  In this article, we theoretically investigate a spaser (surface plasmon
amplification by stimulated emission of radiation), which consists of a
spherical silver nanoparticle surrounded by four-level gain medium of quantum
dots (QDs). The spaser system is pumped coherently and incoherently with the
same excitation rate, and the characteristics of coherent localized surface
plasmon (LSP) mode, thus produced, are compared for the two pumping scenarios.
We provide a detailed analytical expression for the steady state and show that
the incoherent pump is more suitable for the continuous spaser mode. The reason
is better understood by studying the temporal evolution of number of LSP (N_n
), where the oscillation of LSP starts early for incoherent drive and relaxes
to steady state with a large value of N_n. At a large pump rate, spaser curve
shows saturation. In addition, we have found that the resonance peak of spaser
field is independent of coherent as well as incoherent pumping, while the peak
amplitude of field depends on the pump rate.
