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

Topological Surface-plasmon-polaritons on Corrugated Metal-dielectric Surfaces