Interference traps waves in open system: Bound states in the continuum

TL;DR

This paper reviews various mechanisms of bound states in the continuum (BICs) in open wave systems, highlighting their physical origins, types, and the theoretical methods used to identify them across microwave, acoustic, and quantum systems.

Contribution

It provides a comprehensive classification and explanation of BIC mechanisms, including symmetry protected, Friedrich-Wintgen, Fabry-Perot, and accidental BICs, with a focus on their physical realization and detection methods.

Findings

Identifies four main BIC mechanisms in open cavities.

Highlights the role of destructive interference in BIC formation.

Uses effective non-Hermitian Hamiltonian to detect BICs.

Abstract

I review the four mechanisms of bound states in the continuum (BICs) in application to microwave and acoustic cavities open to directional waveguides. The most simple are the 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 result of full destructive interference of outgoing resonant modes. The third type of the BICs, the Fabry-Perot BICs, occur in a double resonator system when each resonator can serve as an ideal mirror. At last, 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 by a smooth deformation of the eigenmode. We also review the one-dimensional systems in which the BICs occur owing to full destructive interference of two waves separated by spin or polarization or by paths in the Aharonov-Bohm rings. We widely use the method of effective non-Hermitian Hamiltonian equivalent to the coupled mode theory which detects bound states in the continuum (BICs) by finding zero widths resonances.