Optical solitons in media with focusing and defocusing saturable nonlinearity and a parity-time-symmetric external potential

We report results for solitons inmodels of waveguides with focusing or defocusing saturable nonlinearity and a parity-time (PT )-symmetric complex-valued external potential of the Scarf-II type. The model applies to the nonlinear wave propagation in gradedindex optical waveguides with balanced gain and loss. We find both fundamental and multipole solitons for both focusing and defocusing signs of the saturable nonlinearity in such PT -symmetric waveguides. The dependence of the propagation constant on the solitons power is presented for different strengths of the nonlinearity saturation, S. The stability of fundamental, dipole, tripole and quadrupole solitons is investigated by means of the linear-stability analysis and direct numerical simulations of the corresponding (1+1)-dimensional nonlinear Schrödinger-type equation. The results show that the instability of the stationary solutions can be mitigated or completely suppressed, increasing the value of S.