Scientists find holes in light by tying it in knots

August 1, 2018, University of Bristol
Experimentally measured polarisation singularity trefoil knot. Credit: University of 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 may appear to be a single, tightly focused beam. In fact, it's an electromagnetic field, vibrating in an ellipse shape at each point in space. This multidirectional light is said to be 'polarised'.

The effect can be seen with polarised sunglasses, which only allow one direction of light to penetrate. By holding them up to the sky and rotating them, viewers will see darker and brighter patches as light flowing in different directions appears and disappears.

Now, scientists have been able to use holographic technology to twist a polarised 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, 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 ' 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 structures known as 'polarisation singularities'.

Discovered by Professor John Nye in Bristol over 35 years ago, polarisation singularities occur at points where the polarisation ellipse is circular, with other polarisations wrapping around them. In 3 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.

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."

Explore further: Tying light in knots

More information: Hugo Larocque et al. Reconstructing the topology of optical polarization knots, Nature Physics (2018). DOI: 10.1038/s41567-018-0229-2

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3 / 5 (2) Aug 01, 2018
Among other things, what is meant by "light" doesn't seem to be firm here. Is it a single photon, a pencil of light rays, the electromagnetic nature of light?
"Polarized" light is light composed of rays oscillating only in one plane perpendicular to the direction of travel, "unpolarized" light has light rays oscillating in all directions! A polarizing lens should not show darker and brighter patches as it is rotated, unless there are inhomogenous regions in the light.
5 / 5 (3) Aug 01, 2018
"The effect can be seen with polarised sunglasses, which only allow one direction of light to penetrate. By holding them up to the sky and rotating them, viewers will see darker and brighter patches as light flowing in different directions appears and disappears."

I will have to try that to test my new polarised sunglasses. I suppose that different areas of the polarised lenses are produced/manufactured to exhibit either the one-directional or the scattering of photons, depending on the strength of the light entering the lenses, as well as if the wearer is driving in an unlit tunnel or in bright sunshine. But I'm not entirely certain.
not rated yet Aug 02, 2018
#JP, atmospheric effects and, especially, surface reflections polarise sun-light, which is why polarised filters usually mitigate reflected glare. As eg 'driving glasses' are set to block road-based and other near-horizontal reflections, they're not so good for vertical window glass.

#SEU, filtering reflected glare helps, but what is left is often too bright for comfort, so there may be a 'neutral density' filter, too. If high-tech, this tint may be nimbly photo-chromic.

Um, used to be that a pair of polarised sunglasses came with a test-card with a small window of filter. By rotating this versus the glasses, you could see the effect sinusoidally rise and fall from partial to near-total obscuration.
Such an 'Aha' moment trumps many thousand words of explanation...
not rated yet Aug 03, 2018
Yeah we know, superposition of the field applies! What else ya got!

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