Calculation of the colliding pulse mode locking in CW dye ring lasers

A calculation of the influence of a transient absorber grating on the pulse parameters of a dye laser in the "colliding pulse mode-locking" (CPM) regime is given. It is shown that, compared to other passive methods, considerably shorter pulses with a more favorable stability region can be obtained. Within the stability range of single pulse operation the shortest pulses in the CPM are obtained by operating far above threshold where the saturation energy of the amplifier is much greater than that of the absorber. Deviation from an amplifier position that is symmetric with respect to the amplification of the counter-running pulses leads to different energies of the pulses and to a strong decrease of the stability range. Taking the dispersive properties of absorber and amplifier into consideration, equations for the time dependent phase of the laser pulse are established and solved by an analytical ansatz. The resulting pulse chirp is shown to be mainly dependent on the detuning of the pulse frequency from the center frequency of the saturable absorber. The estimated values for the pulse duration and the down-chirp for typical experimental conditions of a rhodamine 6G-DODCI CPM laser agree well with the measured ones.