'Edge-First Flying Doughnut' Rewrites Rules on Angular Momentum

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COLLEGE PARK, Md., May 19, 2021 — Researchers at the University of Maryland have shown that photons in a vacuum can have orbital angular momentum (OAM) vectors that point sideways, at 90° to the direction of propagation. The discovery relies on a spatiotemporal optical vortex (STOV), the pulses of which are already known to hold potential in nonlinear optics applications.

There are two types of rotational momentum in physics: spin and orbital. Both are described by the quantity known as angular momentum (AM). AM is a conserved quantity; it can be broken up and redistributed among particles such as atoms and photons, but the total AM must remain the same.

AM is also a vector, which is a quantity that has a direction, and this direction is perpendicular to the plane in which the rotational circulation occurs.

In a laser beam, photons have both types of AM: spin angular momentum (SAM) and orbital angular momentum (OAM). While photons don’t rotate on axes like planets, their SAM comes from the rotation of the photon’s electric field, and SAM can only point forward or backward with respect to beam direction.

The simplest laser beam in which photons have OAM is the doughnut beam. Shining such a laser on a wall would show a bright doughnut or ring with a dark center. The OAM vector also points forward or backward, and the OAM is the same for every photon in the beam.

Contrary to the decades-long expectation that OAM vectors can only point forward or backward, researchers at the University of Maryland, in the new work, found that photons in a vacuum can have OAM vectors pointing sideways at 90° to the direction of propagation.

The team demonstrated this by generating a doughnut pulse they refer to as an “edge-first flying doughnut,” or STOV. In this case, the doughnut hole is oriented sideways, and because the rotational circulation now occurs around the ring, the AM vector points at right angles to the plane that contains the ring.

To prove that this sideways-pointing OAM is associated with individual photons and not just the overall shape of the flying doughnut, the team sent the pulse through a nonlinear crystal to undergo a process called second harmonic generation, in which two red photons are converted into a single blue photon with double the frequency. This reduces the number of photons by a factor of two. Each blue photon should have twice the sideways pointing OAM. The results of the experiment showed this to be the case.

The AM of the flying doughnut or STOV is the composite effect of a swarm of photons somersaulting in lockstep.

The researchers in the work identified numerous potential applications for STOVs. For example, the AM conservation embodied by somersaulting photons may make STOV beams resistant to breakup by atmospheric turbulence, with potential application to free-space optical communications. Additionally, because STOV photons must occur in pulses of light, such pulses could be used to dynamically excite a wide range of materials or to probe them in ways that exploit the OAM and the doughnut hole.

“STOV pulses could play a big role in nonlinear optics where beams can control the material they propagate in, enabling novel applications in beam focusing, steering, and switching,” said Howard Milchberg, professor of physics at the University of Maryland.

The research was published in Optica (

Published: May 2021
Research & TechnologyLasersphysicsangular momentumorbital angular momentumspin angular momentumdonutdonut beamUniversity of Marylandspatio-temporal optical vortexSTOVopticanonlinear opticsOpticslight properties

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