A research partnership including theoretical physicists from the University of Bristol and Birmingham has formulated a new method of assessing how light flows through space—by tying knots in it.
Experimentally measured polarization singularity trefoil knot. (Image credit: University of Bristol)
Laser light may look like a single, tightly focused beam. In actual fact, it is an electromagnetic field that vibrates in an ellipse shape at each point in space. This multidirectional light is supposed to be ‘polarized’.
The effect can be observed with polarized sunglasses, which only permit one direction of light to penetrate. By holding them up to the sky and rotating them, viewers will view darker and brighter patches as light flowing in various directions appears and disappears.
Currently, researchers have been able to apply holographic technology to twist a polarized laser beam into knots.
Professor Mark Dennis, from the University of Bristol’s School of Physics and University of Birmingham’s School of Physics and Astronomy, headed the theoretical part of the study.
“We are all familiar with tying knots in tangible substances such as shoelaces or ribbon. A branch of mathematics called ‘knot theory’ can be used to analyse such knots by counting their loops and crossings.
“With light, however, things get a little more complex. It isn’t just a single thread-like beam being knotted, but the whole of the space or ‘field’ in which it moves.
“From a maths point of view, it isn’t the knot that’s interesting, it’s the space around it. The geometric and spatial properties of the field are known as its topology.”
With the aim of examining the topology of knotted light fields, scientists from universities in Bristol, Birmingham, Ottowa, and Rochester used polarized light beams to form structures known as ‘polarization singularities’.
Polarization singularities were discovered by Professor John Nye in Bristol more than 35 years ago. They occur at points where the polarization ellipse is circular, with other polarizations wrapping around them. In three dimensions, these singularities take place along lines, in this case forming knots.
The team was able to form knots of much greater complexity than formerly possible in light and examined them in fine detail.
Professor Dennis added: “
One of the purposes of topology is to talk about showing data in terms of lines and surfaces. The real-world surfaces have a lot more holes than the maths predicted.”
The research, which was sponsored by a Leverhulme Trust Research Project Grant, is a significant step forward in the study of optics and polarization, and, say scientists, could pave the way for the creation of new devices which process information through tailored complex light structures.