Analysis of surface plasmon modes and band structures for plasmonic crystals in one and two dimensions

In this study, we employ the interfacial operator approach to compute surface plasmon modes as well as band structures (including longitudinal modes) for plasmonic crystals in one and two dimensions. In particular, we consider the free-electron model for the metal. It is shown that the localized feature of surface plasmon modes can be resolved near the interface by introducing interfacial variables. For a one-dimensional array of metal, convergence of two branches of surface plasmon modes is studied by varying the filling fraction of the metal. For two-dimensional metallic structures, band flattening, band broadening, and plasmonic band gaps are observed and discussed. The highly degenerate nature and infinite number of surface plasmon modes can be explained by employing the Rayleigh quotient for the TE modes. The cutoff behavior in the TM modes is made clear by considering the energy density of the electromagnetic fields. The transverse electric fields, surface charges, and polarization currents are visualized to help understand various properties of surface plasmon modes. Moreover, the effect of plasma frequency and the transition from dispersive metals to perfect conductors are also explored. Finally, the contribution of Drude damping is considered by perturbation analysis.