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Light takes off for Lévy flight

22 May 2008

Researchers in Italy have for the first time engineered an optical material to support Lévy flights, which fundamentally alter the way that light waves travel through the material.

Lévy flight

A new optical material that acts as a "superdiffusor" has been created by Diederik Wiersma and colleagues at the European Laboratory for Non-linear Spectroscopy (LENS) in Florence, Italy. Light travels through the material not by conventional Brownian diffusion, but in a random series of shorter and longer steps that together form a Lévy flight.

"Lévy flights are of fundamental importance in many transport phenomena, such as animals searching for food, earthquake patterns and human travel," Wiersma told optics.org. "But this is the first time that Lévy flights have been observed in a material. It's fascinating to see that light waves, animals and earthquakes all follow the same basic laws."

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. As a result, each step contributes equally to the average transport properties of the material.

A Lévy flight is also characterized by a random walk, but in this case 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.

In fact, says Wiersma, normal diffusion is just a limiting case of Lévy flights, which offer a much more general description of transport processes. "We have made a translucent material that breaks this very powerful diffusion approximation for the first time. Due to its very rapid scattering process, you can also say that it behaves as a superdiffusor."

The material, which Wiersma and colleagues have dubbed a "Lévy glass", is made by embedding particles of titanium dioxide in a glass matrix. These particles scatter light efficiently because of their high refractive index, and the scientists control the local density of these scattering particles by also incorporating glass microspheres of different sizes into the material.

The glass microspheres do not scatter, but they alter the spatial distribution of scattering events that occur inside the material. "The size distribution of the glass spheres determines the density fluctuations of the scattering elements – the titania spheres. This is the key to obtain a Lévy flight," said Wiersma.


Comparing light transmission through samples of the Lévy glass and a normal diffusive material reveals some interesting differences. For a start, the intensity of light transmission through a Lévy glass decays much more slowly with distance than for a conventional material. But more intriguing are the large variations in both the intensity and spread of the light output after transmission through the Lévy glass, while in the normal diffusive case both of these parameters remain almost constant.

According to Wiersma, the properties of the new material can easily be tuned, which could help researchers to understand the behaviour of light in disordered systems such as random lasers and image reconstruction. It also provides a unique experimental system that could offer new insights into Lévy flight phenomena in other fields, such as biology, economics and sociology. "By creating a material in which light waves exhibit this physics you can study this transport phenomenon in an easy and controlled way," he said.

And, in the future, the unusual properties of Lévy glasses could lead to new opaque optical materials, such as paints with novel visual effects, and even lasers based on superdiffusive feedback. "These applications are meant as ideas for future developments," cautioned Wiersma. "If you really knew the killer application you would probably not talk about it, but patent it and try to make it."

The researcher's reported their work in Nature.

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