扭曲圆波导阵列中的时空动力学
Spatiotemporal dynamics in a twisted, circular waveguide array
摘要：
研究了光脉冲在扭曲多芯光纤中传输的非线性离散局域解的存在性和谱稳定性。通过考虑一个偶数，$N$，波导，我们推导出渐近表达式的解决方案，其中大部分的光强度集中作为一个孤立的脉冲局限于一个单一的波导。得到的首阶项与数值计算结果符合得很好。此外，如在没有时间色散的模型中那样，当扭转参数$ϕ$由$ϕ= π/N$给出时，这些驻波表现出光学抑制，其中单个波导保持未被激发到首阶。光谱计算和数值演化实验表明，这些驻波解决方案是稳定的耦合参数小于临界值的值，在这一点上的光谱不稳定性的结果从碰撞的内部特征值的本征值在原点。当$ϕ= π/N$。
英文摘要：
We consider the existence and spectral stability of nonlinear discrete localized solutions representing light pulses propagating in a twisted multi-core optical fiber. By considering an even number, $N$, of waveguides, we derive asymptotic expressions for solutions in which the bulk of the light intensity is concentrated as a soliton-like pulses confined to a single waveguide. The leading order terms obtained are in very good agreement with results of numerical computations. Furthermore, as in the model without temporal dispersion, when the twist parameter, $ϕ$, is given by $ϕ= π/N$, these standing waves exhibit optical suppression, in which a single waveguide remains unexcited, to leading order. Spectral computations and numerical evolution experiments suggest that these standing wave solutions are stable for values of the coupling parameter less than a critical value, at which point a spectral instability results from the collision of an internal eigenvalue with the eigenvalues at the origin. This critical value has a maximum when $ϕ= π/N$.
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