Spatiotemporal mode-locked (STML) fiber lasers have become an excellent platform in nonlinear optics research due to the rich nonlinear evolution process. In order to overcome modal walk-off and realize phase locking of different transverse modes, it is usually crucial to reduce the modal group delay difference in the cavity. In this paper, we use long-period fiber grating (LPFG) to compensate the large modal dispersion and differential modal gain in the cavity, realizing the spatiotemporal mode-locking in step-index fibers cavity. The LPFG inscribed in few-mode fiber could induce strong mode coupling, which has wide operation bandwidth based on dual-resonance coupling mechanism. By using dispersive Fourier transform involved intermodal interference, we show that there is a stable phase difference between the transverse modes constituting the spatiotemporal soliton. These results would be beneficial for the study of spatiotemporal mode-locked fiber lasers.

Dissipative systems form various self-organized states owing to the abundant attractor structures. The study of the response of different self-organized states under collision perturbation is of great significance for understanding the dissipative nonlinear systems. The collision dynamics of single soliton and soliton molecules can not only assist the stability analysis of attractors, but also reveal the rich physical connotations of soliton interactions. Here, for the first time, the collision processes of single soliton and soliton molecules in different excited states are detected using the dispersive Fourier transform technology. The collision processes include the disintegration and rebuilding of soliton molecules as well as chaotic oscillating evolution, accompanied by the emergence of transition states such as triple binding state, soliton fusion and acceleration. According to whether the soliton molecule can return to its initial excited state, the collisions are classified as elastic and inelastic. The different interaction strength between solitons is an important condition for rebuilding stable soliton molecules. Numerical simulations show that the gain dynamics are the main physical origin of collisions. Our research will stimulate in-depth research on the interaction of self-organized states in nonlinear systems such as chemical molecules, and have potential applications in optical logic gates.

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