“…The numerical investigation demonstrates the SM formation can refer to the direct soliton-soliton interaction as the oscillating tails overlapped, and the SMs can stably exist in the cavity when phase differences are 0, π, and ± π/2. Heretofore, various SMs have been exemplified in mode-locked fiber lasers based on nonlinear polarization rotation (NPR) [13], nonlinear optical loop mirror (NOLM / NALM) [14,15], real saturable absorbers (SAs) (e.g., graphene [16], carbon nanotubes [17,18], MoS 2 / fluorine mica Langmuir Blodgett film [19]), nonlinear multimode interference effect [20], and spatiotemporal mode-locking [21] et al In Ref. [22], the generation and propagation of various SMs were summarized, and pointed out that the SMs can be formed with fundamental unit of conventional solitons, stretched pulses, parabolic pulses, or gain-guided solitons.…”