In this paper a surface plasmon polariton laser (spaser), which generates surface plasmons in graphene nanoflake, is considered. The peculiarities of spaser, such as strong material dispersion, require revision of basic laser equations. We provide a
full derivation of equations of the spaser dynamics starting from the Maxwell-Bloch equations. Optical Bloch equations and rate equations are obtained and the relation of the equation parameters through the physical ones is given. In the case of graphene realization, the numerical parameter values are estimated.
We show that net amplification of surface plasmons is achieved in channel in a metal plate due to nonradiative excitation by quantum dots. This makes possible lossless plasmon transmission lines in the channel as well as the amplification and generat
ion of coherent surface plasmons. As an example, a ring channel spaser is considered.
