Sunday, February 24, 2008

The Dark Side of Light: Brownian Fractals

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Light may not seem very interesting in our everyday lives. But to scientists, light’s properties are a constant source of intrigue. The nature of light as both wave and particle, light as the universal speed limit, and the way light interacts with magnetic fields in the atmosphere to form auroras are a just a few examples of light’s fascinating behavior.

Recently, researchers from the University of Glasgow and the University of Bristol in the UK have discovered another unusual property of light – or, more accurately, the darkness within light. As the researchers explain, natural light fields are threaded by lines of darkness, which create optical vortices that appear as black points within the light. The group has modeled this phenomenon, and found that the lines of darkness exhibit fractal properties with Brownian (random) characteristics. Further, the characteristics of these optical vortices suggest universal properties, which could help connect different areas of physics.

Many people have noticed the phenomenon of laser speckle, which occurs when coherent, monochromatic laser light bounces off a rough surface, giving the surface a speckled appearance. The black specks are interference patterns generated by a superposition of highly coherent light waves reflected from different points on the rough surface. Sometimes the speckled pattern can even appear to sparkle when the viewer moves relative to the surface.

In a recent issue of Physical Review Letters, the UK researchers describe how they developed a model of the superpositions that create the dark optical vortices, using numerical simulations and experiments. In their experiments, they created laser speckle with a 10-mm-diameter helium neon laser beam shining through a screen made of ground glass.

By measuring the superpositions with an interferometer, the scientists could generate a 3D map of the structure of the optical vortices. They found two types of vortices. Infinite vortex lines, which account for about 73% of the dark vortices, percolate entirely through the light beam. The remaining 27% of the vortices form closed loops, which occur when a vortex line returns to its starting point within a small enough area.

When investigating the lines of darkness further, the researchers found that they exhibit scale invariance. In other words, the vortices look the same no matter how much you zoom out – they are fractals. Lead author Kevin O’Holleran of the University of Glasgow said that, while he and his colleagues suspected vortex lines to exhibit fractal properties, they were quite surprised to find that the fractality was of a Brownian nature.

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