Generation and Annihilation of Topologically Protected Bound States in the Continuum and Circularly Polarized States by Symmetry Breaking

We demonstrate by breaking the C_{6} symmetry for higher-order at-Γ bound states in the continuum (BICs) with topological charge -2 in photonic crystals (i) deterministic generation of off-Γ BICs from the at-Γ BIC and (ii) a variety of pair-creation and annihilation processes of circularly polarized states with opposite topological charges and the same handedness. To explain these phenomena, we introduce the handedness-wise topological charge quantized to a half-integer. The handedness-wise charge gives a unified picture of various phenomena involving BICs and circularly polarized states.