Stability and Dynamics of Bragg Grating Solitons in a semilinear Dual-Core System with Cubic-Quintic Nonlinearity

Abstract

Bragg grating soliton dynamics in a semilinear coupler, in which one core has Bragg grating with cubic-quintic nonlinearity and the other is linear are studied. The system's linear spectrum contains two bandgaps, namely the upper and lower gaps when the group velocity mismatch term c in the linear core is zero. For c ≠ 0, an additional genuine central gap results in. In the moving case, three bandgaps exist. For quiescent cases, the edges of the bandgaps are almost independent of c for a given coupling coefficient κ. However, in the case of moving solitons, the bandgap edges strongly depend on soliton velocity s and group velocity mismatch c. The system supports two disjoint families of solitons, referred to as ‘Type 1’ and ‘Type 2’; both of which exist throughout the upper and lower gaps only. The stability of solitons is investigated using systematic numerical techniques. Investigations reveal that all Type 2 solitons are highly unstable, while vast regions exist where Type 1 solitons are stable. The stability border depends on system parameters, such as q, κ, c and s. The presence of quintic nonlinearity greatly improves the robustness of the solitons. The interaction dynamics of co-propagating solitons gives rise to several interesting outcomes. Generally, in-phase solitons attract and out-of-phase solitons repel. In-phase interactions result in a variety of outcomes, such as destruction of the solitons; symmetric or asymmetric separation; and, more interestingly, the fusion into a single one and 2→3 transformation. Further, collisions of stable counter-propagating solitons are systematically investigated. In-phase collisions exhibit diverse outcomes, which may include passage through with unchanged, reduced, increased or different velocities; destruction of the solitons; merger into a single one; and three soliton process. The merger and three soliton process are mostly significant and may have potential applications in slow light generation.