Physicists from Harvard University have elucidated that the trajectory of an optical rotatum conforms to a logarithmic spiral, a geometric configuration frequently observed in the development of seashells and galactic structures.
The progression of a light beam endowed with optical rotatum, depicted across its propagation distance. Image attribution: Dorrah et al., doi: 10.1126/sciadv.adr9092.
“This phenomenon represents a nascent characteristic of light, manifesting as an optical vortex that traverses space and undergoes peculiar transformations,” stated Professor Federico Capasso, the senior progenitor of this investigation.
“Its capabilities could be instrumental in the precise manipulation of minuscule matter.”
In a remarkable revelation, the research cohort discovered that the beam of light, which carries orbital angular momentum, develops according to a mathematically discernible pattern prevalent throughout the natural world.
Echoing the generative principles of the Fibonacci sequence, their optical rotatum follows a logarithmic helical path, a form also apparent in the chambers of a nautilus shell, the seed arrangements in a sunflower, and the branching architecture of arboreal specimens.
“This emergent characteristic was one of the unanticipated discoveries of this research endeavor,” remarked Dr. Ahmed Dorrah, the principal author of this study.
“It is our hope that this work may stimulate further exploration by specialists in applied mathematics, encouraging them to scrutinize these light patterns and derive novel insights from their universal imprimatur.”
This current research builds upon prior investigations where the team employed a metasurface—a diaphanous lens meticulously patterned with light-refracting nanostructures—to engineer a light beam possessing controlled polarization and orbital angular momentum along its trajectory, effectively transforming any incident light into varied structures that evolve as they propagate.
Now, an additional dimension of control has been incorporated into their light manipulation capabilities, allowing for the modification of its spatial torque during propagation.
“We are demonstrating an enhanced degree of control, achievable through continuous modulation,” commented Alfonso Palmieri, a contributing author to this research.
Prospective applications for such an unconventional light beam encompass the precise handling of microscopic entities, such as colloidal suspensions, by introducing a novel force dictated by the light’s distinctive torque.
Furthermore, it holds the potential to facilitate the development of highly accurate optical tweezers for the micro-manipulation of minute objects.
Whereas prior demonstrations of torque-modifying light have necessitated high-intensity lasers and cumbersome apparatus, these scientists achieved their results using a singular liquid crystal display and a low-intensity beam.
By successfully generating a rotatum within an industry-standard, integrated device, the practical implementation of their technology faces substantially fewer impediments than previously encountered.
“Our findings broaden the existing body of knowledge concerning structured light, presenting novel avenues for light-matter interactions, enhanced communications, and advanced sensing technologies, while also suggesting analogous phenomena within condensed matter physics and Bose-Einstein condensates,” they concluded.
The investigation has been published in the esteemed journal Science Advances.
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Ahmed H. Dorrah et al. 2025. Rotatum of light. Science Advances 11 (15); doi: 10.1126/sciadv.adr9092
