We demonstrate by breaking the $C_6$ symmetry for higher-order at-$\mathrm{\Gamma }$ bound states in the continuum (BICs) with topological charge $-2$ in photonic crystals (i) deterministic generation of off-$\mathrm{\Gamma }$ BICs from the at-$\mathrm{\Gamma }$ 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.

中文翻译：

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通过对称破坏在连续谱和圆极化状态中拓扑受保护的束缚态的产生和An灭。

我们通过打破 $C_6$ 高阶at的对称性$\mathrm{\Gamma }$ 具有拓扑电荷的连续体（BIC）中的束缚态 $-2$ 在光子晶体中（i）确定性产生$\mathrm{\Gamma }$ 来自at的BIC$\mathrm{\Gamma }$BIC和（ii）具有相反拓扑电荷和相同惯性的各种圆极化状态的成对和an灭过程。为了解释这些现象，我们引入了量化为半整数的按惯用方式进行拓扑计算。灵巧的电荷给与BIC和圆极化状态的各种现象一个统一的画面。