Study of transition dynamics from breathing single pulse to higher-order pulses and hysteresis in a figure-of-9 fiber laser

This study investigates the nonlinear dynamics and hysteresis phenomena in a figure-of-9 fiber laser. The laser cavity consists of an Erbium doped nonlinear amplifying loop mirror (NALM) containing a Dispersion Compensation Fiber (DCF) segment, coupled to a nonlinear optical loop mirror (NOLM). A lumped-element model is developed for the laser cavity accounting for bi-directional light propagation. The model is based on the modified nonlinear Schrödinger equation (NLSE) with coefficients directly related to the parameters of each cavity segment. Gain saturation is taken into consideration for stable laser operation. The numerical results show that self-starting passive mode-locking and self-structuration of soliton lattices occur in the cavity of the laser. The soliton structuring is based on the concept of dissipative solitons, which requires a balance between dispersion-nonlinearity and gain-loss. The gain-loss parameters influence both the temporal pulse interactions and the NALM's transmission, leading to a large variety of single and multiple breathing dissipative soliton dynamics. In that context, riveting studies of the transition dynamics from breathing single pulses to high-order multiple breathing dissipative solitons and hysteresis with respect to unsaturated amplifier gain in a figure-of-9 all-fiber laser are explored.