A canonical quantization scheme for localized surface plasmons (LSPs) in a metal nanosphere is presented based on a microscopic model composed of electromagnetic fields, oscillators that describe plasmons, and a reservoir that describes excitations other than plasmons. The eigenmodes of this fully quantum electrodynamic theory show a spectrum that includes radiative depolarization and broadening, including redshifting from the quasi-static LSP modes, with increasing particle size. These spectral profiles correctly match those obtained with exact classical electrodynamics (Mie theory). The present scheme provides the electric fields per plasmon in both near- and far-field regions whereby its utility in the fields of quantum plasmonics and nano-optics is demonstrated.
Assuming that the resonant surface plasmons on a spherical nanoparticle is formed by standing waves of two counter-propagating surface plasmon waves along the surface, by using Mie theory simulation, we find that the dispersions of surface plasmon resonant modes supported by silver nanospheres match that of the surface plasmons on a semi-infinite medium-silver interface very well. This suggests that the resonant surface plasmons of a metal nanosphere can be treated as a propagating surface plasmon wave.
In this work, the plasmon coupling effect between two gold nanospheres on a gold slab is investigated. At plasmon resonance frequencies, electrons on the surface of the slab are absorbed into spheres and contribute to plasmon oscillation. This effect can help enhance the local electric field and optical coupling force between the two spheres.
Nanometer-sized metal particles exhibit broadening of the localized surface plasmon resonance (LSPR) in comparison to its value predicted by the classical Mie theory. Using our model for the LSPR dependence on non-local surface screening and size quantization, we quantitatively relate the observed plasmon width to the nanoparticle radius $R$ and the permittivity of the surrounding medium $ε_m$. For Ag nanospheres larger than 8 nm only the non-local dynamical effects occurring at the surface are important and, up to a diameter of 25 nm, dominate over the bulk scattering mechanism. Qualitatively…
The Dicke subradiance and superradiance resulting from the interaction between surface plasmons of a nanosphere and an ensemble of quantum emitters have been investigated using a Green function approach. Based on such an investigation, we propose a scheme for a deterministic multiqubit quantum phase gate. As an example, twoqubit, threequbit, and fourqubit quantum phase gates have been designed and analyzed in detail. Phenomena due to the losses in the metal are discussed. Potential applications of these phenomena to quantuminformation processing are anticipated.
When metallic (or plasmonic) nanospheres are nearly touching, strong concentration of light can occur in the narrow gap regions. This phenomenon has a potential application in nanophotonics, biosensing and spectroscopy. The understanding of the strong interaction between the plasmonic spheres turns out to be quite challenging. Indeed, an extremely high computational cost is required to compute the electromagnetic field. Also, the classical method of image charges, which is effective for dielectric spheres system, is not valid for plasmonic spheres because of their negative permittivities. Here…
Inspired by recent measurements on individual metallic nanospheres that can not be explained with traditional classical electrodynamics, we theoretically investigate the effects of nonlocal response by metallic nanospheres in three distinct settings: atomic spontaneous emission, electron energy loss spectroscopy, and light scattering. These constitute two near-field and one far-field measurements, with zero-, one-, and two-dimensional excitation sources, respectively. We search for the clearest signatures of hydrodynamic pressure waves in nanospheres. We employ a linearized hydrodynamic model …
Theoretical description of oscillations of electron liquid in large metallic nanospheres (with radius of few tens nm) is formulated within random-phase-approximation semiclassical scheme. Spectrum of plasmons is determined including both surface and volume type excitations. It is demonstrated that only surface plasmons of dipole type can be excited by homogeneous dynamical electric field. The Lorentz friction due to irradiation of electro-magnetic wave by plasmon oscillations is analyzed with respect to the sphere dimension. The resulting shift of resonance frequency turns out to be strongly s…
The random-phase-approximation semiclassical scheme for description of plasmon excitations in large metallic nanospheres (with radius 10--100 nm) is developed for a case of presence of dynamical electric field. The spectrum of plasmons in metallic nanosphere is determined including both surface and volume type excitations and their mutual connections. It is demonstrated that only surface plasmons of dipole type can be excited by a homogeneous dynamical electric field. The Lorentz friction due to irradiation of e-m energy by plasmon oscillations is analysed with respect to the sphere dimension.…
