Bidirectional Feedback and Correlation Analysis of Soliton-State Transitions Mediated by a Quasi-Continuous-wave Background

The quasi-continuous-wave background (qCWB) is a common phenomenon in the nonlinear dynamics of ultrafast fiber lasers, yet its role in soliton-state transitions remains insufficiently understood. Here, we confirm the presence of qCWB by combining soliton filtering with short-time Fourier transform measurements. Mutual information and Pearson correlation analyses reveal that qCWB plays a decisive role in nonequilibrium switching between soliton molecules and pulsating soliton molecules. We further identify a bidirectional feedback mechanism, in which qCWB induces soliton-state switching via positive feedback, while the resulting soliton states exert negative feedback on qCWB, thereby maintaining dynamic balance. This mechanism enables a qCWB-based optical encoding platform for active control of ultrafast laser states.