Dynamics at threshold in mesoscale lasers

The threshold properties of very small lasers (down to the nanoscale) are a topic of active research in light of continuous progress in nanofabrication. With the help of a simple rate equation model, we analyze the intrinsic, macroscopic dynamics of threshold crossing for (class B) lasers whose response is adequately described by interplay of the intracavity photon number and the population inversion (energy reservoir). We use the deterministic aspects of the basic rate equations to extract some fundamental time constants from an approximate analysis of laser dynamics in the threshold region. Approximate solutions for the population inversion and the field intensity, up to the point where the latter reaches macroscopic levels, are found and discussed. The resulting time scales characterize the laser's ability to respond to perturbations (external modulation or intrinsic fluctuations in the lasing transition region). Numerical verifications test the accuracy of these solutions and confirm their validity. The predictions are used to interpret experimental results obtained in mesoscale lasers (VCSELs) and to speculate about their extension to nanolasers.