Real-time observation of dual-periodic dual-pulse synchronous and asynchronous pulsations in a spatiotemporal mode-locked fiber laser

We report the firstly experimental observation of dual-periodic dual-pulse synchronous pulsation (DDSP) and dual-periodic dual-pulse asynchronous pulsation (DDAP) in a spatiotemporal mode-locked fiber laser, composed of a short-period pulsation (SPP) lasting for tens of round-trip times (RTs) and a long-period pulsation (LPP) lasting for hundreds of RTs. It is found that the DDSP displays in-phase modulations between two pulses during the dual-periodic pulsation, while the DDAP demonstrates out-phase modulations in the SPP. Notably, the study reveals consistent pulsation periods across various transverse modes whether in the DDSP or DDAP, and the LPPs exhibit synchronization for different transverse modes, while the SPPs are asynchronous. Our findings illustrate that transverse modes do not influence the periodic modulation between two pulses. This exploration enhances the comprehension of multi-period pulsations in spatiotemporal mode-locked fiber lasers, and contributes to investigating high-dimensional nonlinear phenomena.