Study of polarization-dependent band inversions and edge states from two-dimensional square lattice plasmonic crystals

When two topologically trivial and nontrivial systems are brought together, a localized energy state is formed at the interface. For crystalline quantum and classical systems, their topology can be determined by studying the eigenmode symmetries at high symmetry points (HSPs) in the Brillouin zone. As electromagnetic systems are usually leaky, their radiations retain the eigenmode information, thus providing a means for probing the band topology. Here, we formulate the far-field characteristics of the eigenmodes at HSPs in 2D square lattice plasmonic systems and reveals, unlike the conventional tight-binding model, several polarization-dependent band inversions occur at the{\Gamma}and X points, rendering subtle changes in their band topology. In particular, by carefully tuning the system geometry to facilitate trivial and non-trivial phases, polarization selective 0D and 1D edge states that possess distinct field symmetries are realized. The evolution of 0D or 1D edge state depends on the degree of bulk-edge overlapping. We perform angle- and polarization-resolved diffraction spectroscopy on 2D Au plasmonic nanohole arrays to verify the theory and observe such states. Our study demonstrates the applicability of simple far-field technique for diagnosing the band topology of various crystalline classical systems in electromagnetics and acoustics.