Three-level Spaser System: a Semi-Classical Analysis

We theoretically study a nanospaser system, which consists of a spherical silver nanoparticle embedded inside a sphere composed of dye molecules. The gain of the system, dye molecules, are described by a three-level model, where the transition frequency between the lowest two energy levels is close to the surface plasmon frequency of the nanosphere. Contrary to a two-level model of spaser, the three-level model takes into account finite relaxation time between the high energy levels of the gain medium. These relaxation processes affect both the spaser threshold and the number of generated plasmons in the continuous wave regime. While for a two-level model of a spaser the number of generated plasmons has a linear dependence on the gain, for the three-level model this dependence becomes quadratic.