We demonstrate that multiple higher-order topological transitions can be triggered via the continuous change of the geometry in kagome photonic crystals composed of three dielectric rods. By tuning a single geometry parameter, the photonic corner and edge states emerge or disappear with higher-order topological transitions. Two distinct higher-order topological insulator phases and a normal insulator phase are revealed. Their topological indices are obtained from symmetry representations. A photonic analog of the fractional corner charge is introduced to distinguish the two higher-order topological insulator phases. Our predictions can be readily realized and verified in configurable dielectric photonic crystals.

中文翻译：

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可调 C3 对称光子晶体中的高阶拓扑相

我们证明了可以通过由三个介电棒组成的 kagome 光子晶体中几何形状的连续变化来触发多个高阶拓扑跃迁。通过调整单个几何参数，光子角和边缘状态随着高阶拓扑跃迁而出现或消失。揭示了两个不同的高阶拓扑绝缘体相和一个正常绝缘体相。它们的拓扑指数是从对称表示中获得的。引入分数角电荷的光子模拟来区分两个高阶拓扑绝缘体相。我们的预测可以在可配置的介电光子晶体中轻松实现和验证。