Chaotic polarization dynamics of dissipative vector solitons in mode-locked fiber lasers

Chaotic dissipative solitons have attracted increasing attention in recent years as paradigmatic objects for exploring nonequilibrium nonlinear dynamics with direct relevance to a wide range of physical systems. However, this progress has been largely confined to scalar frameworks. In comparison, how chaos emerges and evolves in dissipative soliton systems endowed with additional internal degrees of freedom remains largely unexplored. Here we address this problem in vector solitons of a mode-locked fiber laser numerically, where orthogonally polarized field components are intrinsically coupled. We show that the route to chaos is not universal but strongly conditioned by the polarization state. For polarization-locked vector solitons, chaotic behavior predominantly manifests in the intensity dynamics, while the polarization remains constrained by nonlinear phase locking. In contrast, polarization-rotating vector solitons undergo a clear period-bifurcation route to chaos, during which the polarization states evolve from a fixed point to discrete multi-period trajectories and eventually delocalize over the Poincaré sphere, indicating simultaneous chaos in both intensity and polarization. These results highlight polarization dynamics as a key ingredient in dissipative soliton physics and reveal chaotic regimes that emerge only from polarization-resolved dynamics, extending the landscape of dissipative soliton dynamics beyond scalar soliton models.