论文标题
在周期性波导中连续体中结合状态的频率扰动理论
Frequency perturbation theory of bound states in the continuum in a periodic waveguide
论文作者
论文摘要
在无损周期性结构中，连续体（BIC）中的绑定状态的特征是真实的频率和一个真实的bloch波动向量，在周围介质中存在波动或从无限传播的波。对于应用程序，重要的是要分析对BIC附近的波形自然存在的高Q $共振，或者在结构扰动时出现。现有的理论为由于结构扰动或波形变化而出现的共振模式的复杂频率（以及$ q $ factor）提供了定量结果。当周期性结构被视为周期性波导时，经常为给定的真实频率分析本征谱。在本文中，我们考虑使用BIC的周期性波导，并研究了在BIC频率附近的真实频率的特征模。事实证明，BIC附近的这种本征始终具有复杂的Bloch波数，但是它们可能是泄漏的模式或可能不会在横向上辐射到无穷大的泄漏模式。这些本征码也可以是复杂的模式，在侧向方向上呈指数衰减。我们的研究与BIC在光学波导中的应用有关，也有助于分析在BIC频率附近运行的光子设备。
In a lossless periodic structure, a bound state in the continuum (BIC) is characterized by a real frequency and a real Bloch wavevector for which there exist waves propagating to or from infinity in the surrounding media. For applications, it is important to analyze the high-$Q$ resonances that either exist naturally for wavevectors near that of the BIC or appear when the structure is perturbed. Existing theories provide quantitative results for the complex frequency (and the $Q$-factor) of resonant modes that appear/exist due to structural perturbations or wavevector variations. When a periodic structure is regarded as a periodic waveguide, eigenmodes are often analyzed for a given real frequency. In this paper, we consider periodic waveguides with a BIC, and study the eigenmodes for given real frequencies near the frequency of the BIC. It turns out that such eigenmodes near the BIC always have a complex Bloch wavenumber, but they may or may not be leaky modes that radiate out power laterally to infinity. These eigenmodes can also be complex modes that decay exponentially in the lateral direction. Our study is relevant for applications of BICs in optical waveguides, and it is also helpful for analyzing photonic devices operating near the frequency of a BIC.
