Natural light fields are threaded by lines of darkness. For monochromatic light, the phenomenon is familiar in laser speckle—the black points that appear in scattered light because of destructive interference. Those points, known as optical vortices, become lines in three dimensions; when multiple plane waves interfere, the vortices can form a complicated tangle throughout the volume of the light field. Using techniques from mathematics and optical wavefront engineering, Mark Dennis (University of Bristol), Miles Padgett (University of Glasgow), and their UK colleagues have now demonstrated that those lines of zero intensity can be shaped into linked loops and knots. The trick lay in finding the exotic solutions to Maxwell’s equations—or more precisely, the paraxial wave equation—that do the job. Last year Dennis and student Robert King realized they could exploit a topological technique known as Milnor mapping to construct a complex scalar function for a knot. To imprint the function into an optical field, Padgett and students Kevin O’Holleran and Barry Jack used a diffractive hologram to generate the proper destructive interference pattern onto an incoming laser beam. They spatially mapped out the resulting knot (shown here red) by measuring where the phases (different colors in the cross section) become singularities. One goal of the research is to better understand the role knotted vortices may play in systems as diverse as cold turbulent superfluids and hot magnetized plasmas. (M. R. Dennis et al., Nat. Phys. 6, 118, 2010.)—R. Mark Wilson
