Model for Describing Plasmonic Nanolasers using Maxwell-Liouville Equations

We present a theoretical study of lasing action when plasmonic metallic structures that show lattice plasmon resonances are embedded in a gain medium. Our model combines classical electrodynamics for arrays of gold nanoparticles with a four-level quantum Liouville model of the laser dye photophysics. Numerical solution was implemented using finite-difference time-domain calculations coupled with a finite difference solution to the Liouville equation. A particular focus of this work is the influence of dephasing in the quantum dynamics on the emission intensity at the threshold for lasing. We find that dephasing in the quantum system leads to reduced lasing emission, but with little effect on the long term population inversion. We also examine rate equation models with and without constraints arising from the Pauli Exclusion Principle. There are factor of two differences between the Maxwell-Liouville results (greater emission intensities and narrower widths) compared to the corresponding results of rate-equation models of the dye states, which indicates the importance of using the Maxwell-Liouville approach in modeling these systems.