Analysis of the uniform rate equation model of laser dynamics

The spatially independent laser rate equation model is generalized to include multimode effects, and it is also shown that the same description of laser behavior as provided by the single-mode model results. Analytical expressions for the steady-state values of the variables in all modes are derived. It is shown that a singularity at the oscillation threshold exists in the steady-state equations which is responsible for the laser action. It is further demonstrated that the inverted population and the photon density in off-axis modes saturates above threshold, whereas the photon density in the primary mode increases linearly with pump rate above threshold. The exact time-dependent solutions are determined numerically, and it was found that the spiking separation and decay time could change by more than 50 percent of their values at the start of laser emission to the region of steady-state oscillation, even when the pump is assumed to be time independent. The linearized expressions for the spiking parameters are, therefore, inadequate-despite their frequent use-to describe phenomena appearing in the early portions of the spiking trace. A comparison with five experimental cases is also made. It was found that this model, with all modes included, provides no improvement over the single mode model, and cannot account for the irregular or undamped spiking or even the multimode oscillations observed experimentally.