Enhanced Smith–Purcell radiation from bound states in the continuum of metallic gratings

Abstract

The enhancement of Smith–Purcell radiation (SPR) produced by electrons moving closely to a grating is a longstanding topic of interest. Here, we systematically investigate the resonant enhancement of SPR for planar metallic gratings. Using an analytic solution for the amplitude of SPR, we show that metallic gratings with a small dutycycle support two type of bound states in the continuum (BICs), i.e. symmetry-protected BICs and accidental BICs, both of which enable the SPR to be enhanced by orders of magnitude at the resonant frequency. The required electron energy for the excitation of BICs can be reduced by employing a higher-order diffraction wave for SPR. Our results present a mechanism for enhancing the SPR produced by metallic gratings, and may find applications in free-electron lasers.