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Levy flight moves light in mysterious ways

09 Dec 2008

Levy flights in an optical material were observed by a team of scientists for the first time in May this year. Marie Freebody speaks to Diederik Wiersma, the man at the head of the group, to find out the significance of this type of light travel and its possible applications.

Diederik Wiersma is research director at the European Laboratory for Nonlinear Spectroscopy at the University of Florence, and at the National Institute for the Physics of Matter, in Italy. He heads up a research group that deals with photonic materials on micro and nanometre length scales. His group has played a leading role in the understanding of light transport in periodic, quasi-crystalline and disordered structures, including the observation of phenomena such as light localization and random lasers. Recently, the group was the first to observe the optical analogy of Lévy flights and super diffusion of photons in a newly developed material – Lévy glass.

Can you explain the concept of Lévy flights?
Lévy flight is a term used to describe the motion of light when it travels not by conventional Brownian diffusion, but in a random series of shorter and longer steps that together form a Lévy flight.

In conventional diffusion – which is usually used to describe the light transmission through an opaque or translucent material – the movement of light is approximated by a random walk in which the lengths of individual steps are about the same. Each step contributes equally to the average transport properties of the material.

A Lévy flight is also characterized by a random walk, but the step length varies considerably and in some cases extremely long jumps can occur. In this case, the longer steps dominate the transport of light through the material.

It turns out that many processes in nature are based on Lévy flights. An important example is the search pattern that animals follow to find food. Bees that are placed in a new environment will perform a Lévy flight to find the flowers in the area. By doing this they can cover a much vaster area than by performing a normal random walk, and they gain very detailed local information.

Why are Lévy flights important?
Light diffusion has become a powerful tool for studying diffusive transport, thanks to the analogies that exist between light diffusion and diffusion of particles in other fields of research, such as solid-state physics, acoustics and atomic physics. Light has the advantage that it allows for high-precision experiments with relatively simple tools. From such optical experiments it is possible to learn about important concepts that can then be applied to other fields.

Light diffusion is easy to study in disordered optical materials (materials in which light rays are heavily scattered and perform a random walk). What we did was implement Lévy flights in a new diffusive optical material that we call Lévy glass. In such a glass, photons follow a random walk with a step-length distribution given by Lévy statistics – that is the photons occasionally make very large jumps. The final result is an optical super diffuser.

What are the main applications and when do you expect them to occur?
Lévy glass has a new optical appearance, which could make it interesting for jewellery or art. Another interesting property is its very efficient diffusive power. Lévy glass breaks the powerful diffusion approximation due to its rapid scattering process and acts as an optical super diffuser. This can help the redistribution of the emission from LED light sources for environmental lighting or create new visual effects from an optical source. It can also improve the interaction between light and electro-optical materials such as silicon, to enhance the efficiency of solar cells.

What would you say is the most important recent advance?
Research on light diffusion and disordered photonic structures in general has seen an enormous boost in recent years. One of the reasons for this is that most photonic materials, and especially photonic crystals, intrinsically suffer from structural disorder. It is impossible to make a perfect photonic crystal without some level of randomness. This made it important to understand how disorder affects the propagation of light and how the physics behind disorder relates to optical phenomena. It also became clear that disorder is not necessarily a disadvantage. It was found that disorder in photonic crystals can lead to a very efficient trapping mechanism for optical waves. This is promising for optical memory applications and slow light devices in which disorder can be an advantage.

What will the next breakthrough be?
Lévy processes occur in so many different fields that it is hard to tell where the next breakthrough will be. The trend of the stock market, the distribution of human travel and the diffusion of liquids in the Earth's crust are all examples of Lévy processes.

We need a better understanding of the link between the scattering elements in a Lévy glass and the resulting anomalous transport process. Dimensionality of the system and finite size effects are thereby crucial and so far not well understood. From the experimental and practical point of view I think you will soon see an exploration of all of the possibilities that Lévy glasses have to offer from a fundamental research and applications point of view.

• This article originally appeared in the December 2008 issue of Optics & Laser Europe magazine.

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