UNIDIRECTIONAL FLOW OF THE DISCRETE DARK SOLITONS AND EXCITATION OF THE DISCRETE X-WAVES IN PT-SYMMETRIC OPTICAL WAVEGUIDE ARRAYS

We study two types of discrete nonlinear waves based on discrete optical waveguides. One is the scattering problem of the spatial discrete dark solitons, and the other one is the excitation of the discrete X-waves. The unidirectional flow of the discrete dark solitons is found by the interaction between a mobile discrete dark soliton and an embedded defect created by a pair of parity-time (PT) symmetric waveguides with mutually balanced gain and loss. The scattering is an inelastic process, where the discrete dark soliton can be reflected, transmitted or trapped depending on its transversal speed and strengths of the embedded defects. We show numerically the unidirectional flow of the discrete dark solitons and the trapping of discrete dark soliton by two of PT-symmetric defects. Thus it is possible to perform the diode effect and the storage of single and multiple discrete dark solitons. We numerically demonstrate that the optical discrete X-waves can be excited for a wide range of initial conditions, namely by the interplay between discrete diffraction, normal temporal dispersion, and nonlinearity in PT-symmetric waveguide arrays.