Pulsating Period-Doubled Soliton Molecules in a Passive Mode-Locked Fiber Laser

The period-doubling bifurcation, which marks a transition from steady states to chaotic regimes, has been widely studied both theoretically and experimentally. However, the complex nonlinear dynamical phenomena underlying these transitions remain to be fully investigated. In this paper, the complex dynamics of pulsating period-doubled soliton molecules (PDSMs) were experimentally and numerically investigated in a passively mode-locked fiber laser. Two distinct pulsating period-doubled soliton molecules (PDSMs) were experimentally generated by adjusting the polarization controller (PC), including the single-period and double-period varieties. Transient pulsating characteristics of these soliton molecules were captured using dispersive Fourier transform technique, revealing the presence of multiple energy modulation periods in PDSMs. Numerical simulations reproduced the interplay of multiple bifurcation behaviors, which was in good agreement with the experimental observations. These findings provide new insights into complex bifurcation phenomena, offering valuable perspectives for nonlinear science and applications.