An international team of physicists, led by Dr Thomas Bauer from the Max Planck Institute for the Science of Light and the Friedrich-Alexander-University Erlangen-Nuremberg in Germany, has experimentally produced a three-dimensional geometrical structure called Möbius strip from the polarization of light.
Numerically calculated and experimentally observed optical polarization Möbius strips. Image credit: Thomas Bauer et al, 10.1126/science.1260635.
Light is an electromagnetic wave, and as such it has an electromagnetic field. The direction in which the electric component of this field oscillates is commonly referred to as the light’s polarization.
Polarization, for example, is the key to understanding glare-reducing polarized sunglasses and making 3D cinema possible.
The polarization of sunlight beams is usually random, which means the orientation of the electric field is independent from one beam to another.
But when light is reflected from many objects, the reflected light becomes polarized in a specific direction, parallel to the surface that is reflecting the light.
“Demonstrating that a Möbius strip can be made of polarization states of light is interesting not only for improving the fundamental understanding of optical polarization but also because it could be used to generate complex structures at micro and nanoscales,” said Dr Bauer and his colleagues, who reported the results in the journal Science.
In their experiment, the team used a specific, rather exotic, type of light beam: a tightly focused laser beam that they refer to as structured light.
Structured light has a very specific polarization and intensity distribution in the light beam – and therefore the electromagnetic field oscillates differently for different parts of the beam. It is not always at right angles to the direction the light is moving in, as would be the case in a standard laser beam.
In this highly structured beam, there will be components of the electric field in all three dimensions. Moreover, different parts of the beam will have different electric field components in different directions.
To create the structured beam and measure its polarization, Dr Bauer and his colleagues used a series of optical tools.
The laser light is first passed through a q-plate – a liquid crystal lens. To image the polarization they used a nanoparticle. This particle was scanned over the cross-section of the beam and they observed the light it scattered.
By determining how the light was scattered, and effectively using it as an interferometer, the polarization of the light beam at the focus is detected, and consequently the Möbius strips emerge.
The Möbius strips show how the electric field is oriented at each position on a circular path surrounding the axis of the laser beam.
Depending on the particulars of the structure of laser beam, the scientists observe Möbius strips of polarization having 3/2 or 5/2 twists.
“These strips demonstrate the rich structure that a light beam can possess at very small, subwavelength distance scales,” said Prof Robert Boyd of the University of Rochester and the University of Ottawa.
“Moreover, the measurement technique used here holds great promise for probing the nanostructure of other sorts of light beams.”
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Thomas Bauer et al. Observation of optical polarization Möbius strips. Science, published online January 29, 2015; doi: 10.1126/science.1260635
