Stability of Bragg grating solitons in a semilinear dual-core system with cubic–quintic nonlinearity

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• 作者：Md. Jahirul Islam ; Javid Atai
• 关键词：Bragg grating soliton ; Fiber Bragg grating ; Cubic–quintic nonlinearity
• 刊名：Nonlinear Dynamics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：87
• 期：3
• 页码：1693-1701
• 全文大小：
• 刊物类别：Engineering
• 刊物主题：Vibration, Dynamical Systems, Control; Classical Mechanics; Mechanical Engineering; Automotive Engineering;
• 出版者：Springer Netherlands
• ISSN：1573-269X
• 卷排序：87

文摘

The existence and stability of quiescent Bragg grating solitons in a dual-core fiber, where one core contains a Bragg grating with cubic–quintic nonlinearity, and the other is a linear are studied. The model admits two disjoint bandgaps when the relative group velocity in the linear core, c, is zero: one in the upper half and the other in the lower half of the system’s linear spectrum. In the general case (i.e., \(c\ne 0\)), a central gap (which is a genuine gap) is formed, while the lower and upper gaps overlap with one branch of continuous spectrum, and therefore, they are not genuine bandgaps. For quiescent solitons, exact analytical solutions are found in implicit form for \(c=0\). For nonzero c, soliton solutions are obtained numerically. The system supports two disjoint families (referred to as Type 1 and Type 2) of zero-velocity soliton solutions, separated by a border. Both Type 1 and Type 2 soliton solutions exist throughout the upper and lower gaps but not in the central gap. The stability of both soliton families is investigated by means of systematic numerical simulations. It is found that Type 2 solitons are always unstable and are destroyed upon propagation. On the other hand, unstable Type 1 solitons may either decay into radiation or radiate some energy and evolve into a moving Type 1 soliton. Also, in the case of Type 1 solitons, we have identified stable regions in the plane of quintic nonlinearity and frequency. The influence of coupling coefficient and the relative group velocity in the linear core on the stability of solitons are analyzed.