Quantum statistics of light after saturated two-photon emission processes and the photon statistics of a two-photon laser

Starting with the Master equation for the photon distribution of a single-mode light beam derived by Scully and Lamb for one-photon emission processes it is straightforward to find corresponding Master equations for saturated k-photon emission. These can be solved without one-photon losses analytically. We discuss the resulting photon statistics in a two-photon laser by careful investigation of the solution and subsequent inclusion of one-photon losses.