六方晶格光子晶体平板中连续谱束缚态的对称性性质
Symmetry Properties of Bound States in the Continuum in Hexagonal Lattice Photonic Crystal Slabs
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中文总结 AI 辅助
本文通过群论和$k \cdot p$微扰理论分析$C_{6v}$对称光子晶体平板中的连续谱束缚态，揭示其对称性决定的场分布、远场偏振及质量因子缩放规律。
中文摘要 AI 辅助
光子晶体（PhC）腔内的连续谱束缚态（BICs）尽管位于辐射模式的连续谱内，却能实现光的完全限制。尽管其多样化的实际应用吸引了大量研究兴趣，但对BICs基础理解的发展对于未来器件的设计至关重要。本文采用群论方法确定具有$C_{6v}$空间群对称性的光子晶体的不可约表示（irreps）的基函数，由此可以确定腔内电磁场的空间分布。此外，利用电场的反射奇偶性和$k \cdot p$微扰理论方法来确定每个不可约表示的远场偏振。$k \cdot p$微扰解释了为何$E_2$不可约表示具有拓扑电荷$-2$，并表明拓扑电荷不一定指示BIC的存在。另外，研究发现模式的质量因子不一定按$Q \propto 1/|k|^{2|q|}$缩放，而是依赖于$k \cdot p$微扰中与辐射模式的耦合，该耦合由每个不可约表示的对称性决定。
英文摘要
Bound states in the continuum (BICs) within photonic crystal (PhC) cavities realise the full confinement of light despite lying within the continuum of radiation modes. While their diverse practical applications has attracted considerable research interest, developing the fundamental understanding of BICs is important for the design of future devices. This paper uses a group theoretical approach to determine the basis functions of the irreducible representations (irreps) of a PhC with the symmetry of the $C_{6v}$ space group, from which the spatial distribution of the electromagnetic fields within the cavity can be determined. Furthermore, the reflection parity of the electric field and a $k \cdot p$ perturbation theory approach are used to determine the far-field polarisation of each irrep. The $k \cdot p$ perturbation explains why the $E_2$ irrep has a topological charge of $-2$, as well as showing that a topological charge does not necessarily indicate the presence of a BIC. Additionally, it is found that the quality factor of the modes do not necessarily scale as $Q \propto 1/|k|^{2|q|}$, but are instead dependent on the coupling to the radiative mode in the $k \cdot p$ perturbation, which is determined from the symmetry of each irrep.
发表机构
- School of Physical, Chemical, and Environmental Sciences, Cardiff University（卡迪夫大学物理、化学与环境科学学院）
机构由 AI 辅助整理，请以论文原文为准。
