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

As the knowledge of the eigenmode symmetries at high symmetry points (HSPs) in the Brillouin zone is essential in studying the topological properties of electronic and electromagnetic systems, how one can acquire it precisely has become a subject of interest. Here, we employ temporal coupled mode theory (CMT) to determine the irreducible representations of the energy bands at the HSPs in 2D square lattice photonic systems. Our CMT on plasmonic nanohole arrays formulates how Bloch-like surface plasmon polaritons (SPPs) interact not only with each other and but also with the continuum, revealing the importance of mode coupling in defining the field symmetries as well as their radiative and nonradiative characteristics. Such formulation facilitates the assignments of the band representations. From the representations, we find, unlike the conventional 2D tight-binding model, several band inversions occur at the {\Gamma}and X points as hole size increases, leading to changes in band topology in a subtle manner. In addition, the radiations arising from the coupled SPPs that carry different field symmetries are strongly polarization- and phase-dependent. We then conduct angle- and polarization-resolved diffraction spectroscopy on plasmonic arrays to verify the theory. Our study paves a simple way toward the probing of the band topology of non-Hermitian systems via far-field.