Transient Evolution of the Field Power Spectrum during the Switch-on of a Detuned Laser

We describe the time evolution of the nite window eld power spectrum during the switch-on transient of a detuned laser. We derive an analytical expression for a stochastic map that generates a time series of the eld over time steps of the order of the fast time scale of evolution. The diierent eeects of static initial intensity noise and phase noise along the evolution are disentangled. Initiation of laser emission can be viewed as a process of noise ampliication. For this reason noise eeects are particularly important during the transient dynamics. The statistics of laser switch-on processes have been considered in a variety of situations 1{11], including