Model for describing plasmon-enhanced lasers that combines rate equations with finite-difference time-domain

We report a theoretical study of lasing when plasmonic metallic structures are embedded in a gain medium. The model used is a dynamic semi-quantumapproach that accounts for stimulated and spontaneous emission wherein molecules constituting the laser dye are described using a four-level rate equation model, which is coupled to an electrodynamics description of the entire system including metal particles. Based on 3D simulations in which electromagnetic fields for both the pump and emitted photons are accurately determined for an array of elliptical gold nanorods, we numerically demonstrate lasing action above an intensity threshold for a narrow range of wavelengths close to the plasmon maximum. We also show numerically that this lasing action clamps the population inversion above threshold. The dye molecule photophysics near the nanoparticle was also studied, and it is demonstrated that stimulated emission dominates over spontaneous emission above threshold, with most of the stimulated emission being associated with the near-field region near the metal nanorods. The effect of the Purcell factor on the lasing action is also studied. This theoretical work provides the basic framework for investigation and optimization of light emission arising from the coupling of gain media and plasmonic nanostructures.