论文标题
$ \ cal {pt} $中的离散孤子动力学 - 对称寡聚物，带有复杂的耦合
Discrete solitons dynamics in $\cal{PT}$-symmetric oligomers with complex-valued couplings
论文作者
论文摘要
我们考虑在光学波导设备中的一系列双寡聚物。系统的数学模型是耦合的离散非线性schrödinger（NLS）方程，其中增益和损坏参数有助于复杂值值的线性耦合。该数组适应了平均时间（$ \ cal {pt} $）的光学模拟 - 耦合臂之间的对称属性。该系统承认基本的明亮离散解决方案。我们使用扰动理论分析研究了它们的存在和光谱稳定性。这些分析发现将使用Newton-Raphson方法和标准特征问题解决者进行数值验证。我们的研究侧重于孤子子的两种自然离散模式：单个和双激发位置，分别称为现场和场地模式。这些模式中的每一个都获得了二聚体臂之间的三种不同构型，即对称，不对称和反对称。尽管场地和现场离散孤子通常都不稳定，但后者可以稳定，具体取决于传播常数，水平线性耦合系数和增益损失参数的组合值。
We consider an array of double oligomers in an optical waveguide device. A mathematical model for the system is the coupled discrete nonlinear Schrödinger (NLS) equations, where the gain-and-loss parameter contributes to the complex-valued linear coupling. The array caters to an optical simulation of the parity-time ($\cal{PT}$)-symmetry property between the coupled arms. The system admits fundamental bright discrete soliton solutions. We investigate their existence and spectral stability using perturbation theory analysis. These analytical findings are verified further numerically using the Newton-Raphson method and a standard eigenvalue-problem solver. Our study focuses on two natural discrete modes of the solitons: single- and double-excited-sites, also known as onsite and intersite modes, respectively. Each of these modes acquires three distinct configurations between the dimer arms, i.e., symmetric, asymmetric, and antisymmetric. Although both intersite and onsite discrete solitons are generally unstable, the latter can be stable, depending on the combined values of the propagation constant, horizontal linear coupling coefficient, and gain-loss parameter.
