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Tying Knots in Light

CANBERRA, Australia, Oct. 31, 2012 — Light can be coaxed to tie itself into knots, but under the right conditions the knot-tying can happen spontaneously, new research suggests. 

Australian National University physicists have produced a model from physics and mathematical concepts that generates optical vortices with dark cores in a bright laser beam, which tangle into knots. The light knots have potential applications in quantum computing, laser beams and advanced modern optics.

While it has been shown previously that light can be induced to tie itself in knots, for the first time researchers have caused the phenomenon to happen spontaneously, forming little cores of darkness in bright laser beams. Courtesy of Australian National University.

“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,” said study co-author Dr. Anton Desyatnikov at ANU’s Nonlinear Physics Centre. “It is 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.”

Unlike previous research that produced knots in light artificially, the new research focuses on models in which knots form spontaneously, similar to the tangles in power cords.

However, unlike electrical cables, light does not form knots easily, Desyatnikov said.

An initially deformed vortex-free soliton develops vortex lines during propagation in a self-focusing saturable medium. (yellow arrow is the optical z-axis). Here we distinguish isolated vortex rings (unknots) in pink, linked vortex rings (Hopf links) in green and orange, and vortex (trefoil) knots in blue. Courtesy of Scientific Reports.

“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,” he said. “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, but once you do, the knots are virtually guaranteed.”

It is not possible, however, to predict where exactly the knots will form, he said.

“Just that under these specific circumstances, the optical vortices will spontaneously nucleate and tie themselves into little knots,” Desyatnikov said.

The study appeared in Scientific Reports (doi:10.1038/srep00771

See also: Light Tied in Knots

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why golden ratio optimizes knot compression: (the math) animating the perfect (golden ratio) slip knot (origin of hebrew:
11/13/2012 5:10:06 PM

What is the "self-focusing saturable medium" referenced in above article?
11/4/2012 3:24:28 PM

I remember that the 1980s promise of solitons as an outstanding solution to increase the bit rate of optical transmission never came to fruition. So, this story about light vortices emerging as a practical solution for quantum computers still has a long way to go.
11/2/2012 12:42:47 AM

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