Cerjan Alexander, Loring Terry A
Center for Integrated Nanotechnologies, Sandia National Laboratories, Albuquerque, NM 87185, USA.
Department of Mathematics and Statistics, University of NM, Albuquerque, NM 87131, USA.
Nanophotonics. 2022 Nov 14;11(21):4765-4780. doi: 10.1515/nanoph-2022-0547. eCollection 2022 Dec.
Recently, the study of topological structures in photonics has garnered significant interest, as these systems can realize robust, nonreciprocal chiral edge states and cavity-like confined states that have applications in both linear and nonlinear devices. However, current band theoretic approaches to understanding topology in photonic systems yield fundamental limitations on the classes of structures that can be studied. Here, we develop a theoretical framework for assessing a photonic structure's topology directly from its effective Hamiltonian and position operators, as expressed in real space, and without the need to calculate the system's Bloch eigenstates or band structure. Using this framework, we show that nontrivial topology, and associated boundary-localized chiral resonances, can manifest in photonic crystals with broken time-reversal symmetry that lack a complete band gap, a result that may have implications for new topological laser designs. Finally, we use our operator-based framework to develop a novel class of invariants for topology stemming from a system's crystalline symmetries, which allows for the prediction of robust localized states for creating waveguides and cavities.
最近，光子学中的拓扑结构研究引起了广泛关注，因为这些系统可以实现稳健的、非互易的手性边缘态和类似腔的受限态，这在线性和非线性器件中都有应用。然而，目前用于理解光子系统拓扑结构的能带理论方法对可研究的结构类别产生了根本性限制。在此，我们开发了一个理论框架，用于直接从光子结构在实空间中表示的有效哈密顿量和位置算符来评估其拓扑结构，而无需计算系统的布洛赫本征态或能带结构。使用这个框架，我们表明，非平凡拓扑以及相关的边界局域手性共振可以在具有破缺时间反演对称性且缺乏完整带隙的光子晶体中表现出来，这一结果可能对新型拓扑激光设计有影响。最后，我们使用基于算符的框架来开发一类源于系统晶体对称性的新型拓扑不变量，这使得能够预测用于创建波导和腔的稳健局域态。
