Extended Data Fig. 2: Start-up in the presence of gain-induced nonlinearity and thermal nonlinearity: single soliton formation.
Numerical propagation for Eqs. (1–4) in Supplementary Section S1, modelling a microresonator-filtered fibre laser with the inclusion of a saturable gain and gain-induced nonlinearity in the amplifying cavity, and a thermal nonlinearity in the microcavity. The system parameters are ΓT = 5, τT = 8 × 103, η = 0.4, τg = 4 × 104, Θ = −13, g = 0.25 and Δ + ΘgP = −0.21. a, Pseudo-colour map of the electric field intensity in the microcavity, in the normalized units of Eqs. (1–4), as a function of the position in the microresonator x (which is normalized against the microcavity roundtrips) and time t (which is normalized against the main-cavity roundtrips). b, Temporal evolution of the peak intensity. The colours varying for increasing times matches with the plot inside panel e (showing the attractor). c, Temporal evolution of the effective detuning Δb-Δa. The colours varying for increasing times matches with the plot in panel e. d, Temporal evolution of the gain. The colours varying for increasing times matches with the plot in panel e. e, Map of the attractor for the peak intensity, detuning and gain, as in c, d, following the colour code of b–d as a function of time. The attractor is superimposed to the soliton (orange) and zero state (blue) stability regions. Figure 2a of the main text reproduces this map.
