The logarithmic spiral produced by optical rotatum follows a pattern often found in nature, including nautilus shells. [Image: Capasso Lab / Harvard SEAS]
Researchers at Harvard University, USA, have shown that a light beam can be shaped into an optical vortex that can spiral inwards or outwards, tracing out the same pattern that is seen in the formation of natural systems such as hurricanes and seashells (Sci. Adv., doi: 10.1126/sciadv.adr9092). This new form of structured light, which Federico Capasso and colleagues have dubbed optical “rotatum,” provides access to a complex combination of optical forces that could offer new ways to control particles and their properties.
Twisted light
Light beams that evolve as a vortex have already been exploited in a variety of applications, ranging from free-space communications through to optical tweezers and quantum information processing. Such corkscrew-shaped paths are generated by light beams that carry orbital angular momentum (OAM), which are produced using tools such as spatial light modulators, metasurfaces and geometric phase plates. More recent work has shown that the OAM can be varied linearly along the optical path, which has proved particularly useful for manipulating small particles on attosecond timescales.
In a new twist, the Harvard team demonstrated that the OAM of the propagating beam can be altered using any polynomial function, producing new and complex patterns in the optical path. In particular, increasing the OAM along a parabolic curve causes the vortex to grow or decay in a logarithmic spiral, similar to the swirling arms of a galaxy or the growth pattern of a nautilus shell. The researchers call this effect optical rotatum, borrowing a term from classical mechanics that refers to the rate of change in torque on an object. “This is a new behavior of light consisting of an optical vortex that propagates through space and changes in unusual ways,” said Capasso.
When this complex field profile is synthesized with a standard setup for digital holography, the interference between the beams produces a helical wavefront that repeatedly deforms its twist along the optical path.
Achieving optical rotatum
To achieve this parabolic dependence, the helical twist of the light must evolve continuously as it propagates. This requires different parts of the beam to propagate with slightly different phase delays along the direction of propagation, which the researchers accomplish by creating a series of vortex beams with slightly different bend angles. When this complex field profile is synthesized with a standard setup for digital holography, the interference between the beams produces a helical wavefront that repeatedly deforms its twist along the optical path.
In the parabolic regime of rotatum, the researchers show that the optical beam can evolve from a flat profile to a helical pattern with five spirals over a propagation distance of 20 cm, with the growth of the spiral pattern close to Fibonacci's golden ratio. The team believes that the combination of optical forces within such complex optical vortices could be exploited, for example, to enhance the interactions between light and matter, to manipulate small particles in three dimensions, or to enable novel applications in spintronics and lightwave electronics. “We envision this work to enrich the science and applications of wave physics, singular optics, structured light and beyond,” Capasso and his colleagues conclude.