Influence of natural phase fluctuations on active mode locking

An analysis is made of the influence of the spontaneous radiation noise on the operation of a mode-locked laser with an inhomogeneously broadened line. Mode locking is achieved by modulation of the losses. The system of equations for the perturbations of the phases of individual modes is replaced by a parabolic stochastic differential equation in which the mode number is considered to be an independent continuous variable. The boundary conditions and requirements for a Langevin source in the parabolic equation are formulated. It is shown that the phase of the nth mode drifts from that of the mth mode in accordance with the random walk law. A limit is derived for the total number of modes which can be locked when the fluctuation strength (the spectral width of a free-running mode) and the modulation depth are fixed.