Multiple excitation of confined graphene plasmons by single free electrons

Toward Complete Optical Coupling to Confined Surface Polaritons

Optical coupling between propagating light and confined surface polaritons plays a pivotal role in the practical design of nanophotonic devices. However, the coupling efficiency decreases dramatically with the degree of mode confinement due to the mismatch that exists between the light and polariton wavelengths, and despite the intense efforts made to explore different mechanisms proposed to circumvent this problem, the realization of a flexible scheme to efficiently couple light to polaritons remains a challenge. Here, we experimentally demonstrate an efficient coupling of light to surface-plasmon polaritons assisted by engineered dipolar scatterers placed at an optimum distance from the surface. Specifically, we fabricate gold disks separated by a silica spacer from a planar gold surface and seek to achieve perfect coupling conditions by tuning the spacer thickness for a given scatterer geometry that resonates at a designated optical frequency. We measure a maximum light-to-plasmon coupling cross section of the order of the square of the light wavelength at an optimum distance that results from the interplay between a large particle-surface interaction and a small degree of surface-driven particle-dipole quenching, both of which are favored at small separations. Our experiments, in agreement with both analytical theory and electromagnetic simulations, support the use of optimally placed engineered scatterers as a disruptive approach to solving the long-standing problem of in/out-coupling in nanophotonics.

Toward Optimum Coupling between Free Electrons and Confined Optical Modes

Free electrons are excellent tools to probe and manipulate nanoscale optical fields with emerging applications in ultrafast spectromicroscopy and quantum metrology. However, advances in this field are hindered by the small probability associated with the excitation of single optical modes by individual free electrons. Here, we theoretically investigate the scaling properties of the electron-driven excitation probability for a wide variety of optical modes including plasmons in metallic nanostructures and Mie resonances in dielectric cavities, spanning a broad spectral range that extends from the ultraviolet to the infrared region. The highest probabilities for the direct generation of three-dimensionally confined modes are observed at low electron and mode energies in small structures, with order-unity (∼100%) coupling demanding the use of <100 eV electrons interacting with eV polaritons confined down to tens of nanometers in space. Electronic transitions in artificial atoms also emerge as practical systems to realize strong coupling to few-eV free electrons. In contrast, conventional dielectric cavities reach a maximum probability in the few-percent range. In addition, we show that waveguide modes can be generated with higher-than-unity efficiency by phase-matched interaction with grazing electrons, suggesting a practical method to create multiple excitations of a localized optical mode by an individual electron through funneling the so-generated propagating photons into a confining cavity─an alternative approach to direct electron-cavity interaction. Our work provides a roadmap to optimize electron-photon coupling with potential applications in electron spectromicroscopy as well as nonlinear and quantum optics at the nanoscale.

High-Efficiency Coupling of Free Electrons to Sub-λ3 Modal Volume, High-Q Photonic Cavities

We report on the design, realization, and experimental investigation by spatially resolved monochromated electron energy loss spectroscopy (EELS) of high-quality-factor cavities with modal volumes smaller than λ3, with λ being the free-space wavelength of light. The cavities are based on a slot defect in a 2D photonic crystal slab made up of silicon. They are optimized for high coupling of electrons accelerated to 100 kV to quasi-transverse electrical modes polarized along the slot direction. We studied the cavities in two geometries and took advantage of the deep sub-optical wavelength spatial resolution of the electron microscope and high spectral resolution of the monochromator to comprehensively describe the optical excitations of the slab. The first geometry, for which the cavities have been designed, corresponds to an electron beam traveling along the slot direction. The second consists of the electron beam traveling perpendicular to the slab. In both cases, a large series of modes is identified. The dielectric slot mode energies are measured to be in the 0.8-0.85 eV range, as per design, and surrounded by two bands of dielectric and air modes of the photonic structure. The dielectric even slot modes, to which the cavity mode belongs, are highly coupled to the electrons with up to 3.2% probability of creating a slot photon per incident electron. Although the experimental spectral resolution (around 30 meV) alone does not allow to disentangle cavity photons from other slot photons, the excellent agreement between the experiments and finite-difference time-domain simulations allows us to deduce that among the photons created in the slot, around 30% are stored in the cavity mode. A systematic study of the energy and coupling strength as a function of the photonic band gap parameters permits us to foresee an increase of coupling strength by fine-tuning phase-matching. Our work demonstrates free electron coupling to high-quality-factor cavities with low mode densities and sub-λ3 modal volumes, making it an excellent candidate for applications such as quantum nano-optics with free electrons.

