Abstract
A quantum approach is proposed to describe the Smith-Purcell free-electron laser (SP-FEL) where the interacting electron is described quantum mechanically as a wave packet with a finite width. A quantum regime for the SP-FEL operation is newly defined when the electron wave packet width is larger or comparable to the interaction length. This quantum regime can be realized in SP-FELs in periodic nanostructures enabled by current nanofabrication advances. In this quantum regime, the gain linewidth is determined by the longitudinal size of the electron wave packet. The latter result can be used in measuring the spreading length of a free-electron quantum wave packet. It is found that as the width of the electron wave packet increases, the coherence of the emitted radiation is enhanced. Finally, whether in the classical or quantum regime, an analytical expression for the gain in a SP-FEL is derived. Then we propose an efficient scheme for a SP-FEL amplifier to generate terahertz radiation. (C) 2021 Optical Society of America