Faraday effect, inverse magnetooptical effects. 2 ABSTRACT. Graphene is a unique material to study fundamental limits of plasmonics. Apart from the ultimate single-layer thickness, its carrier concentration can be tuned by chemical doping or applying an electric field. In this manner the electrodynamic properties of graphene can be varied from highly conductive to dielectric. Graphene supports strongly confined, propagating surface plasmon-polaritons (SPPs) in a broad spectral range from terahertz to midinfrared frequencies. It also possesses a strong magneto-optical response and thus provides complimentary architectures to conventional magneto-plasmonics based on magneto-optically active metals or dielectrics. Despite of a large number of review articles devoted to plasmonic properties and applications of graphene, little is known about graphene magneto-plasmonics and topological effects in graphene-based nanostructures, which represent the main subject of this review. We discuss several strategies to enhance plasmonic effects in topologically distinct closed surface landscapes, i.e. graphene nanotubes, cylindric nanocavities and toroidal nanostructures. A novel phenomenon of the strongly asymmetric SPP propagation on chiral meta-structures and fundamental relations between structural and plasmonic topological indices are reviewed.
I. IntroductionGraphene opens up wide prospects for numerous flatland photonic and plasmonic applications [1-7]. Graphene-based waveguides support localized electromagnetic SPP waves, both TE-and TM-polarized [8-16]. Their tight confinement and long propagation length allow for observing strong light-matter interactions in graphene-based structures [17]. Optical properties of graphene transformations give rise to distinct topological indices, which largely determine the properties of plasmonic modes. The interplay of the intrinsic (elliptic versus hyperbolic) topology of SPPs propagating on a flat 2D-meta-surface and the geometrical 3D-topology of nanostructures can induce novel plasmonic effects: a giant azimuthal rotation of intensity distribution of particular SPP modes upon propagation, one-way propagation of SPPs, vanishing of the Fabry-Perot resonances in finite length meta-tubes, unidirectional circulating Mach-Zehnder-like resonances in a meta-torus, etc.Figure 1: (A) An array of densely packed graphene stripes with sub-wavelength periodicity Λ forms a metasurface which may support both elliptic (B) and hyperbolic SPPs (C). A rolled-up meta-surface forms a meta-tube and its donut-like shape is a meta-torus (D). In (B) and (C) Λ = 50 nm, A = 45 nm, B = 5 nm. 5The cylindrical geometry deserves a particular attention as it provides a common basis for plasmonics in chiral media [38][39][40][41][42] and non-reciprocal magneto-optics in waveguides. It is known that the parallel external magnetic field can rotate a spatially inhomogeneous intensity distribution (i.e. speckle-pattern) of light in the cross-section plane upon its propagation along an optical fiber [43][44][45][46]. Rec...