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Based on a rate equation model for single-mode two-level lasers, twoalgorithms for stochastically simulating the dynamics and steady-statebehaviour of micro- and nanolasers are described in detail. Both methods leadto steady-state photon numbers and statistics characteristic of lasers, but oneof the algorithms is shown to be significantly more efficient. This algorithm,known as Gillespie's First Reaction Method (FRM), gives up to a thousandfoldreduction in computation time compared to earlier algorithms, while alsocircumventing numerical issues regarding time-increment size and ordering ofevents. The FRM is used to examine intra-cavity photon distributions, and it isfound that the numerical results follow the analytics exactly. Finally, the FRMis applied to a set of slightly altered rate equations, and it is shown thatboth the analytical and numerical results exhibit features that are typicallyassociated with the presence of strong inter-emitter correlations innanolasers.

Efficient stochastic simulation of rate equations and photon statistics of nanolasers