Theory of internally pumped mode-locked CW dye laser

A closed-form solution for the pulses of an internally pumped mode-locked CW dye laser, where the mode locking is achieved by a fast saturable absorber, is presented. The pulse shape is found to be secant hyperbolic in time. The pulsewidth and the pulse power are expressed as functions of the system parameters. The pulses are found to be bandwidth limited by the amplifier of relatively longer relaxation time.