Pierre Barthelemy

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. 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. Lévy flights have accordingly turned out to be applicable to a diverse range of fields, describing animal foraging patterns, the distribution of human travel and even some aspects of earthquake behaviour. Transport based on Lévy flights has been extensively studied numerically, but experimental work has been limited and, to date, it has not seemed possible to observe and study Lévy 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 Lévy flight. The key parameters that determine the transport behaviour can be easily tuned, making this an ideal experimental system in which to study Lévy flights in a controlled way. The development of a material in which the diffusive transport of light is governed by Lévy statistics might even permit the development of new optical functionalities that go beyond normal light diffusion.

Engineering of light confinement in strongly scattering disordered media

Disordered photonic materials can diffuse and localize light through random multiple scattering, offering opportunities to study mesoscopic phenomena, control light-matter interactions, and provide new strategies for photonic applications. Light transport in such media is governed by photonic modes characterized by resonances with finite spectral width and spatial extent. Considerable steps have been made recently towards control over the transport using wavefront shaping techniques. The selective engineering of individual modes, however, has been addressed only theoretically. Here, we experimentally demonstrate the possibility to engineer the confinement and the mutual interaction of modes in a two-dimensional disordered photonic structure. The strong light confinement is achieved at the fabrication stage by an optimization of the structure, and an accurate and local tuning of the mode resonance frequencies is achieved via post-fabrication processes. To show the versatility of our technique, we selectively control the detuning between overlapping localized modes and observe both frequency crossing and anti-crossing behaviours, thereby paving the way for the creation of open transmission channels in strongly scattering media.

Optical Levy flights and super diffusion of light

People working with optics and lasers usually try to avoid dust on their equipment as much as possible. Dust particles scatter light randomly in all directions and this is often detrimental to the performance of optical devices and lasers. In this articles we will see that it is possible to turn this situation upside down and actually make use of multiple light scattering to study interesting physical phenomena. In particular, we will discuss optical Lévy flights and super diffusion, and various interference effects like weak and strong localization of light waves.

Photons, Dust and Honey Bees

Light transport is a new optical material called Levy glass is reported in which photons exhibit a Levy flight and hence super diffusion.