“…where λ is the radiation wavelength, θ (shown in figure 1) indicates the radiation direction, L is the structural period, β is the ratio of the beam velocity to light velocity, and n is a negative integer that indicates the harmonic order. More recently, the Smith-Purcell free electron laser (SP-FEL) [6][7][8], which is the coherent SPR from premodulated electron bunches (generated previously by the accelerator or by the beam-wave interaction on the periodic surface), has been extensively studied for its potential in generating radiation that can not be easily obtained by other methods, especially for terahertz (THz) wave generation [9,10]. In SP-FEL, the SPR becomes coherent in some specific directions, where the SPR frequency is harmonic of bunching frequency, and the radiation intensity is remarkably increased since it is proportional to the square of the bunch number.…”