Super-poissonian fluctuations of number of photons in the radiation of a single-mode laser operating near active particles number threshold

It is shown that considerably exceeding the threshold pump power for laser oscillation is not sufficient for attaining Poissonian statistics of laser-emitted photons. The necessary and sufficient condition for achieving the Poissonian level of fluctuations of the number of photons in a laser mode consists in simultaneously considerably exceeding the threshold level with respect to the pumping rate and the threshold with respect to the number of active particles of the laser medium. In the case of arbitrarily large pump-power excess over the threshold, but close to the threshold with respect to the number of active particles, fluctuations of the number of photons are substantially higher than the shot noise level (super-Poissonian statistics of photons) and can reach the level of fluctuations of thermal (chaotic) light.