An operator-based approach to topological photonics
An operator-based approach to topological photonics
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DOI：
10.1515/nanoph-2022-0547
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发表时间：
2022-09
期刊：
影响因子：
7.5
通讯作者：
A. Cerjan;T. Loring
中科院分区：
文献类型：
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作者：
A. Cerjan;T. Loring
摘要近年来，光子学中拓扑结构的研究引起了人们极大的兴趣，因为这些系统可以实现鲁棒的、非互易的手征边缘态和腔状受限态，在线性和非线性器件中都有应用。然而，目前的能带理论的方法来理解光子系统中的拓扑结构产生的基本限制类的结构，可以研究。在这里，我们开发了一个理论框架，直接从其有效的哈密顿量和位置算子，在真实的空间表示，而不需要计算系统的布洛赫本征态或能带结构的光子结构的拓扑结构进行评估。使用这个框架，我们表明，非平凡的拓扑结构，以及相关的边界本地化的手征共振，可以体现在光子晶体中的时间反演对称性，缺乏一个完整的带隙，结果可能会影响新的拓扑激光器的设计。最后，我们使用我们的运营商为基础的框架，开发一类新的不变量的拓扑结构源于系统的晶体对称性，它允许预测强大的本地化状态创建波导和腔。
Abstract 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.