Theory of Passive Mode Locking of a Laser Having Two Laser Amplifiers of Unequal Relaxation Time with a Slow Saturable Absorber

This paper presents a closed-form solution for the pulses of a laser having two homogeneously broadened laser amplifiers of unequal relaxation time mode locked by a ‘slow’ saturable absorber. The pulse shape is found to be secant-hyperbolic. It is found that the gains of both amplifiers participate in time-modulating the pulse and that the pulses are bandwidth-limited by the amplifier with a relaxation time longer than the cavity round-trip time. We have also shown that the model of a ‘slow’ saturable absorber and an amplifier of relaxation time longer than the cavity round-trip time does not give self-starting, mode-locking solutions.