Engineering 2D Material Exciton Line Shape with Graphene/h-BN Encapsulation

Control over the optical properties of atomically thin two-dimensional (2D) layers, including those of transition metal dichalcogenides (TMDs), is needed for future optoelectronic applications. Here, the near-field coupling between TMDs and graphene/graphite is used to engineer the exciton line shape and charge state. Fano-like asymmetric spectral features are produced in WS2, MoSe2, and WSe2 van der Waals heterostructures combined with graphene, graphite, or jointly with hexagonal boron nitride (h-BN) as supporting or encapsulating layers. Furthermore, trion emission is suppressed in h-BN encapsulated WSe2/graphene with a neutral exciton red shift (44 meV) and binding energy reduction (30 meV). The response of these systems to electron beam and light probes is well-described in terms of 2D optical conductivities of the involved materials. Beyond fundamental insights into the interaction of TMD excitons with structured environments, this study opens an unexplored avenue toward shaping the spectral profile of narrow optical modes for application in nanophotonic devices.

Generation of entangled waveguided photon pairs by free electrons

Entangled photons are a key resource in quantum technologies. While intense laser light propagating in nonlinear crystals is conventionally used to generate entangled photons, such schemes have low efficiency due to the weak nonlinear response of known materials and losses associated with in/out photon coupling. Here, we show how to generate entangled polariton pairs directly within optical waveguides using free electrons. The measured energy loss of undeflected electrons heralds the production of counter-propagating polariton pairs entangled in energy and emission direction. For illustration, we study the excitation of plasmon polaritons in metal strip waveguides that strongly enhance light-matter interactions, rendering two-plasmon generation dominant over single-plasmon excitation. We demonstrate that electron energy losses detected within optimal frequency ranges can reliably signal the generation of plasmon pairs entangled in energy and momentum. Our proposed scheme is directly applicable to other types of optical waveguides for in situ generation of entangled photon pairs.

Radiative loss of coherence in free electrons: a long-range quantum phenomenon

Quantum physics rules the dynamics of small objects as they interact over microscopic length scales. Nevertheless, quantum correlations involving macroscopic distances can be observed between entangled photons as well as in atomic gases and matter waves at low temperatures. The long-range nature of the electromagnetic coupling between charged particles and extended objects could also trigger quantum phenomena over large distances. Here, we reveal a manifestation of quantum mechanics that involves macroscopic distances and results in a nearly complete depletion of coherence associated with which-way free-electron interference produced by electron-radiation coupling in the presence of distant extended objects. This is a ubiquitous effect that we illustrate through a rigorous theoretical analysis of a two-path electron beam interacting with a semi-infinite metallic plate and find the inter-path coherence to vanish proportionally to the path separation at zero temperature and exponentially at finite temperature. The investigated regime of large distances originates in the coupling of the electron to radiative modes assisted by diffraction at material structures but without any involvement of material excitations. Besides the fundamental interest of this macroscopic quantum phenomenon, our results suggest an approach to measuring the vacuum temperature and nondestructively sensing the presence of distant objects.

Shaping free-electron radiation via van der Waals heterostructures

The van der Waals heterostructures with aperiodic stackings have been exploited to shape the spatiotemporal wavefront of free-electron X-ray radiation.

Multi-plasmon effects and plasmon satellites in photoemission from nanostructures

Plasmons can be excited during photoemission and produce spectral photoelectron features that yield information on the nanoscale optical response of the probed materials. However, these so-called plasmon satellites have so far been observed only for planar surfaces, while their potential for the characterization of nanostructures remains unexplored. Here, we theoretically demonstrate that core-level photoemission from nanostructures can display spectrally narrow plasmonic features, reaching relatively high probabilities similar to the direct peak. Using a nonperturbative quantum-mechanical framework, we find a dramatic effect of nanostructure morphology and dimensionality as well as universal scaling laws for the plasmon-satellite probabilities. In addition, we introduce a pump-probe scheme in which plasmons are optically excited prior to photoemission, leading to plasmon losses and gains in the photoemission spectra and granting us access to the ultrafast dynamics of the sampled nanostructure. These results emphasize the potential of plasmon satellites to explore multi-plasmon effects and ultrafast electron-plasmon dynamics in metal-based nanoparticles and two-dimensional nanoislands.

