Perturbation theories for symmetry-protected bound states in the continuum on two-dimensional periodic structures

TL;DR

This paper develops perturbation theories for symmetry-protected bound states in the continuum (BICs) in 2D periodic structures, showing how to achieve higher Q-factors through specific perturbations and conditions.

Contribution

It derives conditions on perturbations that significantly increase Q-factors of BICs in 2D periodic structures, extending understanding of resonance behavior.

Findings

Q-factors can be increased to O(1/δ^4) or O(1/δ^6) with specific perturbations.

Q-factors near resonant modes scale as O(1/β^2), but can reach O(1/β^6) under certain conditions.

Symmetry-protected BICs are robust to symmetric perturbations but become high-Q resonances under non-symmetric perturbations.

Abstract

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 non-symmetric. 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) periodic structures with a 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 periodic structures, the $Q$-factors of nearby resonant modes are typically $O(1/\beta^2)$, where $\beta$ is the Bloch wavenumber. We show that the $Q$-factors can be $O(1/\beta^6)$ if the ASW satisfies a simple condition.