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首页> 外文期刊>Philosophical transactions of the Royal Society. Mathematical, physical, and engineering sciences >Pinned modes in two-dimensional lossy lattices with local gain and nonlinearity
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Pinned modes in two-dimensional lossy lattices with local gain and nonlinearity

机译：具有局部增益和非线性的二维有损晶格中的固定模式

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摘要

We introduce a system with one or two amplified nonlinear sites ('hot spots', HSs) embedded into a twodimensional linear lossy lattice. The system describes an array of evanescently coupled optical or plasmonic waveguides, with gain applied to selected HS cores. The subject of the analysis is discrete solitons pinned to the HSs. The shape of the localized modes is found in quasi-analytical and numerical forms, using a truncated lattice for the analytical consideration. Stability eigenvalues are computed numerically, and the results are supplemented by direct numerical simulations. In the case of self-focusing nonlinearity, the modes pinned to a single HS are stable and unstable when the nonlinearity includes the cubic loss and gain, respectively. If the nonlinearity is selfdefocusing, the unsaturated cubic gain acting at the HS supports stable modes in a small parametric area, whereas weak cubic loss gives rise to a bistability of the discrete solitons. Symmetric and antisymmetric modes pinned to a symmetric set of two HSs are also considered.
机译：我们介绍了一种系统，该系统具有嵌入到二维线性有损晶格中的一个或两个放大的非线性位点（“热点”，HS）。该系统描述了一个of逝耦合的光波导或等离激元波导的阵列，增益应用于选定的HS磁芯。分析的主题是固定在HS上的离散孤子。局部模式的形状以准解析和数字形式找到，使用截短的格子进行分析。通过数值计算稳定性特征值，并通过直接数值模拟对结果进行补充。在自聚焦非线性的情况下，当非线性分别包括三次损耗和增益时，固定到单个HS的模式是稳定的和不稳定的。如果非线性是自散焦的，则作用于HS的不饱和立方增益在较小的参数区域中支持稳定模式，而弱的立方损耗会导致离散孤子的双稳态。还考虑了固定到两个HS的对称集的对称和反对称模式。

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