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 find the conditions upon the amplitude and frequency of an external electromagnetic field at which the dipole moment of a Bergman-Stockman spaser oscillates in antiphase with the field. For these values of the amplitude and frequency the losses in
metal nanoparticles is exactly compensated of by gain. This shows that spasers may be used as inclusions in designing lossless metamaterials.
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.
We demonstrate that when the frequency of the external field differs from the lasing frequency of an autonomous spaser, the spaser exhibits stochastic oscillations at low field intensity. The plasmon oscillations lock to the frequency of the external
field only when the field amplitude exceeds a threshold value. We find a region of values of the external field amplitude and the frequency detuning (the Arnold tongue) for which the spaser synchronizes with the external wave.
