Dye laser statistics and the phase transition

By an analytic examination of the photon probability distribution derived by Schaefer and Willis it is shown that, under the conditions for a second order phase transition, the dye laser statistics may be indistinguishable from those of a conventional laser, despite the presence of the triplet states. Under the conditions for a first order phase transition the statistics change, and for some combinations of parameters the change is manifest in the behavior of the normalized second factorial moment of the photon number. Curves are presented that should be directly verifiable by photoelectric counting experiments.