Topological edge and corner states based on the transformation and combination of photonic crystals with square lattice

The topological edge state (TES) and the topological corner state (TCS) have provided new method of manipulating the behavior of light. In this paper, we propose topological photonic crystals (PCs) with C-4 symmetry, and the electric field distribution and polarization of eigenmodes are investigated via the finite element method. Through the lattice transformation, different Zak phases and polarizations of eigenmodes in the PCs can be obtained. Further, one-dimensional TES and zero-dimensional TCS with strong robustness are realized by the combination of PCs with different Zak phases. This work paves a new way for manipulating the behavior of light based on the properties of TES and TCS, which will promote the development of the integrated optical field.