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.

我回顾了连续介质 (BIC) 中束缚态在微波和声学腔应用中对定向波导开放的四种机制。最简单的是受对称保护的 BIC，由于本征模式与波导传播模式的正交性，它们位于腔内。然而，最普遍和最有趣的是 Friedrich-Wintgen 机制，当 BIC 是输出谐振模式的完全破坏性干扰的结果。第三种类型的 BIC，Fabry-Perot BIC，出现在双谐振器系统中，此时每个谐振器都可以用作理想的镜子。最后，偶然的 BIC 可以在不对称的开放腔中实现，就像开放的西奈台球一样，其中谐振器的本征模式可能由于本征模式的平滑变形而意外地与波导的连续体正交。我们还回顾了一维系统，其中由于自旋或极化或阿哈罗诺夫-玻姆环中的路径分开的两个波的完全相消干涉而发生 BIC。我们广泛使用等效于耦合模式理论的有效非厄米哈密顿量方法，该方法通过寻找零宽度共振来检测 BIC。