Theory of passively mode-locked lasers for the case of a nonlinear complex-propagation coefficient

Abstract

We examine passive mode locking, to which not only net-gain saturation but also group-velocity dispersion and self-phase modulation contribute significantly. Different sources of self-phase modulation are considered, and closed-form analytical solutions are obtained. The case of the colliding-pulse mode locking is discussed, and an ideal case is considered, in which the self-phase modulation and group-velocity dispersion are balanced so as to take maximum advantage of this additional shaping mechanism. This mechanism is shown to be similar to that which causes solitons in optical fibers; it provides additional reduction of the pulse width and significantly improves the stability against fluctuations in net gain.