Photon statistics of a bad-cavity laser near threshold

A simple model of a bad-cavity laser is presented based on Haken's master equation for N pumped two-level atoms in a cavity. Via adiabatic elimination of fast variables the whole photon statistics is solved analytically near threshold. It is shown that the second order coherence function $g^{(2)}(0)$ has a very different behavior near threshold for a bad-cavity laser compared to a good-cavity laser. The power spectrum illustrates nicely the different time scales involved in the dynamics