论文标题
四倍的非铁相变和非晶体耦合谐振器光学波导
Four-fold non-Hermitian phase transitions and non-reciprocal coupled resonator optical waveguides
论文作者
论文摘要
非热系统可以表现出对边界条件的特别敏感性。鉴于拓扑边界模式和非炎性皮肤效应可以共存或单独出现在非热门系统中，因此，呈现一个综合的非铁相图具有巨大的价值，以在现实的非官方系统中进行进一步的灵活控制。在这里，我们在数学水平上揭示了四个非热相变的四倍，其中I期仅表现出拓扑边界模式，II期同时显示拓扑边界模式和皮肤模式，III阶段仅表现出皮肤模式，而第四阶段无法表现出任何边界模式。通过得出非热的绕组数，分析表达了拓扑边界模式的存在或不存在条件，这与通过迭代Green的函数方法获得的数值结果一致。结合了关于非炎性皮肤效应的研究，我们严格地建立了四倍的相图。我们还设计了一系列耦合的谐振器光学波导。光子结构中非热性引入引起的现象类似于拓扑绝缘体中的带反转，表明光子带中存在拓扑边界模式。
Non-Hermitian systems can exhibit extraordinary sensitivity to boundary conditions. Given that topological boundary modes and non-Hermitian skin effects can either coexist or individually appear in non-Hermitian systems, it is of great value to present a comprehensive non-Hermitian phase diagram, for further flexible control in realistic non-Hermitian systems. Here, we reveal four-fold non-Hermitian phase transitions at a mathematically level, where phase I exhibits only topological boundary modes, phase II displays both topological boundary modes and skin modes, phase III exhibits only skin modes, and phase IV cannot manifest any boundary modes. By deriving non-Hermitian winding numbers, the existence or non-existence condition of topological boundary modes are analytically expressed, consistent with the numerical results obtained through the iterative Green's function method. Combining with the study on non-Hermitian skin effects, we rigorously establish the four-fold phase diagram. We also design an array of coupled resonator optical waveguides. The introduction of non-Hermiticity in the photonic structure induces a phenomenon similar to band inversion in topological insulators, indicating the presence of topological boundary modes in the photonic bands.
