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

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.

Review: 48 pages, 42 figures

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• Enhanced sum-frequency generation from etchless lithium niobate empowered by dual quasi-bound states in the continuum
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• Multiple symmetry protected BIC lines in two dimensional synthetic parameter space
• Highly directional and coherent emission from dark excitons enabled by bound states in the continuum
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• Exceptional points in dielectric spheroid
• Desktop laboratory of bound states in the continuum in metallic waveguide with dielectric cavities
• Non-Hermitian extended midgap states and bound states in the continuum
• Degenerate bound states in the continuum in square and triangular open acoustic resonators
• Acoustic Bound States in the Continuum in Coupled Helmholtz Resonators
• Parametric dependence of bound states in the continuum: a general theory
• Enhanced light absorption in Tamm metasurface with a bound state in the continuum
• Approximating transmission and reflection spectra near isolated nondegenerate resonances
• Spectral continuum in the Rabi-Stark model
• Robustness of Bound States in the Continuum in Bilayer Structures against Symmetry Breaking
• Bound state in the continuum in an anisotropic photonic crystal supported by full-wave phase plate
• Real transmission and reflection zeros of periodic structures with a bound state in the continuum
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• How many parameters do we need to obtain a BIC in symmetric and asymmetric structures?
• Bound states in the continuum induced via local symmetries in complex structures
• Thermo-optic hysteresis with bound states in the continuum
• Solitary Spectrally-Discrete Bound States in the Continuum in an Open System
• Experimental Study of Fabry-Perot BICs in a Microwave Waveguide
• Computing diffraction anomalies as nonlinear eigenvalue problems
• Observing S-Matrix Pole Flow in Resonance Interplay: Cold Collisions of Ultracold Atoms in a Miniature Laser-based Accelerator
• Discrete embedded solitary waves and breathers in one-dimensional nonlinear lattices
• Lattice-induced sound trapping in biperiodic metasurfaces of acoustic resonators
• Temporal coupled mode theory for high-$Q$ resonances in dielectric metasurfaces
• Bound states in the continuum in cuprous oxide quantum wells
• Frequency perturbation theory of bound states in the continuum in a periodic waveguide
• Singular value decomposition to describe bound states in the continuum in periodic metasurfaces
• CPA-lasing associated with the quasibound states in the continuum in asymmetric non-Hermitian structures
• Trapped-mode excitation in all-dielectric metamaterials with loss and gain
• Complex Band Structure and Bound States in the Continuum: A Unified Theoretical Framework
• Dispersive bands of bound states in the continuum