Topological plasmonic waveguides in triharmonic metal gratings

We study topological surface-plasmon-polaritons at optical frequencies in tri-harmonic diffraction gratings formed at a metal-dielectric interface. The latter are shown to well approximate a bipartite Kronig-Penney model. Topologically protected localised modes are then predicted to occur at the edges of the grating and at defects formed by the combination of two mirror antisymmetric corrugations, whose bulk invariant is a step-wise varying Zak phase in both cases. An interesting special case wherein the defect state is in-fact forbidden is also observed that reveals the fragility of such states despite their topological nature.