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ScienceWise - Summer 2013

Smoke & mirrors

Article Illustration
Smoke rings are not a new phenomena but mathematics developed to describe them has applications in modern optics

Scientists learn to tie knots in light

You might have seen people with cigarettes blow rings of smoke that spin in the air. Such rings are stable vortices of air currents so they can persist and move for several seconds, whereas other patterns in smoke quickly dissipate.

Smoke rings are not a new thing. Back in the nineteenth century the physicist Lord Kelvin was fascinated by them and the amazing stability they exhibited. It even inspired him to propose the idea that atoms consisted of knot-like structures in the aether – a substance that was then believed to permeate all space.

Whilst concepts like knots in the aether are now confined to the history books, the mathematics that was developed to describe those knots and vortices is still alive and well today and finding applications in the most advanced modern optics.

Drs Anton Desyatnikov of the ANU Nonlinear Physics Centre and Mark Dennis from Bristol University are part of an international team of scientists who are designing knots in light.

“If a laser beam is created and twisted in a suitable way, an optical vortex can occur in the form of a dark core down the centre of the beam.” Dr Desyatnikov explains, “So when such a ‘doughnut’ shaped beam propagates in air, the central vortex is a straight line, a thread of darkness. But where things really begin to get interesting and knotty, is when instead of air, that vortex beam travels through a non-linear medium,”

A non-linear medium is one whose optical properties vary with the intensity of the light travelling through it. If a laser enters a lump of window glass it will be refracted (bent) slightly. It doesn’t matter how dim or bright the beam is, the amount of bending will be exactly the same. In a non-linear medium, the light actually alters the properties of the glass. So a bright beam changes the properties of the medium and is bent differently to a dim one.

Why that’s important is that it makes things like self-focusing possible. A bright beam in effect, creates a little lens in the heart of the material that focuses it down, makes it brighter so focuses it more etc.

A combination of vortices and nonlinearity can literally lead to the light getting tied up in knots. “The idea of a knot of light is something scientists have been exploring for years,” Dr Desyatnikov says, “And a few groups have managed to achieve just that by precisely engineering laser beams with “artificial” or “hand-made” knots. But what we’ve been working on are models in which the knots spontaneously form on their own, just like those annoying knots that you always get in electrical cables!”

However unlike electrical cables which love to form knots, light doesn’t. Scientists have found that inducing knots to form in laser beams by introducing perturbations in the form of laser speckle only very rarely induces knots.

“Our models suggest that you have to get the key parameters of the light in a certain range before you can easily tie the light in knots,” Dr Desyatnikov explains “But once you do, the knots are virtually guaranteed.  The really interesting thing is that we can’t predict exactly where they will form. Just that under these specific circumstances the optical vortices will spontaneously nucleate and tie themselves into little knots.”

“Apart from their curiosity value, what’s really interesting and useful about these knots of darkness is that they show you what the power flow is doing. It’s part of the incredible progress science is making in the field of optics, we’re beginning to do things with light that would have once seemed impossible.”

Knots in light also illustrate the beauty of physics and mathematics. Concepts from one area such as waves and vortices in fluids like air can be adapted and applied in what may seem like a totally different area, light in a laser beam.

These results are published in the paper freely available online

“Spontaneous knotting of self-trapped waves” by Desyatnikov, A.S., Buccoliero, D., Dennis, M.R. & Kivshar, Y.S., Scientific Reports 2, 771; DOI:10.1038/srep00771 (2012).

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