Bistability in spatiotemporal mode-locking with dynamic multimode gain

Three-dimensional (3D) dissipative soliton existed in spatiotemporal mode-locked (STML) multimode fiber laser has been demonstrated to be a promising formalism for generating high-energy femtosecond pulses, which unfortunately exhibit diverse spatiotemporal dynamics that have not been fully understood. Completely modeling the STML multimode fiber lasers can shed new light on the underlying physics of the spatiotemporal dynamics and thus better manipulate the generation of high-quality energic femtosecond pulses, which however is still largely unmet. To this end, here we theoretically investigate a dynamic multimode gain model of the STML multimode fiber laser by exploring the multimode rate equation (MMRE) in the framework of generalized multimode nonlinear Schr\"odinger equation. Using this dynamic multimode gain model, the attractor dissection theory is revisited to understand the dominant effects that determine the modal composition of 3D dissipative soliton. Specifically, by varying the numerical aperture of the multimode gain fiber (MMGF), different gain dynamics that correspond to distinct types of gain attractors are observed. As a result, two distinguishing STML operation regimes, respectively governed by the multimode gain effect and spatiotemporal saturable absorption, are identified. In the latter regime, especially, 3D dissipative solitons present bistability that there exist bifurcated solutions with two different linearly polarized (LP) mode compositions. To verify the theoretical findings, the experimental implementation shows that the state of STML can be switched between different LP modes, and confirms the presence of bistability. Particularly, the 3D-soliton shaping mechanism that is governed by the multimode gain effect is testified for the first time, to the best of our knowledge.