The random-phase-approximation semiclassical scheme for description of plasmon excitations in large metallic nanospheres, with radius range 10-60 nm, is formulated in an all-analytical version. The spectrum of plasmons is determined including both surface and volume type excitations and their mutual connections. The various channels for damping of surface plasmons are evaluated and the relevant resonance shifts are compared with the experimental data for metallic nanoparticles of different size located in dielectric medium or on the semiconductor substrate. The strong enhancement of energy tra…
With recent experiments investigating the optical properties of progressively smaller plasmonic particles, quantum effects become increasingly more relevant, requiring a microscopic description. Using the density matrix formalism we analyze the photo-excited few-electron dynamics of a small nanosphere. Following the standard derivation of the bulk plasmon we particularly aim on elucidating the role of the Coulomb interaction. Calculating the dielectric susceptibility spectrum in the linear optical response we find discrete resonances resulting from a collective response mediated by the Coulomb…
We show that a dimer made of two gold nanospheres exhibits a remarkable efficiency for second-harmonic generation under femtosecond optical excitation. The detectable nonlinear emission for the given particle size and excitation wavelength arises when the two nanoparticles are as close as possible to contact, as in situ controlled and measured using the tip of an atomic force microscope. The excitation wavelength dependence of the second-harmonic signal supports a coupled plasmon resonance origin with radiation from the dimer gap. This nanometer-size light source might be used for high-resolut…
Localized surface plasmon resonances (LSPRs) have recently been identified in extremely diluted electron systems obtained by doping semiconductor quantum dots. Here we investigate the role that different surface effects, namely electronic spill-out and diffuse surface scattering, play in the optical properties of these ultra-low electron density nanosystems. Diffuse scattering originates from imperfections or roughness at a microscopic scale on the surface. Using an electromagnetic theory that describes this mechanism in conjunction with a dielectric function including the quantum size effect,…
We report on the nanoparticle-size-dependent onset of quantum tunneling of electrons across the sub-nanometer gaps in three different sizes (30, 50, and 80 nm) of highly uniform gold nanosphere dimers. For precision plasmonics, the gap distance is systematically controlled at the level of single C-C bonds via a series of alkanedithiol linkers (C2-C16). The corresponding single-particle scattering spectra reveal that for the larger dimers the onset of quantum effects occurs at larger gap distances: C6 for 80 nm, C5 for 50 nm, and C4 for 30 nm dimers. 2D non-local and quantum-corrected model (QC…
We present an analytical derivation of the electromagnetic response of a spherical object coated by a conductive film, here exemplified by a graphene coating. Applying the framework of Mie-Lorenz theory augmented to account for a conductive boundary condition, we derive the multipole scattering coefficients, modified essentially through the inclusion of an additive correction in numerator and denominator. By reductionist means, starting from the retarded response, we offer simple results in the quasistatic regime by analyzing the multipolar polarizability and associated dispersion equation for…
The selective optical detection of individual metallic nanoparticles (NPs) with high spatial and temporal resolution is a challenging endeavour, yet is key to the understanding of their optical response and their exploitation in applications from miniaturised optoelectronics and sensors to medical diagnostics and therapeutics. However, only few reports on ultrafast pump-probe spectroscopy on single small metallic NPs are available to date. Here, we demonstrate a novel phase-sensitive four-wave mixing (FWM) microscopy in heterodyne detection to resolve for the first time the ultrafast changes o…
Collective electron dynamics in plasmonic nanosystems can unfold on timescales in the attosec- ond regime and the direct measurements of plasmonic near-field oscillations is highly desirable. We report on numerical studies on the application of attosecond nanoplasmonic streaking spectroscopy to the measurement of collective electron dynamics in isolated Au nanospheres. The plasmonic field oscillations are induced by a few-cycle NIR driving field and are mapped by the energy of photoemitted electrons using a synchronized, time-delayed attosecond XUV pulse. By a detailed analysis of the amplitud…
When intense laser fields interact with nanoscale targets, strong-field physics meets plasmonic near-field enhancement and sub-wavelength localization of light. Photoemission spectra reflect the associated attosecond optical and electronic response and encode the collisional and collective dynamics of the solid. Nanospheres represent an ideal platform to explore the underlying attosecond nanophysics because of their particularly simple geometry. This review summarizes key results from the last decade and aims to provide the essential stepping stones for students and researchers to enter this f…
