Collective Effects in Nanolasers

In this thesis, a model of nanolasers is presented, in which the typically neglected correlations between emitters in the gain material are incorporated. The model is closely related to the traditional rate equation model of lasers, which describes the dynamics of the mean photon number and emitter populations in the laser, but extends the description minimally by including equations for the emitter-field and emitter-emitter correlations. The effect on the steady-state behaviour of the mean particle numbers is studied by analytically solving both the traditional and extended rate equations. It is found that the model presented here can capture some of the collective features like “excitation trapping,” which are also found in experiments and more intricate models. By considering the spectral properties of the modelled systems, it is found that both lasers and LEDs can be described. Moreover, it is found that a spectral splitting may occur, which signals strong collective emitter-field coupling, and it is shown that only lasers (not LEDs) may exhibit such a collective Rabi splitting. The connection between the excitation trapping and the spectral splitting is examined, and a parameter-space symmetry is identified. Finally, the photon noise and statistics are considered using a method of stochastic simulation, which was recently developed for the traditional rate equations. A few attempts at applying this to the extended rate equations are presented, and for some of these, the photon statistics exhibit features, which are found in experiments and other theories involving inter-emitter correlations. This approach may thus be the first step in developing a simple numerical description of laser noise including emitter cross-correlations.