Fig. 2: Phase-defined regimes of soliton assemblies.

a Gradually saturated total energy (black curve), increasing temporal separation (red curve) and well-defined phase-evolving velocity (blue curve), all nonlinearly fitted. Frame-by-frame manipulation is implemented by a stepwise increase in pump power, from 212.7 mW to 255.6 mW, with a step of 1.3 mW. Two constituents are amplified by the increased gain supply, resulting in a saturated tendency of total energy. The soliton pairs are governed by the gain supply and defined into three regimes with respect to their different internal phase evolutions. Three representative averaged multishot optical spectra are shown in the insets, with the pump powers of 220.5 mW, 233.5 mW, and 250.4 mW, respectively. The free spectral ranges indicate the different temporal separations. b A 3D interaction space is introduced to show the frame-by-frame evolving trajectories of (τ, φ), especially the variation in phase-evolving velocity. Each frame represents 1000 roundtrips. The related frame-by-frame first-order autocorrelation traces in the SP regime are shown in the inset. c–e Successive spectral interferograms of the three soliton assemblies. Different drifting of spectral fringes implies intramolecular phase evolutions. f Three molecular phases. The different tendencies are regard as the symbols to identify the phase-defined regimes. g Three temporal separations. Each vibrating period corresponds to a 2π variation in the molecular phase