Design optimization of spasers considering the degeneracy of excited plasmon modes

We model spaser as an n-level quantum system and study a spasing geometry comprising of a metal nanosphere resonantly coupled to a semiconductor quantum dot (QD). The localized surface plasmons are assumed to be generated at the nanosphere due to the energy relaxation of the optically excited electron-hole pairs inside the QD. We analyze the total system, which is formed by hybridizing spaser's electronic and plasmonic subsystems, using the density matrix formalism, and then derive an analytic expression for the plasmon excitation rate. Here, the QD with three nondegenerate states interacts with a single plasmon mode of arbitrary degeneracy with respect to angular momentum projection. The derived expression is analyzed, in order to optimize the performance of a spaser operating at the triple-degenerate dipole mode by appropriately choosing the geometric parameters of the spaser. Our method is applicable to different resonator geometries and may prove useful in the design of QD-powered spasers.