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

TL;DR

This paper derives a general condition for special bound states in the continuum (BICs) on periodic structures, which exhibit extremely high quality factors over a broad range of wavevectors, with implications for practical resonator applications.

Contribution

It introduces a new general condition for identifying special BICs with higher quality factor scaling on 2D periodic structures, supported by numerical examples.

Findings

Derived a condition for special BICs with Q ∝ 1/|β - β*|^4

Numerically identified antisymmetric standing wave BICs on circular cylinder arrays

Showed these BICs have large Q over a wide β range

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 $1/|\beta - \beta_*|^2$, where $\beta$ and $\beta_*$ are the Bloch wavevectors of the resonant modes and the BIC, respectively. But for some special BICs, the quality factors are proportional to $1/|\beta -\beta_*|^4$. 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 $\beta$.