Topological edge and corner states in a two-dimensional photonic Su-Schrieffer-Heeger lattice

Implementation of topology on photonics has opened new functionalities of photonic systems such as topologically protected boundary modes. We theoretically present polarization-dependent topological properties in a 2D Su-Schrieffer-Heeger lattice by using a metallic nanoparticle array and considering the polarization degree of freedom. We demonstrate that when eigenmodes are polarized parallel to the plane of the 2D lattice, it supports longitudinal edge modes that are isolated from the bulk states and transverse edge modes that are overlapped with the bulk states. Also, the in-plane polarized modes support a second-order topological phase under an open boundary condition by breaking the four-fold rotational symmetry. This work will offer polarization-based multifunctionality in compact photonic systems that have topological features.