Fig. 1. Schematic diagram of the passively mode-locked fiber laser in the experiment

Fig. 2. Schematic diagram of single soliton without modulation signal. (a) Real-time observed spectrum of the single soliton; (b) comparison of spectra obtained by traditional optical spectrum snalyzer and the DFT technology, with an inset showing a schematic of the autocorrelation of single soliton pulse

Fig. 3. Vibrational soliton molecule under modulation signal amplitude of 0.266 V. (a) Real-time spectral observation of the soliton molecule; (b) evolution process diagram of the relative phase between the two pulses of the soliton molecules with the number of round trips; (c) evolution process diagram of the pulse spacing between the two pulses of the soliton molecules with the number of round trips; (d)‒(g) spectra of the soliton molecule at round trips 431, 443, 449, and 459, respectively.

Fig. 4. Double soliton molecule with in-phase vibration obtained with modulation signal amplitude of 0.701 V. (a) Real-time spectral observation of the double soliton molecule; (b)(c) evolution process diagrams of the relative phase and temporal of the two pulses in the left soliton molecule; (d)(e) evolution process diagrams of the relative phase and temporal of the two pulses in the right soliton molecule; (f)‒(i) spectra of the double soliton molecule at round trips 197, 203, 212 and 220, respectively

Fig. 5. Double soliton molecule with out-of-phase vibration obtained with modulation signal amplitude of 0.719 V. (a) Real-time observed spectrum of the double soliton molecule; (b)(c) evolution process diagrams of the relative phase and temporal of the two pulses in the left soliton molecule; (d)(e) evolution process diagrams of the relative phase and temporal of the two pulses in the right soliton molecule; (f)‒(i) spectra of the double soliton molecule at round trips 130, 140, 148 and 156, respectively