An analytical general analysis of the electromagnetic Dyadic Greens Function for two-dimensional sheet (or a very thin film) is presented, with an emphasis on on the case of graphene. A modified steepest descent treatment of the fields from a point d
ipole given in the form of Sommerfeld integrals is performed. We sequentially derive the expressions for both out-of-plane and in-plane fields of both polarizations. It is shown that the analytical approximation provided is very precise in a wide range of distances from a point source, down to a deep subwavelength region (1/100 of wavelength). We separate the contribution from the pole, the branch point and discuss their interference. The asymptotic expressions for the fields are composed of the plasmon, Norton wave and the components corresponding to free space.
Resonance diffraction in the periodic array of graphene micro-ribbons is theoretically studied following a recent experiment [L. Ju et al, Nature Nanotech. 6, 630 (2011)]. Systematic studies over a wide range of parameters are presented. It is shown
that a much richer resonant picture would be observable for higher relaxation times of charge carriers: more resonances appear and transmission can be totally suppressed. The comparison with the absorption cross-section of a single ribbon shows that the resonant features of the periodic array are associated with leaky plasmonic modes. The longest-wavelength resonance provides the highest visibility of the transmission dip and has the strongest spectral shift and broadening with respect to the single-ribbon resonance, due to collective effects.
Surface plasmon modes supported by graphene ribbon waveguides are studied and classified. The properties of both modes with the field concentration within the ribbon area (waveguiding modes) and on the edges (edge modes) are discussed. The waveguide
and edge modes are shown to be separated from each other by a gap in wavenumbers. The even-parity hybridized edge mode results to be the fundamental electromagnetic mode of the ribbon, possessing also the lowest losses. All the plasmonic modes in the ribbons have an optimum frequency, at which the absorption losses are minimum, due to competition between the plasmon confinement and the frequency dependence of absorption in graphene.
The extraordinary properties of graphene make it a very promising material for use in optoelectronics. However, this is still a nascent field, where some basic properties of the electromagnetic field in graphene must be explored. Here we report on th
e fields radiated by a nanoemitter lying on a graphene sheet. Our results show that this field presents a rich dependence on both frequency, distance to the source and dipole orientation. This behavior is attributed to distinct peculiarities on the density of electromagnetic states in the graphene sheet and the interaction between them. The field is mainly composed of an core region of high-intensity electromagnetic field, dominated by surface plasmons, and an outer region where the field is practically the same it would be for an emitter in vacuum. Within the core region, the intensity of the electric field is several orders of magnitude larger than what it would be in vacuum. Importantly, the size of this core region can be controlled thorough external gates, which opens up many interesting applications in, for instance, surface optics and spectroscopy. Additionally, the large coupling between nanoemitters and surface plasmons makes graphene sheets a propitious stage for quantum-optics, in which the interaction between quantum objects could be externally tailored at will.
The electromagnetic field on the metal surface launched by a subwavelength slit is analytically studied, for the case when the fundamental mode inside the slit has a wavevector component along the slit axis (conical mount). Both near-field and far-fi
eld regions are discussed, and the role of surface plasmon-polaritons and Norton waves is revealed. It is shown that the distance from the slit at which NW are more intense than surface plasmons decrease with parallel wavevector, which could help experimental studies on Norton waves. Additionally, it is found that the s-polarization component, while present for any non-zero parallel wavevector, only weakly contributes to the NWs.
Surface electromagnetic modes supported by metal surfaces have a great potential for uses in miniaturised detectors and optical circuits. For many applications these modes are excited locally. In the optical regime, Surface Plasmon Polaritons (SPPs)
have been thought to dominate the fields at the surface, beyond a transition region comprising 3-4 wavelengths from the source. In this work we demonstrate that at sufficiently long distances SPPs are not the main contribution to the field. Instead, for all metals, a different type of wave prevails, which we term Norton waves for their reminiscence to those found in the radio-wave regime at the surface of the Earth. Our results show that Norton Waves are stronger at the surface than SPPs at distances larger than 6-9 SPPs absorption lengths, the precise value depending on wavelength and metal. Moreover, Norton waves decay more slowly than SPPs in the direction normal to the surface.
