A Levy flight for light

A random walk is a stochastic process in which particles or waves travel along random trajectories. The first application of a random walk was in the description of particle motion in a fluid (brownian motion); now it is a central concept in statistical physics, describing transport phenomena such as heat, sound and light diffusion(1). Levy flights are a particular class of generalized random walk in which the step lengths during the walk are described by a 'heavy-tailed' probability distribution. They can describe all stochastic processes that are scale invariant(2,3). Levy flights have accordingly turned out to be applicable to a diverse range of fields, describing animal foraging patterns(4), the distribution of human travel(5) and even some aspects of earthquake behaviour(6). Transport based on Levy flights has been extensively studied numerically(7-9), but experimental work has been limited(10,11) and, to date, it has not seemed possible to observe and study Levy transport in actual materials. For example, experimental work on heat, sound, and light diffusion is generally limited to normal, brownian, diffusion. Here we show that it is possible to engineer an optical material in which light waves perform a Levy flight. The key parameters that determine the transport behaviour can be easily tuned, making this an ideal experimental system in which to study Levy flights in a controlled way. The development of a material in which the diffusive transport of light is governed by Levy statistics might even permit the development of new optical functionalities that go beyond normal light diffusion.