Multiscale Modeling &Simulation, Volume 21, Issue 3, Page 827-848, September 2023.
Abstract. Motivated by topologically protected states in wave physics, we study localized eigenmodes in one-dimensional periodic media with defects. The Su–Schrieffer–Heeger model (the canonical example of a one-dimensional system with topologically protected localized defect states) is used to demonstrate the method. Our approach can be used to describe two broad classes of perturbations to periodic differential problems: those caused by inserting a finite-sized piece of arbitrary material and those caused by creating an interface between two different periodic media. The results presented here characterize the existence of localized eigenmodes in each case and, when they exist, determine their eigenfrequencies and provide concise analytic results that quantify the decay rate of these modes. These results are obtained using both high-frequency homogenization and transfer matrix analysis, with good agreement between the two methods.

中文翻译：

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局部缺陷模式的渐近表征：Su-Schrieffer-Heeger 及相关模型

多尺度建模与仿真，第 21 卷，第 3 期，第 827-848 页，2023 年 9 月。
抽象的。受波动物理学中拓扑保护态的推动，我们研究了具有缺陷的一维周期性介质中的局域本征模。Su-Schrieffer-Heeger 模型（具有拓扑保护局部缺陷态的一维系统的典型示例）用于演示该方法。我们的方法可用于描述周期性微分问题的两大类扰动：由插入有限尺寸的任意材料引起的扰动和由在两种不同周期性介质之间创建界面引起的扰动。这里给出的结果描述了每种情况下局部本征模态的存在性，并且当它们存在时，确定它们的本征频率并提供量化这些模态的衰减率的简明分析结果。