Imaging the field inside nanophotonic accelerators

Controlling optical fields on the subwavelength scale is at the core of nanophotonics. Laser-driven nanophotonic particle accelerators promise a compact alternative to conventional radiofrequency-based accelerators. Efficient electron acceleration in nanophotonic devices critically depends on achieving nanometer control of the internal optical nearfield. However, these nearfields have so far been inaccessible due to the complexity of the devices and their geometrical constraints, hampering the design of future nanophotonic accelerators. Here we image the field distribution inside a nanophotonic accelerator, for which we developed a technique for frequency-tunable deep-subwavelength resolution of nearfields based on photon-induced nearfield electron-microscopy. Our experiments, complemented by 3D simulations, unveil surprising deviations in two leading nanophotonic accelerator designs, showing complex field distributions related to intricate 3D features in the device and its fabrication tolerances. We envision an extension of our method for full 3D field tomography, which is key for the future design of highly efficient nanophotonic devices.

Jaynes-Cummings interaction between low-energy free electrons and cavity photons

The Jaynes-Cummings Hamiltonian is at the core of cavity quantum electrodynamics; however, it relies on bound-electron emitters fundamentally limited by the binding Coulomb potential. In this work, we propose theoretically a new approach to realizing the Jaynes-Cummings model using low-energy free electrons coupled to dielectric microcavities and exemplify several quantum technologies made possible by this approach. Using quantum recoil, a large detuning inhibits the emission of multiple consecutive photons, effectively transforming the free electron into a few-level system coupled to the cavity mode. We show that this approach can be used for generation of single photons, photon pairs, and even a quantum SWAP gate between a photon and a free electron, with unity efficiency and high fidelity. Tunable by their kinetic energy, quantum free electrons are inherently versatile emitters with an engineerable emission wavelength. Hence, they pave the way toward new possibilities for quantum interconnects between photonic platforms at disparate spectral regimes.

Complete Excitation of Discrete Quantum Systems by Single Free Electrons

We reveal a wealth of nonlinear and recoil effects in the interaction between individual low-energy electrons (≲100  eV) and samples comprising a discrete number of states. Adopting a quantum theoretical description of combined free-electron and two-level systems, we find a maximum achievable excitation probability of 100%, which requires specific conditions relating to the coupling strength and the transition symmetry, as we illustrate through calculations for dipolar and quadrupolar modes. Strong recoil effects are observed when the kinetic energy of the probe lies close to the transition threshold, although the associated probability remains independent of the electron wave function even when fully accounting for nonlinear interactions with arbitrarily complex multilevel samples. Our work reveals the potential of free electrons to control localized excitations and delineates the boundaries of such control.

Optical Excitations with Electron Beams: Challenges and Opportunities

Free electron beams such as those employed in electron microscopes have evolved into powerful tools to investigate photonic nanostructures with an unrivaled combination of spatial and spectral precision through the analysis of electron energy losses and cathodoluminescence light emission. In combination with ultrafast optics, the emerging field of ultrafast electron microscopy utilizes synchronized femtosecond electron and light pulses that are aimed at the sampled structures, holding the promise to bring simultaneous sub-Å-sub-fs-sub-meV space-time-energy resolution to the study of material and optical-field dynamics. In addition, these advances enable the manipulation of the wave function of individual free electrons in unprecedented ways, opening sound prospects to probe and control quantum excitations at the nanoscale. Here, we provide an overview of photonics research based on free electrons, supplemented by original theoretical insights and discussion of several stimulating challenges and opportunities. In particular, we show that the excitation probability by a single electron is independent of its wave function, apart from a classical average over the transverse beam density profile, whereas the probability for two or more modulated electrons depends on their relative spatial arrangement, thus reflecting the quantum nature of their interactions. We derive first-principles analytical expressions that embody these results and have general validity for arbitrarily shaped electrons and any type of electron-sample interaction. We conclude with some perspectives on various exciting directions that include disruptive approaches to noninvasive spectroscopy and microscopy, the possibility of sampling the nonlinear optical response at the nanoscale, the manipulation of the density matrices associated with free electrons and optical sample modes, and appealing applications in optical modulation of electron beams, all of which could potentially revolutionize the use of free electrons in photonics.

