Topological Edge State in the Two-Dimensional Stampfli-Triangle Photonic Crystals

A two-dimensional Stampfli-triangle photonic crystal (2D S-T PC), which arranges the basic structural unit of a Stampfli-type photonic quasicrystal (PQC) in a triangular lattice, is proposed. The relationship between the structural parameters and the topological trivial or nontrivial state generated in the 2D S-T PC and the relationship between the structural parameters and the frequency of the one-way propagation are analyzed. One-way propagation based on a U-shaped waveguide composed of 2D S-T PCs, with topological trivial and nontrivial states sharing a common band gap, is realized. The topological edge state, which satisfies C-6 symmetry, is realized by changing just the diameters of the cylinders in the 2D S-T PC. This provides an idea for the generation of a topological edge state based on a 2D PQC and increases the diversity and adjustability of the method to realize the topological edge state.