Energy-increasing driven hierarchical transition of weakly dissipative pure-sextic soliton to multi-breather soliton molecules

We systematically investigated the mechanism of multi-state hierarchical evolution of pure- sextic soliton (PSS) regulated by saturation energy (Esat) in normal-dispersion fiber lasers. At low Esat, the weak gain saturation effect fails to balance the normal dispersion and nonlinear effects such as self-phase modulation (SPM), resulting in PSS exhibiting a weakly dissipative state with limited spectral broadening. With increased Esat, significant accumulation of pulse power and nonlinear effects triggers modulation instability, leading the PSS to transition into a breathing state through periodic energy redistribution, thereby releasing the excessive nonlinear phase shift accumulated by SPM. When Esat is further increased, the synergistic effect of SPM and modulation instability breaks through the clamping threshold, driving the splitting of PSS and gradually evolving into two-, four-, and six-breathing soliton molecules states. The symmetric adjacent soliton pairs in the multi-soliton states maintain their stability through periodic energy exchange. This work elucidates the multi-stage transition mechanism of PSS, establishing a theoretical basis for experimentally manipulating multi-breathing PSS bound states through pump power control.