Plasmonics of magnetic and topological graphene-based nanostructures

Abstract

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...

Dispersion features of complex waves in a graphene-coated semiconductor nanowire

“…related to the TM 0n modes and TE 0n modes, respectively. In practice, similar to the case of cylindrical dielectric waveguides coated by a resistive film [10], the axially symmetric modes can be excited in a graphene-coated nanowire either by using specific excitation methods or by creating a particular anisotropy of the graphene sheet [2]. By solving the corresponding dispersion equation one can obtain the dependence of the complex propagation constant β of the m-th order non-symmetric hybrid EH mn and HE mn modes or axially symmetric TM 0n and TE 0n modes on frequency or geometrical parameters of the waveguide.…”

“…The dispersion equations for the TM modes of surface plasmons are obtained from Eqs. (5) and (7) providing the following substitutions: κ 2 1,2 = β 2 − ω 2 ε 1,2 µ 1,2 ; J m (·) → I m (·); H (2) m (·) → K m (·), where I m (·) and K m (·) are modified Bessel functions of the first and second kinds, respectively. The results of our calculations are summarized in Figs.…”

“…m (·) and H(2) m (·) are the Hankel function of the second kind and its derivative, respectively.A formal substitution of m = 0 into the dispersion equation(5) related to the non-symmetric hybrid modes does not instantly lead to appearance of two separate dispersion equations related to the axially symmetric transverse magnetic (TM 0n ;…”

Optical Transport Properties of Graphene Surface Plasmon Polaritons in Mid-Infrared Band

“…The mid-infrared band is a technologically important wave band, which has important applications in different fields including spectroscopic sensing and environmental monitoring [23]. It was found that graphene supports SPPs from the THz to mid-infrared band [24][25][26]. Graphene SPPs show excellent properties simultaneously, including ultra-compact mode confinement, dynamic tunability, and lower loss [19,27].…”

Electrical Phase Control Based on Graphene Surface Plasmon Polaritons in Mid-infrared

“…Due to their tunability and small size, these graphene-based devices have advantages over traditional devices. In addition, graphene has been proven to support SPPs from a mid-infrared band to THz and SPPs bound to the surface of doped graphene, which exhibit a number of favorable properties [16,17]. The ability to fabricate large-sized, high-crystalline samples enables the lifetime of SPPs to reach hundreds of optical cycles, making graphene a potential alternative for precious metal SPPs [12].The phase modulation of light is at the core of many applications and much research [18].…”