Symmetric and asymmetric solitons supported by a 𝒫𝒯-symmetric potential with saturable nonlinearity: bifurcation, stability and dynamics

The symmetry breaking bifurcation of solitons in an optical waveguide with focusing saturable nonlinearity and parity-time ()-symmetric complex-valued external potentials is investigated. As the soliton power increases, it is found that the branches of asymmetric solitons split off from the base branches of -symmetric fundamental soliton. The bifurcation diagrams, consisting essentially of the propagation constants of optical solitons, indicate that symmetric fundamental and multipole solitons, as well as asymmetric solitons can exist. The stabilities and the dynamics characteristics of solitons are comprehensively investigated. We find the different instability scenarios of the symmetric solitons, but the symmetry breaking bifurcation is caused only by the onset of instability of the symmetric fundamental solitons. This result is further confirmed by the numerical examples with the different saturable nonlinearity parameters. In particular, we find that the soliton power and the stability of soliton at the bifurcation points are significantly changed by varying the strength of the saturable nonlinearities. These results provide additional way to control symmetry breaking bifurcations in -symmetric optical waveguide.