We report a numerical investigation on the heat transfer through one dimensional arrays of metallic nanoparticles closely spaced in a host material. Our simulations show that the multipolar interactions play a crucial role in the heat transport via collective plasmons. Calculations of the plasmonic thermal conductance and of the thermal conductivity in ballistic and diffusive regime, respectively have been carried out. (a) Using the Landauer-Buttiker formalism we have found that, when the host material dielectric constant takes positive values, the multipolar interactions drastically enhance by several order of magnitude the ballistic thermal conductance of collective plasmons compared with that of a classical dipolar chain. On the contrary, when the host material dielectric constant takes negative values, we have demonstrated the existence of non-ballistic multipolar modes which annihilate the heat transfer through the chains. (b) Using the kinetic theory we have also examined the thermal behavior of chains in the diffusion approximation. We have shown that the plasmonic thermal conductivity of metallic nanoparticle chains can reach 1% of the bulk metal thermal conductivity . This result could explain the anomalously high thermal conductivity observed in many colloïdal suspensions, the so called nanofluids.
We develop a general quantum theory of the coupled plasmonic modes resulting from the near-field interaction between localized surface plasmons in a heterogeneous metallic nanoparticle dimer. In particular, we provide analytical expressions for the frequencies and decay rates of the bright and dark plasmonic modes. We show that, for sufficiently small nanoparticles, the main decay channel for the dark plasmonic mode, which is weakly coupled to light and, hence, immune to radiation damping, is of nonradiative origin and corresponds to Landau damping, i.e., decay into electron-hole pairs.
We predict the electromagnetic field driven nucleation of nanoparticles that provide plasmonic oscillations in resonance with the field frequency. The oscillations assume a phase that maximizes the particle polarization and energy gain due to nucleation. We derive closed form expressions for the corresponding nucleation barrier and particle shape vs. field frequency and strength, metal plasma frequency, conductivity, and the host dielectric permittivity. We show that the plasmonic polarization allows for nucleation of particles that would not be stable in zero field.
Here, extending our previous work on this topic, we derive a dynamic closed-form dispersion relation for a rigorous analysis of guided wave propagation along coupled parallel linear arrays of plasmonic nanoparticles, operating as optical 'two-line' waveguides. Compared to linear arrays of nanoparticles, our results suggest that these waveguides may support longer propagation lengths and more confined beams, operating analogously to transmission-line segments at lower frequencies. Our formulation fully takes into account the whole dynamic interaction among the infinite number of nanoparticles c…
The non-oxidizing catalytic noble metal rhodium is introduced for ultraviolet plasmonics. Planar tripods of 8 nm Rh nanoparticles, synthesized by a modified polyol reduction method, have a calculated local surface plasmon resonance near 330 nm. By attaching p-aminothiophenol, local field-enhanced Raman spectra and accelerated photo-damage were observed under near-resonant ultraviolet illumination, while charge transfer simultaneously increased fluorescence for up to 13 minutes. The combined local field enhancement and charge transfer demonstrate essential steps toward plasmonically-enhanced ul…
A simple and highly reproducible technique is demonstrated for the fabrication of metallic electrodes with nanometer separation. Commercially available bare gold colloidal nanoparticles are first trapped between prefabricated large-separation electrodes to form a low-resistance bridge by an ac electric field. A large dc voltage is then applied to break the bridge via electromigration at room temperature, which consistently produces gaps in the sub-10 nm range. The technique is readily applied to prefabricated electrodes with separation up to 1 micron, which can be defined using optical lithogr…
We present a variant of the recently developed quantum corrected model (QCM) for plasmonic nanoparticles [Nature Commun. 3, 825 (2012)] using non-local boundary conditions. The QCM accounts for electron tunneling in narrow gap regions of coupled metallic nanoparticles, leading to the appearance of new charge transfer plasmons. Our approach has the advantages that it emphasizes the non-local nature of tunneling and introduces only contact resistance, but not ohmic losses through tunneling. Additionally, it can be implemented much easier in boundary element method (BEM) approaches. We develop th…
We consider the relaxation of an excited two-level system (TLS) positioned near a spherical plasmonic nanoparticle (NP). The transition frequency of the TLS is assumed to coincide with the frequency of the condensation point of NP plasmonic resonances. We show that the relaxation of the TLS excitation is a two-step process. Following an initial exponential decay, the TLS breaks in to Rabi oscillations. Depending upon the distance between the TLS and NP, the probability of the TLS being in the excited state exhibits either chaotic or nearly regular oscillations. In the latter case, the eigenfre…
