PHYSICAL REVIEW B 86, 235440 (2012) Excitation of terahertz surface plasmons on graphene surfaces by an elementary dipole and quantum emitter: Strong electrodynamic effect of dielectric support George W. Hanson, 1,* Ebrahim Forati, 1,† Whitney Linz, 1,‡ and Alexander B. Yakovlev 2,§ 1 Department of Electrical Engineering, University of Wisconsin-Milwaukee, 3200 N. Cramer St., Milwaukee, Wisconsin 53211, USA 2 Center for Applied Electromagnetic Systems Research (CAESR), Department of Electrical Engineering, The University of Mississippi, University, MS 38677, USA (Received 11 September 2012; published 26 December 2012) The excitation of transverse magnetic (TM) surface plasmons by a point dipole in the vicinity of a multilayered graphene/dielectric system is examined. It was previously shown that the surface plasmon (SP) excited by a vertical dipole on an isolated graphene sheet exhibits a strong excitation peak in the THz region; here we show that, in the presence of a finite-thickness dielectric support layer such as SiO 2 , considerable spectral content is transferred to a second (perturbed dielectric slab) mode, greatly decreasing and redshifting the excitation peak. The presence of a Si half-space also diminishes the excitation strength, but for graphene on top of SiO 2 -Si the presence of the SiO 2 layer creates a spacer restoring the excitation peak. A two-level quantum emitter is also considered, where it is shown that the addition of a thin dielectric support slab and SiO 2 -Si geometries affects the spontaneous decay rate in a manner similar to the classical dipole SP excitation peak. DOI: 10.1103/PhysRevB.86.235440 PACS number(s): 78.67.Wj, 78.20.Bh, 41.20.Jb I. INTRODUCTION Recently, large-area graphene has been fabricated, 1,2 al- lowing for graphene plasmonic applications in the far- through near-infrared range of frequencies. Graphene has been proposed for applications such as THz plasmon oscillators, 3 polarizers, 4,5 filters, 6 antennas, 7,8 surface plasmon modulators, 9 and in tunable waveguiding structures and interconnects, 10–17 among a host of other applications such as Fourier optics and beam scanning 18,19 and cloaking. 20 For plasmonic applications there are four important at- tributes of the surface plasmon (SP): (1) attenuation, (2) propagation constant, (3) mode confinement and field profile, and (4) excitation strength. The first three fundamental plasmon properties have been studied in previous works (e.g., Refs. 21–24), and in Ref. 25 the existence of transverse electric/magnetic graphene plasmons was examined in light of the intraband and interband contributions to the conductivity. In our previous work 26 we have examined the dipole excitation problem of a single graphene sheet at the intersection of two dielectric half-spaces (see also Refs. 27 and 28 for the quantum emitter case). In the THz regime it was shown that surface plasmons on graphene have higher attenuation, but also much better field confinement, than a thin metal layer. Furthermore, in the low THz regime it was found that the surface plasmon can be strongly excited, with the electric field being several orders of magnitude larger than the field in the absence of the graphene sheet (which is not the case for thin metal sheets). These strong surface plasmon absorption peaks at THz frequencies have been measured for several graphene structures. 29,30 Further, recent scattering-type scanning near- field optical microscopy (SNOM) imaging experiments 31 have shown in real space the existence of graphene surface plasmons on finite graphene structures, and confirmed some basic SP properties predicted by previous models, as well as some of the results obtained here. Most of the results in Ref. 26 and many of the results in other previous theoretical/simulation studies of electrodynamic ef- fects predominately considered the graphene sheet to reside in vacuum (i.e., suspended graphene 32,33 ). Other than suspended graphene, graphene is often used in various multilayer environ- ments, such as graphene-SiO 2 -Si and supported graphene on SiO 2 or other thin layers. 34,35 In Ref. 26 it was shown that the introduction of a dielectric half-space tends to depress the ex- citation peak, and increase field confinement and attenuation. In this work, we again study the four above-mentioned surface plasmon attributes based on the dipole excitation problem, and focus on the electrodynamic effect of a finite- thickness dielectric slab, and, more generally, a multilayered graphene/dielectric system on graphene-supported surface plasmons. The electromagnetic fields are governed by classical Maxwell’s equations, and the graphene is represented by a conductivity surface arising from a semiclassical (intraband) and quantum-dynamical (interband) model. It is shown that surface plasmons on supported graphene on SiO 2 are considerably different than on suspended graphene, and that even an electrically-thin dielectric support can elimi- nate the SP excitation peak exhibited by an isolated graphene layer, and decrease field confinement by transferring spectral content to a dielectric-slab surface mode weakly bound to the substrate. However, the graphene rapidly (in space) decouples from a dielectric support by introducing a low-permittivity gap between the graphene sheet and the dielectric, restoring the SP excitation peak. For graphene on silicon, enhanced field confinement depresses the excitation peak, but the addition of a low-permittivity spacer can restore the peak. Finally, we consider a two-level quantum emitter and examine the effect of the dielectric environment on the spontaneous decay rate, 28 where, similar to the classical excitation case, the presence of the dielectric support tends to decrease the decay rate by opening additional decay channels into dielectric slab modes. In the presence of a Si half-space, as with the classical dipole, the addition of a spacer layer enhances the decay rate. In the following all units are in the SI system, and the time variation (suppressed) is e jωt , where j is the imaginary unit. II. DESCRIPTION Figure 1 depicts a laterally infinite graphene sheet having conductivity σ (S) above a dielectric slab having permittivity 235440-1 1098-0121/2012/86(23)/235440(9) ©2012 American Physical Society