This book is meant as an introduction to graphene plasmonics and aims at the advanced undergraduate and graduate students entering the field of plasmonics in graphene. In it different theoretical methods are introduced, starting with an elementary description of graphene plasmonics and evolving towards more advanced topics. This book is essentially self-contained and brings together a number of different topics about the field that are scattered in the vast literature. The text is composed of eleven chapters and of a set of detailed appendices. It can be read in two different ways: Reading only the chapters to get acquainted with the field of plasmonics in graphene or reading the chapters and studying the appendices to get a working knowledge of the topic. The study of the material in this book will bring the students to the forefront of the research in this field.
The versatile control of graphene's plasmonic modes via an external gate-voltage inspires us to design efficient electro-optical graphene plasmonic logic gates at the midinfrared wavelengths. We show that these devices are superior to the conventional optical logic gates because the former possess cut-off states and interferometric effects. Moreover, the designed six basic logic gates (i.e., NOR/AND, NAND/OR, XNOR/XOR) achieved not only ultracompact size lengths of less than λ/28 with respect to the operating wavelength of 10 μm, but also a minimum extinction ratio as high as 15 dB. These grap…
The concept and analysis of a Terahertz (THz) frequency-reconfigurable antenna using graphene are presented. The antenna exploits dipole-like plasmonic resonances that can be frequency-tuned on large range via the electric field effect in a graphene stack. In addition to efficient dynamic control, the proposed approach allows high miniaturization and good direct matching with continuous wave THz sources. A qualitative model is used to explain the excellent impedance stability under reconfiguration. These initial results are very promising for future all-graphene THz transceivers and sensors. K…
Visible surface plasmon resonances (SPRs) could be excited by TE wave polarization in one-dimensional photonic crystals (PCs) coated by a graphene layer under the Kretschmann configuration. In this work, the plasmonic Bloch wave properties beyond Dirac points in a one-dimensional graphene-based photonic sensing structure have been numerically studied. We demonstrate that emergent plasmonic dips in the reflectance spectra of the suggested photonic device in the visible region exhibit tunable characteristics upon modulation of the chemical potential and the hopping parameter. The sensitivity of …
Doped graphene emerges as a strong contender for active plasmonic material in the mid-infrared wavelengths due to the versatile external-control of its permittivity-function and also its highly-compressed graphene surface plasmon (GSP) wavelength. In this paper, we design active plasmonic waveguide devices based on electrical-modulation of doped graphene nanoribbons (GNRs) on a voltage-gated inhomogeneous dielectric layer. We first develop figure-of-merit (FoM) formulae to characterize the performance of passive and active graphene nanoribbon waveguides. Based on the FoMs, we choose optimal GN…
The concept, analysis, and design of series switches for graphene-strip plasmonic waveguides at near infrared frequencies are presented. Switching is achieved by using graphene's field effect to selectively enable or forbid propagation on a section of the graphene strip waveguide, thereby allowing good transmission or high isolation, respectively. The electromagnetic modeling of the proposed structure is performed using full-wave simulations and a transmission line model combined with a matrix-transfer approach, which takes into account the characteristics of the plasmons supported by the diff…
A graphene sheet gated with a ridged ground plane, creating a soft-boundary (SB) graphene nanoribbon, is considered. By adjusting the ridge parameters and bias voltage a channel can be created on the graphene which can guide TM surface plasmon polaritons (SPP). Two types of modes are found; fundemental and higher-order modes with no apparent cutoff frequency and with energy distributed over the created channel, and edge modes with energy concen-trated at the soft-boundary edge. Dispersion curves, electric near-field patterns, and current distributions of these modes are determined. Since the l…
An active plasmonic switch based on single- and few-layer doped graphene ribbon array operating in the mid-infrared spectrum is investigated with theoretical and numerical calculations. It is shown that significant resonance wavelength shifts and modulation depths can be achieved with a slight variation of the doping concentration of the graphene ribbon. The few-layer graphene ribbon array device outperforms the single-layer one in terms of the achievable modulation depth. Our simulations reveal that, by modulating the Fermi-energy level between 0.2 eV and 0.25 eV, a four-layer graphene ribbon…
Graphene is a unique material to study fundamental limits of plasmonics. Apart from the ultimate single-layer thickness, its carrier concentration can be tuned by chemical doping or applying an electric field. In this manner the electrodynamic properties of graphene can be varied from highly conductive to dielectric. Graphene supports strongly confined, propagating surface plasmon-polaritons (SPPs) in a broad spectral range from terahertz to mid-infrared frequencies. It also possesses a strong magneto-optical response and thus provides complimentary architectures to conventional magneto-plasmo…
