Localized modes and dark solitons sustained by nonlinear defects

Abstract

Dark solitons and localized defect modes against periodic backgrounds are considered in arrays of waveguides with defocusing Kerr nonlinearity constituting a nonlinear lattice. Bright defect modes are supported by local increase of the nonlinearity, while dark defect modes are supported by a local decrease of the nonlinearity. Dark solitons exist for both types of the defect, although in the case of weak nonlinearity they feature side bright humps making the total energy propagating through the system larger than the energy transferred by the constant background. All considered defect modes are found stable. Dark solitons are characterized by relatively narrow windows of stability. Interactions of unstable dark solitons with bright and dark modes are described.