Knots in optical vortices
Phase singularities: In physics, wave propagation is traditionally analyzed by means of regular solutions of wave equations. These solutions often possess singularities, the points or lines in space at which mathematical quantities that describe physical properties of waves become infinite or change abruptly. For example, at the point of phase singularity, the phase of the wave is undefined and wave intensity vanishes. Phase singularities are now recognized as important features common to all waves. The earliest known scientific description of phase singularity was made in the 1830′s by Whewell, as discussed by M. Berry in “Making waves in physics,” Nature (London) 403, 21 (2000).While Whewell studied the ocean tides, he came to the extraordinary conclusion that rotary systems of tidal waves possess a singular point at which all cotidal lines meet and at which tide height vanishes.
Vortices: Waves that possess a phase singularity and a rotational flow around the singular point are called vortices. They can be found in physical systems of different nature and scale, ranging from water whirlpools and atmospheric tornadoes to quantized vortices in superfluids and quantized lines of magnetic flux in superconductors. In a light wave, the phase singularity forms an optical vortex: The wave rotates around the vortex core in a given direction; at the center, the velocity of this rotation is infinite and the light intensity vanishes (black spots). Because of the twisting (like a corkscrew around its axis of travel), the light waves at the axis itself cancel each other out. When projected onto a flat surface, an optical vortex looks like a ring of light, with a dark hole in the center. This corkscrew of light, with darkness at the center, is called an wave-front screw dislocations or optical vortex.
Understanding and controlling the properties of optical vortices could lead to numerous applications in the future, ranging from optical communications and data storage to the trapping, control, and manipulation of particles and cold atoms. Indeed, optical vortices provide an efficient way to control light by creating reconfigurable waveguides in bulk media. The study of phase singularities in optical parametric processes not only suggests new directions of fundamental research in optics but also provides links to other branches of physics. For e.g., the recent discovery of a rich variety of exotic topological defects in unconventional superfluids (such as 3He-A) and superconductors points to the likelihood that deep analogies exist between vortices in complex superfluids and multifrequency light waves. Recent theoretical analysis of two color parametric optical vortices has demonstrated that such vortices possess unexpected properties that make them even more exotic than quantized vortices in unconventional superfluids.
Source: http://wwwrsphysse.anu.edu.au/nonlinear/papers/pdf/OPN_2001_04_00026.pdf
Knots in optical vortices
Optical vortices can be created with holograms which direct the flow of light. A team of physicists working at the universities of Bristol, Glasgow and Southampton have 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”. Dr Mark Dennis from the University of Bristol said “The study of knotted vortices was initiated by Lord Kelvin back in 1867 in his quest for an explanation of atoms. This work opens a new chapter in that history.”
Source: http://www.bristol.ac.uk/news/2010/6792.html
January 18, 2010