Temporal Soliton “Molecules” in Mode-Locked Lasers: Collisions, Pulsations, and Vibrations

A few years after the discovery of the stable dissipative soliton pairs in passively mode-locked lasers, a large variety of multi-soliton complexes were studied in both experiments and numerical simulations, revealing interesting new behaviors. This chapter focuses on the following three subjects: collisions between dissipative solitons, pulsations of dissipative solitons, and vibrations of soliton pairs. Different outcomes of collisions between a soliton pair and a soliton singlet are discussed, showing possible experimental control in the formation or dissociation of ‘soliton molecules’. Long-period pulsations of single and multiple dissipative solitons are presented as limit cycles and observed experimentally. Finally, one possible manifestation of long-period pulsation for a soliton pair results in a vibrational motion. All these behaviors that enrich the life of multi-soliton complexes make them akin to molecules. However, the analogy has clear limitations, since these ‘soliton molecules’ are inherently strongly dissipative and require a sustained energy supply from the gain medium.