Discrete solitons in an array of linear waveguides with a nonlinear 𝒫𝒯-symmetric defect

Abstract

A one-dimensional linear waveguide array with a parity-time[Formula: see text]([Formula: see text])-symmetric defect, which is represented by a pair of waveguides carrying equal amount of nonlinear gain and loss, is considered. Compared to the system with linear [Formula: see text]-symmetric defect, a different instability of solitons is exhibited in this model, in which the unstable fundamental discrete solitons suffer either decay or blowup. The effect of nonlinear [Formula: see text]-symmetry on the stability of fundamental solitons is investigated numerically by obtaining the stability region of the solitons. The region has a finite threshold of total power as the coupling within the defect is less than the counterpart of other linear waveguides, while the threshold is absent as the coupling within the defect is larger than the one between other linear waveguides. The stability region is intensely enlarged by the increase of the coupling strength within the defect, and descends exponentially with the increase of the total power.