With the unique possibilities for controlling light in nanoscale devices, graphene plasmonics has opened new perspectives to the nanophotonics community with potential applications in metamaterials, modulators, photodetectors, and sensors. This paper briefly reviews the recent exciting progress in graphene plasmonics. We begin with a general description for optical properties of graphene, particularly focusing on the dispersion of graphene-plasmon polaritons. The dispersion relation of graphene-plasmon polaritons of spatially extended graphene is expressed in terms of the local response limit …
Towards twisted, topological, and quantum graphene plasmonics
University of Porto（波尔图大学）；University of Minho（米尼奥大学）；International Iberian Nanotechnology Laboratory（国际伊比利亚纳米技术实验室）；University of Southern Denmark（南丹麦大学）
Plasmon polaritons in van der Waals (vdW) materials hold promise for next-generation photonics. The ability to deterministically imprint spatial patterns of high carrier density in cavities and circuitry with nanoscale features underlies future progress in nonlinear nanophotonics and strong light-matter interactions. Here, we demonstrate a general strategy to atomically imprint low-loss graphene plasmonic structures using oxidation-activated charge transfer (OCT). We cover graphene with a monolayer of WSe$_2$, which is subsequently oxidized into high work-function WOx to activate charge transf…
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…
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…
Two rich and vibrant fields of investigation, graphene physics and plasmonics, strongly overlap. Not only does graphene possess intrinsic plasmons that are tunable and adjustable, but a combination of graphene with noble-metal nanostructures promises a variety of exciting applications for conventional plasmonics. The versatility of graphene means that graphene-based plasmonics may enable the manufacture of novel optical devices working in different frequency ranges, from terahertz to the visible, with extremely high speed, low driving voltage, low power consumption and compact sizes. Here we r…
We appraise a waveguide-integrated plasmonic graphene photodetector based on the hot carrier photo-bolometric effect, with performance characterized simultaneously by high responsivity, on the scale of hundreds of AW-1, and high speed on the scale of 100s of GHz. Performance evaluation is based on a theory of bolometric effect originating from the band nonparabolicity of graphene. Results compare favorably with the state-of-the-art plasmonic bolometric photodetectors, predicting up to two orders of magnitude increase in a responsivity while keeping speed on the same level, defined by the elect…
We theoretically demonstrate a high-sensitivity, graphene-plasmon based refractive index sensor working in the mid-infrared at room temperature. The bulk figure of merit of our sensor reaches values above $10$, but the key aspect of our proposed plasmonic sensor is its surface sensitivity which we examine in detail. We have used realistic values regarding doping level and electron relaxation time, which is the limiting factor for the sensor performance. Our results show quantitatively the high performance of graphene-plasmon based refractive index sensors working in the mid-infrared.
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 propose and discuss terahertz electro-absorption modulators based on graphene plasmonic structures. The active device consists of a self-gated pair of graphene layers, which are patterned to structures supporting THz plasmonic resonances. These structures allow for efficient control of the effective THz optical conductivity, thus absorption, even at frequencies much higher than the Drude roll-off in graphene where most previously proposed graphene-based devices become inefficient. Our analysis shows that reflectance-based device configurations, engineered so that the electric field is enhan…
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…
We present a magnetically biased graphene-ferrite structure discriminating the TE and TM plasmonic modes of graphene. In this structure, the graphene TM plasmons interact reciprocally with the structure. In contrast, the graphene TE plasmons exhibit nonreciprocity. This nonreciprocity is manifested in unidirectional TE propagation in a frequency band close to the interband threshold frequency. The proposed structure provides a unique platform for the experimental demonstration of the unusual existence of the TE plasmonic mode in graphene.
Plasmonic Faraday rotation in nanowires manifests itself in the rotation of the spatial intensity distribution of high-order surface plasmon polariton (SPP) modes around the nanowire axis. Here we predict theoretically the giant Faraday rotation for SPP propagating on graphene-coated magneto-optically active nanowires. Upon the reversal of the external magnetic field pointing along the nanowire axis some high-order plasmonic modes may be rotated by up to ~ 100 degrees on scale of about 500 nm at mid-infrared frequencies. Tuning carrier concentration in graphene by chemical doping or gate volta…
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…
We study the mid-infrared plasmonic response in Bernal-stacked bilayer graphene. Unlike its monolayer counterpart, bilayer graphene accommodates optically active phonon modes and a resonant interband transition at infrared frequencies. They strongly modifies the plasmonic properties of bilayer graphene, leading to Fano-type resonances, giant plasmonic enhancement of infrared phonon absorption, narrow window of optical transparency, and a new plasmonic mode at higher energy than the classical plasmon.
