  In this paper, a possible way to achieve lasing from THz to extreme UV domain
due to stimulated scattering of graphene plasmons on the free electrons is
considered. The analytical-quantitative description of the proposed FEL scheme
is based on the self-consistent set of the Maxwell--Vlasov equations. We study
the downconversion as well as the upconversion. It is shown that the coherent
downconversion of infrared radiation to THz one can be achieved using a source
of very non-relativistic electrons at the resonant coupling with the graphene
plasmons. Due to the strongly confined graphene plasmons, the upconversion of
mid-infrared to extreme UV radiation can be achieved with the mildly
relativistic electron beams. The latter is a promising mechanism for the
tabletop short-wavelength free electron nanolaser.
