Realization of edge and corner states in photonic crystals with kagome lattices through topological insulator generators

High-order topological insulators can be realized via two-dimensional photonic crystals (PCs) with different lattices including honeycomb, square and kagome lattices. In this paper, we utilize the kagome lattices to build a two-dimensional all-dielectric PCs platform with two kinds of topological insulator generators, obtaining the topological edge states in different frequency bands, and realizing the dual-band single channel waveguide and frequency divider. In addition, we research the origins of the two types of corner states in the combined triangle and parallelogram box-shaped structures, which consist of nontrivial PCs and trivial PCs, realizing the superimposed corner states and further enhancing the localized energy intensity in the PCs platform. These works have great potential for application in integrated nanophotonic devices.