▎ 摘　　要

In this article, we propose a quantum regime for Cherenkov free-electron laser (CFEL) and surface plasmon polaritons (SPPs) excited in dielectric and multilayer graphene waveguides, respectively. This quantum regime is realized when the momentum spread induced in the interaction is smaller than the photon recoil. The discrete momentum exchange characterizing this interaction yields a significantly narrow single emission line. To determine the condition of the quantum regime, we derive an expression for the gain in the Cherenkov effect using a quantum mechanical treatment. It is assumed that the effective spread in momentum is due to the finite interaction length L (or the propagation length in the case of SPPs). For both cases, CFEL and SPPs, the effects of electron beam and waveguide parameters on the possibility of the quantum regime are studied. We conclude that the quantum regime can be basically verified at low electron beam energy (<40 keV) and at emission wavelengths in the near infrared range (<5 mu m) when L is in the order of millimeters. In the case of SPPs, we also show that the feasibility to realize quantum SPPs is enhanced by increasing the chemical potential and number of graphene layers. (C) 2018 Elsevier B.V. All rights reserved.