Twisting Light into Knots

This is an experimentally measured polarization singularity trefoil knot. (Source: U. Bristol)

A research colla­boration including theo­retical physicists from the Univer­sity of Bristol and Birming­ham has found a new way of eva­luating how light flows through space – by tying knots in it. Laser light may appear to be a single, tightly focused beam. In fact, its electro­magnetic field vibrates in an ellipse shape at each point in space, it shows polari­zation. Now, scientists have been able to use holo­graphic tech­nology to twist a pola­rized laser beam into knots.

Mark Dennis, from the Univer­sity of Bristol’s School of Physics and University of Bir­mingham’s School of Physics and Astro­nomy, led the theo­retical part of the research. He said: “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. In order to analyse the topology of knotted light fields, researchers from univer­sities in Bristol, Bir­mingham, Ottowa and Rochester used polarised light beams to create polari­zation singu­larities.

Discovered by John Nye in Bristol over 35 years ago, polari­zation singu­larities occur at points where the polari­zation ellipse is circular, with other polari­zations wrapping around them. In three dimensions, these singu­larities occur along lines, in this case creating knots. The team were able to create knots of much greater complexity than pre­viously possible in light and analysed them in fine detail. 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.” (Source: U. Bristol)

Reference: H. Larocque et al.: Reconstructing the topology of optical polarization knots, Nat. Phys., online 30 July 2018; DOI: 10.1038/s41567-018-0229-2

Link: H. H. Wills Physics Laboratory, University of Bristol, Bristol, UK

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