Unified approach to multiphoton lasers and multiphoton bistability

This paper presents a unified theory of nonequilibrium transitions which occur in radiation interacting via an $n$-photon transition with atomic systems inside optical cavities. Incoherent pumping of the atoms and coherent driving of the cavity are included. Examples of such systems are the $n$-photon laser, the $n$-photon laser with injected signal, and $n$-photon optical bistability. The state equation and stability conditions for these phenomena are derived. Fluctuations are included via a Fokker-Planck equation in the constant-diffusion approximaton for which potential solutions may be obtained in the steady state. When these solutions are used, moments of the photon distribution can be calculated for the above systems in the specific cases of one- and two-photon transitions.