In the design proposed by the Southampton-led group, concentric rings of azimuthally oriented linear dipole resonators would produce different frequency dispersion patterns at different spatial points, leading to the creation of a “flying doughnut” pulse from an ordinary input pulse. [Image: Reprinted with permission from N. Papasimakis et al., Phys. Rev. B 97, 201409(R) (2018); © 2018 by American Physical Society] [Enlarge image]
A team of researchers headed by OSA Fellow Nikolay Zheludev of the University of Southampton, U.K., and Nanyang Technological University, Singapore, has proposed a metamaterials-based scheme to realize flying electromagnetic doughnuts, a theoretical solution to Maxwell’s equations that’s never been achieved experimentally (Phys. Rev. B, doi: 10.1103/PhysRevB.97.201409). The researchers believe that their recipe, which they’re now working to realize in the lab, could open up some new possibilities in communications, sensor design and spectroscopy.
Exotic toroidal pulses
We’re all familiar with the plane-wave solutions to Maxwell’s celebrated equations—ordinary light waves in which the electromagnetic field is oriented at right angles to the wave’s propagation direction. But the equations also have a few surprises up their sleeve. In particular, they allow exotic solutions in the form of short pulses with a toroidal, or doughnut-like, shape that would propagate in free space, and that include a strong electromagnetic-field component in the direction of propagation rather than transverse to it.
These unusual pulses—fancifully christened flying doughnuts (FDs), and first described theoretically more than 20 years ago—have a number of characteristics that would open up intriguing application possibilities. For example, the specifics of the doughnuts’ predicted energy density suggest that they could act as highly efficient particle accelerators. Even more important, while plane waves, Gaussian pulses and other, more familiar solutions of Maxwell’s equations can be written as the product of separate space-dependent and time-dependent functions, the spatial and temporal structure of FDs is inextricably linked. That means that the frequency spectrum of the pulse varies in space, in ways that might be exploited for new kinds of encoding in communications and spectroscopy applications.
Unfortunately, that same spatiotemporal coupling makes FDs very difficult to create in the real world. It’s been suggested, for example, that one can make the toroidal pulses through special arrays of electrically controlled optical antennas, emitting at different frequencies in a specific spatial pattern that would create the FD structure in the far field. But controlling such a complex antenna array on the required fast timescale, especially at optical frequencies, has been a nonstarter.
A metamaterials approach
The Zheludev-led group at Southampton, which also included researchers from National Taiwan University and the U.K. Defense Science and Technology Laboratory, looked at a different approach for generating FDs: Start with a conventional light pulse, and use metamaterials to convert it into a flying doughnut.
According to the paper’s lead author, Nikitas Papasimakis at Southampton, the team’s solution began by separating the problem into several steps. “The first is to have the right topology, this toroidal shape,” he says, which the team’s proposed design would achieve with a segmented waveplate. The waveplate acts as a polarization converter, transforming a plane-polarized input pulse into an azimuthally polarized one, in which polarization is rotated by specific, varying amounts in different parts of the pulse.
With that geometric task taken care of, Papasimakis continues, the second part of the solution is designed to “imprint the space-time coupling” characteristic of FDs on the Gaussian input pulse, which is still separable into space-dependent and time-dependent components. To do that, the pulse would be passed through a concentric array of azimuthally oriented dipole antennas, the distribution of which would be carefully designed to result in the spatial frequency distribution predicted for FDs. “Essentially,” Papasimakis says, “we tried to mimic the electromagnetic phase distribution created by the [doughnut] pulse using a metasurface, with dipole resonators.”
Application possibilities
In numerical simulations of its FD recipe, the team found that its designed structure closely aligned with the morphology and spatial frequency distribution predicted for the doughnuts from Maxwell’s equations. The results were encouraging enough, Papasimakis reports, that the team is now working on an experimental proof of concept, with some preliminary results reported at the recent CLEO conference.
Realizing the doughnuts could lead to some interesting new applications, according to Papasimakis. “One of the most interesting things is that you have field components along the propagation direction,” he notes—particularly at the center of the toroid. That has made FDs intriguing as a possible vehicle for particle acceleration and energy transfer (a potential application that was, in fact, explored in the initial theoretical paper introducing the concept in 1996).
Other applications, Papasimakis says, relate to the space-time inseparability of FDs, a significant difference from other solutions of Maxwell’s equations. “You could think of a spectroscopic scheme where you send a [FD] pulse through the material you want to interrogate, and some frequency components are absorbed and some aren’t,” he suggests. Because the frequency structure of the pulse varies spatially, says Papasimakis, one could imagine a scheme where the altered spectral signature, and thus the material composition, could be read directly by imaging the pulse wavefront, rather than by using a separate spectrometer.
In a similar way, the spatial frequency distribution could open up new communications applications in encoding information on the toroidal pulses, and reading them at the back end. “You could do operations in the frequency domain in telecommunications,” says Papasimakis, “by simply acting on the spatial structure of the pulse.”