Serving as a new two-dimensional plasmonic material, graphene has stimulated an intensive study of its optical properties which benefit from the unique electronic band structure of the underlying honeycomb lattice of carbon atoms. In classical electrodynamics, nanostructured graphene is commonly modeled by the computationally demanding problem of a three-dimensional conducting film of atomic-scale thickness. Here, we propose an efficient alternative two-dimensional electrostatic approach where all the calculation procedures are restricted to the plane of the graphene sheet. To explore possible…
Plasmons in graphene nanostructures show great promise for mid-infrared applications ranging from a few to tens of microns. However, mid-infrared plasmonic resonances in graphene nanostructures are usually weak and narrow-banded, limiting their potential in light manipulation and detection. Here we investigate the coupling among graphene plasmonic nanostructures and further show that by engineering the coupling, enhancement of light-graphene interaction strength and broadening of spectral width can be achieved simultaneously. Leveraging the concept of coupling, we demonstrate a hybrid 2-layer …
Electronic control of blackbody emission from graphene plasmonic resonators on a silicon nitride substrate is demonstrated at temperatures up to 250 C. It is shown that the graphene resonators produce antenna-coupled blackbody radiation, manifest as narrow spectral emission peaks in the mid-IR. By continuously varying the nanoresonators carrier density, the frequency and intensity of these spectral features can be modulated via an electrostatic gate. We describe these phenomena as plasmonically enhanced radiative emission originating both from loss channels associated with plasmon decay in the…
Recent advancements in metamaterials and plasmonics have promised a number of exciting applications, in particular at terahertz and optical frequencies. Unfortunately, the noble metals used in these photonic structures are not particularly good conductors at high frequencies, resulting in significant dissipative loss. Here, we address the question of what is a good conductor for metamaterials and plasmonics. For resonant metamaterials, we develop a figure-of-merit for conductors that allows for a straightforward classification of conducting materials according to the resulting dissipative loss…
Graphene is used as the thinnest possible spacer between gold nanoparticles and a gold substrate. This creates a robust, repeatable, and stable sub-nanometre gap for massive plasmonic field enhancements. White light spectroscopy of single 80 nm gold nanoparticles reveals plasmonic coupling between the particle and its image within the gold substrate. While for a single graphene layer, spectral doublets from coupled dimer modes are observed shifted into the near infra-red, these disappear for increasing numbers of layers. These doublets arise from plasmonic charge transfer, allowing the direct …
We propose an on-chip CMOS compatible graphene plasmonic photodetector based on the photo-thermoelectric effect (PTE) that occurs across an entire homogeneous graphene channel. The proposed photodetector incorporates the long-range dielectric-loaded surface plasmon polariton (LR-DLSPP) waveguide with a metal stripe serving simultaneously as a plasmon supporting metallic material and one of the metal electrodes. Large in-plane component of the transverse magnetic (TM) plasmonic mode can couple efficiently to the graphene causing large temperature increases across an entire graphene channel with…
We investigate the excitation of quantum plasmonic states of light in graphene using end-fire and prism coupling. In order to model the excitation process quantum mechanically we quantize the transverse-electric and transverse-magnetic surface plasmon polariton (SPP) modes in graphene. A selection of regimes are then studied that enable the excitation of SPPs by photons and we show that efficient coupling of photons to graphene SPPs is possible at the quantum level. Futhermore, we study the excitation of quantum states and their propagation under the effects of loss induced from the electronic…
We theoretically examine the role of Kerr nonlinearities for graphene plasmonics in nanostructures, specifically in nanoribbons. The nonlinear Kerr interaction is included semiclassically in the intraband approximation. The resulting electromagnetic problem is solved numerically by self-consistent iteration with linear steps using a real-space discretization. We derive a simple approximation for the resonance shifts in general graphene nanostructures, and obtain excellent agreement with numerics for moderately high field strengths. Near plasmonic resonances the nonlinearities are strongly enha…
We report experimental signatures of plasmonic effects due to electron tunneling between adjacent graphene layers. At sub-nanometer separation, such layers can form either a strongly coupled bilayer graphene with a Bernal stacking or a weakly coupled double-layer graphene with a random stacking order. Effects due to interlayer tunneling dominate in the former case but are negligible in the latter. We found through infrared nano-imaging that bilayer graphene supports plasmons with a higher degree of confinement compared to single- and double-layer graphene, a direct consequence of interlayer tu…
In this minireview, we explore the main features and the prospect of plasmonics with two-dimensional semiconductors. Plasmonic modes in each class of van der Waals semiconductors have their own peculiarities, along with potential technological capabilities. Plasmons of transition-metal dichalcogenides share features typical of graphene, due to their honeycomb structure, but with damping processes dominated by intraband rather than interband transitions, unlike graphene. Spin-orbit coupling strongly affects the plasmonic spectrum of buckled honeycomb lattices (silicene and germanene), while the…
We report an on-chip integrated metal-graphene-silicon plasmonic Schottky photodetector with 85mA/W responsivity at 1.55 um and 7% internal quantum efficiency. This is one order of magnitude higher than metal-silicon Schottky photodetectors operated in the same conditions. At a reverse bias of 3V, we achieve avalanche multiplication, with 0.37A/W responsivity and avalanche photogain~2. This paves the way to graphene integrated silicon photonics.
