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.
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