Manipulation of topological edge and corner states in photonic Kagome crystals through different combinations

Abstract

Recently, the topological edge states (TESs) and topological corner states (TCSs) have been demonstrated in the system of second-order topological photonic crystals (TPCs) with different lattices and have attracted extensive attention in the field of optics. In this paper, we realize TESs and TCSs in TPCs based on the ‘breathing’ Kagome lattice with rhomboid dielectric columns. We investigate the influence of Wannier center on TESs and TCSs in TPCs with Kagome lattice by constructing different combination structures consisting of topologically trivial and topologically non-trivial photonic crystals (PCs), and illustrate the robustness of TESs and TCSs to defects. Thereby, we propose a rhomboidal hybrid structure composed of topologically trivial and topologically non-trivial PCs, which can realize the frequency division and beam splitting simultaneously. In addition, we also construct a parallelogram box-shaped structure of topologically non-trivial PCs with Kagome lattices surrounded by topologically trivial PCs with Kagome lattices, and find that TCSs only appear in the close regions of acute-angled corners in this structure. And by interchanging the positions of two different types of TPCs, we also demonstrate that the frequencies of TCSs can be affected by their combination manner. Moreover, there are one kind of TCSs with strong localization characteristic resulting from the nearest-neighbor coupling and another kind of TCSs resulting from the next-nearest-neighbor coupling appearing in the close regions of an acute-angled corner. This work provides a new approach for integrated optical devices based on TPCs.