Topological plasmonic waveguides in triharmonic metal gratings

We study topological surface-plasmon-polaritons at optical frequencies in diffraction gratings formed by bipartite corrugated metal-dielectric gratings. To do so we implement the theory as developed Della Valle and Longhi to describe amplitude of field an emergent Schr\"odinger-like equation. The tri-harmonic grating generates a Kronig-Penney model. Topologically protected localised modes are then predicted occur edges defects combination two mirror antisymmetric corrugations, whose bulk invariant is step-wise varying Zak phase both cases.