Spontaneous and stimulated electron-photon interactions in nanoscale plasmonic near fields

The interplay between free electrons, light, and matter offers unique prospects for space, time, and energy resolved optical material characterization, structured light generation, and quantum information processing. Here, we study the nanoscale features of spontaneous and stimulated electron-photon interactions mediated by localized surface plasmon resonances at the tips of a gold nanostar using electron energy-loss spectroscopy (EELS), cathodoluminescence spectroscopy (CL), and photon-induced near-field electron microscopy (PINEM). Supported by numerical electromagnetic boundary-element method (BEM) calculations, we show that the different coupling mechanisms probed by EELS, CL, and PINEM feature the same spatial dependence on the electric field distribution of the tip modes. However, the electron-photon interaction strength is found to vary with the incident electron velocity, as determined by the spatial Fourier transform of the electric near-field component parallel to the electron trajectory. For the tightly confined plasmonic tip resonances, our calculations suggest an optimum coupling velocity at electron energies as low as a few keV. Our results are discussed in the context of more complex geometries supporting multiple modes with spatial and spectral overlap. We provide fundamental insights into spontaneous and stimulated electron-light-matter interactions with key implications for research on (quantum) coherent optical phenomena at the nanoscale.

Graphene Plasmon Excitation with Ground-State Two-Level Quantum Emitters

The transmission of a two-level quantum emitter in its ground state through a graphene nanosheet is investigated. The graphene plasmons (GPs) field distribution, especially the opposite orientations of the vertical electric field components on the two sides of the graphene nanosheet, produces a significant nonadiabatic process during the interaction between the emitter and the localized GPs. By taking into account the counterrotating terms, the excitation of the quantum emitter with simultaneous emission of a GP has a large probability. This happens for emitter speeds of about 10^{-4} times the speed of light. For accelerated emitters, the GPs exhibit thermal field photon distribution with a high temperature. As a consequence, this study provides a promising platform to observe the dynamical Casimir effect as well as a simulation of the Unruh effect.

Efficient excitation of hybrid modes on a double-layer graphene with metallic slit grating

The excitation of double-layer hybrid plasmonic modes is investigated by the finite element method. The hybrid modes, verified as the standing even order of both symmetric and anti-symmetric modes, are effectively generated. There are several advances in comparison with using the Si grating: the metallic grating not only compensates phase mismatch, but also acts as a magnetic polariton. The dependences of each hybrid mode on the geometric parameters are analyzed respectively. Interestingly, a second spectra splitting occurs at each hybrid resonant mode with an obliquely incident light. At last, the excitation efficiency can be further enhanced to 90% using the Salisbury screen. The proposed hybrid system can be utilized to design various double-layer graphene-based plasmonic devices, including tunable optical switches, thermal emitters, multiband absorbers, sensors, etc.

Nonlinear Interactions between Free Electrons and Nanographenes

Free electrons act as a source of highly confined, spectrally broad optical fields that are widely used to map photonic modes with nanometer/millielectronvolt space/energy resolution through currently available electron energy-loss and cathodoluminescence spectroscopies. These techniques are understood as probes of the linear optical response, while nonlinear dynamics has escaped observation with similar degree of spatial detail, despite the strong enhancement of the electron evanescent field with decreasing electron energy. Here, we show that the field accompanying low-energy electrons can trigger anharmonic response in strongly nonlinear materials. Specifically, through realistic quantum-mechanical simulations, we find that the interaction between ≲100 eV electrons and plasmons in graphene nanostructures gives rise to substantial optical nonlinearities that are discernible as saturation and spectral shifts in the plasmonic features revealed in the cathodoluminescence emission and electron energy-loss spectra. Our results support the use of low-energy electron-beam spectroscopies for the exploration of nonlinear optical processes in nanostructures.

Controlling free electrons with optical whispering-gallery modes

Free-electron beams are versatile probes of microscopic structure and composition^1,2, and have revolutionized atomic-scale imaging in several fields, from solid-state physics to structural biology³. Over the past decade, the manipulation and interaction of electrons with optical fields have enabled considerable progress in imaging methods⁴, near-field electron acceleration^5,6, and four-dimensional microscopy techniques with high temporal and spatial resolution⁷. However, electron beams typically couple only weakly to optical excitations, and emerging applications in electron control and sensing^8-11 require large enhancements using tailored fields and interactions. Here we couple a free-electron beam to a travelling-wave resonant cavity mode. The enhanced interaction with the optical whispering-gallery modes of dielectric microresonators induces a strong phase modulation on co-propagating electrons, which leads to a spectral broadening of 700 electronvolts, corresponding to the absorption and emission of hundreds of photons. By mapping the near-field interaction with ultrashort electron pulses in space and time, we trace the lifetime of the the microresonator following a femtosecond excitation and observe the spectral response of the cavity. The natural matching of free electrons to these quintessential optical modes could enable the application of integrated photonics technology in electron microscopy, with broad implications for attosecond structuring, probing quantum emitters and possible electron-light entanglement.

