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

We report results for solitons in models of waveguides with focusing or defocusing saturable nonlinearity and a parity-time ( )-symmetric complex-valued external potential of the Scarf-II type. The model applies to the nonlinear wave propagation in graded-index 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 -symmetric waveguides. The dependence of the propagation constant on the soliton’s 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 . This article is part of the theme issue ‘Dissipative structures in matter out of equilibrium: from chemistry, photonics and biology (part 1)’.