色散谐振器阵列中的亚波长异常点
Subwavelength exceptional points in dispersive resonator arrays
浏览论文内容
中文总结 AI 辅助
本文通过Lippmann-Schwinger公式研究色散谐振器阵列中的亚波长异常点，推导出缺陷特征值条件与逆设计条件，并证明无源阻尼和失谐可产生异常点，数值实验验证了理论。
中文摘要 AI 辅助
异常点为非厄米波系统产生强光谱灵敏度提供了一种机制。然而，对于具有高度色散材料参数的亚波长谐振器，谐振问题在频率上并非线性特征值问题。本文利用Lippmann-Schwinger公式及相关的体积势约化来研究色散谐振器阵列中的异常点。该约化导出一个有限维非线性矩阵束，其元素同时编码局部材料响应和谐振器之间的体积介导相互作用。我们将异常点表征为该束的亏损特征值，并为二聚体和更高阶系统推导出显式条件。我们证明，无源阻尼和失谐可以在不施加增益的情况下产生异常点，并提出了在指定频率处放置此类简并的逆设计条件。我们还证明了相应的Puiseux分裂定律，并识别了材料色散如何进入前导灵敏度前置因子。数值实验（包括受卤化物钙钛矿启发的二聚体和三聚体）验证了该理论，并表明异常点机制对于显式的高度色散无源材料定律仍然成立。
英文摘要
Exceptional points provide a mechanism for producing strong spectral sensitivity in non-Hermitian wave systems. For subwavelength resonators with highly dispersive material parameters, however, the resonance problem is not a linear eigenvalue problem in the frequency. In this paper, we use the Lippmann-Schwinger formulation and the associated volume-potential reduction to study exceptional points in dispersive resonator arrays. The reduction leads to a finite-dimensional nonlinear matrix pencil whose entries encode both the local material response and the volume-mediated interaction between the resonators. We characterize exceptional points as defective characteristic values of this pencil and derive explicit conditions for dimers and higher-order systems. We show that passive damping and detuning can generate exceptional points without imposed gain, and we formulate an inverse-design condition for placing such degeneracies at prescribed frequencies. We also prove the corresponding Puiseux splitting laws and identify how material dispersion enters the leading sensitivity prefactor. Numerical experiments, including halide-perovskite-inspired dimers and trimers, illustrate the theory and show that the exceptional-point mechanism persists for explicit highly dispersive passive material laws.
发表机构
- MAP5, Université Paris Cité, CNRS（巴黎西岱大学数学与应用数学研究所（MAP5），法国国家科学研究中心（CNRS））
机构由 AI 辅助整理，请以论文原文为准。
