A Möbius Strip Made of Light

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Illustration: University of Ottawa

Most nerdy kids, of the type that would grow up to read IEEE Spectrum, were excited when they first learned about the Möbius strip, a three-dimensional shape with only one surface. Many immediately fashioned their own, by cutting a thin strip of paper, twisting it, and joining one end to the other to make a continuous surface. Now scientists have figured out how to make a Möbius strip out of light.

The researchers, from Canada, Europe, and the United States, were able to twist the polarization of a light beam in order to form a 3-D structure out of an electric field that had the same topology as a Möbius strip made of matter would. Lightwaves consist of both an electric and a magnetic field, which oscillate perpendicular to each other. Polarization refers to the direction in which the electric field oscillates.

Under normal circumstances the polarization does not change as the lightwave moves through space. But  the team managed to change those circumstances, says Ebrahim Karimi, a postdoctoral fellow in Robert Boyd’s Quantum Photonics group at the University of Ottawa, and one of the authors of the paper explaining the results in this week’s Science Express. The device that does the job, which they call a “q plate,” consists of a series of liquid crystals. Instead of all being lined up in the same direction, the individual liquid crystals are set at various angles to each other, forming a complex pattern through which the light can pass. Shooting a laser through the q plate creates an interference pattern that twists the polarization along the path of the light beam.

Normally, the polarization is perpendicular to the direction in which the light is moving; . But things were different when the researchers took the beam they’ve passed through the q plate and focused it through a microscope lens onto a spherical gold nanoparticle.

What they see is an oscillating electric field that twists around in a band with only one side, just like a Möbius strip. They made a more standard version that has one and a half twists, then with a different q plate made one with four and half twists.

Karimi says eliciting this new behavior from light might help physicists understand more about the fundamental nature of optics and physics. It might have a practical application as well. If they can shape a light beam in three dimensions, they could conceivably use that ability to fabricate 3-D structures in the sort of photolithography processes used to build electronic circuits. “You’d have a beam that you could control in all directions,” he says.

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