Coherent interaction between free electrons and a photonic cavity

Advances in the research of interactions between ultrafast free electrons and light have introduced a previously unknown kind of quantum matter, quantum free-electron wavepackets^1-5. So far, studies of the interactions of cavity-confined light with quantum matter have focused on bound electron systems, such as atoms, quantum dots and quantum circuits, which are considerably limited by their fixed energy states, spectral range and selection rules. By contrast, quantum free-electron wavepackets have no such limits, but so far no experiment has shown the influence of a photonic cavity on quantum free-electron wavepackets. Here we develop a platform for multidimensional nanoscale imaging and spectroscopy of free-electron interactions with photonic cavities. We directly measure the cavity-photon lifetime via a coherent free-electron probe and observe an enhancement of more than an order of magnitude in the interaction strength relative to previous experiments of electron-photon interactions. Our free-electron probe resolves the spatiotemporal and energy-momentum information of the interaction. The quantum nature of the electrons is verified by spatially mapping Rabi oscillations of the electron spectrum. The interactions between free electrons and cavity photons could enable low-dose, ultrafast electron microscopy of soft matter or other beam-sensitive materials. Such interactions may also open paths towards using free electrons for quantum information processing and quantum sensing. Future studies could achieve free-electron strong coupling^6,7, photon quantum state synthesis⁸ and quantum nonlinear phenomena such as cavity electro-optomechanics⁹.

Entanglements of Electrons and Cavity Photons in the Strong-Coupling Regime

This Letter sets a road map towards an experimental realization of strong coupling between free electrons and photons and analytically explores entanglement phenomena that emerge in this regime. The proposed model unifies the strong-coupling predictions with known electron-photon interactions. Additionally, this Letter predicts a non-Columbic entanglement between freely propagating electrons. Since strong coupling can map entanglements between photon pairs onto photon-electron pairs, it may harness electron beams for quantum communication, thus far exclusive to photons.

Ultrafast Multiharmonic Plasmon Generation by Optically Dressed Electrons

Interactions between electrons and photons are a source of rich physics from atomic to astronomical scales. Here, we examine a new kind of electron-photon interaction in which an electron, modulated by light, radiates multiple harmonics of plasmons. The emitted plasmons can be femtosecond in duration and nanometer in spatial scale. The extreme subwavelength nature of the plasmons lowers the necessary input light intensity by at least 4 orders of magnitude relative to state-of-the-art strong-field processes involving bound or free electrons. The results presented here reveal a new means of ultrafast (10-1000 fs) interconversion between photonic and plasmonic energy, and a general scheme for generating spatiotemporally shaped ultrashort pulses in optical materials. More generally, our results suggest a route towards realizing analogues of fascinating physical phenomena like nonlinear Compton scattering in plasmonics and nanophotonics with relatively low intensities, slow electrons, and on nanometer length scales.

Stimulated electron energy loss and gain in an electron microscope without a pulsed electron gun

