Enhancing free-electron radiation using photonic flatbands

Highlighting the preprint "Observation of enhanced free-electron radiation from photonic flatband resonances" that appeared on arXiv the other day.

 

The efficiency at which free electrons radiate electromagnetic energy is dictated by phase matching between the electron and photons. In other words, the two should remain in phase. Phase matching requires an intersection in momentum (k) space between the electronic and photonic dispersion relations. 

In a uniform medium, phase matching can occur when the electron travels faster than the speed of light in the medium, corresponding to Cherenkov radiation. For periodic media, phase matching is no longer limited to a single wavevector, but can occur at a discrete set of points thanks to the periodicity of the Brillouin zone, known as Smith-Purcell resonances. 

Fine-tuning the band structure of a photonic crystal, one can achieve phase matching along a continuous line of momenta in the Brllouin zone. The authors predict orders-of-magnitude enhancement of the radiation intensity due to a flatband resonance, observing a 100-fold enhancement in their experiments. Discrepancies between simulations and observations are attributed to electron beam-induced doping of their photonic crystal.

I found this study particularly noteworthy for a few reasons:

• One of the main selling points of photonic flatbands is their ability to enhance nonlinear optical effects, which are most commonly considered in the framework of nonlinear Schrodinger-type equations describing phenomena such as solitons and lasing. This work establishes a new application of flatbands: mediating efficient interactions between free-electrons and light by bridging their distinct spatial scales.
• Flatbands are usually studied under the tight binding approximation, where they occur exactly. In photonic crystals the tight binding approximation doesn't hold, making it hard to achieve a sufficiently flat dispersion throughout the entire Brillouin zone (we tried this unsuccessfully in the past). However, enhancement of free electron-light interaction does not require a perfectly flat 2D dispersion relation, but merely flat dispersion along 1D line in the Brillouin zone. Such line degeneracies occur more generically at critical points between elliptic and hyperbolic isoenergy contours. This makes it easier to design and harness flatbands in practical systems.