Rotatum of light

Vortices are ubiquitous in nature and can be observed in fluids, condensed matter, and even in the formation of galaxies. Light, too, can evolve like a vortex. Optical vortex beams are exploited in light-matter interaction, free space communications, and imaging. Here, we introduce optical rotatum, a behavior of light in which an optical vortex beam experiences a quadratic chirp in its orbital angular momentum along the optical path. We show that such an adiabatic deformation of topology is associated with the accumulation of a Gouy phase factor, which, in turn, perturbs the propagation constant (spatial frequency) of the beam. The spatial structure of optical rotatum follows a logarithmic spiral-a signature that is commonly seen in the pattern formation of seashells and galaxies. Our work expands the previous literature on structured light, offers new modalities for light-matter interaction, communications, and sensing, and hints at analogous effects in condensed matter physics and Bose-Einstein condensates.