  In this article, a spaser (surface plasmon amplification by stimulated
emission of radiation) system consisting of a metal nanoparticle surrounded by
a large number of quantum dots (QDs) is studied. Usually, the effect of
electron-phonon interaction is neglected in the spaser related literature. But
some gain media, attributed by the large Raman scattering cross-section,
exhibit stronger electron-phonon interaction. No such study has been performed
for a QD-based spaser. Hence, it warrants investigation of the same in spaser
system. In the present work, we investigate the effects of electron-phonon
interaction on a three-level QD-based spaser. We consider two types of
interaction potentials, linear and quadratic, and analyze their effects
individually. First, we focus on the linear electron-phonon interaction that
perturbs the electrons present in the excited state. This yields a periodic
steady-state number of localized surface plasmon (LSP). The accompanying
analytic solution reveals that the population inversion of the gain medium
depends on the linear potential strength (Frohlich constant) but does not
affect the threshold of spaser considerably for the given numerical parameters.
In addition to the LSP, phonons may be generated during this process, the
temporal dynamics of which are also detailed. Initially, the number of phonons
exhibit decaying periodic oscillations, whose amplitude depends on the strength
of the electron-phonon interaction. Under continuous pumping, at later times,
the number of phonons reaches a steady-state value, which may find application
in realization of continuous phonon nanolasers. Further, the effect of the
quadratic potential is studied phenomenologically by increasing the
excited-state decay rate. This results in a large number of LSP and an intense
spaser spectrum.
