Soliton-soliton dynamics in a dual-core system with separated nonlinearity and nonuniform Bragg grating

Abstract

The interactions between stable quiescent Bragg grating solitons are investigated systematically in a dual-core system where one core is uniform and has Kerr nonlinearity and other is linear and is equipped with a Bragg grating with dispersive reflectivity. In a previous work, it has been shown that the model supports stable quiescent Bragg solitons which may contain sidelobes in their profile in case of strong dispersive reflectivity. The interactions of in-phase solitons may lead to a variety of outcomes in the absence of sidelobes including merger into a quiescent soliton, destruction of both solitons, symmetric or asymmetric separation of solitons and generation of three solitons. In case of $$\pi $$ -out-of-phase solitons without sidelobes, the solitons repel each other. However, in the presence of sidelobes, for both in-phase and $$\pi $$ -out-of-phase solitons, the interactions may result in the repulsion of solitons or the formation of a long-lasting bound state that eventually disintegrates into two separating solitons. We have identified the regions for different interaction outcomes in the plane of dispersive reflectivity and frequency.