Bound states in the continuum on periodic structures: perturbation theory and robustness

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 crucially depend on the symmetry of the structure. In this Letter, a perturbation theory is developed for propagating BICs on two-dimensional periodic structures. The Letter shows that these BICs are robust against structural perturbations that preserve the symmetry, indicating that these BICs, in fact, are implicitly protected by symmetry.