Spectral-temporal transition dynamics of dichromatic soliton molecules in synchronous mode-locked fiber lasers

Dichromatic soliton molecules (DSMs), comprising multiple optical solitons with two carrier frequencies, can exhibit static or breathing states, akin to real chemical molecules. Although these two states have been extensively studied individually, comprehending the intricate transitions between them is crucial for effectively controlling lasing states. Here, we experimentally observe spectral-temporal transition dynamics between these DSM states in a synchronous mode-locked fiber laser, leveraging dispersive Fourier transform and dispersive temporal interferometry techniques. Our findings reveal obvious transient breathing processes during the transition from breathing to static states, while the reverse transformation is not evident. Numerical simulations, utilizing a model integrating equations for population inversion in mode-locked lasers and cross-phase-modulation-coupled complex Ginzburg-Landau equations, reproduce similar dynamics. This investigation elucidates transition dynamics in nonequilibrium systems, providing insights for intelligent manipulation of lasing states.