Topological boundary states of two-dimensional restricted isosceles triangular photonic crystals

We propose an all-media photonic crystal (PC) composed of isosceles triangle dielectric cylinders that realizes the topological phase transition by simply rotating the isosceles triangular dielectric cylinders. Additionally, the topological phase transition is closely linked with the size parameters and rotation angle of the isosceles triangle. The topological boundary states with lossless transmission are constructed on the interface of two different topological structures, and the optical quantum spin Hall effect is simulated. Further, we verified that the boundary state is unidirectional and immune to disorder, cavity, and sharp bend defects. By rotating the angle of the triangle to control the transmission path of the pseudo-spin state, we realize diverse transport pathways of light, such as the "straight line" shape, "Z" shape, "U" shape, and "Y" shape. This topological system shows a higher degree of freedom, which can promote the research on topological boundary states and the development of topological insulators in practical applications.