We investigated the dimensionality transition behavior of graphene localized plasmon resonances in confinement-controlled graphene devices. We first demonstrated a possibility of dimensionality transition, based on the devices carrier-density dependence, from a two-dimensional plasmon resonance to a one-dimensional plasmon one. We fabricated optical transparent devices and electrical transport devices on the same optical transparent wafer. These devices allow detailed control and analysis between carrier density and plasmon resonance peak positions. The carrier density from square root n (two-dimensional) to constant (one-dimensional) is consistent with the theoretical predictions based on the Dirac Fermion carriers in linear-band structure materials.
Recent progress in the fabrication of materials has made it possible to create arbitrary non-periodic two-dimensional structures in the quantum plasmon regime. This paves the way for exploring the plasmonic properties of electron gases in complex geometries such as fractals. In this work, we study the plasmonic properties of Sierpinski carpets and gaskets, two prototypical fractals with different ramification, by fully calculating their dielectric functions. We show that the Sierpinski carpet has a dispersion comparable to a square lattice, but the Sierpinski gasket features highly localized p…
Resonant Raman spectroscopy is realized on closely spaced nanowire based quantum wells. Phonon quantization consistent with 2.4 nm thick quantum wells is observed, in agreement with cross-section transmission electron microscopy measurements and photoluminescence experiments. The creation of a high density plasma within the quantized structures is demonstrated by the observation of coupled plasmon-phonon modes. The density of the plasma and thereby the plasmon-phonon interaction is controlled with the excitation power. This work represents a base for further studies on confined high density ch…
We investigate plasmon resonances in graphene with periodic carrier density modulation. The period is 8 um, and each period consists of 1.7- and 6.3-um-wide ribbons with different density. Using terahertz spectroscopy, we show two plasmon modes with their electric field mostly localized in the 1.7- or 6.3-um-wide ribbon arrays. We also show that plasmons are excited only in one of the micro-ribbon arrays when the Fermi energy of the other micro-ribbon array is set close to the charge neutrality point. These results indicate that plasmons can be confined by the carrier density modulation.
The ability to confine light into tiny spatial dimensions is important for applications such as microscopy, sensing and nanoscale lasers. While plasmons offer an appealing avenue to confine light, Landau damping in metals imposes a trade-off between optical field confinement and losses. We show that a graphene-insulator-metal heterostructure can overcome that trade-off, and demonstrate plasmon confinement down to the ultimate limit of the lengthscale of one atom. This is achieved by far-field excitation of plasmon modes squeezed into an atomically thin hexagonal boron nitride dielectric h-BN s…
Graphene plasmons were predicted to possess ultra-strong field confinement and very low damping at the same time, enabling new classes of devices for deep subwavelength metamaterials, single-photon nonlinearities, extraordinarily strong light-matter interactions and nano-optoelectronic switches. While all of these great prospects require low damping, thus far strong plasmon damping was observed, with both impurity scattering and many-body effects in graphene proposed as possible explanations. With the advent of van der Waals heterostructures, new methods have been developed to integrate graphe…
Quantum confinement of graphene carriers is an effective way to engineer its properties. It is commonly realized through physical edges that are associated with the deterioration of mobility and strong suppression of plasmon resonances. Here, we demonstrate a simple, large-area, edge-free nanostructuring technique, based on amplifying random nanoscale structural corrugations to a level where they efficiently confine carriers, without inducing significant inter-valley scattering. This soft confinement, allows the low-loss lateral ultra-confinement of graphene plasmons, scaling up their resonanc…
Recently, it was demonstrated that a graphene/dielectric/metal configuration can support acoustic plasmons, which exhibit extreme plasmon confinement an order of magnitude higher than that of conventional graphene plasmons. Here, we investigate acoustic plasmons supported in a monolayer and multilayers of black phosphorus (BP) placed just a few nanometers above a conducting plate. In the presence of a conducting plate, the acoustic plasmon dispersion for the armchair direction is found to exhibit the characteristic linear scaling in the mid- and far-infrared regime while it largely deviates fr…
In this paper we propose and discuss coherent terahertz sources based on charge density wave (plasmon) amplification in two dimensional graphene. The coupling of the plasmons to interband electron-hole transitions in population inverted graphene layers can lead to plasmon amplification through stimulated emission. Plasmon gain values in graphene can be very large due to the small group velocity of the plasmons and the strong confinement of the plasmon field in the vicinity of the graphene layer. We present a transmission line model for plasmon propagation in graphene that includes plasmon diss…
