Theory of passively modelocked lasers for the case of a nonlinear complex propagation coefficient.

We examine passive modelocking where not only net gain saturation, but also group velocity dispersion and self-phase modulation contribute significantly to pulse shaping. Different sources of self-phase modulation are considered and closed form analytical solutions are obtained. The case of the colliding pulse modelocking is discussed, and an "ideal" case is considered, where the self-phase modulation and group velocity dispersion are balanced so as to take maximum advantage of this additional shaping mechanism.