Hot carriers produced from the decay of localized surface plasmons in metallic nanoparticles are intensely studied because of their optoelectronic, photovoltaic and photocatalytic applications. From a classical perspective, plasmons are coherent oscillations of the electrons in the nanoparticle, but their quantized nature comes to the fore in the novel field of quantum plasmonics. In this work, we introduce a quantum-mechanical material-specific approach for describing the decay of single quantized plasmons into hot electrons and holes. We find that hot carrier generation rates differ signific…
Electron energy loss spectroscopy (EELS) has emerged as a powerful tool for the investigation of plasmonic nanoparticles, but the interpretation of EELS results in in terms of optical quantities, such as the photonic local density of states, remains challenging. Recent work has demonstrated that under restrictive assumptions, including the applicability of the quasistatic approximation and a plasmonic response governed by a single mode, one can rephrase EELS as a tomography scheme for the reconstruction of plasmonic eigenmodes. In this paper we lift these restrictions by formulating EELS as an…
The combination of single photon emitters (quantum dots) and tailored metal nanoparticles with defined size and shape allows a detailed study of the interaction between light and matter. The enhanced optical near-field of the nanoparticles can strongly influence the absorption and emission of nearby fluorescent quantum dots. We show that a controlled spatial arrangement enables the analysis and understanding of polarization dependent coupling between a metal nanoparticle and few or single fluorescent quantum dots. Modifications in the fluorescence spectrum and lifetime are analyzed and compare…
We investigate the radiative heat transport along a Su-Schrieffer-Heeger chain of InSb nanoparticles. We show that in the topological non-trivial phase, the edge modes dominate the radiative heat transport despite their strong localization at the edges of the finite chain due to a long-range coupling of the first and last particle. We further discuss the scaling laws of the heat transfer with respect to the chain length for the longitudinal and transversal band- and edge modes and conclude that both type of modes obey the same scaling law.
Background: Semiconductor-doped glasses are treated actively through many years and continue to be of great interest because challenged features of nanosized semiconductors of various chemical nature. Copper chalcogenides have discovered the plasmonic properties in line with quantum confinement effects specific for major of semiconductor nanoparticles. Objective: The aim of this work is to study structural and optical features of the sol-gel derived silica glasses with copper selenide nanoparticles demonstrating appearance of the plasmonic light absorption in the near IR range. Method: The sam…
Strategies for ultrafast optical control of magnetism have been a topic of intense research for several decades because of the potential impact in technologies such as magnetic memory, spintronics, and quantum computation, as well as the opportunities for non-linear optical control and modulation in applications such as optical isolation and non-reciprocity. Here we report the first experimental quantification of optically induced magnetization in plasmonic Au nanoparticles due to the inverse Faraday effect (IFE). The induced magnetic moment in nanoparticles is found to be ~1,000x larger than …
Plasmonic nanocrystals with hot spots are able to localize optical energy in small spaces. In such physical systems, near-field interactions between molecules and plasmons can become especially strong. This paper considers the case of a nanoparticle dimer and a chiral biomolecule. In our model, a chiral molecule is placed in the gap between two plasmonic nanoparticles, where the electromagnetic hot spot occurs. Since many important biomolecules have optical transitions in the UV, we consider the case of Aluminum nanoparticles, as they offer strong electromagnetic enhancements in the blue and U…
In this letter, we address the thermal processes occurring in plasmonic nanoparticles. We determine constrains imposed upon the plasmonic excitation in such nanoparticle by the resulting heat generation. Taking into account temperature dependence of the metal losses, we predict the existence of the critical number of plasmons in the nanoparticle. We also allow for the temperature dependencies of the thermal-conductivity coefficient of the environment and the Kapitza heat boundary resistance. We show that the latter can dominate the overall heat resistance in the system. Strength limitations ca…
MNPBEM is a Matlab toolbox for the simulation of metallic nanoparticles (MNP), using a boundary element method (BEM) approach. The main purpose of the toolbox is to solve Maxwell's equations for a dielectric environment where bodies with homogeneous and isotropic dielectric functions are separated by abrupt interfaces. Although the approach is in principle suited for arbitrary body sizes and photon energies, it is tested (and probably works best) for metallic nanoparticles with sizes ranging from a few to a few hundreds of nanometers, and for frequencies in the optical and near-infrared regime…
We present a quantum mechanical approach to calculate broadening of plasmonic resonances in metallic nanostructures due to collisions of electrons with the surface of the structure. The approach is applicable if the characteristic size of the structure is much larger than the de Broglie electron wavelength in the metal. The approach can be used in studies of plasmonic properties of both single nanoparticles and arrays of nanoparticles.
