Intensity distribution for a Q-switched laser

We examine the nonlinear dynamics of the turn-on of a
Q
-switched laser (or maser) oscillator. The description of the laser is fully quantal, including fluctuations. We use the coherent state representation for the field, and treat the atoms adiabatically. We obtain for the first time an accurate analytical solution for the distribution, which describes the probability, in an ensemble of identically prepared lasers, that the field intensity has a certain value at a certain time after the initiation of the
Q
-switch. The most easily observable fluctuation effect is a timing jitter in the turn-on, amounting to about two and one-half times the time constant, which describes the early exponential rise of the field intensity. An example is presented, using parameters approximating those of a 1-mW helium-neon laser.