Twisted physics

A group of UK scientists has light theory all tied up in a paper published in the February 2010 issue of Nature Physics. Using lasers under holographic control, Dr. Mark Dennis and fellow physicists at the universities of Bristol, Glasgow and Southampton have successfully twisted light into knots for the first time.

Demonstrating such advanced control of light has important implications for laser technology and could be applied to future optical trapping schemes or superresolved fluorescence imaging.

This image represents the theoretical construction of a trefoil knot.

Tying light into knots draws on an abstract branch of mathematics, known as “knot theory.” Although beams of light appear to flow in straight lines, they actually contain lines of zero intensity that flow in whirls and eddies, much the same way water flows in a river. These revolving lines of zero intensity, or blackness, are called optical vortices, and, although they can’t be seen, they fill the light all around us.

“The aim was to understand how to create optical vortex knots and create them experimentally using lasers under holographic control,” Dennis said. “Optical vortices are the most general form of destructive interference, and therefore are ubiquitous in optical fields. Without understanding them, we cannot understand the fine structure of light fields.”

This image represents the theoretical construction of a trefoil knot. Images courtesy of Mark Dennis, Robert King, Barry Jack, Kevin O’Holleran and Miles Padgett.

Following Dennis’ theory, the Glasgow side of the collaboration optimized the knot recipe to compute the desired knotted field in the waist plane of the laser. The phase and intensity were embedded onto a computer-controlled hologram (based on a first-order diffraction scheme). Next, an incoming laser beam acquired the phase and intensity pattern of the hologram, and a CCD camera mounted on a motorized stage measured the intensity and phase of the knot field, plane by plane.

“By understanding [that] how an optical vortex (as a strand of darkness) sits in a bright light beam is related to the way looped curves occupy the 3-D space, we were able to apply abstract mathematical knot theory to find solutions of the laser paraxial equation, which have knotted vortices,” Dennis said.

These techniques frequently are used in sculpting the bright patterns in light beams for applications such as optical trapping, but now the researchers have shown that it is possible to manipulate the 3-D structure of the dark regions of a beam.