A Lévy flight for light

Flights of fancy: 'Lévy glass' opens a window on new optical materials 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 Lévy flight, where a moving entity can occasionally take unusually large steps, thereby transforming a system's behaviour. Lévy 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 'Lévy glass', rather than regular diffusion, light waves perform a Lévy flight, in which photons spread around extremely efficiently. This will be an ideal model for studying Lévy 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 Lévy 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 diffusion 1 . Lévy 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 . Lévy 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 Lévy flights has been extensively studied numerically 7 , 8 , 9 , but experimental work has been limited 10 , 11 and, to date, it has not seemed possible to observe and study Lévy transport in actual materials. For example, experimental