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 analyze the plasmonic modes of a metal nanoparticle circular array. Closed form solutions to the eigenmode problem are given. For each polarization, the plasmonic mode with the highest quality is found to be an antiphase mode. We found that the significant suppression in radiative loss can be understood as the cancellation of the dipolar radiation term in the radiative linewidth. The remaining finite radiative linewidth decreases exponentially as the number of particle increases.
We derive a general expression for electric and magnetic part of the near-field energy density of $N$ dipoles of temperatures $T_1, \ldots, T_N$ immersed in a background field having a different temperature $T_b$. In contrast to former expressions this inclusion of the background field allows for determining the energy density of heated or cooled isotropic dipolar objects within an arbitrary environment which is thermalized at a different temperature. Furthermore, we show how the energy density is related to the local density of states. We use this general expression to study the near-field en…
Optical properties of colloidal plasmonic titanium nitride nanoparticles are examined with an eye on their photothermal via transmission electron microscopy and optical transmittance measurements. Single crystal titanium nitride cubic nanoparticles with an average size of 50 nm exhibit plasmon resonance in the biological transparency window. With dimensions optimized for efficient cellular uptake, the nanoparticles demonstrate a high photothermal conversion efficiency. A self-passivating native oxide at the surface of the nanoparticles provides an additional degree of freedom for surface funct…
We present analytical expressions for the resonance frequencies of the plasmonic modes hosted in a cylindrical nanoparticle within the quasistatic approximation. Our theoretical model gives us access to both the longitudinally and transversally polarized dipolar modes for a metallic cylinder with an arbitrary aspect ratio, which allows us to capture the physics of both plasmonic nanodisks and nanowires. We also calculate quantum mechanical corrections to these resonance frequencies due to the spill-out effect, which is of relevance for cylinders with nanometric dimensions. We go on to consider…
For plasmonic nanoparticles, we investigate the influence of surface roughness inherent to top-down fabrication on the optical properties, and find that it has a surprisingly small influence on the position and width of the plasmon peaks. Our experimental observation is supported by simulations based on the boundary element method approach. Using a perturbation approach, suitable for metallic nanoparticles with a moderate degree of surface roughness, we demonstrate that the reason for this lies in motional narrowing where the plasmon averages over the random height fluctuations. Surface roughn…
Anisotropic plasmon coupling in closely-spaced chains of Ag nanoparticles was visualized using the electron energy loss spectroscopy in a scanning transmission electron microscope. For dimers as the simplest chain, mapping the plasmon excitations with nanometers' spatial resolution and 0.27 eV energy resolution intuitively identified two coupling plasmons. The in-phase mode redshifted from the ultraviolet region as the inter-particle spacing was reduced, reaching the visible range at 2.7 eV. Calculations based on the discrete dipole approximation confirmed its optical activeness, where the lon…
While plasmonic particles can provide optical resonances in a wide spectral range from the lower visible up to the near-infrared, often symmetry effects are utilized to obtain particular optical responses. By breaking certain spatial symmetries, chiral structures arise and provide robust chiroptical responses to these plasmonic resonances. Here, we observe strong chiroptical responses in the linear and nonlinear optical regime for chiral L-handed helicoid III nanoparticles and quantify them by means of an asymmetric factor, the so-called g-factor. We calculate the linear-optical g-factors for …
Plasmonic nanoarrays which support collective surface lattice resonances (SLRs) have become an exciting frontier in plasmonics. Compared with the localized surface plasmon resonance (LSPR) in individual particles, these collective modes have appealing advantages such as angle-dependent dispersions and much narrower linewidths. Here, we investigate systematically how the geometry of the lattice affects the SLRs supported by metallic nanoparticles. We present a general theoretical framework from which the various SLR modes of a given geometry can be straightforwardly obtained by a simple compari…
