Statistical amplitude and phase variations in mode-locked lasers

The influence of statistical amplitude or phase variations in the modes of a mode-locked laser on the time-dependent output intensity and on the relative efficiency of nonlinear optical processes is investigated. The ensemble-averaged intensity, the time-dependent distribution of the resulting complex amplitude, and the second-order moment of the intensity distribution are calculated and discussed for both types of variations. As long as no systematic amplitude or phase changes are introduced, the pulse shape is maintained, but superimposed on a fluctuating background, and the efficiency for nonlinear optical processes is reduced. For random phase fluctuations over 2π the pulse behavior disappears completely and the output becomes Gaussian or chaotic light.