Researchers in the United States and Israel have improved the momentum matching between a beam of electrons fired across a photonic crystal and the photons they emit in the process—so boosting emission by a factor of 100. [Image: L. Chen]
The interaction between free electrons and light is central to many modern technologies, among them microscopes, particle accelerators and high-energy lasers. But the strength of this interaction is limited by a mismatch in size between photons, which have a wavelength in the visible spectrum of about 10–7 m, and electrons, whose Compton wavelength is some five orders of magnitude smaller.
Now researchers have shown how to overcome this disparity by exploiting what are known as photonic flatbands (Nature, doi: 10.1038/s41586-022-05387-5). They have found that by carefully tuning the trajectory and velocity of electrons passing over a specially made slab of photonic crystal, it is possible to resonantly boost the particles’ emission of radiation by a factor of 100 compared to previous, more conventional demonstrations.
Mismatch in momentum
Interactions between free electrons and photons come in various guises. One of these is Cherenkov radiation, which is emitted by charged particles when they travel through a medium faster than the associated phase velocity of light. A variation on this is Smith–Purcell radiation, in which a radiating electron exceeds light’s phase velocity by virtue of passing very close and parallel to a periodic grating.
Such emission relies on phase matching—an equivalence between electron and photon phase velocities. But this condition only involves the emitted radiation’s longitudinal momentum. The transverse momentum, in contrast, can take on a range of values. Because not all such momenta values can support photonic modes, there is a mismatch in transverse momentum, which limits the number of photons that can be generated.
Increase in emission probability
In the latest work, Marin Soljačić, Yi Yang and Charles Roques-Carmes of the Massachusetts Institute of Technology (MIT), USA, and colleagues in the United States and Israel have shown how to overcome this problem using photonic flatbands—photonic band structures without dispersion. Already widely used in condensed-matter physics and photonics, flatbands, in this case, allow Smith–Purcell radiation to take on a range of transverse momentum values in a particular dimension—so enhancing interactions between electrons and photons.
The researchers demonstrated this approach with both computer simulations and experiments. In the latter case, they used a scanning electron microscope to fire 20- to 40-keV free electrons across the top of a photonic crystal consisting of an array of shallow 300 nm-diameter air holes etched in a slab of silicon. They measured the resulting radiation using a charge-coupled device and a spectrometer.
The researchers say that the scheme could be used to generate electromagnetic radiation over a wide range of wavelengths by varying the parameters of the photonic crystal and the speed of the electrons.
They were able to generate probability maps of photon emission by measuring the emitted radiation for different values of the free electrons’ velocity and the beam’s direction compared with the photonic crystal orientation. Because the beam was not quite parallel to the photonic crystal surface, the radiation was actually the result of two phenomena—the Smith–Purcell effect and another form of emission specific to free electrons known as incoherent cathodoluminescence.
After combining separate simulations for the two effects, the researchers found a close match between their modeling and the experimental results. Both indicated a roughly 100-fold increase in the probability of emission over a small range of electron velocities and photon frequencies compared with that of conventional Smith–Purcell radiation.
Future directions
The researchers say that the scheme could be used to generate electromagnetic radiation over a wide range of wavelengths by varying the parameters of the photonic crystal and the speed of the electrons—in principle producing anything from radio waves (including sought-after terahertz radiation) to X-rays. They also say it should be possible to invert the scheme and use resonant light waves to accelerate electrons, which, they speculate, might lead to miniature particle accelerators on silicon chips.
However, Soljačić cautions that more work needs to be done before the research can yield practical devices. Among the challenges, he notes, are further developing a chip-based source of fast electrons and hooking up all the optical and electronic components together in a single integrated circuit. “I would say that with some serious effort, in two to five years, such novel sources might start competing in at least some areas of radiation, at least in research settings,” he says.