Pulse statistics of modulated gas lasers

Pulse statistics of modulated class A single mode lasers is analyzed both numerically and analytically. The time evolution of the electric field is described by the following equation where a is the pump parameter and ψ is the spontaneous emission noise of intensity D. An analytic approximation is developed for the switch-on time probability density. In this approximation the time evolution is divided in two regimes: a linear one with noise, where saturation is not important, and a nonlinear deterministic domain. Using a kind of self-consistency condition for the switch–on time probability density P(t), an integral equation is derived for P(t). Numerical simulations show that this approximation is very accurate (see Fig.1).