We report a distributed-feedback behavior in electron-driven dielectric gratings, arising from intrinsic forward-backward wave interactions, relevant to low-threshold coherent emission. Coupled-mode analysis reveals a quasi-stable region in the groove-depth dependence of the distributed-feedback coupling, consistently beginning at a fundamental organ-pipelike resonance. When driven by an electron beam, the guided power exhibits a corresponding resonance landscape, with a peak at the fundamental organ-pipelike resonance followed by regrowth in the quasi-stable region, highlighting a strong correlation between the intrinsic distributed-feedback behavior and electron-surface mode interaction. Based on this framework, we numerically demonstrate a silicon-grating chip-scale distributed-feedback Cherenkov free-electron laser operating in the terahertz (THz) regime and employing a micrometer-scale grating with an optimized groove depth. Small-signal and coupled-mode analyses for the optimized structure predict a milliampere-level oscillation threshold in good agreement with particle-in-cell simulations, while time-domain simulations confirm Bragg-resonant field buildup at 0.328 THz via electron microbunching with sustained guided-field growth along the grating. These results establish a general design principle for low-threshold terahertz sources based on distributed-feedback surface-mode resonances.

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• Integrated optics
• Light-matter interaction
• Free-electron lasers
• Periodic gratings
• Solid state lasers
• Waveguides
• Coupled mode theory
• Terahertz sources