In-phase and out-of-phase period doubling of bound-state solitons in Er-doped mode-locked fiber lasers

We investigate the specific changes of each soliton during the period-doubling of bound solitons in Er-doped mode-locked fiber lasers. Numerical simulations reveal that each soliton in the bound-state soliton can independently undergo period doubling. The different initial states of lasers may lead to in-phase and out-of-phase period doubling of bound-state solitons. These findings are experimentally verified by constructing an Er-doped fiber laser. The real-time spectrum evolution of bound-state solitons was measured using the time-stretched dispersion Fourier transform technique, confirming the existence of in-phase and out-of-phase period-doubling mechanisms in bound-state solitons. This study provides deeper insight into the complex dynamics of solitons in fiber lasers and contributes to the stability analysis of nonlinear systems and the detection of small signals.