具有复值耦合的$\cal{PT}$对称低聚物中的离散孤子动力学
Discrete solitons dynamics in $\cal{PT}$-symmetric oligomers with complex-valued couplings
摘要：
我们考虑了一个光波导器件中的双低聚物阵列。系统的数学模型是耦合的离散非线性薛定谔（NLS）方程，其中增益和损耗参数有助于复值线性耦合。该阵列迎合耦合臂之间的奇偶时间（$\cal{PT}$）对称性的光学模拟。该系统存在基本亮离散孤子解。利用微扰理论分析了它们的存在性和谱稳定性。这些分析结果进一步验证数值使用牛顿-拉夫逊方法和标准的特征值问题求解器。我们的研究集中在两个自然的孤立子离散模式：单和双激发的网站，也被称为现场和intersite模式，分别。这些模式中的每一种在二聚体臂之间获得三种不同的构型，即，对称、不对称和反对称。虽然站点间和现场离散孤子一般是不稳定的，后者可以是稳定的，这取决于传播常数，水平线性耦合系数和增益损耗参数的组合值。
英文摘要：
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.
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