二维光子系统中局域k空间拓扑与贝里相位的群论框架
A Group-Theoretical Framework for Local k-Space Topology and Berry Phase in 2D Photonic Systems
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中文总结 AI 辅助
本文构建了融入光子系统关键特征的群论框架，研究二维光子系统中局域k空间拓扑与贝里相位的对称性起源，分析结构设计与对称性扰动对拓扑特征的操控，相关分析可扩展至多类人工波晶体。
中文摘要 AI 辅助
二维光子晶体（2D PhCs）可在不依赖带占据和天然晶体结构的情况下，对大量布洛赫模式实现精细调控，作为本质上的开放系统，是探索各类拓扑现象的通用平台。本文借鉴固体物理中的不可约表示形式主义，同时明确纳入光子布洛赫系统的关键特征，如辐射耦合与横波条件，构建了一套理论框架。在该框架内，我们研究了局域k空间拓扑（如连续谱中的束缚态、光学涡旋光束）以及两种代表性系统中贝里相位的对称性起源；还从群论角度分析了如何利用定制化结构设计与定向对称性扰动来操控这些拓扑特征，尤其展示了该形式主义在不同截断方式得到的布洛赫模式中的应用，并明确了通用n带构型下每种截断方式的适用范围。该分析可直接扩展至标量类薛定谔算子与两能级处理之外的各类人工波晶体。
英文摘要
Two-dimensional photonic crystals (2D PhCs) enable fine-grained control over a broad set of Bloch modes without the constraints of band occupancy and natural crystal structures, and, as intrinsically open systems, serve as versatile platforms for exploring diverse topological phenomena. Here, we develop a theoretical framework inspired by the irreducible-representation formalism in solid-state physics, while explicitly incorporating key characteristics of photonic Bloch systems, such as radiative coupling and transverse condition. Within this framework, we study the symmetry origins of local k-space topology, e.g., bound-states in the continuum and optical vortex beams, and Berry phase in two representative systems. We further analyze, from a group-theory perspective, how tailored structural designs and targeted symmetry perturbations can be exploited to manipulate these topological features. In particular, we showcase the application of the formalism to Bloch modes from distinct truncation approaches and specify the preferable regimes for each, both under a generic $n$-band configuration. The analysis can thereby be readily extended to a wide range of artificial wave crystals beyond scalar Schrödinger-like operators and two-level treatment.
