Buildup of laser oscillations from quantum noise.

Buildup of laser oscillation is expressed in terms of the probabilities p(n)(t) that there are n photons in the laser cavity. These probabilities obey a coupled set of difference-differential equations of motion. The method and results of numerical integration of these equations are given here for the initial condition that no photons exist (radiation field vacuum). Corresponding equations of motion for the moments of the photon distribution are derived, and their time dependences are given. A movie showing the time development of the p(n) from an initial vacuum is given on the corners of the November 1970 issue of Applied Optics and can be seen by flipping through the pages.