Using a realistic quantum master equation we show that the resonance fluorescence spectra of a two-level artificial atom (quantum dot) can be tuned by adjusting its photonic local density of states via biasing of one or more graphene monolayers. The structured photon reservoir is included using a photon Green function theory which fully accounts for the loss and dispersion. The field-driven Mollow triplet spectrum can be actively controlled by the graphene bias in the THz frequency regime. We also consider the effect of a dielectric support environment, and multiple graphene layers, on the emi…
The unique gate-voltage dependent optical properties of graphene make it a promising electrically-tunable plasmonic material. In this work, we proposed in-situ control of the polarization of nanoantennas by combining plasmonic structures with an electrostatically tunable graphene monolayer. The tunable polarizer is designed based on an asymmetric cross nanoantenna comprising two orthogonal metallic dipoles sharing the same feed gap. Graphene monolayer is deposited on a Si/SiO2 substrate, and inserted beneath the nanoantenna. Our modelling demonstrates that as the chemical potential is incremen…
The recent developments in the emerging field of plasmonics in graphene and other Dirac systems are reviewed and a comprehensive introduction to the standard models and techniques is given. In particular, we discuss intrinsic plasmon excitations of single and bilayer graphene via hydrodynamic equations and the random phase approximation, but also comment on double and multilayer structures. Additionally, we address Dirac systems in the retardation limit and also with large spin-orbit coupling including topological insulators. Finally, we summarize basic properties of the charge, current and ph…
The gate-controllable complex conductivity of graphene offers unprecedented opportunities for reconfigurable plasmonics at THz and mid-IR frequencies. However, the requirement of a gating electrode close to graphene and the single `control knob' that this approach offers for graphene conductivity limits the practical implementation and performance of graphene-controllable plasmonic devices. Herein, we report on graphene stacks composed of two or more graphene monolayers separated by electrically thin dielectrics and present a simple and rigorous theoretical framework for their characterization…
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…
Graphene plasmonics is a rapidly growing field with multiple potential applications. One of the standard ways to study plasmons in graphene is by fabricating an array of graphene nanoribbons where nanoribbon edges provide the efficient photon-plasmon coupling. We systematically analyze the problem of optical plasmonic response in such systems and demonstrate the purely geometric nature of the size quantization condition for graphene plasmons. Accurate numerical calculations allowed us to tabulate the universal geometric parameters of plasmon size quantization, which is expected to become usefu…
Using the hydrodynamic model in the electrostatic approximation, we describe the formation of graphene surface plasmons when a charge is in motion either perpendicular or parallel to a graphene sheet. In the first case, the electron-energy loss (EEL) spectrum of the electron is computed, showing that the resonances in the spectrum are linked to the frequency of the graphene surface plasmons. In the second case, we discuss the formation of plasmonic wakes due to the dragging of the surface plasmons induced by the motion of the charge. This effect is similar to Coulomb drag between two electron …
Plasmonics has established itself as a branch of physics which promises to revolutionize data processing, improve photovoltaics, increase sensitivity of bio-detection. A widespread use of plasmonic devices is notably hindered (in addition to high losses) by the absence of stable and inexpensive metal films suitable for plasmonic applications. This may seem surprising given the number of metal compounds to choose from. Unfortunately, most of them either exhibit a strong damping of surface plasmons or easily oxidize and corrode. To this end, there has been continuous search for alternative plasm…
We propose a terahertz radiation source based on the excitation of plasma resonances in graphene structures by means of mixing two NIR laser signals with a THz difference frequency. The process is the photo-thermo-electric effect which has recently been demonstrated to be operative at THz frequencies in graphene. An antenna couples the THz radiation out of the sub-wavelength graphene element and into the far field. The emission is monochromatic with a bandwidth determined by that of the NIR laser sources. The output power of the device as a function of the emitter frequency is estimated at ten…
We study localized plasmonic excitations in bilayer graphene (BLG) nanodisks, comparing AA-stacked and AB-stacked BLG and contrasting the results to the case of two monolayers without electronic hybridization. The electrodynamic response of the BLG electron gas is described in terms of a spatially homogeneous surface conductivity, and an efficient alternative two-dimensional electrostatic approach is employed to carry out all the numerical calculations of plasmon resonances. Due to a unique electronic band structures, the resonance frequency of the traditional dipolar plasmonic mode in the AA-…
The collective excitations of electrons in the bulk or at the surface, namely plasmons, play an important role in the properties of materials, and have generated the field of plasmonics. We report the observation of a highly unusual plasmon mode on the surface of Van der Waals heterostructures of graphene monolayer on 2D transition metal dichalcogenide substrate. Since the exponentially decaying fields of surface plasmon wave propagating along interface is highly sensitive to the ambient refractive index variations, such heterostructures are useful for ultra-sensitive bio-sensing.
