The phase picked up by a graphene plasmon upon scattering by an abrupt edge is commonly assumed to be $-pi$. Here, it is demonstrated that for high plasmon momenta this reflection phase is $approx -3pi/4$, virtually independent on either chemical pot
ential, wavelength or dielectric substrate. This non-trivial phase arises from a complex excitation of highly evanescent modes close to the edge, which are required to satisfy the continuity of electric and magnetic fields. A similar result for the reflection phase is expected for other two-dimensional systems supporting highly confined plasmons (very thin metal films, topological insulators, transition polaritonic layers, etc.). The knowledge of the reflection phase, combined with the phase picked up by the plasmon upon propagation, allows the estimation of resonator properties from the dispersion relation of plasmons in the infinite monolayer.
Placing graphene on uniaxial substrates may have interesting application potential for graphene-based photonic and optoelectronic devices. Here we analytically derive the dispersion relation for graphene plasmons on uniaxial substrates and discuss th
eir momentum, propagation length and polarization as a function of frequency, propagation direction and both ordinary and extraordinary dielectric permittivities of the substrate. We find that the plasmons exhibit an anisotropic propagation, yielding radially asymmetric field patterns when a point emitter launches plasmons in the graphene layer.
An analytical method for diffraction of a plane electromagnetic wave at periodically-modulated graphene sheet is presented. Both interface corrugation and periodical change in the optical conductivity are considered. Explicit expressions for reflecti
on, transmission, absorption and transformation coefficients in arbitrary diffraction orders are presented. The dispersion relation and decay rates for graphene plasmons of the grating are found. Simple analytical expressions for the value of the band gap in the vicinity of the first Brillouin zone edge is derived. The optimal amplitude and wavelength, guaranteeing the best matching of the incident light with graphene plasmons are found for the conductivity grating. The analytical results are in a good agreement with first-principle numeric simulations.
A single graphene sheet, when subjected to a perpendicular static magnetic field provides Faraday rotation that, per atomic layer, greatly surpasses that of any other known material. This Giant Faraday rotation originates from the cyclotron resonance
of massless electrons, which allows dynamical tuning through either external electrostatic or magnetostatic setting. Furthermore, the rotation direction can be controlled by changing the sign of the carriers in graphene, which can be done by means of an external electric field. However, despite these tuning possibilities, the requirement of large magnetic fields hinders application of the Faraday effect in real devices, especially for frequencies higher than few THz. In this work we demonstrate that, for a given value of the static external magnetic field, giant Faraday rotation can be achieved in arrays of graphene microribbons at frequencies much higher than the corresponding cyclotron frequency. The main feature in the magneto-optical response of graphene ribbons is not associated with the cyclotron resonance but rather with the fundamental magnetoplasmon excitation of a single ribbon. The magnetoplasmon nature of Faraday rotation in graphene ribbons opens great possibilities, as the resonance frequency can be locally selected by appropriately choosing the width of the ribbon while still preserving the tuning capability through a (smaller) external magnetic field.
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.
We show that a graphene sheet perforated with micro- or nano-size antidots have prominent absorption resonances in the microwave and terahertz regions. These resonances correspond to surface plasmons of a continuous sheet perturbed by a lattice. They
are excited in different diffraction orders, in contrast to cavity surface plasmon modes existing in disconnected graphene structures. The resonant absorption by the antidot array can essentially exceed the absorption by a continuous graphene sheet, even for high antidot diameter-to-period aspect ratios. Surface plasmon-enhanced absorption and suppressed transmission is more efficient for higher relaxation times of the charge carriers.
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.
