Steering Smith-Purcell radiation angle in a fixed frequency by the Fano-resonant metasurface

Smith-Purcell radiation (SPR) is a kind of electromagnetic wave radiation that happens when an energetic beam of electrons passes very closely parallel to the surface of a ruled optical diffraction grating. The frequency of radiation waves varies in the upper and lower space of the grating for different electron velocity, satisfying the SPR relationship. In this study, a Fano-resonant metasurface was proposed to steer the direction of the SPR waves at the fixed resonant frequency by changing the velocity of the electron beam without varying the geometric parameters or adding extra coupling structure. The maximum emission power always locates at the resonant frequency by utilizing the integration of the Poynting vector. The relative radiated efficiency can reach to a maximum value of 91% at the frequency of 441 GHz and the efficiency curve has a dip when the direction of SPR is nearly vertical due to the high transmission. There is a great consistence of steering radiation angle from 65 degrees to 107 degrees by altering the velocity of electron beam from 0.6c to 0.95c both in analytical calculation and PIC (particle-in-cell of CST) simulation at terahertz frequencies, where c is the speed of light in vacuum. Furthermore, the destructive interference of Fano resonance between the magnetic mode and the toroidal mode shows the underlying physics of steering SPR in a fixed frequency. Our study indicates that the proposed structure can produce direction-tunable THz radiation waves at resonant frequency by varying the velocity of the electron beam, which is promising for various applications in a compact, tunable, high power millimeter wave and THz wave radiation sources.