Dynamical properties of nanolasers based on few discrete emitters

We investigate the dynamical properties of nanolasers comprising a few two-level emitters coupled to an optical cavity. A set of rate equations is derived, which agree very well with a solution of the full master equation model and makes it simple to investigate the properties of the system. Using a linearized version of these rate equations, we can analytically express the response of the nanolaser to a modulation of the pumping rate. These results are compared to the modulation response obtained directly from the master equation using a novel method. Using the rate equation method, we calculate the modulation bandwidth and show that, contrary to conventional semiconductor lasers, the nanolaser is typically over-damped and displays a dip in the modulation bandwidth as the two-level systems become inverted. Both these features can be traced back to the modeling of the emitters as two-level systems that are incoherently pumped.Comment: 11 pages, 5 figure