Passive mode locking of a femtosecond Ti:sapphire laser with pulsed synchronous pumping by a finite train of picosecond pulses

An analysis is made, with the aid of the self-consistent nonlinear ABCD matrix method, of the specific features of the mechanism of passive mode locking of a femtosecond Ti:sapphire laser under conditions of pulsed synchronous pumping. The conditions of stable laser operation are studied. It is proposed to use an additional aperture as an element of negative feedback for the stabilisation of passive mode locking. Practical recommendations concerning the optimisation of a femtosecond laser are given.