The optical solitons in the Scarff parity-time symmetric potentials

We investigate the existence and stability of solitons in parity-time (PT) symmetric Scarff complex potentials, including linear case, and self-focusing and self-defocusing nonlinear cases. For linear case, the PT-breaking points, the eigenvalues and eigenfunction for different modulated depths of PT symmetry Scarff complex potential are obtained numerically. For nonlinear cases, the existence and stability of fundamental and multipole solitons are studied in self-focusing and self-defocusing media. For a fixed modulated depth, the eigenvalue for fundamental or multipole linear modes is equal to the critical propagation constant bc of fundamental and multipole solitons existence. Fundamental solitons are stable in the self-defocusing nonlinear media and low power region for the self-focusing nonlinear case. Multipole solitons are stable with the propagation constants close to bc both for self-focusing and self-defocusing nonlinearities.