  Period-doubling bifurcation is a universal dynamic of nonlinear systems,
which has been extensively investigated in laser systems with a single
transverse mode. This study presents an experimental observation and
theoretical investigation of the period-doubling bifurcation in spatiotemporal
mode-locked (STML) multimode fiber lasers. In the period-doubling state, it is
observed that the pulse train modulation varies with the transverse-mode, and
the output beam profile fluctuates rapidly and periodically. The numerical
simulations conducted in this study are in good agreement with the experimental
observations. Furthermore, a simple iterative model is proposed by considering
the mode-dependent saturable absorption effect, and the experimental results
can be qualitatively interpreted by this model. Based on these results,
spatiotemporal saturable absorption is believed to be the key factor for the
unique spatiotemporal characteristic of period-doubling bifurcation in
multimode lasers. This study contributes to the understanding of the complex
spatiotemporal dynamics in STML multimode lasers and to the discovery of novel
dynamics in high-dimensional nonlinear systems.