Graphene plasmonic resonators have been broadly studied in the terahertz and mid-infrared ranges because of their electrical tunability and large confinement factors which can enable dramatic enhancement of light-matter coupling. In this work, we demonstrate that the characteristic scaling laws of graphene plasmons change for smaller (< 40 nm) plasmonic wavelengths, expanding the operational frequencies of graphene plasmonic resonators into the near-infrared (NIR) and modifying their optical confinement properties. We utilize a novel bottom-up block copolymer lithography method that substantia…
Graphene plasmons have recently attracted a great deal of attention because of their tunability, long lifetime, and high degree of field confinement in the vertical direction. Nearby metal gates have been shown to modify the graphene plasmon dispersion and further confine their electric field. We study the plasmons of a graphene sheet deposited on a metal, in the regime in which metal bands do not hybridize with massless Dirac fermion bands. We derive exact results for the dispersion and lifetime of the plasmons of such hybrid system, taking into account metal nonlocalities. The graphene plasm…
Owing to its excellent electrical, mechanical, thermal and optical properties, graphene has attracted great interests since it was successfully exfoliated in 2004. Its two dimensional nature and superior properties meet the need of surface plasmons and greatly enrich the field of plasmonics. Recent progress and applications of graphene plasmonics will be reviewed, including the theoretical mechanisms, experimental observations, and meaningful applications. With relatively low loss, high confinement, flexible feature, and good tunability, graphene can be a promising plasmonic material alternati…
Plasmonic excitations such as surface-plasmon-polaritons (SPPs) and graphene-plasmons (GPs), carry large momenta and are thus able to confine electromagnetic fields to small dimensions. This property makes them ideal platforms for subwavelength optical control and manipulation at the nanoscale. The momenta of these plasmons are even further increased if a scheme of metal-insulator-metal and graphene-insulator-metal are used for SPPs and GPs, respectively. However, with such large momenta, their far-field excitation becomes challenging. In this work, we consider hybrids of graphene and metallic…
In recent years, we have seen a rapid progress in the field of graphene plasmonics, motivated by graphene's unique electrical and optical properties, tunabilty, long-lived collective excitation and their extreme light confinement. Here, we review the basic properties of graphene plasmons; their energy dispersion, localization and propagation, plasmon-phonon hybridization, lifetimes and damping pathways. The application space of graphene plasmonics lies in the technologically significant, but relatively unexploited terahertz to mid-infrared regime. We discuss emerging and potential applications…
Surface plasmons in graphene may provide an attractive alternative to noble-metal plasmons due to their tighter confinement, peculiar dispersion, and longer propagation distance. We present theoretical studies of the nonlinear difference frequency generation of terahertz surface plasmon modes supported by two-dimensional layers of massless Dirac electrons, which includes graphene and surface states in topological insulators. Our results demonstrate strong enhancement of the DFG efficiency near the plasmon resonance and the feasibility of phase-matched nonlinear generation of plasmons over a br…
Metamaterials and plasmonics are powerful tools for unconventional manipulation and harnessing of light. Metamaterials can be engineered to possess intriguing properties lacking in natural materials, such as negative refractive index. Plasmonics offers capabilities to confine light in subwavelength dimensions and to enhance light-matter interactions. Recently,graphene-based plasmonics has revealed emerging technological potential as it features large tunability, higher field-confinement and lower loss compared to metal-based plasmonics. Here,we introduce hybrid structures comprising graphene p…
The two-dimensionality of graphene and other layered materials can be exploited to simplify the theoretical description of their plasmonic and polaritonic modes. We present an analytical theory that allows us to simulate these excitations in terms of plasmon wave functions (PWFs). Closed-form expressions are offered for their associated extinction spectra, involving only two real parameters for each plasmon mode and graphene morphology, which we calculate and tabulate once and for all. Classical and quantum-mechanical formulations of this PWF formalism are introduced, in excellent mutual agree…
We calculate the linear transverse current current response function for graphene at finite temperature and chemical potential. Within the Random Phase Approximation, we then discuss general aspects of transverse plasmons beyond the local response such as their dependence on temperature and on the surrounding dielectric media. We find, e.g., maximal confinement of this mode for a homogeneous dielectric media with refractive index $n\simeq 40$. Confinement can further be enhanced by placing the graphene sheet inside an optical cavity, but there exists a critical width below which no transverse …
We investigate through analytic calculations the surface plasmon dispersion relation for monolayer graphene sheets and a separated parallel pair of graphene monolayers. An approximate form for the dispersion relation for the monolayer case was derived, which was shown to be highly accurate and offers intuition to the properties of the supported plasmon mode. For parallel graphene pairs separated by small gaps, the dispersion relation of the surface plasmon splits into two branches, one with a symmetric and the other with an antisymmetric magnetic field across the gap. For the symmetric (magnet…
