Non-Hermitian physics has found a fertile ground in optics. Recently, the study of mode coalescence, i.e., exceptional points, has led to the discovery of intriguing and counterintuitive phenomena. Degeneracies are typically modeled through the coupled mode theory to determine the behavior of eigenstates and eigenvalues. However, the complex nature of the eigenvalues makes their characterization from the response spectrum difficult. Here, we demonstrate that a coherent interferometric excitation allows estimation of both the real and imaginary parts of the eigenvalues. We study the clockwise and counter-clockwise modes in optical microresonators both in the case of Hermitian and non-Hermitian intermodal coupling. We show the conditions by which a resonant doublet, due to the dissipative coupling of counter-propagating modes caused by surface roughness backscattering, merges to a single Lorentzian. This permits us to estimate the optimal quality factor of the microresonator in the absence of modal coupling caused by backscattering. Furthermore, we demonstrate that a taiji microresonator working at an exceptional point shows a degeneracy splitting only in one propagation direction and not in the other. This follows from the strongly non-Hermitian intermodal coupling caused by the inner S-shaped waveguide.

中文翻译：

---

估计非厄米特两能级光学系统特征值的干涉方法

非厄米物理学在光学领域找到了肥沃的土壤。最近，对模态合并，即异常点的研究，导致了一些有趣和违反直觉的现象的发现。简并通常通过耦合模式理论建模，以确定本征态和本征值的行为。然而，特征值的复杂性使得从响应谱中对其进行表征变得困难。在这里，我们证明了相干干涉激发允许估计特征值的实部和虚部。我们研究了在厄米特和非厄米特模态耦合的情况下光学微谐振器中的顺时针和逆时针模式。我们展示了共振双峰的条件，由于由表面粗糙度反向散射引起的反向传播模式的耗散耦合，合并为单个洛伦兹。这使我们能够在没有由反向散射引起的模态耦合的情况下估计微谐振器的最佳品质因数。此外，我们证明了工作在异常点的太极微谐振器仅在一个传播方向上显示简并分裂，而在另一个传播方向上没有。这是由内部 S 形波导引起的强非厄米特模态耦合造成的。我们证明了工作在异常点的太极微谐振器仅在一个传播方向上显示简并分裂，而在另一个传播方向上没有。这是由内部 S 形波导引起的强非厄米特模态耦合造成的。我们证明了工作在异常点的太极微谐振器仅在一个传播方向上显示简并分裂，而在另一个传播方向上没有。这是由内部 S 形波导引起的强非厄米特模态耦合造成的。