Stationary states of parity-time symmetric dark solitons in super-Gaussian potential

Abstract

Objective:The study of super-Gaussian PT-symmetric potential is of great interest as it addresses all types of confining refractive index profiles ranging from step index to smooth guides. In super-Gaussian potential, though bright solitons have been studied, the studies on dark solitons are limited. The influence of the imaginary potential on the fundamental and higher eigenmodes of the dark soliton has been analysed due to its potential applications. The role of nonlinearity and the coefficient of real potential on the PT-symmetry has also been studied. Methods:The stationary states are modelled by ordinary differential equation and the eigenvalues and eigenmodes of ground and excited states have been found numerically. The linear stability of the stationary states has been analysed using the linearised Bogoliubov-de Genes(BDG) equations and the stability of dynamical states has been studied using finite difference method. Results:The studies have shown that, even in the presence of imaginary potential, the real eigenvalue spectrum and symmetric eigenfunction exist in the PT-symmetric region. PT-symmetry breaking occurs at the threshold value of imaginary potential above which the eigenvalues are complex. The nonlinearity enhances the PT-symmetry. Also, the threshold value decreases with the coefficient of real potential. The stationary and dynamical states are stable in PT-symmetric region.