  Vector soliton operation of erbium-doped fiber lasers mode locked with atomic
layer graphene was experimentally investigated. Either the polarization
rotation or polarization locked vector dissipative solitons were experimentally
obtained in a dispersion-managed cavity fiber laser with large net cavity
dispersion, while in the anomalous dispersion cavity fiber laser, the phase
locked NLSE solitons and induced NLSE soliton were experimentally observed. The
vector soliton operation of the fiber lasers unambiguously confirms the
polarization insensitive saturable absorption of the atomic layer graphene when
the light is incident perpendicular to its 2D atomic layer.
