Free-electron-driven Vortex Smith-Purcell Radiation with Higher-order Topological Charge

A free-electron-based vortex Smith-Purcell radiation with the higher-order topological charge is proposed in this paper based on uniform helical grating. Due to the spiral constraint of azimuth, the evanescent field of the electron beam will be diffracted and possess the orbital angular momentum. When the wave vectors of the diffraction wave match those of the free space, the vortex beam will be generated with different topological charges. Moreover, the higher-order topological charge can be affirmatively generated by utilizing the higher spatial harmonics according to Bloch's theorem of the helical periodic system. Moreover, the vortex beam with mixed orbital angular momentum can also be achieved. Furthermore, and the mode purities of these vortex beams are analyzed. The proposed scheme may facilitate the journey of the vortex beam from optical into terahertz band.