发表机构
Virginia Tech; City University of Hong Kong（弗吉尼亚理工大学; 香港城市大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出基于傅里叶模态方法的数值工具，用于高效求解BIC附近共振态的微扰方程，捕捉高阶渐近标度，助力BIC理论分析与器件设计。
AI 中文摘要
周期性光子结构支持的连续谱中束缚态（BICs）被高Q值共振所包围，并在动量空间中充当偏振涡旋的中心，这使得它们对广泛的应用具有吸引力。最近，针对BIC附近的共振态提出了一种微扰理论，该理论产生了一系列方程，其解直接近似共振态并确定其Q因子和偏振的渐近行为。因此，高效求解这些方程至关重要。由于许多关于BIC的研究涉及层状结构，我们开发了一种基于傅里叶模态方法的方法。数值算例证实了所提出方法的有效性，并展示了其捕捉高阶渐近标度的能力。我们的工作为BIC的理论分析提供了一个实用工具，也可能有助于基于BIC的光子器件的设计。
英文摘要
Bound states in the continuum (BICs) supported by periodic photonic structures are surrounded by high-$Q$ resonances and serve as centers of polarization vortices in momentum space, making them attractive for a wide range of applications. Recently, a perturbation theory has been formulated for resonant states near BICs, yielding a hierarchy of equations whose solutions directly approximate the resonant states and determine the asymptotic behavior of their $Q$ factors and polarizations. Efficiently solving these equations is therefore essential. Since many studies of BICs concern layered structures, we develop an approach based on the Fourier modal method. Numerical examples confirm the effectiveness of the proposed method and demonstrate its ability to capture higher-order asymptotic scaling. Our work provides a practical tool for the theoretical analysis of BICs and may also facilitate the design of BIC-based photonic devices.