Metallic nano-structures characterised by multiple geometric length scales support low-frequency surface-plasmon modes, which enable strong light localization and field enhancement. We suggest studying such configurations using singular perturbation methods, and demonstrate the efficacy of this approach by considering, in the quasi-static limit, a pair of nearly touching metallic nano-spheres subjected to an incident electromagnetic wave polarized with the electric field along the line of sphere centers. Rather than attempting an exact analytical solution, we construct the pertinent (longitudi…
Optimisation and Precision Tuning of Localised Surface Plasmon Resonance in AuFON Systems
Universidad de Pamplona-Colombia（潘普洛纳大学）；Centro Atómico Bariloche e Instituto Balseiro, Comisión Nacional de Energía Atómica (CNEA) - Universidad Nacional de Cuyo (UNCUYO)（巴里洛切原子中心与巴尔塞罗研究所，国家原子能委员会（CNEA）- 昆卡约国立大学 (UNCUYO)）；Instituto de Nanociencia y Nanotecnología (INN-Bariloche), Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET)（纳米科学与技术研究所（INN-巴里洛切），国家科学研究委员会（CONICET)）
Raza et al. recently observed the extraordinarily large energy blueshifts of localized surface plasmon resonances and additional surface plasmon resonances in silver nanoparticles encapsulated in silicon nitride, which are not fully understood yet. By using the quantum model consisting of two subsystems respectively for describing the center of mass and intrinsic motions of conduction electrons of a metallic nanosphere and a coupling occurred between the center of mass and conduction electrons outside the metallic nanosphere, we firstly deduced the general energy and line broadening size-depen…
Sub-nanometer 3D morphometric precision of polarisation-resolved wide-field optical extinction microscopy determines the roundness of individual gold nanospheres
Plasmon-enhanced Raman scattering (PERS) becomes nonlinear when phonon pumping and phonon-stimulated scattering come into play. It is fundamental to the understanding of PERS and its photobleaching behavior. By quantization of the molecular vibration coherent state into phonon number states, we theoretically predict a stepwise dependence of PERS intensity on laser power. Experimental evidence is presented by measuring a monolayer of malachite green isothiocyanate molecules sandwiched in individual gold nanosphere-plane antennas, under radially polarized laser excitation of sub-microWatt powers…
We show that the Higgs mode of a superconductor, which is usually challenging to observe by far-field optics, can be made clearly visible using near-field optics by harnessing ultraconfined graphene plasmons. As near-field sources we investigate two examples: graphene plasmons and quantum emitters. In both cases the coupling to the Higgs mode is clearly visible. In the case of the graphene plasmons, the coupling is signaled by a clear anticrossing stemming from the interaction of graphene plasmons with the Higgs mode of the superconductor. In the case of the quantum emitters, the Higgs mode is…
Plasmonic resonance of a metallic nanostructure results from coherent motion of its conduction electrons driven by incident light. At the resonance, the induced dipole in the nanostructure is proportional to the number of the conduction electrons, hence $10^{7}$ times larger than that in an atom. The interaction energy between the induced dipole and fluctuating virtual field of the incident light can reach a few tenths of an eV. Therefore, the classical electromagnetism dominating the field becomes inadequate. We argue that quantum electrodynamics (QED) should be used instead as the fundamenta…
We develop a theoretical model of the surface plasmon resonance of metallic nanospheres in the size range down to the single nanometer size. Within this model we explicitly show how different microscopic mechanisms, namely quantization due to size (QSE) and electron spill-out, affect the energy of the surface plasmon. We demonstrate, that electron spill-out effects, which can move the surface plasma energy both toward the red or the blue, can be comparable to or even stronger than QSE. Thus, depending on circumstances, QSE may only be observed for ultrasmall metal nanoparticles much closer to …
We study the optical responses of metal nanoparticle chains. Multiple scattering calculations are used to study the extinction cross sections of silver nanosphere chains of finite length embedded in a glass matrix. The transmission and reflection coefficients of periodic 2D arrays of silver nanospheres are also calculated to understand the interaction between nanoparticle chains. The results are in agreement with recent experiments. The splitting of plasmon-resonance modes for different polarizations of the incident light are explored. Results on the effect of disorder are also presented.
Beyond the Quantum Picture: The Electrodynamic Origin of Chiral Nanoplasmonics
University of Rome Tor Vergata（罗马托尔维加塔大学）；Università di Pisa（比萨大学）；Umeå University（于默奥大学）；CNR Institute of Chemistry of OrganoMetallic Compounds (CNR-ICCOM)（国家研究委员会有机金属化合物化学研究所）
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…
We consider a biased molecular junction subjected to external time-dependent electromagnetic field. The field for two typical junction geometries (bowtie antennas and metal nanospheres) is calculated within finite-difference time-domain technique. Time-dependent transport and optical response of the junctions is calculated within non-equilibrium Green's function approach expressed in a form convenient for description of multi-level systems. We present numerical results for a two-level (HOMO-LUMO) model, and discuss influence of localized surface plasmon polariton modes on transport.
