Photon diffusion

Abstract: Translucent materials such as milk, clouds and biological tissues owe their appearance to the way they interact with light, randomly scattering an incident ray many times before it re-emerges. This process — analogous to the brownian motion of particles in a fluid — is called a random walk, a concept central to statistical physics. It is used, for example, to describe the diffusion of heat, light and sound. An extension of this idea is the Levy flight, where a moving entity can occasionally take unusually large steps, thereby transforming a system's behaviour. Levy flights have been recognized in systems as diverse as earthquakes and animal food searches. Barthelemy et al. have now engineered such behaviour into an optical material (titanium dioxide particles in a glass matrix). In the resulting 'Levy glass', rather than regular diffusion, light waves perform a Levy flight, in which photons spread around extremely efficiently. This will be an ideal model for studying Levy flights, and may also lead to novel optical materials. The cover the photons' path, with the light source top right. Photo by Diederik and Leonardo Wiersma An extension of the concept of a random walk is the Levy flight, in which the moving entity can occasionally take unusually large steps. Pierre Barthelemy and colleagues show how such behaviour can be engineered into an optical material. 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 diffusion1. 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 invariant2,3. Levy flights have accordingly turned out to be applicable to a diverse range of fields, describing animal foraging patterns4, the distribution of human travel5 and even some aspects of earthquake behaviour6. Transport based on Levy flights has been extensively studied numerically7,8,9, but experimental work has been limited10,11 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.