Second-Order Topological Photonic Modes in Dipolar Arrays

Higher-order topological insulators (HOTIs) are insulators that have novel topological boundary states on the hinges and corners. Herein, we generalize them to photonic HOTIs beyond conventional scalar coupling by considering the dipolar breathing Kagome lattice. The photonic Kagome lattice supports out-of-plane and in-plane modes through tensorial dipole-dipole interaction. The topological properties of both modes are protected by generalized chiral symmetry. We demonstrate that the topological modes of the out-of-plane mode are similar to those of scalar models. Interestingly, in addition to in-plane corner states in the lower gap, the in-plane mode hosts multiple gapless symmetric and antisymmetric hinge modes along or transversal to the zigzag and armchair boundaries. These features have no counterparts in scalar models. Our findings demonstrate that photonic HOTIs have richer physics compared with their scalar counterparts, offering opportunities for engineering novel electromagnetic applications with topological constraints.