Theory of mode-locked pumping of dye lasers

A system of equations is derived to describe the pulse shape in a train of ultrashort pulses in the active mode-locking regime. Unlike other investigations, this system allows for the multilevel properties of the active medium, for the dispersion of the group velocities of the interacting pulses, and also for depletion of the pump pulse during propagation and for the transient nature of the polarization of the lasing transition. In the degenerate case, theoretical analyses are made of these equations and analytic expressions are obtained for the parameters of the laser pulse. It is found that the minimum of the lasing pulse duration is shifted into the range of negative detunings as a result of mismatch of the group velocities and that there is a certain pump pulse energy for which the duration of the laser pulse has a minimum. Numerical investigations are made of the shape and parameters of ultrashort pulses for various mismatches of the resonator lengths.