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. ![]() When driven by a train of single electrons repeating at 0.1 PHz, the nano-grating waveguide emits strong laser radiation at the second harmonic of the excitation frequency. 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- µm laser-like radiation at the Bragg resonance of a 31- µm long silicon grating with a 400-nm thickness and 310-nm period. 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. Unfortunately, those keV emitters from electron microscopes or dielectric laser accelerators usually deliver a small current with discrete moving electrons separated by a distance of a few or tens of microns. 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. ![]() A conventional free-electron laser is useful but large, driven by a beam with many relativistic electrons.
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