Periodic dissipative soliton dynamics with tunable spectral notch depth in an all-polarization-maintaining nonlinear amplifying loop mirror fiber laser

Control of dissipative solitons has long been a key research focus due to their high energy and compressibility in ultrafast fiber systems. However, achieving controllable dissipative solitons in all-polarization-maintaining fiber lasers remains a major challenge, owing to the lack of flexible tuning methods to balance nonlinearity, dispersion, gain, and loss. Here, we propose a vector-analysis-based model to elucidate spectral modulation in soliton pulsations, enabling stepwise insight into nonlinear phase shifts and soliton evolution. To explore system behavior and stability, we numerically solve the nonlinear Schrödinger equation (NLSE) under controlled fiber-length variations in a nonlinear amplifying loop mirror (NALM), effectively tuning the relative nonlinear phase shift. Simulations show that precise control of this shift achieves pronounced modulation in both temporal and spectral domains, reveals a classical period-doubling route to chaos, and compensates for nonlinear variation of the gain coefficient itself, thereby facilitating complex dynamical behaviors under tightly coupled conditions. This provides a feasible approach for all-fiber spectral shaping amplification.