Single-electron Nano-chip Free-electron Laser

A conventional free-electron laser is useful but large, driven by a beam with many relativistic electrons. Although, recently, keV electron beams have been used to excite broadband radiation from material chips, there remains a quest for a chip-size free-electron laser capable of emitting coherent radiation. Unfortunately, those keV emitters from electron microscopes or dielectric laser accelerator usually deliver a small current with discrete moving electrons separated by a distance of a few or tens of microns. To envisage a chip-size free-electron laser as a powerful research tool, we study in this paper achievable laser radiation from a single electron and an array of single electrons atop a nano-grating dielectric waveguide. In our study, thanks to the strong coupling between the electron and the guided wave in a structure with distributed feedback, a single 50-keV electron generates 1.5-um laser-like radiation at the Bragg resonance of a 31-um long silicon grating with a 400-nm thickness and 310-nm period. When driven by a train of single electrons repeating at 0.1 PHz, the nano-grating waveguide emits a strong laser radiation at the second harmonic of the excitation frequency. A discrete spectrum of Smith-Purcell radiation mediated by the waveguide modes is also predicted in theory and observed from simulation in the vacuum space above the grating waveguide. This study opens up the opportunity for applications requiring combined advantages from compact high-brightness electron and photon sources.