Emission of smith-purcell radiation at the fundamental frequency from a grating equipped with sidewalls

The two-dimensional theory of the Smith-Purcell free-electron laser predicts that coherent Smith-Purcell radiation can occur only at harmonics of the frequency of the evanescent wave that is resonant with the beam. Particle-in-cell simulations have shown that in a three-dimensional context, where the lamellar grating has sidewalls, coherent Smith-Purcell radiation can be copiously emitted at the fundamental frequency, for a well-defined range of beam energy. An experiment at microwave frequencies has confirmed this prediction. The power output is considerably greater than for the previously observed emission at the second harmonic, in agreement with three-dimensional simulations. The dependence of frequency on beam energy and emission angle is in good agreement with three-dimensional theory and simulations. Provided that a reduction in scale can be achieved, a path is open to coherent Smith-Purcell radiation at Terahertz frequency.