Credit: ROBERT KING/MARK DENNIS

The interaction of multiple light beams in a medium can be thought of as similar to how water flows in a river, with such 'flow' causing the creation of optical vortices — light fields that have characteristic lines of zero intensity in space. Now, using algebraic topology, researchers from the UK have developed a scheme for creating optical vortices in propagating laser fields to form knots and links (Nature Phys. 6, 118–121; 2010).

Mark Dennis and co-workers use mathematical knot theory to construct complex functions in an abstract 3D space on a periodic braid. The knot function is then embedded in a propagating light beam, with the knots forming as dark interference lines from overlapping laser modes.

To experimentally realize the knots, a hologram made by a computer-controlled liquid-crystal display is used to imprint a carefully designed phase pattern of laser light. Observation of the optical knots is possible using a numerical optimization algorithm to increase the contrast in light intensity, making the structures easier to see.

“The technology by which we display the holograms has a limited dynamic range, which in turn makes controlling the dark regions of the beam difficult,” the team explained to Nature Photonics. Indeed, one objective of the work is to investigate how the beam parameters can be modified such that the required contrast in the hologram is reduced.

The work by Dennis et al. shows how physicists can adapt pure mathematics, such as knot theory, for use in physical phenomena. The proposed knot-formation technique may be useful for designing optical landscapes for the blue-detuned trapping of particles or super-resolved fluorescence imaging.