连续谱中束缚态的相流拓扑

中文摘要 AI 辅助

控制连续谱中束缚态（BIC）的拓扑电荷对于先进的拓扑光子学至关重要。因此，需要一个严谨的理论框架来理解这些电荷的形成，以推动该领域的进一步发展。然而，当没有单一多极子主导模式时，传统的多极子形式主义往往无法预测拓扑电荷。为解决这一基本问题，我们提出了一个严谨的动力系统框架来描述拓扑电荷的形成。该方法在偏振涡旋与矢量偏振场的局部结构之间建立了直接联系。在所提出的框架内，我们挑战了将拓扑电荷等同于主导多极子的Hopf指数的既有识别方式，并证明了多极子系数的导数在决定电荷方面所起的重要作用。我们的理论框架通过半解析多极子分解和周期性介质超表面的全波数值模拟得到了验证。此外，我们展示了晶胞对称性如何影响BIC周围偏振场的局部结构，并确定了形成高拓扑电荷的必要条件。我们的发现为分析BIC的拓扑性质提供了更严谨的基础，为拓扑光子学中的先进应用铺平了道路。

英文摘要

Control of topological charges of bound states in the continuum (BICs) is essential for advanced topological photonics. A rigorous theoretical framework for understanding the formation of these charges is therefore necessary for further progress in this field. However, conventional multipolar formalism often fail to predict the topological charge when no single multipole dominates the mode. To address this fundamental issue, we present a rigorous dynamical systems framework for describing formation of topological charges. This attitude provides a direct link between polarization vortex and the local structure of the vector polarization field. Within the proposed framework, we challenge the established identification of the topological charge with the Hopf index of the dominant multipole and demonstrate the significant role played by derivatives of the multipolar coefficients in determining the charge. Our theoretical framework is validated within semi-analytical multipolar decompositions and full-wave numerical simulations of periodic dielectric metasurfaces. Furthermore, we show how the symmetry of the unit cell influences the local structure of the polarization field around BIC and identify the necessary conditions for the formation of high topological charges. Our findings provide a more rigorous basis for analysing BICs' topological properties, paving the way for advanced applications in topological photonics.

发表机构

• School of Physics and Engineering, ITMO University（ITMO大学物理与工程学院）

机构由 AI 辅助整理，请以论文原文为准。

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7 pages, 3 figures