All-analytical semiclassical theory of spaser performance in a plasmonic nanocavity

Experimental approaches to manipulating light-matter interaction at the nanoscale level have quickly advanced in recent years, leading to the use of surface plasmon amplification by stimulated emission of radiation (spaser) in plasmonic nanocavities. Yet, a well-understood analytical theory to quantitatively explain certain characteristics of the spaser system has still been lacking and is greatly needed. Here, we develop an all-analytical semiclassical theory to investigate the energy exchange between active materials and fields and the spaser performance in a plasmonic nanocavity. The theory incorporates the four-level atomic rate equations in association with the classical oscillator model for active materials and Maxwell's equations for fields, thus allowing one to uncover the relationship between the characteristics of the spaser (the output power, saturation, and threshold) and the nanocavity parameters (quality factor, mode volume, loss, and spontaneous emission efficiency), atomic parameters (number density, linewidth, and resonant frequency), and external parameters (pumping rate). The semiclassical theory has been employed to analyze previous spaser experiments and shows that using a single gold nanoparticle plasmonic nanocavity to ignite the spaser is very difficult due to its high threshold. The theory can be commonly used in understanding and designing all novel microlaser, nanolaser, and spaser systems.