In this chapter, laser rate equations were used to derive another set of simpler rate equations that couple cavity photon number and the population of excited active atoms as the dynamical variables describing the laser. These equations were used to explore the buildup of laser oscillations from noise in a laser cavity and the remarkable growth of cavity photon number as the laser crosses threshold of oscillation. These modified rate equations were used to derive a Master equation for the cavity photon number probabilities. The steady-state solution of this equation was used to discuss equally remarkable transformation of photon statistics of laser light near threshold. The effect of spontaneous emission on setting the ultimate limit on laser linewidth was also discussed.
Rate equations for the population dynamics of multilevel systems in laser-induced fluorescence spectroscopy are solved by the aid of perturbation theory. This leads to a general expression for the population of the level pumped by the laser radiation. Arbitrary laser pulse shapes as well as collisional processes are admitted. In the first-order approximation three functions depending on time and the properties of the laser pulse remain. These functions have been tabulated for a bell-shaped laser pulse. The results are used in several characteristic situations and are compared with the numerical solutions of the rate equations.