We study emission of photoelectrons from plasmonic nanoparticles into surrounding matrix. We consider two mechanisms of the photoelectric effect from nanoparticles - surface and volume ones, and use models of these two effects which allow us to obtain analytical results for the photoelectron emission rates from nanoparticle. Calculations have been done for the step potential at surface of spherical nanoparticle, and the simple model for the hot electron cooling have been used. We highlight the effect of the discontinuity of the dielectric permittivity at the nanoparticle boundary in the surfac…
We investigate an array of metal nanoparticles as a channel for nanophotonic quantum communication and the generation of quantum plasmonic interference. We consider the transfer of quantum states, including single-qubits as plasmonic wavepackets, and highlight the necessity of a quantum mechanical description by comparing the predictions of quantum theory with those of classical electromagnetic theory. The effects of loss in the metal are included, thus putting our investigation into a practical setting and enabling the quantification of the performance of realistic nanoparticle arrays as plas…
Single-molecule surface enhanced Raman scattering (SM-SERS) is one of the vital applications of plasmonic nanoparticles. The SM-SERS sensitivity critically depends on plasmonic hot-spots created at the vicinity of such nanoparticles. In conventional fluid-phase SM-SERS experiments, plasmonic hot-spots are facilitated by chemical aggregation of nanoparticles. Such aggregation is usually irreversible, and hence, nanoparticles cannot be re-dispersed in the fluid for further use. Here, we show how to combine SM-SERS with plasmon-polariton assisted, reversible assembly of plasmonic nanoparticles at…
Non-equilibrium quantum plasmonics in nanoparticle-on-mirror nanocavities
Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China（电子科技大学前沿科学技术研究院）；Photonics Research Centre, Universiti Malaya（马来亚大学光子研究中心）；Nanophotonics Centre, Cavendish Laboratory, Department of Physics, University of Cambridge（剑桥大学物理系卡文迪许实验室纳米光子学中心）
Numerous applications of nanotechnologies rely on the wide availability of high-quality crystalline nanoparticles (NPs). Although the chemical synthesis of noble metal nanoparticles (gold and silver) is well mastered, pushing the optical response of metallic nanoparticles towards the ultraviolet requires other materials, such as aluminum. Although a few demonstrations of chemical synthesis of Al nanoparticles have been reported so far, an elaboration path allowing for a wide range of NP size that is compatible with mass production has yet to be demonstrated. In this article, we report on the p…
We theoretically investigate the creation of a magnetic moment in gold nanoparticles by circularly polarized laser light. To this end, we describe the collective electron dynamics in gold nanoparticles using a semiclassical approach based on a quantum hydrodynamic model that incorporates the prin- cipal quantum many-body and nonlocal effects, such as the electron spill-out, the Hartree potential, and the exchange and correlation effects. We use a variational approach to investigate the breathing and the dipole dynamics induced by an external electric field. We show that gold nanoparticles can …
We theoretically investigate equilibrium behaviors and photothermal effects of a flexible plasmonic metamaterial composed of aramid nanofibers and gold nanoparticles. The fiber matrix is considered as an external field to reconfigure a nanoparticle assembly. We find that the heating process tunes particle-particle and fiber-particle interactions, which alter adsorption of nanoparticles on fiber surfaces or clustering in pore spaces. Thus, it is possible to control the nanoparticle self-assembly by laser illumination. Gold nanoparticles strongly absorb radiations and efficiently dissipate absor…
Bimetallic plasmonic nanoparticles enable tuning of the optical response and chemical stability by variation of the composition. The present numerical simulation study compares Ag-Au alloy, Ag@Au core-shell, and Au@Ag core-shell bimetallic plasmonic nanoparticles of both spherical and anisotropic (nanotriangle and nanorods) shapes. By studying both spherical and anisotropic (with LSPR in the near-infrared region) shapes, cases with and without interband transitions of Au can be decoupled. Explicit comparisons are facilitated by numerical models supported by careful validation and examination o…
We demonstrate an efficient eigen-decomposition method for analyzing the guided modes in metal nanoparticle chains. The proposed method has the advantage of showing the dispersion relation and mode quality simultaneously. It can also separate the material and geometrical properties, so its efficiency does not depend on the complexity of the material polarizability. The method is applied to analyze the guided modes of a single and a pair of metal chains. The more accurate dynamic dipole polarizability typically gives a red-shift compared with the results obtained with the broadly used quasistat…