Many promising nanophotonics endeavours hinge upon the unique plasmonic properties of nanometallic structures with narrow non-metallic gaps, which support super-concentrated bonding modes that singularly redshift with decreasing separations. In this letter, we present a descriptive physical picture, complemented by elementary asymptotic formulae, of a nonlocal mechanism for plasmon-redshift saturation at subnanometric gap widths. Thus, by considering the electron-charge and field distributions in the close vicinity of the metal-vacuum interface, we show that nonlocality is asymptotically manif…
In this work, a new structure is suggested for spasing. The presented spaser is made up of a graphene nanosphere, which supports localized surface plasmon modes, and a quantum dot array, acting as a gain medium. The gain medium is pumped by an external laser source. Since all the plasmons are carried on a graphene platform, the structure features coherent surface plasmons with high confinement and large life time. All the structure is analyzed theoretically using full quantum mechanical description. The main advantage of the proposed spaser is the simple tuning capability of it by changing gra…
Plasmons are commonly interpreted with classical electrodynamics, while nonclassical effects may influence the dynamics of plasmon resonances as the plasmon confinement is approaching the few--nanometer scale. However, an unambiguous approach to quantify the degree of nonclassical dynamics remains. We propose a nonclassical-impact parameter (NCI) to characterize the degree of nonclassical effects from an energy perspective, i.e. which fraction of the total electromagnetic energy is attributed to classical electrodynamic terms and which fraction is correspondingly to be assigned to nonclassical…
A hot-spot of high local field can be created in between two closely placed metal nanoparticles by irradiating them with an appropriate wavelength and polarization of incident light. The strength of the field at the hot-spot is expected to get enhanced by even up to six orders of magnitude than that of the applied field. Placing a semiconductor quantum dot or an analyte molecule at the hot-spot is an essential step towards harnessing the enhanced field for applications. In this article, we show that it is possible to position a CdTe quantum dot (QD) between two larger silver nanospheres in col…
Historically, the field of plasmonics has been relying on the framework of classical electrodynamics, with the local-response approximation of material response being applied even when dealing with nanoscale metallic structures. However, when approaching the atomic-scale confinement of the electromagnetic radiation, mesoscopic effects are anticipated to become observable, e.g., those associated with the nonlocal electrodynamic surface response of the electron gas. We investigate nonlocal effects in propagating gap surface plasmon modes in ultrathin metal--dielectric--metal planar waveguides, e…
Quantum effects of plasmonic phenomena have been explored through ab-initio studies, but only for exceedingly small metallic nanostructures, leaving most experimentally relevant structures too large to handle. We propose instead an effective description with the computationally appealing features of classical electrodynamics, while quantum properties are described accurately through an infinitely thin layer of dipoles oriented normally to the metal surface. The nonlocal polarizability of the dipole layer is mapped from the free-electron distribution near the metal surface as obtained with 1D q…
Plasmonic resonances of nanoparticles have drawn lots of attentions due to their interesting and useful properties such as strong field enhancements. These systems are typically studied using either classical electrodynamics or fully quantum theory. Each approach can handle some aspects of plasmonic systems accurately and efficiently, while having its own limitation. The self-consistent hydrodynamics model has the advantage that it can incorporate the quantum effect of the electron gas into classical electrodynamics in a consistent way. We use the method to study the plasmonic response of poly…
When in close contact, plasmonic resonances interact and become strongly correlated. In this work we develop a quantum mechanical model, using the language of continuous variables and quantum information, for an array of coupled particle plasmons. This model predicts that when the coupling strength between plasmons approaches or surpasses the local dissipation, a sizable amount of entanglement is stored in the collective modes of the array. We also prove that entanglement manifests itself in far-field images of the plasmonic modes, through the statistics of the quadratures of the field, in wha…
We develop a consistent quantum description of surface plasmons interacting with quantum emitters and external electromagnetic field. Within the framework of macroscopic electrodynamics in dispersive and absorptive medium, we derive, in the Markov approximation, the canonical Hamiltonian, commutation relations, and coupling parameters for the plasmon modes in metal-dielectric structures of an arbitrary shape whose characteristic size is well below the diffraction limit. We then develop a new quantum approach bridging the macroscopic and canonical schemes which describes the interacting plasmon…
We consider a biased molecular junction subjected to external time-dependent electromagnetic field. We discuss local field formation due to both surface plasmon-polariton excitations in the contacts and the molecular response. Employing realistic parameters we demonstrate that such self-consistent treatment is crucial for proper description of the junction transport characteristics.
