Dispersion Analysis of Ultrathin Grating for Free-Electron-Driven Frequency Comb

The utility of free-electron radiation spans numerous fields, including biological imaging, particle detection, and light generation across a wide frequency range, from microwave to X-ray. Despite extensive efforts to manipulate properties such as directionality, phase, and polarization using metamaterials, the intrinsic broadband spectra of free-electron radiation have yet to be fully exploited for the generation of frequency combs, which represent state-of-the-art technology in metrology and spectroscopy. In this study, we demonstrate the analysis of the dispersion of ultrathin grating for the generation of a free-electron-driven frequency comb. By assuming the decay rate of arbitrary mode is the same in all directions of the designed structure, a rational and adaptable platform for generating a specific frequency comb is presented, which has the potential to advance the development of metrology and spectroscopy in the terahertz band.