Using the dyadic Green function (GF) with a multilayer medium, we propose an eigendecomposition (ED) analysis of a plasmonic system composed of a one-dimensional periodic metal nanoparticle chain and planar layered structure. An effective eigenpolarizability involving the collective effects of both the chain and the layered structure is well defined to characterize the dispersion relation and the mode quality of the plasmonic modes. Applying this method, we demonstrate that the interplay between the surface plasmon polaritons (SPPs) at the metal–dielectric interface and the localized plasmon in the chain enables strong mode splitting. In particular, for the polarization perpendicular to layer surface, high-quality modes can be present inside the light cone even if the chain is open to the surrounding air. A slow-light band is also predicted to exist as long as the layered medium supports a SPP mode that can couple to the chain mode.
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