Suppression of symmetry breaking of nonlinear modes by defocusing saturable nonlinearity in parity-time symmetric potentials

Symmetry breaking of nonlinear localized modes and suppression of symmetry-breaking bifurcations are reported in the framework of the nonlinear Schrodinger equation with defocusing saturable nonlinearity in parity-time symmetric potentials. We found that, beyond a critical point, one type of the nonlinear modes with asymmetric profiles bifurcates from the branch of the first excited state. We prove that the bifurcation is essentially triggered by instability of the first excited state by linear stability analysis, which implies the symmetry breaking of the nonlinear modes is steerable by changing the stability of the first excited state of the nonlinear mode. A suppressing effect is that the symmetry-breaking bifurcation of the nonlinear modes can be completely suppressed by adjusting the strength of the saturable nonlinearity. This suppressing effect of symmetry-breaking bifurcation is illuminated by analyzing the stability behaviors of the nonlinear modes.