Double-periodic pulsating solitons in 2.8 μm mid-infrared fiber laser

This study systematically investigates double-periodic pulsating solitons in mid-infrared ultrafast fiber lasers based on the complex Ginzburg-Landau equation. By adjusting the pump power in a 2.8 μm Er³⁺-doped fluoride mode-locked fiber laser, we demonstrate the transitions from single-pulse steady operation to pulsating solitons, two-soliton bound-state, and ultimately three- and four-soliton molecular numerically. We observed several double-periodic pulsating solitons with short periods of 13, 9, 4, 11, 7, 10, and 3 and long periods of 425, 86, 105, 216, 648, 823, and 90, respectively. These solitons exhibit hybrid dynamics characterized by the coexistence of both short- and long-period pulsation features. Furthermore, we analyzed double-periodic pulsating solitons with a short period of 3. Within a specific range of increasing pump power, these solitons maintained a constant short period while exhibiting an increase in their long period. Compared to the Yb³⁺-, Er³⁺-, and Tm³⁺-doped silica fibers used in near-infrared fiber lasers, the Er³⁺-doped fluoride fiber employed in 2.8 μm mid-infrared fiber lasers exhibits a smaller nonlinear coefficient and weaker nonlinear effects, with distinct higher-order nonlinear characteristics in theoretical modeling. Therefore, this paper presents the first theoretical investigation of double-periodic pulsating soliton dynamics in mid-infrared fiber lasers. These findings deepen the understanding of pulse nonlinear dynamics in anomalous-dispersion-dominated systems and offer novel insights for optimizing pulses in mid-infrared ultrafast lasers, with potential applications in molecular spectroscopy and precision material processing.