We report on a novel way of performing stimulated electron energy-loss and energy-gain spectroscopy (sEELS/sEEGS) experiments that does not require a pulsed gun. In this scheme, a regular scanning transmission electron microscope (STEM) equipped with a conventional continuous electron gun is fitted with a modified EELS detector and a light injector in the object chamber. The modification of the EELS detector allows one to expose the EELS camera during tunable time intervals that can be synchronized with nanosecond laser pulses hitting the sample, therefore allowing us to collect only those electrons that have interacted with the sample under light irradiation. Using  ∼ 5 ns laser pulses of  ∼ 2 eV photon energy on various plasmonic silver samples, we obtain evidence of sEELS/sEEGS through the emergence of up to two loss and gain peaks in the spectra at  ± 2 and  ± 4 eV. Because this approach does not involve any modification of the gun, our method retains the original performances of the microscope in terms of energy resolution and spectral imaging with and without light injection. Compared to pulsed-gun techniques, our method is mainly limited to a perturbative regime (typically no more that one gain event per incident electron), which allows us to observe resonant effects, in particular when the plasmon energy of a silver nanostructure matches the laser photon energy. In this situation, EELS and EEGS signals are enhanced in proportion to n+1 and n, respectively, where n is the average plasmon population due to the external illumination. The n term is associated with stimulated loss and gain processes, and the term of 1 corresponds to conventional (spontaneous) loss. The EELS part of the spectrum is therefore an incoherent superposition of spontaneous and stimulated EEL events. This is confirmed by a proper quantum-mechanical description of the electron/light/plasmon system incorporating light-plasmon and plasmon-electron interactions, as well as inelastic plasmon decay.

Photothermal Engineering of Graphene Plasmons

Nanoscale photothermal sources find important applications in theranostics, imaging, and catalysis. In this context, graphene offers a unique suite of optical, electrical, and thermal properties, which we exploit to show self-consistent active photothermal modulation of its nanoscale response. In particular, we predict the existence of plasmons confined to the optical landscape tailored by continuous-wave external-light pumping of homogeneous graphene. This result relies on the high electron temperatures achievable in optically pumped clean graphene while its lattice remains near ambient temperature. Our study opens a new avenue toward the active optical control of the nanophotonic response in graphene with potential application in photothermal devices.

Phonon-Polariton Mediated Thermal Radiation and Heat Transfer among Molecules and Macroscopic Bodies: Nonlocal Electromagnetic Response at Mesoscopic Scales

Thermal radiative phenomena can be strongly influenced by the coupling of phonons and long-range electromagnetic fields at infrared frequencies. Typically employed macroscopic descriptions of thermal fluctuations often ignore atomistic effects that become relevant at nanometric scales, whereas purely microscopic treatments ignore long-range, geometry-dependent electromagnetic effects. We describe a mesoscopic framework for modeling thermal fluctuation phenomena among molecules near macroscopic bodies, conjoining atomistic treatments of electronic and vibrational fluctuations obtained from density functional theory in the former with continuum descriptions of electromagnetic scattering in the latter. The interplay of these effects becomes particularly important at mesoscopic scales, where phonon polaritons can be strongly influenced by the objects' finite sizes, shapes, and nonlocal or many-body response to electromagnetic fluctuations. We show that, even in small but especially in elongated low-dimensional molecules, such effects can modify thermal emission and heat transfer by orders of magnitude and produce qualitatively different behavior compared to predictions based on local, dipolar, or pairwise approximations.

Topologically protected Dirac plasmons in a graphene superlattice

Topological optical states exhibit unique immunity to defects, rendering them ideal for photonic applications. A powerful class of such states is based on time-reversal symmetry breaking of the optical response. However, existing proposals either involve sophisticated and bulky structural designs or can only operate in the microwave regime. Here we show a theoretical demonstration for highly confined topologically protected optical states to be realized at infrared frequencies in a simple two-dimensional (2D) material structure—a periodically patterned graphene monolayer—subject to a magnetic field of only 2 tesla. In our graphene honeycomb superlattice structures, plasmons exhibit substantial nonreciprocal behavior at the superlattice junctions under moderate static magnetic fields, leading to the emergence of topologically protected edge states and localized bulk modes. This approach is simple and robust for realizing topologically nontrivial optical states in 2D atomic layers, and could pave the way for building fast, nanoscale, defect-immune photonic devices.

Current proposals suitable for experimental realization of topologically protected optical states rely on complicated structures or only operate in the microwave regime. Here, Pan et al. propose topological Dirac plasmons to be realized at infrared frequencies in a periodically patterned graphene monolayer, subject to a magnetic field of only 2 Tesla.

