Plasmonic response of graphene nanostructures

Graphene is a planar monolayer of carbon atoms tightly packed into a 2D honeycomb lattice. Since the first experimental isolation in 2004, graphene has attracted an enormous interest due to its extraordinary optoelectronic properties for nanophotonics. The unique band structure of graphene consists of a lower or valence band and an upper or conduction band, which at low energies resemble the shape of two inverted cones touching at one point (the so-called Dirac point) that marks the Fermi level in the neutral state. In this state, the valence band is completely filled with electrons, while the conduction band is empty. Interestingly, when extra electrons are added to graphene (doping), they start filling unoccupied states in the conduction band up to a certain level that corresponds to the new Fermi level EF=ħvF(n)½, where n is the electronic density per unit area, and vFc/300 their velocity. The collective oscillations of these extra electrons are known as Dirac plasmons, and they are subdivided into two different subgroups: surface plasmon polaritons (SPPs) and localized surface plasmons (LSPs). In the second chapter of this thesis, we classically study Dirac plasmons assuming an inhomogeneous distribution of n in different graphene nanostructures (ribbons and disks), and also a periodic distribution in extended graphene layers. When the characteristic length of the nanostructure is of the order of the Fermi wavelength, classical electromagnetism is no longer valid, and a quantum-mechanical approach is necessary. In the third chapter of this thesis, we provide extensive quantum calculations of the response of LSPs sustained on narrow nanoribbons.The fourth chapter of this thesis is devoted to the study of the strong nonlinear plasmonic response of doped graphene. Finally, in the fifth chapter, we show the outstanding potential of graphene LSPs to resolve the chemical identity of molecules

Plasmons in electrostatically doped graphene

Graphene has raised high expectations as a low-loss plasmonic material in which the plasmon properties can be controlled via electrostatic doping. Here, we analyze realistic configurations, which produce inhomogeneous doping, in contrast to what has been so far assumed in the study of plasmons in nanostructured graphene. Specifically, we investigate backgated ribbons, co-planar ribbon pairs placed at opposite potentials, and individual ribbons subject to a uniform electric field. Plasmons in backgated ribbons and ribbon pairs are similar to those of uniformly doped ribbons, provided the Fermi energy is appropriately scaled to compensate for finite-size effects such as the divergence of the carrier density at the edges. In contrast, the plasmons of a ribbon exposed to a uniform field exhibit distinct dispersion and spatial profiles that considerably differ from uniformly doped ribbons. Our results provide a road map to understand graphene plasmons under realistic electrostatic doping conditions.Comment: 9 pages, 9 figure

Second-order quantum nonlinear optical processes in single graphene nanostructures and arrays

Intense efforts have been made in recent years to realize nonlinear optical interactions at the single-photon level. Much of this work has focused on achieving strong third-order nonlinearities, such as by using single atoms or other quantum emitters while the possibility of achieving strong second-order nonlinearities remains unexplored. Here, we describe a novel technique to realize such nonlinearities using graphene, exploiting the strong per-photon fields associated with tightly confined graphene plasmons in combination with spatially nonlocal nonlinear optical interactions. We show that in properly designed graphene nanostructures, these conditions enable extremely strong internal down-conversion between a single quantized plasmon and an entangled plasmon pair, or the reverse process of second harmonic generation. A separate issue is how such strong internal nonlinearities can be observed, given the nominally weak coupling between these plasmon resonances and free-space radiative fields. On one hand, by using the collective coupling to radiation of nanostructure arrays, we show that the internal nonlinearities can manifest themselves as efficient frequency conversion of radiative fields at extremely low input powers. On the other hand, the development of techniques to efficiently couple to single nanostructures would allow these nonlinear processes to occur at the level of single input photons.Comment: 25 pages, 6 figure

Quantum nonlocal effects in individual and interacting graphene nanoribbons

We show that highly doped graphene ribbons can support surface plasmons at near-infrared frequencies when their width is in the nanometer range, leading to important nonlocal and finite quantum-size corrections, such as sizable blueshifts. The magnitude of these effects is assessed by comparing classical and quantum-mechanical models to describe graphene plasmons. More precisely, we examine individual and interacting 6–8 nm wide zigzag and armchair ribbons doped to 0.4–1.5 eV Fermi energies. We find a strong influence of nonlocal effects on the orientation of graphene edges, with plasmons in zigzag ribbons undergoing strong quenching when their energy is below the Fermi level. Nonlocality is also affecting the hybridization between ribbon plasmons in dimers and arrays for separations below a few nanometers. Remarkably, the removal of a single row of atomic bonds in a ribbon produces a strong plasmon frequency shift, whereas the removal of bonds along an array of rows separated by several nanometers in an extended sheet causes a dramatic increase in the absorption. Besides the fundamental interest of these results, our work supports the use of narrow ribbons to achieve electro-optical modulation in the near infrared.Peer ReviewedPostprint (published version

Plasmonic energy transfer in periodically doped graphene

12 pags., 3 figs., 1 app. -- Open Access funded by Creative Commons Atribution Licence 3.0We predict unprecedentedly large values of the energy-transfer rate between an optical emitter and a layer of periodically doped graphene. The transfer exhibits divergences at photon frequencies corresponding to the Van Hove singularities of the plasmonic band structure of the graphene. In particular, we find flat bands associated with regions of vanishing doping charge, which appear in graphene when it is patterned through gates of spatially alternating signs, giving rise to intense transfer rate singularities. Graphene is thus shown to provide a unique platform for fast control of optical energy transfer via fast electrostatic inhomogeneous doping. © IOP Publishing and Deutsche Physikalische Gesellschaft.This work was partially supported by the European Union (FP7-ICT-2009-4-248855-N4E), the Spanish MEC (MAT2010-14885 and Consolider NanoLight.es) and Ibercivis. AM acknowledges financial support from the Spanish FPU

Quantum nonlocal effects in individual and interacting graphene nanoribbons

We show that highly doped graphene ribbons can support surface plasmons at near-infrared frequencies when their width is in the nanometer range, leading to important nonlocal and finite quantum-size corrections, such as sizable blueshifts. The magnitude of these effects is assessed by comparing classical and quantum-mechanical models to describe graphene plasmons. More precisely, we examine individual and interacting 6–8 nm wide zigzag and armchair ribbons doped to 0.4–1.5 eV Fermi energies. We find a strong influence of nonlocal effects on the orientation of graphene edges, with plasmons in zigzag ribbons undergoing strong quenching when their energy is below the Fermi level. Nonlocality is also affecting the hybridization between ribbon plasmons in dimers and arrays for separations below a few nanometers. Remarkably, the removal of a single row of atomic bonds in a ribbon produces a strong plasmon frequency shift, whereas the removal of bonds along an array of rows separated by several nanometers in an extended sheet causes a dramatic increase in the absorption. Besides the fundamental interest of these results, our work supports the use of narrow ribbons to achieve electro-optical modulation in the near infrared.Peer Reviewe