The properties of surface plasmons localized at the interface between graphene and kerr-type nonlinear medium in three dimensions are investigated. Compared with surface plasmons at the surface of metal, with the inevitable nonlinear refractive effect, the confinement of plasmon can be improved to three times than graphene plasmons without nonlinear contribution, but also with almost the same relative propagation length. Moreover, the dispersion relation and propation distance of graphene plasmons can be easily controlled by changing the fermi energy, temperature and relaxation time of graphen…
Boundaries and edges of a two dimensional system lower its symmetry and are usually regarded, from the point of view of charge transport, as imperfections. Here we present a first study of the behavior of graphene plasmons in a strong magnetic field that provides a different perspective. We show that the plasmon resonance in micron size graphene disks in a strong magnetic field splits into edge and bulk plasmon modes with opposite dispersion relations, and that the edge plasmons at terahertz frequencies develop increasingly longer lifetimes with increasing magnetic field, in spite of potential…
Plasmon in graphene possesses many unique properties. It originates from the collective motion of massless Dirac fermions and the carrier density dependence is distinctively different from conventional plasmons. In addition, graphene plasmon is highly tunable and shows strong energy confinement capability. Most intriguing, as an atom-thin layer, graphene and its plasmon are very sensitive to the immediate environment. Graphene plasmons strongly couple to polar phonons of the substrate, molecular vibrations of the adsorbates, and lattice vibrations of other atomically thin layers. In this revie…
Graphene plasmons (GPs) have been found to be an exciting plasmonic platform, thanks to their high field confinement and low phase velocity, motivating contemporary research to revisit established concepts in light-matter interaction. In a conceptual breakthrough that is now more than 80 years old, Čerenkov showed how charged particles emit shockwaves of light when moving faster than the phase velocity of light in a medium. To modern eyes, the Čerenkov effect (ČE) offers a direct and ultrafast energy conversion scheme from charge particles to photons. The requirement for relativistic particles…
Optical properties of metallic nanoparticles are most often considered in terms of plasmons, the coupled states of light and quasi-free electrons. Here we predict that confinement of electrons inside the nanostructure leads to another, very different, type of resonance, which determines the optical properties in the frequency range significantly below the plasmonic resonance. We demonstrate that closely placed confinement-induces resonances typically join into a single composite "super-resonance" which produces giant nonlinearity at low frequencies. Our simulations show how such nonlinearities…
The unique optical and electronic properties of graphene allow one to realize active optical devices. While several types of graphene-based photonic modulators have already been demonstrated, the potential of combining the versatility of graphene with subwavelength field confinement of plasmonic/metallic structures is not fully realized. Here we report fabrication and study of hybrid graphene-plasmonic modulators. We consider several types of modulators and identify the most promising one for light modulation at telecom and near-infrared. Our proof-of-concept results pave the way towards on-ch…
We report theoretical evidence that bulk nonlinear materials weakly interacting with highly localized plasmonic modes in ultra-sub-wavelength metallic nanostructures can lead to nonlinear effects at the single plasmon level in the visible range. In particular, the two-plasmon interaction energy in such systems is numerically estimated to be comparable with the typical plasmon linewidths. Localized surface plasmons are thus predicted to exhibit a purely nonclassical behavior, which can be clearly identified by a sub-Poissonian second-order correlation in the signal scattered from the quantized …
Plasmons in van der Waals heterostructures comprised of graphene and related layered materials demonstrate deep subwavelength confinement and large propagation length. In this letter, we show that graphene-insulator-graphene tunnel structures can serve as plasmonic gain media. The gain stems from the stimulated electron tunneling accompanied by the emission of coherent plasmons under interlayer population inversion. The probability of tunneling with plasmon emission appears to be resonantly large at certain values of frequency and interlayer voltage corresponding to the transitions between ele…
We use excited-state quantum chemistry techniques to investigate the intraband absorption of doped semiconductor nanoparticles as a function of doping density, nanoparticle radius, and material properties. The excess electrons are modeled as interacting particles confined in a sphere. We compare the predictions of various single-excitation theories, including time-dependent Hartree-Fock, the random-phase approximation, and configuration interaction with single excitations. We find that time-dependent Hartree-Fock most accurately describes the character of the excitation, as compared to equatio…
