Statistical light-mode dynamics of multipulse passive mode locking

We study the multipulse formation in passive mode locking in the framework of the statistical light-mode dynamics theory. It is a many-body theory that treats the complex many-mode laser system by statistical mechanics. We give a detailed theory and experimental verification for the important case of multiple-pulse formation in the laser cavity. We follow and extend our former work on the subject. We give a detailed analysis with a rigorous calculation of the partition function, the free energy, and the order parameter in the coarse-graining method within the mean-field theory that is exact in the light-mode system. The outcome is a comprehensive picture of multipulse formation and annihilation, pulse after pulse, in an almost quantized manner, as the noise ("temperature") or the light power is varied. We obtain the phase diagram of the system, showing a series of first-order phase transitions, each belonging to a different number of pulses. We also study the hysteresis behavior, typical for such thermodynamic systems. We elaborate on the role of the saturable absorber structure in determining the multipulse formation. The theoretical results are compared to experimental measurements that we obtained with mode-locked fiber lasers, and we find an excellent agreement.