I review the four mechanisms of bound states in the continuum (BICs) in the application of microwave and acoustic cavities open to directional waveguides. The most simple are symmetry-protected BICs, which are localized inside the cavity because of the orthogonality of the eigenmodes to the propagating modes of waveguides. However, the most general and interesting is the Friedrich-Wintgen mechanism, when the BICs are the result of the fully destructive interference of outgoing resonant modes. The third type of BICs, Fabry-Perot BICs, occurs in a double resonator system when each resonator can serve as an ideal mirror. Finally, the accidental BICs can be realized in the open cavities with no symmetry like the open Sinai billiard in which the eigenmode of the resonator can become orthogonal to the continuum of the waveguide accidentally due to a smooth deformation of the eigenmode. We also review the one-dimensional systems in which the BICs occur owing to the fully destructive interference of two waves separated by spin or polarization or by paths in the Aharonov-Bohm rings. We make broad use of the method of effective non-Hermitian Hamiltonian equivalent to the coupled mode theory, which detects BICs by finding zero-width resonances.

中文翻译：

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干扰将波捕获在开放系统中：连续状态中的束缚状态。

在微波和声腔向定向波导开放的应用中，我回顾了连续体（BIC）中束缚态的四种机理。最简单的是对称保护的BIC，由于本征模与波导的传播模正交，所以它们位于腔体内。但是，当BIC是输出共振模的完全破坏性干涉的结果时，最普遍和有趣的是Friedrich-Wintgen机制。当每个谐振器都可以用作理想镜时，第三种类型的BIC（法布里-珀罗BIC）出现在双谐振器系统中。最后，偶然的BIC可以在没有对称性的开放腔中实现，就像开放的Sinai台球那样，由于本征模的平滑变形，谐振器的本征模可能偶然地正交于波导的连续体。我们还回顾了由于自旋或极化或Aharonov-Bohm环中的路径分开的两个波的完全破坏性干涉而导致BIC发生的一维系统。我们广泛使用等效于耦合模式理论的有效非Hermitian哈密顿量方法，该方法通过查找零宽度共振来检测BIC。