Discrete dark solitons in parity–time-symmetric waveguide arrays with gain and loss

Abstract

We demonstrate that discrete dark solitons can be self-trapped in binary self-defocusing parity–time-symmetric waveguide arrays with gain and loss. The discrete dark solitons appear in the form of a localized dip on the Bloch-wave background. When the appropriate boundary condition is satisfied in such finite arrays, the analytical and numerical solutions of discrete dark solitons exist and can both be stable in the one-dimensional case; the stable fundamental discrete vortex solitons can be numerically gained in the two-dimensional case. Interestingly, such one-dimensional discrete dark solitons do not exhibit displacement properties.