FULL QUANTUM THEORY OF OPTICALLY PUMPED THREE-LEVEL LASER
光泵三能级激光的全量子理论

The Langevin quantum theory has been used to treat the optically pumped three-level laser system. We derive an equation of motion for laser field in the type of Van der Pol equation when the photon number of the laser field is not too high. It includes not only both incoherent and coherent pumping, but also both strong and weak optical pumping. If an average over reservoir is taken, the equation will give all the semi-classical results. Our results show that the laser gain comes from two basic processes, i.e., a two-photon process and a two-step process. When the pumping strength is larger than some value, the dynamic Stark effect will appear. The laser linewidth is mainly contributed by the thermal noise, the vaecum fluctuation, the spontaneous emissions between the laser levels and the spontaneous Raman scattering.