Investigation of spatiotemporal mode-locked fiber lasers with hybrid dispersion.

In this work, by controlling the magnitude of the fourth-order dispersion (FOD) values introduced in the multimode fiber mode-locked laser system, the influence of hybrid dispersion (mainly second-order and FOD) on the spatiotemporal mode-locked fiber laser was studied. The numerical study results showed that the introduction of extra FOD enhanced the output pulse energy of the spatiotemporal mode-locked fiber laser and improved the energy stability range of the laser. In addition, the spatiotemporal mode-locked fiber laser system generated pump power-dependent mode competition by the combined effect of FOD and Raman effect, achieving bi-stable spatiotemporal mode-locking with mode complementarity. Specifically, following entry into the pulsating state from the steady-state mode-locking regime with increasing pump power, the system can re-enter a steady state with additional pump power elevation. However, the spatial mode composition involved in the steady-state mode-locking changes during this transition. Notably, this bi-stable behavior has not been reported in previous studies. These findings demonstrate that spatial mode modulation is achievable by rational utilization of FOD and nonlinear effect synergies. For the first time, to our knowledge, this study reveals the critical role of FOD in multimode fiber laser systems, providing new insights into spatiotemporal dynamics of higher-order dispersion and offering novel design strategies for high-energy lasers.