Evolution of vortex and quadrupole solitons in the complex potentials with saturable nonlinearity

We investigate the evolution of vortex and quadrupole solitons in the parity-time (PT)-symmetric optical lattices with self-focusing saturable nonlinearity. It is found that the saturable parameter plays a significant role on the existence and stability of vortex solitons. There exists a threshold for saturable parameter, above which the single-charged vortex solitons can be stable. The strength of gain-loss component of the PT-symmetric potential can affect the existence and stability of vortex solitons dramatically. We find that the single-charged vortex solitons can exist even at the phase transition point of the PT-symmetric potential, but diffuse fast during propagation. In addition, it is also found that the direction of the angular momentum has little effect on the properties of vortex solitons. Dramatically, the stable regions of out-of-phase quadrupole solitons are broader than that of the single-charged vortex solitons, while the stable regions of in-phase quadrupole solitons are narrower than that of the single-charged vortex solitons.