Gap Soliton Dynamics In Coupled Bragg Gratings With Cubic-Quintic Nonlinearity

Abstract

The dynamics of gap solitons in a system of two linearly coupled Bragg gratings with cubic-quintic nonlinearity are investigated. It is found that the model supports two disjoint families of solitons, known as Type 1 and Type 2 solitons, which fill the entire bandgap. There exist symmetric and asymmetric gap solitons within each family. These gap solitons can have any velocity between zero and the speed of light in the medium. The border separating the soliton families has been identified. The stability of solitons is investigated by means of systematic numerical stability analysis. For moving solitons, the stability region is approximately independent of soliton velocities in the standard coupled Bragg gratings model. However, in the case of cubic-quintic model, the velocities of solitons have a significant effect on the stability regions. Type 1 gap solitons are adequately robust against strong perturbations; credited to quintic nonlinearity. Interactions of co-propagating quiescent gap solitons have been systematically investigated. Generally speaking, attraction is present between in-phase quiescent gap solitons interactions, while repulsion arises when the initial phase difference is at π or π/2. The interactions of in-phase Type 1 asymmetric solitons has been proven to result in a range of outcomes, namely, fusion into a single zero-velocity soliton, asymmetrical separation of solitons, symmetrical separation of solitons, formation of three solitons, and the destruction of solitons. Collisions of counter-propagating moving gap solitons are studied numerically. Collisions of in-phase Type 1 asymmetric moving gap solitons can exhibit a range of outcomes, such as the separation of solitons with identical, reduced, increased, or asymmetric velocities. The generation of a quiescent soliton, either through merger or through 2→3 transformation, is a particularly significant outcome. Compared to the merger, 2→3 transformation is deemed to be more stable.