Strong Coupling of Surface Plasmon Polaritons in Monolayer Graphene Sheet Arrays

Abstract

Here we investigate theoretically and numerically the coupling between surface plasmon polaritons (SPPs) in monolayer graphene sheet arrays that have a period much smaller than the wavelength. We show that when the collective SPP is excited with an out-of-phase illumination, the beam tends to propagate toward the opposite direction of the Bloch momentum, reflecting a negative coupling between the constituent SPPs. In contrast, for in-phase illumination, the incident beam is split into two collective SPPs that are highly collimated and display low propagation loss. Moreover, the coupling between the individual SPPs results in a reduction of the modal wavelength of the SPP in comparison with that of a single graphene sheet. DOI: 10.1103/PhysRevLett.109.073901 PACS numbers: 42.82.Et, 42.25.Fx, 42.79.Fm, 73.20.Mf Graphene, an allotrope of carbon consisting of sp 2 bonded carbon atoms arranged in one atom thick honeycomb lattice, has attracted extensive attention since the practical production of stable graphene in 2004 [1]. A great diversity of electronic and optical effects have been found in graphene such as integer and fractional quantum Hall effect at room temperature, tunable band gap, ballistic electronic propagation, optical saturable absorption and luminescence [2][3][4]. The optical response of graphene is characterized by its surface conductivity which greatly relates to its chemical potential (Fermi energy). Graphene manifests strong absorption of light in the near-infrared and visible range [5]. At lower frequencies such as THz and far-infrared range, the intraband transition of electrons dominates and graphene behaves like a metal. The transverse magnetic (TM) polarized surface plasmon polaritons (SPPs) could therefore be supported by graphene. SPPs in graphene possess unique features as compared with metals, such as huge modal index, relatively low loss, and flexible tunability by electric field, magnetic field, and gate voltage [6]. These features make graphene a promising material for SPP-based optical nanodevice applications.So far, the study on graphene plasmonics mostly focused on SPPs in monolayer graphene, graphene ribbons, and double-layer graphene sheets [6][7][8][9][10]. The excitation of SPPs in graphene is theoretically proposed by using nanoemitters in graphene sheets [11,12]. Experimental observation of SPPs in graphene has also been reported by using electron spectroscopy [9] and near-field microscopy [13,14]. As a fundamental issue, the weak coupling of SPPs in between double-layer graphene sheets was recently investigated [15]. The coupling of SPPs in a periodic multilayer graphene system, which is physically different from that in double-layer graphene sheets, is also an important topic but has not been explored yet.In this Letter, we propose a monolayer graphene sheet array (MGSA) composed of periodically stacked monolayer graphene sheets with identical interlayer space. The configuration follows the conventional dielectric and metallic waveguide arrays [16][17][18] that have sho...

Tunable waveguide bends with graphene-based anisotropic metamaterials

“…27) The wavelength of the graphene plasmon is thus λ SPP = 2π/Real(k SPP ) ≈ 0.31 µm, matching the interference pattern in Fig. 2(b) well.…”

“…22) Furthermore, metamaterials based on graphene/dielectric multilayers have also been studied both theoretically 23,24) and experimentally. 25,26) The strong coupling between the surface plasmon polaritons in graphene sheets makes graphene a powerful material for controlling wave radiation 27) and for designing ultrasensitive modulators. 28) Graphene-based metamaterials should also be beneficial in bending electromagnetic waves with proper designs.…”

Tunable Metamaterials Made of Graphene-Liquid Crystal Multilayers

“…(4), one can find that the dispersion of the structure is hyperbolic when ε x ε z < 0 and is elliptic when ε x ε z > 0. The graphene is considered as ultrathin metallic layers with the relative equivalent permittivity of ε g = 1 + iσ g η 0 /(k 0 d 1 ) where k 0 = 2π/λ is the vacuum wavevector, η 0 is the impedance of air and σ g is the surface conductivity of the graphene [18]. σ g is obtained from the Kubo formula [31] including the intraband and interband transition contributions as…”

“…At the frequency ranges of THz and far-infrared, the dissipative loss of graphene is less than the usual metals and its optical response is described by the surface conductivity which is related to its chemical potential and can be controlled and tuned by voltage or chemical doping [16][17][18]. Graphene-based liquid crystal devices, optical modulators and switches can be mentioned as examples [19][20][21][22].…”

“…Also, the optical properties and some applications of the multilayer graphene structures have been investigated by different research groups. For example, Wang et al investigated the coupling between surface plasmon polaritons in a multilayer graphene sheet arrays [18]. Graphene hyperlens for THz radiation have been proposed by Andryieuski using graphene-dielectric multilayered stack [23].…”