Unified Model for Breathing Solitons in Fiber Lasers: Mechanisms across Below- and Above-Threshold Regimes

The emergence of breathing solitons in mode-locked lasers presents a fundamental challenge for the theoretical modeling of mode locking, with the mechanisms underlying below- and above-threshold breathing solitons, and the origins of their distinct nonlinear dynamics, remaining poorly understood. Here, we develop a model that incorporates both spatial and temporal gain dynamics, enabling us to elucidate the origins of these two classes of pulsating states. We show that below-threshold breathing solitons arise from the interplay between Q switching and soliton shaping, whereas Kerr nonlinearity and dispersion dominate the formation of above-threshold breathers. The model further captures the markedly different dynamical properties of these regimes. Experimental observations corroborate the simulations, validating the predictive power of the framework. Beyond providing a refined theoretical basis for ultrafast laser design, this Letter advances the broader understanding of nonequilibrium dynamics in mode-locked lasers and offers new perspectives on breathing soliton phenomena across diverse physical systems.