Recently, plasmons in graphene have been observed experimentally using scattering scanning near-field optical microscopy. In this paper, we develop a simplified analytical approach to describe the behavior in triangular samples. Replacing Coulomb interaction by a short-range one reduces the problem to a Helmholtz equation, amenable to analytical treatment. We demonstrate that even with our simplifications, the system still exhibits the key features seen in the experiment.
Here, we investigate the nonreciprocal propagation and amplification of surface plasmons in drift-current biased graphene, using both Galilean and relativistic-type Doppler shift transformations of the graphene's conductivity. Consistent with previous studies, both conductivity models predict strongly nonreciprocal propagation of surface plasmons due to the drag effect caused by the drifting electrons. In particular, the Galilean Doppler shift model leads to stronger spectral asymmetries in the plasmon dispersion with regimes of unidirectional propagation. Remarkably, it is shown that both con…
We theoretically demonstrate that a system formed by a drift-current biased graphene sheet on a silicon carbide substrate enables loss compensation and plasmon amplification. The active response of the graphene sheet is rooted in the optical pumping of the graphene plasmons with the gain provided by the streaming current carriers. The proposed system behaves as an optical amplifier for the plasmons co-propagating with the drifting electrons and as a strong attenuator for the counter-propagating plasmons. Furthermore, we show that the feedback obtained by connecting the input and output of the …
Large photon drag effect of the massless Dirac Fermions in intrinsic graphene is predicted for a graphene-on-plasmonic-layer system. The surface plasmons in the plasmonic layer enlarge the wave number of photon for hundreds of time of that in vacuum. The evanescent field of the surface plasmons generates directional motion of carriers in the intrinsic graphene, because of the large momentum transfer from the surface plasmon to the excited carriers. A model Hamiltonian is developed on the assumption that the in-plane wavelength of the surface plasmons is much smaller than the mean free path of …
A valley plasmonic crystal for graphene surface plasmons (GSPs) is proposed. We demonstrate that a designer metagate, placed within a few nanometers from graphene, can be used to impose a triangular periodic Fermi energy landscape on the latter. For specific metagate geometries and bias voltages, the combined metagate-graphene structure is shown to produce sufficiently strong Bragg scattering of GSPs to produce complete propagation bandgaps, and to impart the GSPs with nontrivial valley-linked topological properties. Valley-selective kink states supported by a domain wall between differently p…
Plasmonic nanostructures attract tremendous attention as they confine electromagnetic fields well below the diffraction limit while simultaneously sustaining extreme local field enhancements. To fully exploit these properties, the identification and classification of resonances in such nanostructures is crucial. Recently, a novel figure of merit for resonance classification has been proposed 1 and its applicability was demonstrated mostly to toy model systems. This novel measure, the energy-based plasmonicity index (EPI), characterizes the nature of resonances in molecular nanostructures. The …
Inspired by recent advancement of low-power ferroelectic-gated memories and transistors, we propose a design of ferroelectic-gated nanoplasmonic devices based on graphene sheets clamped in ferroelectric crystals. We show that the two-dimensional plasmons in graphene strongly couple with the phonon-polaritons in ferroelectrics at terahertz frequencies, leading to characteristic modal wavelength of the order of 100--200 nm at only 3--4 THz. By patterning the ferroelectrics into different domains, one can produce compact on-chip plasmonic waveguides, which exhibit negligible crosstalk even at 50 …
