Weak Localization of Light in Superdiffusive Random Systems

Abstract

Lévy flights constitute a broad class of random walks that occur in many fields of research, from animal foraging in biology, to economy to geophysics. The recent advent of Lévy glasses allows to study Lévy flights in controlled way using light waves. This raises several questions about the influence of superdiffusion on optical interference effects like weak and strong localization. Super diffusive structures have the extraordinary property that all points are connected via direct jumps, meaning that finite-size effects become an essential part of the physical problem. Here we report on the experimental observation of weak localization in Lévy glasses and compare results with recently developed optical transport theory in the superdiffusive regime. Experimental results are in good agreement with theory and allow to unveil how light propagates inside a finite-size superdiffusive system.PACS numbers: 05.40. Fb, 42.25.Dd Lévy flights are maybe the most general class of random walks, of which the commonly known Brownian motion is a limiting case [1, 2]. They are governed by Lévy statistics [3], which have the fascinating property that, depending on the value of one control parameter, they can exhibit a diverging variance [4]. This leads to a phenomenon called superdiffusion, being a diffusive process in which the mean square displacement increases faster than linear in time [5,6]. Lévy flights are common in nature and appear, for instance, in animal food searches [7,8] The recent development of Lévy glasses [14] and carefully prepared hot atomic vapours [15], have allowed the observation of Lévy flights of light waves and the resulting superdiffusion process. Since interference effects play a dominant role in light transport, this raises the natural question how interference influences optical superdiffusion -a concept which has not been addressed so far. In regular -diffusive -disordered optical systems, interference leads to speckle correlations, and weak and strong localization effects, which all have been studied extensively over the last two decades [16,17]. Localization, in particular, leads to a complete halt of transport that can confine light waves in random patterns. Since the superdiffusion induced by Lévy statistics tends to enhance transport, one would expect it to counter-act localization induced confinement.Among all interference phenomena in random optical materials, maybe the most robust is that of weak localization [16]. It is observed in the form of a cone of enhanced backscattering, which contains information on the path length distribution deep inside the random system, and which has been observed in recent years from several diffusive random structures [18-25] Some of us have recently shown theoretically that weak localization, or coherent backscattering, can be observed from Lévy glasses and that a superdiffusive approximation can be used to predict its behaviour [26]. In this paper we report on the experimental observation of weak localization from superdiffusive materials, which constitu...

Lévy walks

“…Note that the exponent γ is denoted α in the original publications. Adapted from Wiersma, 2008, andBurresi et al, 2012.…”

Cold and Hot Atomic Vapors: A Testbed for Astrophysics?

“…Both the microscopic step size distribution and the macroscopic observables can also be obtained numerically without assuming CFR or neglecting the homogeneous linewidth. We note that in contrast to specifically designed Lévy glass, 36,39 there are no correlations between the location of the scattering and the step size distribution. 40 We are thus closer to an annealed than a quenched disordered system.…”

Steering random walks with kicked ultracold atoms

“…In particular, the lengths of the steps taken by the diffusing particles can have large fluctuations, and they can follow a probability distribution with heavy power-law tails, obeying a generalized central limit theorem [2,3]. Examples of the so-called Lévy [4] random-walk processes are observed in classic transport in complex materials [5][6][7][8][9] and in many interdisciplinary contexts in biology, ecology and economics [2,4,10], making these processes a paradigm of transport and non deterministic evolution in the presence of large deviations.…”