Bragg Soliton Dynamics in Separated Nonlinearity and Bragg Grating with Dispersive Reflectivity

Abstract

The dynamics of Bragg solitons are investigated in a linearly coupled dual-core fiber, where one core is uniform and has Kerr nonlinearity while the other core is linear and has a Bragg grating with dispersive reflectivity. The system’s dispersion relation gives rise to three disjoint bandgaps; a central gap surrounded by two other gaps — one is located in the upper half and the other is in the lower half of the spectrum. Soliton solutions are only found in the upper and lower gaps. It is found that in certain parameter ranges, solitons develop sidelobes. Exact analytical expressions have been developed for all values of relative group velocity to analyse the sidelobes in solitons that are in excellent agreement with numerical solutions. The stability of solitons are analysed in the system by means of systematic numerical simulations. Vast stable regions have been found in the upper and lower gaps. The effect and interplay of dispersive reflectivity, group velocity difference, and grating induced coupling on the stability of solitons are investigated. A key finding is that a stronger grating-induced coupling coefficient counteracts stabilisation effect of dispersive reflectivity. Moving soliton stability depends on its velocity. Further, interactions of quiescent solitons and collisions of counterpropagating solitons are investigated using systematic numerical analysis. Different outcomes of the interactions and collisions are summarised for wide parameter ranges. The outcomes of interactions are strongly affected by initial separation distance and initial phase difference. Solitons interaction containing sidelobes reveal special characteristics. In-phase soliton-soliton collisions result in the formation of zero-velocity quiescent solitons in the lower gaps. Generation of zero/slow Bragg solitons can potentially lead to novel optical devices.