It is by now well established that high-quality graphene enables a gate-tunable low-loss plasmonic platform for the efficient confinement, enhancement, and manipulation of optical fields spanning a broad range of frequencies, from the mid infrared to the Terahertz domain. While all-electrical detection of graphene plasmons has been demonstrated, electrical plasmon injection (EPI), which is crucial to operate nanoplasmonic devices without the encumbrance of a far-field optical apparatus, remains elusive. In this work, we present a theory of EPI in double-layer graphene, where a vertical tunnel …
Due to strong mode-confinement, long propagation-distance, and unique tunability, graphene plasmons have been widely explored in the mid-infrared and terahertz windows. However, it remains a big challenge to push graphene plasmons to shorter wavelengths in order to integrate graphene plasmon concepts with existing mature technologies in the near-infrared region. We investigate localized graphene plasmons supported by graphene nanodisks and experimentally demonstrated graphene plasmon working at 2 μm with the aid of a fully scalable block copolymer self-assembly method. Our results show a promi…
Topological domain walls in dual-gated gapped bilayer graphene host edge states that are gate- tunable and valley polarized. Here we predict that plasmonic collective modes can propagate along these topological domain walls even at zero bulk density, and possess a markedly different character from that of bulk plasmons. Strikingly, domain wall plasmons are extremely long-lived, with plasmon lifetimes that can be orders of magnitude larger than the transport scattering time in the bulk. While most pronounced at low temperatures, long domain wall plasmon lifetimes persist even at room temperatur…
To efficiently integrate cutting-edge terahertz technology into compact devices, the highly confined terahertz plasmons are attracting intensive attentions. Compared to plasmons at visible frequencies in metals, terahertz plasmons, typically in lightly doped semiconductors or graphene, are sensitive to carrier density (n) and thus have an easy tunability, which, however, leads to unstable or imprecise terahertz spectra. By deriving a simplified but universal form of plasmon frequencies, here we reveal a unified mechanism for generating unusual n-independent plasmons (DIPs) in all topological s…
Dirac plasmons in a doped graphene sheet have recently been shown to enable confinement of light to ultrasmall volumes. In this work we calculate the intrinsic lifetime of a Dirac plasmon in a doped graphene sheet by analyzing the role of electron-electron interactions beyond the random phase approximation. The damping mechanism at work is intrinsic since it operates also in disorder-free samples and in the absence of lattice vibrations. We demonstrate that graphene's sublattice-pseudospin degree of freedom suppresses intrinsic plasmon losses with respect to those that occur in ordinary two-di…
We demonstrate that graphene placed on top of structured substrates offers a novel approach for trapping and guiding surface plasmons. A monolayer graphene with a spatially varying curvature exhibits an effective trapping potential for graphene plasmons near curved areas such as bumps, humps and wells. We derive the governing equation for describing such localized channel plasmons guided by curved graphene and validate our theory by the first-principle numerical simulations. The proposed confinement mechanism enables plasmon guiding by the regions of maximal curvature, and it offers a versatil…
Graphene plasmons provide a suitable alternative to noble-metal plasmons because they exhibit much larger confinement and relatively long propagation distances, with the advantage of being highly tunable via electrostatic gating. We report strong light- matter interaction assisted by graphene plasmons, and in particular, we predict unprecedented high decay rates of quantum emitters in the proximity of a carbon sheet, large vacuum Rabi splitting and Purcell factors, and extinction cross sections exceeding the geometrical area in graphene ribbons and nanometer-sized disks. Our results provide th…
Sub-wavelength graphene structures support localized plasmonic resonances in the terahertz and mid-infrared spectral regimes. The strong field confinement at the resonant frequency is predicted to significantly enhance the light-graphene interaction, which could enable nonlinear optics at low intensity in atomically thin, sub-wavelength devices. To date, the nonlinear response of graphene plasmons and their energy loss dynamics have not been experimentally studied. We measure and theoretically model the terahertz nonlinear response and energy relaxation dynamics of plasmons in graphene nanorib…
Nanoplasmonics exploits the coupling between light and collective electron density oscillations (plasmons) to bypass the stringent limits imposed by diffraction. This coupling enables confinement of light to sub-wavelength volumes and is usually exploited in nanostructured metals. Substantial efforts are being made at the current frontier of the field to employ electron systems in semiconducting and semimetallic materials since these add the exciting possibility of realizing electrically tunable and/or active nanoplasmonic devices. Here we demonstrate that a suitable design of the doping profi…
