Physicists Made a Mobius Strip from Dueling Beams of Light

A clever trick opens up new doorways in metamaterial fabrication.

Jan 31 2015, 12:00pm


A group of physicists ​has successfully manipulated beams of laser light into an optical mobius strip. The shape, a classic mindfuck all but nonexistent in nature, has never before been seen in such an immaterial form.

Making a simple mobius strip from a strip of paper is as easy as the result is vexing. Twist once and tape the thing end to end. Ta da: a structure with just one side and one edge. Its single boundary is a closed circle; that is, to get from one "side" of the strip to the other, just follow an edge, which will eventually reveal itself to be the same edge as every other edge found on the mobius strip. Fun.

Even given the sharpest, most focused laser beam, it's still a bit weird to imagine light as having edges and surfaces. Yet, it turns out to be not all that unreasonable to imagine it taking on the unreasonable shape in question. There's a lot more to light than meets the eye.

Image: Wiki

For one thing, light is waves (at least until we force it to act like a particle, but skip that for now). Imagine a straight line from a beam's source to its target; there's really nothing straight about it. What we see is a succession of waves, where the actual electromagnetic field is pointing at 90 degree (right) angles from the beam's direction of travel. It's just like a wave in the ocean—as it travels along in some direction, the waves themselves are always reaching for the sky.

So, we can imagine our beam of light instead as a beam of arrows, all of which are pointing outward from that straight line, like a porcupine with quills of electromagnetic radiation instead of hooked barbs.

It's possible to polarize a beam of light such that the field, while still oscillating at right angles to the beam's direction, rotates in a coordinated way. (Common, non-laser light is usually the result of a jumble of different sources and influences, with the result consisting of a chaotic mess of polarizations, so the field is less spinning than spiking off every which way. Again, imagine the porcupine.)

Image: Wiki

For our idealized laser beam, the polarization looks like the above, a nice even rotation about an axis pointing in the direction of travel. There are actually two parts to our wave, an electric part and a magnetic part, visualized in the first gif.

Together, with both the electric and magnetic components, it already looks a bit like a mobius strip. The physicists, a team based at the Max Planck Institute for the Science of Light, made their strip by making two lasers interfere in just the right way. Using a clever liquid-crystal device, they were able to superimpose two beams on top of each other ("inside" of each other), each having a spin opposite its superimposed partner.

The result was a single waveform, but a single waveform built from a superposition of two different beams with opposite polarizations/rotations. Just imagine one hand twisting right and the other hand twisting left and what that might do to one of the waveforms pictured above. The flat wave "fin" would be rotated in both directions at once, just like the strip of paper in a mobius strip.

The mobius strip is really just one of any number of bizarre possible shapes that might be realized via superimposing two or more beams using the same method. And these possibilities are far from trivial.

"Our results reveal a hidden polarization topology under tight focusing that has not previously been reported in literature," ​the physicists write in Science. "Optical patterns such as those we demonstrate here could for example be used to optically fabricate material microstructures with nontrivial topology for new functional media, e.g., metamaterials with exotic optical properties or molecular shape-selective membranes or substrates."