Spatial solitons and stability in self-focusing and defocusing Kerr nonlinear media with generalized parity-time-symmetric Scarff-II potentials.

We present a unified theoretical study of the bright solitons governed by self-focusing and defocusing nonlinear Schrödinger (NLS) equations with generalized parity-time- (PT) symmetric Scarff-II potentials. Particularly, a PT-symmetric k-wave-number Scarff-II potential and a multiwell Scarff-II potential are considered, respectively. For the k-wave-number Scarff-II potential, the parameter space can be divided into different regions, corresponding to unbroken and broken PT symmetry and the bright solitons for self-focusing and defocusing Kerr nonlinearities. For the multiwell Scarff-II potential the bright solitons can be obtained by using a periodically space-modulated Kerr nonlinearity. The linear stability of bright solitons with PT-symmetric k-wave-number and multiwell Scarff-II potentials is analyzed in detail using numerical simulations. Stable and unstable bright solitons are found in both regions of unbroken and broken PT symmetry due to the existence of the nonlinearity. Furthermore, the bright solitons in three-dimensional self-focusing and defocusing NLS equations with a generalized PT-symmetric Scarff-II potential are explored. This may have potential applications in the field of optical information transmission and processing based on optical solitons in nonlinear dissipative but PT-symmetric systems.