Bound States in the Continuum on Periodic Structures: Perturbation Theory and Robustness

TL;DR

This paper develops a perturbation theory for propagating bound states in the continuum (BICs) on 2D periodic structures, demonstrating their robustness against symmetry-preserving structural perturbations and highlighting their implicit symmetry protection.

Contribution

It introduces a perturbation theory for propagating BICs and shows their robustness, revealing implicit symmetry protection in 2D periodic structures.

Findings

Propagating BICs are robust against symmetry-preserving perturbations.

BICs are implicitly protected by symmetry.

Perturbation theory effectively describes BIC behavior under structural changes.

Abstract

On periodic structures, a bound state in the continuum (BIC) is a standing or propagating Bloch wave with a frequency in the radiation continuum. Some BICs (e.g., antisymmetric standing waves) are symmetry-protected, since they have incompatible symmetry with outgoing waves in the radiation channels. The propagating BICs do not have this symmetry mismatch, but they still depend crucially on the symmetry of the structure. In this Letter, a perturbation theory is developed for propagating BICs on two-dimensional periodic structures. The study shows that these BICs are robust against structural perturbations that preserve the symmetry, indicating that these BICs are in fact implicitly protected by symmetry.