Numerical study on multi-pulse dynamics and shot-to-shot coherence property in quasi-mode-locked regimes of a highly-pumped anomalous dispersion fiber ring cavity

We numerically investigate quasi-mode-locked (QML) multi-pulse dynamics in a fiber ring laser cavity in the anomalous dispersion regime. We show that the laser cavity can operate in five constitutively different QML regimes, depending on the saturation power of the saturable absorber element and the length of the passive fiber section that parameterize the overall nonlinearity and dispersion characteristic of the laser cavity. We classify them into the incoherent noise-like-pulse, partially-coherent noise-like-pulse, symbiotic, partially-coherent multi-soliton, and coherent multi-soliton regimes, accounting for their coherence and multi-pulse formation features. In particular, we numerically clarify and confirm the symbiotic regime for the first time to the best of our knowledge, in which noise-like pulses and multi-solitons coexist stably in the cavity that has recently been observed experimentally. Furthermore, we analyze the shot-to-shot coherence characteristics of the individual QML regimes relative to the amount of the nonlinear-phase shift per roundtrip, and verify a strong correlation between them. We also show that the net-cavity dispersion plays a critical role in determining the multi-pulse dynamics out of the partially-coherent noise-like-pulse, symbiotic, and partially-coherent multi-soliton regimes, when the cavity bears moderate nonlinearity. We quantify and visualize all those characteristics onto contour maps, which will be very useful and helpful in discussing and clarifying the complex QML dynamics.