Title: Non-Hermitian gauged reciprocity and symmetry Show Chinese title

Title: 非厄米规范互易性和对称性

Abstract: The Lorentz reciprocity is a fundamental property in electromagnetism and well known to break down due to an external magnetic field. With a fictitious or imaginary vector potential, however, its behavior is largely unknown. Here we show that in systems with an imaginary vector potential and displaying the non-Hermitian skin effect, the Lorentz reciprocity is broken but still governed by a rigorous mathematical relation, which we term non-Hermitian gauged reciprocity. When mimicking an imaginary vector potential using just linear integrated photonic elements, however, the conditions that lead to the Lorentz reciprocity are still satisfied and hence the latter cannot be broken. Nevertheless, we show that the non-Hermitian gauged reciprocity can still be observed with a proper choice of inputs and outputs, alongside the Lorentz reciprocity. In addition, we also reveal another equal-amplitude response in the same system, which we attribute to a non-Hermitian gauged symmetry. Furthermore, we show that light propagation is not impinged by the non-Hermitian topological funnel effect, highlighting an underappreciated difference between coherently driven and non-driven systems. These findings are confirmed using a tight-binding model and full-wave simulations of coupled optical micro-ring resonators, providing a valuable extension of the Lorentz reciprocity in the non-Hermitian domain. Show Chinese abstract

Abstract: 洛伦兹互易性是电磁学中的一个基本性质，众所周知会由于外部磁场而失效。然而，通过虚构或虚数矢量势，其行为在很大程度上尚不清楚。在这里，我们表明，在具有虚数矢量势并表现出非厄米皮肤效应的系统中，洛伦兹互易性被破坏，但仍由一个严格的数学关系所支配，我们称之为非厄米规范互易性。然而，当仅使用线性集成光子元件模拟虚数矢量势时，导致洛伦兹互易性的条件仍然满足，因此后者无法被破坏。尽管如此，我们表明，通过适当选择输入和输出，仍可以观察到非厄米规范互易性，同时伴随洛伦兹互易性。此外，我们还揭示了同一系统中的另一种等幅响应，我们将其归因于非厄米规范对称性。此外，我们表明，光传播不会受到非厄米拓扑漏斗效应的影响，突显了相干驱动系统与非驱动系统之间被低估的差异。这些发现通过紧束缚模型和耦合光学微环谐振器的全波仿真得到证实，为非厄米领域中的洛伦兹互易性提供了有价值的扩展。