We report a novel behavior of the surface plasmon linewidth in sodium nanospheres Na$_{1760}$ changing with the electron temperature, which monotonically decreases and bears a discontinuous sudden drop at high electron temperatures. Our calculation is based on the model constructed by splitting the total Hamiltonian of all valence electrons of a metallic nanoparticle into two sub-Hamiltonians and their coupling, and obtained results can be verified by the pump-probe femtosecond spectroscopy experiments. In addition, we propose that it is the size uncertainty of small nanoparticles that yields …
We show how a complex Snell's law can be used to describe the refraction of surface plasmon polaritons (SPPs) at an interface between two metals, validating its predictions with 3-D electrodynamics simulations. Refraction gives rise to peculiar SPP features including inhomogeneities in the waveform and dispersion relations that depend on the incident wave and associated material. These features make it possible to generate SPPs propagating away from the interface with significant confinement normal to the propagation direction. We also show that it is possible to encode optical properties of t…
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 numerically study the tuning of the radiative heat transfer between a spherical InSb nanoparticle in the vicinity of a flat SiC surface assisted by a static magnetic field. By changing the value of the applied magnetic field, the dielectric function of the nanosphere becomes anisotropic due to the excitation of magneto-plasmons. In the dipolar approximation, the plasmon resonance of the particle splits into two additional satellite resonances that shift to higher and lower frequencies as the field increases. When one of the particle resonances overlaps with the phonon-polariton frequency of…
Quantum electrodynamics theory of the resonance Raman scattering is developed for an atom in a close proximity to a carbon nanotube. The theory predicts a dramatic enhancement of the Raman intensity in the strong atomic coupling regime to nanotube plasmon near-fields. This resonance scattering is a manifestation of the general electromagnetic surface enhanced Raman scattering effect, and can be used in designing efficient nanotube based optical sensing substrates for single atom detection, precision spontaneous emission control, and manipulation.
A bound state between a quantum emitter (QE) and surface plasmon polaritons (SPPs) can be formed, where the QE is partially stabilized in its excited state. We put forward a general approach for calculating the energy level shift at a negative frequency $ω$, which is just the negative of the nonresonant part for the energy level shift at positive frequency $-ω$. We also propose an efficient formalism for obtaining the long-time value of the excited-state population without calculating the eigenfrequency of the bound state or performing a time evolution of the system, in which the probability a…
We use quantum electrodynamics and the confinement-induced nonlocal dielectric response model based on the Keldysh-Rytova electron interaction potential to study the epsilon-near-zero modes of metallic films in the transdimensional regime. New peculiar effects are revealed such as the plasmon mode degeneracy lifting and the dipole emitter coupling to the split epsilon-near-zero modes, leading to thickness-controlled spontaneous decay with up to three-orders-of-magnitude increased rates.
As characteristic lengths in plasmonics rapidly approach the sub-nm regime, quantum-informed models that can capture those aspects of the quantum nature of the electron gas that are not accessible by the standard approximations of classical electrodynamics, or even go beyond the free-electron description, become increasingly more important. Here we propose a template for comparing and validating the predictions of such models, through the circular dichroism signal of a metallic nanoparticle helix. For illustration purposes, we compare three widely used models, each dominant at different nanopa…
We investigate surface plasmons at a planar interface between a normal dielectric and a topological insulator, where the Fermi-energy lies inside the bulk gap of the topological insulator and gives rise to a two-dimensional charge distribution of free Dirac electrons. We develop the methodology for the calculation of plasmon dispersions, using the framework of classical electrodynamics, with modified constituent equations due to Hall currents in the topological insulator, together with a Lindhard-type description for the two-dimensional charge distribution of free Dirac electrons. For a system…
Strongly nonlinear Bernstein modes in graphene reveal plasmon-enhanced near-field magnetoabsorption
University of Regensburg（雷根斯堡大学）；Institute of High Pressure Physics of the Polish Academy of Sciences（波兰科学院高压物理研究所）；National University of Singapore（新加坡国立大学）；Faculty of Physics, Ivan Franko National University of Lviv（利沃夫伊万·弗兰科国立大学物理学院）