Spatial confinement of matter in functional nanostructures has propelled these systems to the forefront of nanoscience, both as a playground for exotic physics and quantum phenomena and in multiple applications including plasmonics, optoelectronics, and sensing. In parallel, the emergence of monochromated electron energy loss spectroscopy (EELS) has enabled exploration of local nanoplasmonic functionalities within single nanoparticles and the collective response of nanoparticle assemblies, providing deep insight into the associated mechanisms. However, modern synthesis processes for plasmonic …
The concept of quantum plasmonic excitations in plasmonic lattices, which similarly to Frenkel excitons in molecular crystals propagate by hopping from one nanoparticle to another, is introduced. A consistent quantum theory of such plasmonic excitons, beginning with the quantization of localized surface plasmons in a metal nanoparticle and including the radiative relaxation in both 1D and 2D lattices near a reflective substrate surface, is developed. A possible room-temperature Bose-Einstein condensation in the quantum gas of plasmonic excitons is also discussed.
Transport properties of a single plasmon interacting with a hybrid system composed of a semiconductor quantum dot (SQD) and a metal nanoparticle (MNP) coupled to one-dimensional surface plasmonic waveguide are investigated theoretically via the real-space approach. We considered that the MNP-SQD interaction leads to the formation of a hybrid exciton and the transmission and reflection of a single incident plasmon could be controlled by adjusting the frequency of the classical control field applied to the MNP-SQD hybrid nanosystem, the kinds of metallic nanoparticles and the background media, r…
We present an approach to master the well-known challenge of calculating the contribution of d-bands to plasmon-induced hot carrier rates in metallic nanoparticles. We generalise the widely used spherical well model for the nanoparticle wavefunctions to flat d-bands using the envelope function technique. Using Fermi's golden rule, we calculate the generation rates of hot carriers after the decay of the plasmon due to transitions from either a d-band state to an sp-band state or from an sp-band state to another sp-band state. We apply this formalism to spherical silver nanoparticles with radii …
Spatial modulation microscopy is a technique originally developed for quantitative spectroscopy of individual nano-objects. Here, a parallel implementation of the spatial modulation microscopy technique is demonstrated based on a line detector capable of demodulation at kHz frequencies. The capabilities of the imaging system are shown using an array of plasmonic nanoantennas and dendritic cells incubated with gold nanoparticles.
Nanoparticle (NP) arrays of noble metals strongly absorb light in the visible to infrared wavelengths through resonant interactions between the incident electromagnetic field and the metal's free electron plasma. Such plasmonic interfaces enhance light absorption and photocurrent in solar cells. We report a cost effective and scalable room temperature/pressure spin-coating route to fabricate broadband plasmonic interfaces consisting of silver NPs. The NP interface yields photocurrent enhancement (PE) in thin film silicon devices by up to 200% which is significantly greater than previously repo…
Design of nanoscale structures with desired nanophotonic properties are key tasks for nanooptics and nanophotonics. Here, the correlative relationship between local nanoparticle geometries and their plasmonic responses is established using encoder-decoder neural networks. In the im2spec network, the correlative relationship between local particle geometries and local spectra is established via encoding the observed geometries to a small number of latent variables and subsequently decoding into plasmonic spectra; in the spec2im network, the relationship is reversed. Surprisingly, these reduced …
Anomalous resonances in properly shaped plasmonic nanostructures can in principle lead to infinite absorption/gain efficiencies over broad bandwidths. By developing a closed-form analytical solution for the fields scattered by conjoined semicircles, we outline the fundamental physics behind these phenomena, associated with broadband adiabatic focusing of surface plasmons at the nanoscale. We are able to justify the apparent paradox of finite absorption/gain in the limit of infinitesimally small material loss/gain, and we explore the potential of these phenomena in nonlinear optics, spasing, en…
We discuss a self-consistent scheme for treating the optical response of large, hybrid networks of semiconducting quantum dots (SQDs) and plasmonic metallic nanoparticles (MNPs). Our method is efficient and scalable and becomes exact in the limiting case of weakly interacting SQDs. The self-consistent equations obtained for the steady state are analogous to the von Neumann equations of motion for the density matrix of a SQD placed in an effective electric field computed within the discrete dipole approximation. Illustrative applications of the theory to square and honeycomb SQD, MNP, and hybri…
