Using abstract mathematics and holograms, a team of physicists working at the universities of Bristol, Glasgow and Southampton, have been able to produce knotted optical vortices.

Understanding how to control light in this way has important implications for laser technology used in wide a range of industries.

Dr Mark Dennis from the University of Bristol and lead author on the paper, explained: “In a light beam, the flow of light through space is similar to water flowing in a river. Although it often flows in a straight line – out of a torch, laser pointer, etc – light can also flow in whirls and eddies, forming lines in space called ‘optical vortices’.

“Along these lines, or optical vortices, the intensity of the light is zero (black). The light all around us is filled with these dark lines, even though we can’t see them”.

Optical vortices can be created with holograms which direct the flow of light. In this work, the team designed holograms using knot theory – a branch of abstract mathematics inspired by knots in everyday life, such as those that occur in shoelaces and rope. Using these specially designed holograms they were able to create knots in optical vortices.

This new research demonstrates a physical application for a branch of mathematics previously considered completely abstract.

Professor Miles Padgett from Glasgow University, who led the experiments, said: “The sophisticated hologram design required for the experimental demonstration of the knotted light shows advanced optical control, which undoubtedly can be used in future laser devices”.

More from Prof Miles Padgett, “We usually think of light as flowing in straight lines, but it can also be twisted, like a corkscrew, along its axis to create an optical vortex.

“When you do this, the light waves at the axis cancel each other out resulting in the centre of the vortex having a light intensity of zero – in other words there’s no light in the middle, so if you were to shine the light beam on a flat surface, it would appear as a donut-shaped a ring of light.

“What we’ve been able to do is tie these vortices together using specially-designed holograms based on mathematical knot theory to guide and control the vortices.”

This research demonstrates a physical application for a branch of mathematics previously considered completely abstract.

Prof Padgett added: “The sophisticated hologram design required for the experimental demonstration of the knotted light shows advanced optical control, which undoubtedly can be used in future laser devices.”

“The study of knotted vortices was initiated by Lord Kelvin back in 1867 in his quest for an explanation of atoms”, adds Dennis, who began to study knotted optical vortices with Professor Sir Michael Berry at Bristol University in 2000. “This work opens a new chapter in that history.”

We found this presentation on the "Structure of Optical Vortices" if your interested in more on the subject.

Sources - http://www.bristol.ac.uk/news/2010/6792.html and Story from University of Glasgow http://www.gla.ac.uk/news/headline_139979_en.html
This is a link to similar work from another group of researchers published in 2008- Linked and knotted beams of light
Dr Mark Dennis's Web page and Research Highlights
Dr. Miles Padgett's Web Site