizing the standard description of random walks. Unfortunately only macroscopic signatures, obtained by averaging over many random steps, are usually observed in physical systems. We present experimental results investigating the elementary process of anomalous diffusion of photons in hot atomic vapours. We measure the step size distribution of the random walk and show that it follows a power law characteristic of L\'evy flights.Comment: This final version is identical to the one published in Nature Physic

Scattering lengths and universality in superdiffusive L\'evy materials

We study the effects of scattering lengths on L\'evy walks in quenched one-dimensional random and fractal quasi-lattices, with scatterers spaced according to a long-tailed distribution. By analyzing the scaling properties of the random-walk probability distribution, we show that the effect of the varying scattering length can be reabsorbed in the multiplicative coefficient of the scaling length. This leads to a superscaling behavior, where the dynamical exponents and also the scaling functions do not depend on the value of the scattering length. Within the scaling framework, we obtain an exact expression for the multiplicative coefficient as a function of the scattering length both in the annealed and in the quenched random and fractal cases. Our analytic results are compared with numerical simulations, with excellent agreement, and are supposed to hold also in higher dimensionsComment: 6 pages, 8 figure

Diffusive transport of light in two-dimensional granular materials

We study photon diffusion in a two-dimensional random packing of monodisperse disks as a simple model of granular material. We apply ray optics approximation to set up a persistent random walk for the photons. We employ Fresnel's intensity reflectance with its rich dependence on the incidence angle and polarization state of the light. We present an analytic expression for the transport-mean-free path in terms of the refractive indices of grains and host medium, grain radius, and packing fraction. We perform numerical simulations to examine our analytical result.Comment: 9 pages, 3 figure

Optimized White Reflectance in Photonic Network Structures

Three-dimensional disordered networks are receiving increasing attention as versatile architectures for highly scattering materials. However, due to their complex morphology, little is still known about the interplay between their structural and optical properties. Here, we describe a simple algorithm that allows to generate photonic network structures inspired by that of the Cyphochilus beetle, famous for the bright white reflectance of its thin cuticular scales. The model allows to vary the degree of structural anisotropy and filling fraction of the network independently, revealing the key contribution of these two parameters to the overall scattering efficiency. Rigorous numerical simulations show that the obtained structures can exceed the broadband reflectance of the beetle while using less material, providing new insights for the design of advanced scattering materials.Comment: 10 pages, 3 figures. peer reviewed version, published in final form at https://doi.org/10.1002/adom.20190004