We report the investigation of the generation and detection of GHz coherent acoustic phonons in plasmonic gold nanoparticles superlattices (NPS). The experiments have been performed from an optical femtosecond pump-probe scheme across the optical plasmon resonance of the superlattice. Our experiments allow to estimate the collective elastic response (sound velocity) of the NPS as well as an estimate of the nano-contact elastic stiffness. It appears that the light-induced coherent acoustic phonon pulse has a typical in-depth spatial extension of about 45 nm which is roughly 4 times the optical …
Self-organized monocrystalline Au nanoparticles with potential applications in plasmonics are grown in a SrTiO$_3$ matrix by a novel two-step deposition process. The crystalline preferred orientation of these Au nanoparticles is investigated by synchrotron hard x-ray diffraction. Nanoparticles preferentially align with the (111) direction along the substrate normal (001), whereas two in-plane orientations are found with $[110]_{SrTiO_3} \: || \: [110]_{Au}$ and $[100]_{SrTiO_3} \: || \: [110]_{Au}$. Additionally, a smaller diffraction signal from nanoparticles with the (001) direction parallel…
It is challenging to strongly localize temperature in small volumes because heat transfer is a diffusive process. Here we show how to overcome this limitation using electrodynamic hot spots and interference effects in the regime of continuous-wave (CW) excitation. We introduce a set of figures of merit for the localization of temperature and for the efficiency of the plasmonic photo-thermal effect. Our calculations show that the temperature localization in a trimer nanoparticle assembly is a complex function of the geometry and sizes. Large nanoparticles in the trimer play the role of the nano…
The heat-shielding properties of random metasurface, composed of spherical or spheroidal nanoparticles with random displacements and/or random deformation, were theoretically investigated using the finite difference time domain method. The effective coverage was defined using the total area of nanoparticles in the metasurface, and the robustness of the near-infrared light reflection against randomness was investigated. When the effective coverage was high, the near-infrared light reflection was reduced by at least 20% in both nanoparticle arrangement and shape randomness compared to the hexago…
We realise an antibacterial nanomaterial based on the self-limited assembly of patchy plasmonic colloids, obtained by adsorption of lysozyme to gold nanoparticles. The possibility of selecting the size of the assemblies within several hundred nanometres allows for tuning their optical response in a wide range of frequencies from visible to near infrared. We also demonstrate an aggregation-dependent modulation of the catalytic activity, which results in an enhancement of the antibacterial performances for assemblies of the proper size. The gained overall control on structure, optical properties…
We present a rigorous theoretical model for the optical interaction between a nitrogen-vacancy (NV) centre in diamond and a plasmonic metal nanoparticle (MNP), accompanied by a computationally efficient procedure to solve the evolution. The proposed model enables us to successfully explain existing optical emission measurements of NV centres both in the presence and absence of a metal nanoparticle. We show that the NV-plasmon interaction provides a versatile new avenue to enhance and control the optical emission of an NV centre. Changes to the MNP type and size, NV-MNP centre separation, subme…
Ultrafast pump-probe measurements of plasmonic nanostructures probe the non-equilibrium behavior of excited carriers, which involves several competing effects obscured in typical empirical analyses. Here we present pump-probe measurements of plasmonic nanoparticles along with a complete theoretical description based on first-principles calculations of carrier dynamics and optical response, free of any fitting parameters. We account for detailed electronic-structure effects in the density of states, excited carrier distributions, electron-phonon coupling, and dielectric functions which allow us…
We use time-dependent density functional theory to examine the character of various resonances corresponding to peaks in the optical response of small metallic nanoparticles. Each resonance has both "sloshing" and "inversion" character. The sloshing mode is an oscillation in the occupation of the shells nearest the Fermi energy, transferring charge back and forth from below the Fermi level to above it. It results in oscillation in charge density near the surface of the particle. Inversions monotonically move charge from occupied to unoccupied states, and result in oscillation in charge density…