We theoretically investigate the plasmonic heating of graphene-based systems under the mid-infrared laser irradiation, where periodic arrays of graphene plasmonic resonators are placed on dielectric thin films. Optical resonances are sensitive to structural parameters and the number of graphene layers. Under mid-infrared laser irradiation, the steady-state temperature gradients are calculated. We find that graphene plasmons significantly enhance the confinement of electromagnetic fields in the system and lead to a large temperature rise compared to the case without graphene. The correlations b…
Graphene is a novel two-dimensional material with fascinating electrodynamic properties like the ability to support collective electron oscillations (plasmons) accompanied by tight confinement of electromagnetic fields. Our goal is to explore light-matter interaction in graphene in the context of plasmonics and other technological applications but also to use graphene as a platform for studying many body physics like the interaction between plasmons, phonons and other elementary excitations. Plasmons and plasmon-phonon interaction are analyzed within the self-consistent linear response approxi…
Electrons on the liquid helium surface form an extremely clean two dimensional system where different plasmon-excitations can coexist. Under a magnetic field time reversal symmetry is broken and all the bulk magneto-plasmons become gaped at frequencies below cyclotron resonance while chiral one dimensional edge magneto-plasmons appear at the system perimeter. We theoretically show that the presence of a homogeneous density gradient in the electron gas leads to the formation of a delocalized magneto-plasmon mode in the same frequency range as the lowest frequency edge-magnetoplasmon mode. We ex…
Graphene hybrids, made of thin insulators, graphene, and metals can support propagating acoustic plasmons (AGPs). The metal screening modifies the dispersion relation of usual graphene plasmons leading to slowly propagating plasmons, with record confinement of electromagnetic radiation. Here, we show that a graphene monolayer, covered by a thin dielectric material and an array of metallic nanorods can be used as a robust platform to emulate the Su-Schrieffer-Heeger model. We calculate the Zak's phase of the different plasmonic bands to characterise their topology. The system shows bulk-edge co…
We show that it is possible to realize significant nonlinear optical interactions at the few photon level in graphene nanostructures. Our approach takes advantage of the electric field enhancement associated with the strong confinement of graphene plasmons and the large intrinsic nonlinearity of graphene. Such a system could provide a powerful platform for quantum nonlinear optical control of light. As an example, we consider an integrated optical device that exploits this large nonlinearity to realize a single photon switch.
We explore the unusual non-reciprocal and diffraction-less properties of surface plasmon polaritons propagating in drift-biased graphene-based metasurfaces. We show that applying a drift-current on a graphene sheet leads to extremely asymmetric in-plane modal dispersions from terahertz to infrared frequencies, associated with plasmons with low-loss (high-loss and ultra-high confinement) traveling along (against) the bias. Strikingly, truly unidirectional wave propagation is prevented by the intrinsic nonlocal response of a graphene, a mechanism that shapes the energy flow over the surface. We …
The ability to effectively guide electromagnetic radiation below the diffraction limit is of the utmost importance in the prospect of all-optical plasmonic circuitry. Here, we propose an alternative solution to conventional metal-based plasmonics by exploiting the deep subwavelength confinement and tunability of graphene plasmons guided along the apex of a graphene-covered dielectric wedge or groove. In particular, we present a quasi-analytic model to describe the plasmonic eigenmodes in such a system, including the complete determination of their spectrum and corresponding induced potential a…
Plasmon-Enhanced Second-Harmonic Generation in Atomically Thin Crystalline Silver Nanostructures
ICFO–Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology（ICFO-光子科学研究所，巴塞罗那科学技术研究院）；University of Vienna, Faculty of Physics, Vienna Center for Quantum Science and Technology (VCQ)（维也纳大学物理学院，维也纳量子科学与技术中心）；Center for Nanophotonics, NWO Institute AMOLF（纳米光子学中心，NWO AMOLF研究所）；Department of Physics, Dokuz Eylül University（德古兹埃勒大学物理系）；Centro de Física de Materiales CSIC-UPV/EHU and Materials Physics Center（CSIC-巴斯克国立大学物质物理学中心和材料物理中心）
Surface plasmons in graphene provide a compelling strategy for advanced photonic technologies thanks to their tight confinement, fast response and tunability. Recent advances in the field of all optical generation of graphene plasmons in planar waveguides offer a promising method for high speed signal processing in nanoscale integrated optoelectronic devices. Here, we use two counter propagating frequency combs with temporally synchronized pulses to demonstrate deterministic all optical generation and electrical control of multiple plasmon polaritons, excited via difference frequency generatio…
Graphene has emerged as a promising platform to bring nonlinear quantum optics to the nanoscale, where a large intrinsic optical nonlinearity enables long-lived and actively tunable plasmon polaritons to strongly interact. Here we theoretically study the collision between two counter-propagating plasmons in a graphene nanoribbon, where transversal subwavelength confinement endows propagating plasmons with %large effective masses a flat band dispersion that enhances their interaction. This scenario presents interesting possibilities towards the implementation of multi-mode polaritonic gates tha…
