ABSTRACT

Owing to the two-dimensional conguration, the band structure of graphene has Dirac points at the Brillouin zone

(BZ) corners where the electrons are massless and have very high mobility (Castro Neto et al. 2009). The unique features render graphene a promising material that provides an open platform for demonstrating many phenomena in graphene with great scientic signicance and potential applications (Castro Neto et al. 2009; Geim 2009; Das Sarma et al. 2011). Very recently, graphene has stimulated great interest among the nanophotonics community since graphene is found to be able to support surface plasmon polaritons (SPPs) (Hanson 2008a,b; Chen et  al. 2012; Fei et  al. 2012). The graphenesupported SPPs, conventionally known as graphene plasmons (GPs), are guided modes that can propagate along graphene surface with an extremely strong eld connement (Grigorenko et al. 2012). As the chemical potential (Fermi energy) of graphene is larger than half the energy of exciting photons, GPs could be physically excited by metallic tips or quantum dots. Usually, the chemical potential is up to 1 ~ 2 eV (Efetov and Kim 2010; Chen et al. 2011) and hence, GPs could only be observed in the far-infrared and terahertz range. The GPs have many unique features by comparing with SPPs on metals. First, the effective index of GPs is very high. The value could be approaching to more than 100, nearly two orders larger than that of SPPs on metals. The high effective index also suggests the strong connement of the electric eld of GPs. For example, the GPs in the infrared region (λ = 10 µm) have an effective mode width of ~50 nm. That means it can be manipulated deeply below the diffraction limit. Second, the loss of GPs is relatively low since graphene has Dirac electrons with very high mobility at room temperature. The propagation length could reach dozens of wavelengths of the GPs. Finally, the optical properties of graphene can be rapidly tuned by using an external

Abstract ..................................................................................................................................................................................... 457 28.1 Introduction ..................................................................................................................................................................... 457 28.2 Plasmons in a Single Layer of Graphene Sheet ............................................................................................................... 458

28.2.1 Surface Conductivity of Graphene ...................................................................................................................... 458 28.2.2 Plasmons in a Monolayer Graphene .................................................................................................................... 459

28.3 Optical Coupling of Two Graphene Sheets ..................................................................................................................... 460 28.4 Optical Coupling of GPs in Graphene Sheet Arrays ....................................................................................................... 462

28.4.1 Dispersion Relation .............................................................................................................................................. 463 28.4.2 Weak Coupling .................................................................................................................................................... 464 28.4.3 Strong Coupling ................................................................................................................................................... 465 28.4.4 Comparison with Thin Metal Film Arrays .......................................................................................................... 466

28.5 Conclusion ....................................................................................................................................................................... 467 References ................................................................................................................................................................................. 467

changing the chemical potential of graphene. As a result, the optical congurations composed of graphene could be manipulated in real time other than by chemically doping graphene in advance. Owing to the fantastic characteristics, graphene has been reported to nd many great applications in optical modulators (Wang et  al. 2014), couplers (Wang et  al. 2012; Smirnova et  al. 2013), logic gates (Ooi et  al. 2014), and Talbot imaging (Fan et al. 2014).