Dislocated vector asymmetric soliton molecules in birefringence-managed fiber lasers

Optical soliton molecules, the self-organized structures in dissipative systems arising from the equilibrium between attractive and repulsive forces, show great importance for revealing soliton interactions and potential applications in optical communications. Here, we numerically and experimentally demonstrate that two orthogonally polarized components with mirrored profiles can form vector soliton molecules in single-mode fiber lasers containing a section of polarization-maintaining fiber. Due to the dynamic balance between fiber birefringence and chromatic dispersion, the temporal dislocation between two components changes along the cavity while reaching the self-consistent state per round trip. The unequal coupling for orthogonally polarized modes at the input interface of the polarization-maintaining fiber dominates the asymmetric property of subpulses for each component. Such soliton molecules are observed both in erbium-doped and ytterbium-doped fiber lasers, indicating the generality of the vector asymmetric structures. Our work reveals soliton molecules with additional degrees of freedom in polarization and intensity, expanding the understanding of the asymmetric mode interactions in fiber lasers.