Mediated coupling of surface plasmon polaritons by a moving electron beam

The mediated coupling of surface plasmon polaritons (SPPs) by a parallel moving electron beam is demonstrated in this paper. The theoretical analysis shows that the electron beam excited spoof surface plasmon polaritons (SSPs) on the grating placed above the metal films play the role as the excitation source in the mediated coupling. The numerical calculations and particle-in-cell simulations demonstrate the significant advantages of the SSPs mediately coupled SPPs in contrast with that coupled by the parallel moving electron beam directly. The photo density of the mediately coupled SPPs reaches up to 10⁶ per cm² for the electron beam with the charge density 100 nC/cm, which is two orders of magnitude larger than that of the directly coupled SPPs. The tuning band of the mediately coupled SPPs reaches up to 9% for the beam energy ranging from 10 keV to 30 keV, while it almost cannot be tuned for the direct coupling. The lifetime of the mediately coupled SPPs, which reaches up to hundreds of femtoseconds, is also much longer. Accordingly, the mediated coupling may bring great significances for the applications of SPPs.

Transition radiation from graphene plasmons by a bunch beam in the terahertz regime

The terahertz band is an increasingly important spectrum in a wide range of applications from bioimaging and medical diagnostics to security and wireless communications. We propose a tunable terahertz coherent radiation source based on graphene plasmon-induced transition radiation. The transition radiation in terahertz regime arises from the graphene plasmons, which are excited by a normally incident bunched electron beam. We analyze the field-intensities and spectral-angular distributions of the transition radiation with respect to Fermi energy, substrate dielectric permittivity, and electron bunch energy for both the coherent and incoherent radiation. The effect of electron bunching on the radiation pattern is discussed. The mechanism of plasmon frequency-selective transition radiation is discovered.

Padé resummation of many-body perturbation theories

In a typical scenario the diagrammatic many-body perturbation theory generates asymptotic series. Despite non-convergence, the asymptotic expansions are useful when truncated to a finite number of terms. This is the reason for the popularity of leading-order methods such as the GW approximation in condensed matter, molecular and atomic physics. Appropriate truncation order required for the accurate description of strongly correlated materials is, however, not known a priori. Here an efficient method based on the Padé approximation is introduced for the regularization of perturbative series allowing to perform higher-order self-consistent calculations and to make quantitative predictions on the convergence of many-body perturbation theories. The theory is extended towards excited states where the Wick theorem is not directly applicable. Focusing on the plasmon-assisted photoemission from graphene, we treat diagrammatically electrons coupled to the excited state plasmons and predict new spectral features that can be observed in the time-resolved measurements.

Ultrafast radiative heat transfer

Light absorption in conducting materials produces heating of their conduction electrons, followed by relaxation into phonons within picoseconds, and subsequent diffusion into the surrounding media over longer timescales. This conventional picture of optical heating is supplemented by radiative cooling, which typically takes place at an even lower pace, only becoming relevant for structures held in vacuum or under extreme thermal isolation. Here, we reveal an ultrafast radiative cooling regime between neighboring plasmon-supporting graphene nanostructures in which noncontact heat transfer becomes a dominant channel. We predict that more than 50% of the electronic heat energy deposited on a graphene disk can be transferred to a neighboring nanoisland within a femtosecond timescale. This phenomenon is facilitated by the combination of low electronic heat capacity and large plasmonic field concentration in doped graphene. Similar effects should occur in other van der Waals materials, thus opening an unexplored avenue toward efficient heat management.Electron relaxation, which is the dominant release channel of electronic heat in nanostructures, occurs with characteristic times of several picoseconds. Here, the authors predict that an ultrafast (femtosecond) radiative cooling regime takes place in plasmonically active neighboring graphene nanodisks prior to electron relaxation.

Plasmon-assisted high-harmonic generation in graphene

High-harmonic generation in condensed-matter systems is both a source of fundamental insight into quantum electron motion and a promising candidate to realize compact ultraviolet and ultrafast light sources. While graphene is anticipated to efficiently generate high-order harmonics due to its anharmonic charge-carrier dispersion, experiments performed on extended samples using THz illumination have revealed only a weak effect. The situation is further complicated by the enormous electromagnetic field intensities required by this highly nonperturbative nonlinear optical phenomenon. Here we argue that the large light intensity required for high-harmonic generation to occur can be reached by exploiting localized plasmons in doped graphene nanostructures. We demonstrate through rigorous time-domain simulations that the synergistic combination of strong plasmonic near-field enhancement and a pronounced intrinsic nonlinearity result in efficient broadband high-harmonic generation within a single material. Our results support the strong potential of nanostructured graphene as a robust, electrically tunable platform for high-harmonic generation.

