On dielectric periodic structures with a reflection symmetry in a periodic direction, there can be antisymmetric standing waves (ASWs) that are symmetry-protected bound states in the continuum (BICs). The BICs have found many applications, mainly because they give rise to resonant modes of extremely large quality factors ($Q$ factors). The ASWs are robust to symmetric perturbations of the structure, but they become resonant modes if the perturbation is nonsymmetric. The $Q$ factor of a resonant mode on a perturbed structure is typically $O(1/{\delta }^2)$, where $\delta$ is the amplitude of the perturbation, but special perturbations can produce resonant modes with larger $Q$ factors. For two-dimensional (2D) structures with a one-dimensional (1D) periodicity, we derive conditions on the perturbation profile such that the $Q$ factors are $O(1/{\delta }^4)$ or $O(1/{\delta }^6)$. For the unperturbed structure, an ASW is surrounded by resonant modes with a nonzero Bloch wave vector. For 2D structures with a 1D periodicity, the $Q$ factors of nearby resonant modes are typically $O(1/{\beta }^2)$, where $\beta$ is the Bloch wave number. We show that the $Q$ factors can be $O(1/{\beta }^6)$ if the ASW satisfies a simple condition.

• Received 21 November 2019
• Accepted 30 March 2020

DOI:https://doi.org/10.1103/PhysRevA.101.043827