PT-SYMMETRIC OPTICAL MODES AND SPONTANEOUS SYMMETRY BREAKING IN THE SPACE-FRACTIONAL SCHRODINGER EQUATION

We numerically investigate the parity-time (PT) symmetric optical modes in the space-fractional Schrodinger equation. The PT-symmetric optical modes are found below the critical phase-transition points. Beyond the critical phase-transition points, the spontaneous symmetry breaking of the PT-symmetric system occurs for non-PT-symmetric solutions. The diagrams of the eigenvalue spectra of the optical modes are presented as function of the degree of non-Hermiticity of the system. The numerical results reveal that the critical phase-transition point increases monotonously with the increase of the Levy index.