The rotatum: a new "twist" in singular optics

If you’ve ever admired the swirl of cream in your coffee or gazed at the elegant spiral of a seashell, you’ve seen nature’s love for vortices and spirals. From tornadoes to galaxies, swirling patterns are everywhere. But here’s a twist you might not expect: light itself can spiral too.

Physicists have long known that light can carry a kind of "twist" called orbital angular momentum (OAM). Imagine a beam of light not as a straight laser pointer, but as a tiny whirlpool of photons, each carrying a little spin around the beam’s axis. These "optical vortices" have already found uses in everything from more powerful microscopes to futuristic data communication systems.

Now, a team of researchers at Harvard University and Eindhoven University of Technology has added an entirely new layer to this story. In their paper published on Science Advances, Ahmed H. Dorrah, Federico Capasso, Alfonso Palmieri, and Lisa Li, introduce something they call the rotatum of light.

It sounds esoteric, but the idea is beautiful: just as a seashell grows in a spiraling pattern, light too can evolve in spirals as it moves.

Ordinary laser beams march straight ahead. Vortex beams, however, twist like corkscrews. Each photon in such a beam carries angular momentum, which makes these beams behave like tiny whirlwinds of energy. For decades, scientists have learned how to generate and manipulate these beams using holograms, specially engineered materials called metasurfaces, and even spiral-shaped glass plates.

But until now, the "twist" in such beams has been thought of as fixed: a sort of conserved identity of the beam. If you launch light with a given amount of angular momentum, it carries that value through space.

Dorrah and colleagues asked: what if the twist of light itself could change continuously as the beam travels? Not just in steps, but smoothly, like a dancer spinning faster and faster, or slower and slower, as they move across the stage. That’s where rotatum comes in.

To explain rotatum, think about acceleration. In physics, velocity describes how fast something is moving, and acceleration tells you how quickly that speed changes. But what if acceleration itself changes over time? That’s called "jerk." And if jerk changes, you get "snap," and so on. Physicists have long used these higher-order derivatives in mechanics. But no one had seen their equivalents in how light twists.

The team showed that a beam of light can have not just a simple "self-torque" (that is, a linear change in its twist) but also a quadratic change, which they call rotatum. In other words, the twisting of the light doesn’t just change steadily, it curves in its rate of change, like a spiral that tightens or loosens in a parabolic fashion.

And here’s the poetic part: when they created such beams in the lab, their structure revealed a logarithmic spiral, the same mathematical curve that governs seashells and galaxies.

The group achieved this using a clever trick with Bessel beams. These are a special kind of light beam that can travel long distances without spreading out, often described as "non-diffracting" beams. By combining many Bessel beams, each slightly different in angle, they built a beam whose twist evolves as it propagates.

The experiment relied on spatial light modulators, essentially programmable holograms displayed on special computer-controlled screens. By carefully engineering the phase of the incoming light (the fine structure of its wavefront), they could sculpt beams that evolved exactly as predicted: some whose twist grew steadily, some that increased and decreased, and others whose twisting grew quadratically, producing the newly discovered rotatum.

When the researchers looked at the beams under the microscope, they saw dark lines, called "phase singularities", that danced and spiraled inward, feeding the beam’s core with more and more twist. These singularities traced spiral patterns eerily similar to natural growth processes, like the formation of a Nautilus shell.

No, rotatum is not a purely abstract curiosity: history tells us that strange new properties of light often open doors to powerful technologies. Structured light, or, in other words, light that has been shaped in exotic ways, has already given us breakthroughs in many fields. For instance, scientists used optical "tweezers" to move or micromanipulate microscopic objects like cells or nanoparticles. In communications, encoding information in light’s twist enables the transmission of more data through free space. In quantum science, twisted photons are used for secure communication and quantum computing. And finally, in imaging, light structures are used to break past classical resolution limits in microscopes.

Rotatum could extend this toolkit. For example, beams with changing twist could act as ultra-precise depth rulers, measuring distances with extraordinary accuracy. They could sort tiny particles in three dimensions, opening new doors in materials science and biology. And the underlying physics hints at analogies in other wave systems, from sound waves to electron beams. The researchers even suggest possible impacts in quantum materials, where light’s structured angular momentum might drive exotic electronic transitions.

This discovery belongs to the field of singular optics, the study of light fields with unusual structures, like vortices, singularities, and discontinuities. Like many discoveries in physics, the immediate applications of rotatum may not be obvious, but it opens questions such as: can rotatum be harnessed in quantum communication for more secure channels? Could it drive new types of optical forces to control matter at the nanoscale? Will it inspire analogs in other fields, such as acoustics, where sound waves might be engineered with rotatum-like behavior?

The paper ends with a vision: rotatum is about a broader class of "structured waves" across physics. If we can sculpt how waves evolve as they propagate, we might unlock entirely new modes of control over energy and information.

If you want to learn more, the original article titled "Rotatum of light" is available on Science Advances at https://doi.org/10.1126/sciadv.adr9092.