Abstract We formulate and validate a finite element approach to the propagation of a slowly decaying electromagnetic wave, called surface plasmon–polariton, excited along a conducting sheet, e.g., a single-layer graphene sheet, by an electric Hertzian dipole. By using a suitably rescaled form of time-harmonic Maxwell's equations, we derive a variational formulation that enables a direct numerical treatment of the associated class of boundary value problems by appropriate curl-conforming finite elements. The conducting sheet is modeled as an idealized hypersurface with an effective electric conductivity. The requisite weak discontinuity for the tangential magnetic field across the hypersurface can be incorporated naturally into the variational formulation. We carry out numerical simulations for an infinite sheet with constant isotropic conductivity embedded in two spatial dimensions; and validate our numerics against the closed-form exact solution obtained by the Fourier transform in the tangential coordinate. Numerical aspects of our treatment such as an absorbing perfectly matched layer, as well as local refinement and a posteriori error control are discussed.
Plasmonics is considered as one of the most promising candidates for implementing the next generation of ultrafast and ultracompact photonic circuits. Considerable effort has been made to scale down individual plasmonic components into the nanometer regime. However, a compact plasmonic source that can efficiently generate surface plasmon polaritons (SPPs) and deliver SPPs to the region of interest is yet to be realized. Here, bridging the optical antenna theory and the recently developed concept of metamaterials, we demonstrate a subwavelength, highly efficient plasmonic source for directional generation of SPPs. The designed device consists of two nanomagnetic resonators with detuned resonant frequencies. At the operating wavelength, incident photons can be efficiently channeled into SPP waves modulated by the electric field polarization. By tailoring the relative phase at resonance and the separation between the two nanoresonators, SPPs can be steered to predominantly propagate along one specific direct... The authors acknowledge support from the Spanish Ministry of Science and Innovation under Grants No. MAT2009- 06609-C02 and No. CSD2007-046-NanoLight.es. A.Y.N. acknowledges Juan de la Cierva Grant No. JCI-2008-3123 Excitation of the discrete (surface-wave plasmon propagation mode) and continuous (radiation modes) spectrum by a point current source in the vicinity of graphene is examined. The graphene is represented by an infinitesimally thin, local, and isotropic two-sided conductivity surface. The dynamic electric field due to the point source is obtained by complex-plane analysis of Sommerfeld integrals, and is decomposed into physically relevant contributions. Frequencies considered are in the GHz through mid-THz range. As expected, the TM discrete surface wave (surface plasmon) can dominate the response along the graphene layer, although this depends on the source and observation point location and frequency. In particular, the TM discrete mode can provide the strongest contribution to the total electric field in the upper GHz and low THz range, where the surface conductivity is dominated by its imaginary part and the graphene acts as a reactive (inductive) sheet. V C 2011 American Institute of Physics. [doi:10.1063 1.3662883] We discuss the properties of surface plasmons-polaritons in graphene and describe four possible ways of coupling electromagnetic radiation in the terahertz (THz) spectral range to this type of surface waves: (i) the attenuated total reflection (ATR) method using a prism in the Otto configuration, (ii) graphene micro-ribbon arrays or monolayers with modulated conductivity, (iii) a met al stripe on top of the graphene layer, and (iv) graphene-based gratings. The text provides a number of original results along with their detailed derivation and discussion. We derive and interpret solutions of time-harmonic Maxwell’s equations with a vertical and a horizontal electric dipole near a planar, thin conducting film, e.g., graphene sheet, lying between two unbounded isotropic and non-magnetic media. Exact expressions for all field components are extracted in terms of rapidly convergent series of known transcendental functions when the ambient media have equal permittivities and both the dipole and observation point lie on the plane of the film. These solutions are simplified for all distances from the source when the film surface resistivity is large in magnitude compared to the intrinsic impedance of the ambient space. The formulas reveal the analytical structure of two types of waves that can possibly be excited by the dipoles and propagate on the film. One of these waves is intimately related to the surface plasmon-polariton of transverse-magnetic polarization of plane waves. Fundamentals of Plasmonics.- Electromagnetics of Met als.- Surface Plasmon Polaritons at Met al Insulator Interfaces.- Excitation of Surface Plasmon Polaritons at Planar Interfaces.- Imaging Surface Plasmon Polariton Propagation.- Localized Surface Plasmons.- Electromagnetic Surface Modes at Low Frequencies.- Applications.- Plasmon Waveguides.- Transmission of Radiation Through Apertures and Films.- Enhancement of Emissive Processes and Nonlinearities.- Spectroscopy and Sensing.- Metamaterials and Imaging with Surface Plasmon Polaritons.- Concluding Remarks.  We consider the scattering of an incident electromagnetic radiation on a two-dimensional (2D) electron layer with an imbedded met allic contact. We show that the incident wave excites in the system the 2D plasmon polaritons running along the 2D layer and localized near it, and electromagnetic waves reflected back from the system. The ratio of the energy transformed to the 2D plasmon polaritons and reflected back from the layer depends on the frequency and the value of a retardation parameter, which characterizes the importance of retardation effects. When the retardation parameter is large, the energy of the incident radiation is mainly reflected from the 2D electron system and the excitation of the 2D plasmon polaritons is less effective. The results obtained are discussed in connection with recent experiments on the microwave response of the 2D electron systems. Surface plasmons on smooth surfaces.- Surface plasmons on surfaces of small roughness.- Surfaces of enhanced roughness.- Light scattering at rough surfaces without an ATR device.- Surface plasmons on gratings.- Conclusions.