Determination of the irreducible representations at high symmetry points of two-dimensional square lattice plasmonic crystals by far-field radiations

When two topologically trivial and nontrivial systems are brought together, an energy state is formed at the interface that is robust against disorder and perturbation. For crystalline electronic and electromagnetic systems, their band topology can be determined by studying the eigenmode symmetries at high symmetry points (HSPs) in the Brillouin zone. However, such determination is not simple considering the topological properties of a system are highly geometry dependent. For leaky photonic systems, the information of eigenmodes is embedded in the radiation fields, thus providing a means for probing the band topology and designing the interface state. Here, we formulate the far-field characteristics of the energy bands at HSPs in 2D square lattice photonic systems and reveals, unlike the conventional 2D tight-binding model, several polarization-dependent band inversions occur at the Γand X points, leading to changes in their band topology in a subtle manner. As a result, by carefully tuning the system geometry to facilitate p- and s-trivial and non-trivial Zak phases, polarization-selective interface states at the Γand X points can coexist at the same heterojunction. We conduct angle- and polarization-resolved diffraction spectroscopy on 2D Au plasmonic nanohole arrays to verify the theory and observe such interface states.