Bound states in the continuum on periodic structures surrounded by strong resonances

Abstract

Bound states in the continuum (BICs) are trapped or guided modes with their frequencies in the frequency intervals of the radiation modes. On periodic structures, a BIC is surrounded by a family of resonant modes with their quality factors approaching infinity. Typically the quality factors are proportional to $1/|\beta -{\beta }_{\ast }{|}^2$, where $\beta$ and ${\beta }_{\ast }$ are the Bloch wavevectors of the resonant modes and the BIC, respectively. But for some special BICs, the quality factors are proportional to $1/|\beta -{\beta }_{\ast }{|}^4$. In this paper, a general condition is derived for such special BICs on two-dimensional periodic structures. As a numerical example, we use the general condition to calculate special BICs, which are antisymmetric standing waves, on a periodic array of circular cylinders, and show their dependence on parameters. The special BICs are important for practical applications, because they produce resonances with large quality factors for a very large range of $\beta$.

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• Desktop laboratory of bound states in the continuum in metallic waveguide with dielectric cavities
• Conditional robustness of propagating bound states in the continuum on biperiodic structures
• Bound states with complex frequencies near the continuum on lossy periodic structures
• Circularly polarized states and propagating bound states in the continuum in a periodic array of cylinders
• Parametric dependence of bound states in the continuum in periodic structures: vectorial cases
• Parametric Dependence of Bound States in the Continuum on Periodic Structures
• Parametric dependence of bound states in the continuum: a general theory
• On the robustness of bound states in the continuum in waveguides with lateral leakage channels
• A topology optimization of open acoustic waveguides based on a scattering matrix method
• Topologically protected bound states in the continuum and strong phase resonances in integrated Gires-Tournois interferometer
• Frequency perturbation theory of bound states in the continuum in a periodic waveguide
• Bound states in the continuum are universal under the effect of minimal length