Splashing transients of 2D plasmons launched by swift electrons

Launching of plasmons by swift electrons has long been used in electron energy-loss spectroscopy (EELS) to investigate the plasmonic properties of ultrathin, or two-dimensional (2D), electron systems. However, the question of how a swift electron generates plasmons in space and time has never been answered. We address this issue by calculating and demonstrating the spatial-temporal dynamics of 2D plasmon generation in graphene. We predict a jet-like rise of excessive charge concentration that delays the generation of 2D plasmons in EELS, exhibiting an analog to the hydrodynamic Rayleigh jet in a splashing phenomenon before the launching of ripples. The photon radiation, analogous to the splashing sound, accompanies the plasmon emission and can be understood as being shaken off by the Rayleigh jet-like charge concentration. Considering this newly revealed process, we argue that previous estimates on the yields of graphene plasmons in EELS need to be reevaluated.

Efficient plasmonic emission by the quantum Čerenkov effect from hot carriers in graphene

Graphene plasmons 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 over 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 offers a direct and ultrafast energy conversion scheme from charge particles to photons. The requirement for relativistic particles, however, makes Čerenkov emission inaccessible to most nanoscale electronic and photonic devices. Here we show that graphene plasmons provide the means to overcome this limitation through their low phase velocity and high field confinement. The interaction between the charge carriers flowing inside graphene and the plasmons enables a highly efficient two-dimensional Čerenkov emission, giving a versatile, tunable and ultrafast conversion mechanism from electrical signal to plasmonic excitation.

Quantum Effects in the Nonlinear Response of Graphene Plasmons

The ability of graphene to support long-lived, electrically tunable plasmons that interact strongly with light, combined with its highly nonlinear optical response, has generated great expectations for application of the atomically thin material to nanophotonic devices. These expectations are mainly reinforced by classical analyses performed using the response derived from extended graphene, neglecting finite-size and nonlocal effects that become important when the carbon layer is structured on the nanometer scale in actual device designs. Here we show that finite-size effects produce large contributions that increase the nonlinear response of nanostructured graphene to significantly higher levels than those predicted by classical theories. We base our analysis on a quantum-mechanical description of graphene using tight-binding electronic states combined with the random-phase approximation. While classical and quantum descriptions agree well for the linear response when either the plasmon energy is below the Fermi energy or the size of the structure exceeds a few tens of nanometers, this is not always the case for the nonlinear response, and in particular, third-order Kerr-type nonlinearities are generally underestimated by the classical theory. Our results reveal the complex quantum nature of the optical response in nanostructured graphene, while further supporting the exceptional potential of this material for nonlinear nanophotonic devices.

Plasmonics in atomically thin materials

The observation and electrical manipulation of infrared surface plasmons in graphene have triggered a search for similar photonic capabilities in other atomically thin materials that enable electrical modulation of light at visible and near-infrared frequencies, as well as strong interaction with optical quantum emitters. Here, we present a simple analytical description of the optical response of such kinds of structures, which we exploit to investigate their application to light modulation and quantum optics. Specifically, we show that plasmons in one-atom-thick noble-metal layers can be used both to produce complete tunable optical absorption and to reach the strong-coupling regime in the interaction with neighboring quantum emitters. Our methods are applicable to any plasmon-supporting thin materials, and in particular, we provide parameters that allow us to readily calculate the response of silver, gold, and graphene islands. Besides their interest for nanoscale electro-optics, the present study emphasizes the great potential of these structures for the design of quantum nanophotonics devices.

Quantum mechanical origin of the plasmon: from molecular systems to nanoparticles

The surface plasmon resonance (SPR) of noble metal nanoparticles is reviewed in terms of both classical and quantum mechanical approaches. The collective oscillation of the free electrons responsible for the plasmon is well described using classical electromagnetic theory for large systems (from about 10 to 100 nm). In cases where quantum effects are important, this theory fails and first principle approaches like time-dependent density functional theory (TDDFT) must be used. In this paper, we give an account of the current understanding of the quantum mechanical origin of plasmon resonances. We provide some insight into how the discrete absorption spectrum of small noble metal clusters evolves into a strong plasmon peak with increasing particle size. The collective character of the plasmon is described in terms of the constructive addition of single-particle excitations. As the system size increases, the number of single-particle excitations increases as well. A configuration interaction (CI) approach can be applied to describe the optical properties of particles of all shapes and sizes, providing a consistent definition of plasmon resonances. Finally, we expand our analysis to thiolate-protected nanoparticles and analyze the effects of ligands on the plasmon.