Spontaneous symmetry breaking and ghost states in two-dimensional fractional nonlinear media with non-Hermitian potential

Abstract

Abstract The interaction of fractional diffraction and parity-time ( $${{{{{\mathcal{PT}}}}}}$$ PT ) symmetric would bring some unique properties to certain physical system. Here we report a spontaneous symmetry breaking (SSB) phenomenon and ghost states of solitons supported by the two-dimensional (2D) fractional nonlinear Schrödinger (FNLS) equation with focusing and defocusing Kerr media under 2D non-Hermitian $${{{{{\mathcal{PT}}}}}}$$ PT -symmetric potential. The continuous asymmetric soliton bifurcates out in a SSB way. For the focusing regime, as the power exceeds a critical value, the asymmetric soliton bifurcates from fundamental symmetric solitons, and when it turns to the defocusing regime, the symmetry breaking phenomenon is found in the branch of the first excited state. The symmetric solitons (including fundamental one and first excited state) are destabilized at this point. Intriguingly, the branches of asymmetry solitons are existing with complex conjugate propagation constants (alias ghost states), which is solely in fractional media. Moreover, we investigate the dependence of fractional Lévy index (α) on the symmetry breaking of solitons in detail. And the stabilities of fundamental symmetric soliton, asymmetric solitons, as well as the first excited states are explored. Moreover, The management of optical field propagation is achieved by modulation of the external potential. Meanwhile, we find the stable excitations of solitons via adiabatic excitations of system parameters. These results will provide some theoretical basis for the study of SSB phenomena and related physical experiments in the 2D fractional media with $${{{{{\mathcal{PT}}}}}}$$ PT -symmetric potentials.