Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response

Tailoring optical pulling force on gain coated nanoparticles with nonlocal effective medium theory

We study the optical scattering force on the coated nanoparticles with gain core and nonlocal plasmonic shell in the long-wavelength limit, and demonstrate negative optical force acting on the nanoparticles near the symmetric and/or antisymmetric surface plasmon resonances. To understand the optical force behavior, we propose nonlocal effective medium theory to derive the equivalent permittivity for the coated nanoparticles with nonlocality. We show that the imaginary part of the equivalent permittivity is negative near the surface resonant wavelength, resulting in the negative optical force. The introduction of nonlocality may shift the resonant wavelength of the optical force, and strengthen the negative optical force. Two examples of Fano-like resonant scattering in such coated nanoparticles are considered, and Fano resonance-induced negative optical force is found too. Our findings could have some potential applications in plasmonics, nano-optical manipulation, and optical selection.

Probing Gap Plasmons Down to Subnanometer Scales Using Collapsible Nanofingers

Gap plasmonic nanostructures are of great interest due to their ability to concentrate light into small volumes. Theoretical studies, considering quantum mechanical effects, have predicted the optimal spatial gap between adjacent nanoparticles to be in the subnanometer regime in order to achieve the strongest possible field enhancement. Here, we present a technology to fabricate gap plasmonic structures with subnanometer resolution, high reliability, and high throughput using collapsible nanofingers. This approach enables us to systematically investigate the effects of gap size and tunneling barrier height. The experimental results are consistent with previous findings as well as with a straightforward theoretical model that is presented here.

Self-assembled flat-faceted nanoparticles chains as a highly-tunable platform for plasmon-enhanced spectroscopy in the infrared

Self-assembly fabrication methods can produce aggregates of metallic nanoparticles separated by nanometer distances which act as versatile platforms for field-enhanced spectroscopy due to the strong fields induced at the interparticle gaps. In this letter we show the advantages of using particles with large flat facets at the gap as the building elements of the aggregates. For this purpose, we analyze theoretically the plasmonic response of chains of metallic particles of increasing length. These chains may be a direct product of the chemical synthesis and can be seen as the key structural unit behind the plasmonic response of two and three dimensional self-assembled aggregates. The longitudinal chain plasmon that dominates the optical response redshifts following an exponential dependence on the number of particles in the chain for all facets studied, with a saturation wavelength and a characteristic decay length depending linearly on the diameter of the facet. According to our calculations, for small Au particles of 50 nm size separated by a 1 nanometer gap, the saturation wavelength for the largest facets considered correspond to a wavelength shift of ≈ 1200 nm with respect to the single particle resonance, compared to shifts of only ≈ 200 nm for the equivalent configuration of perfectly spherical particles. The corresponding decay lengths are 11.8 particles for the faceted nanoparticles and 3.5 particles for the spherical ones. Thus, large flat facets lead to an excellent tunability of the longitudinal chain plasmon, covering the whole biological window and beyond. Furthermore, the maximum near-field at the gap is only moderately weaker for faceted gaps than for spherical particles, while the region of strong local field enhancement extends over a considerably larger volume, allowing to accommodate more target molecules. Our results indicate that flat facets introduce significant advantages for spectroscopic and sensing applications using self-assembled aggregates.

Quantum Corrections in Nanoplasmonics: Shape, Scale, and Material

The classical treatment of plasmonics is insufficient at the nanometer-scale due to quantum mechanical surface phenomena. Here, an extension of the classical paradigm is reported which rigorously remedies this deficiency through the incorporation of first-principles surface response functions-the Feibelman d parameters-in general geometries. Several analytical results for the leading-order plasmonic quantum corrections are obtained in a first-principles setting; particularly, a clear separation of the roles of shape, scale, and material is established. The utility of the formalism is illustrated by the derivation of a modified sum rule for complementary structures, a rigorous reformulation of Kreibig's phenomenological damping prescription, and an account of the small-scale resonance shifting of simple and noble metal nanostructures.

Detection of electron tunneling across plasmonic nanoparticle-film junctions using nitrile vibrations

The significant electric field enhancements that occur in plasmonic nanogap junctions are instrumental in boosting the performance of spectroscopy, optoelectronics and catalysis. Electron tunneling, associated with quantum effects in small junctions, is reported to limit the electric field enhancement. However, observing and quantitatively determining how tunneling alters the electric fields within small gaps is challenging due to the nanoscale dimensions and heterogeneity present experimentally. Here, we report the use of a nitrile probe placed in the nanoparticle-film gap junctions to demonstrate that the change in the nitrile stretching band associated with the vibrational Stark effect can be directly correlated with the local electric field environment modulated by gap size variations. The emergence of Stark shifts correlates with plasmon resonance shifts associated with electron tunneling across the gap junction. Time dependent changes in the nitrile band with extended illumination further support a build up of charge associated with optical rectification in the coupled plasmon system. Computational models agree with our experimental observations that the frequency shifts arise from a vibrational Stark effect. Large local electric fields associated with the smallest gap junctions give rise to significant Stark shifts. These results indicate that nitrile Stark probes can measure the local field strengths in plasmonic junctions and monitor the subtle changes in the local electric fields resulting from electron tunneling.

Bistable near field and bistable transmittance in 2D composite slab consisting of nonlocal core-Kerr shell inclusions

We carry out a theoretical study on optical bistability of near field intensity and transmittance in two-dimensional nonlinear composite slab. This kind of 2D composite is composed of nonlocal metal/Kerr-type dielectric core-shell inclusions randomly embedded in the host medium, and we derivate the nonlinear relation between the field intensity in the shell of inclusions and the incident field intensity with self-consistent mean field approximation. Numerical demonstration has been performed to show the viable parameter space for the bistable near field. We show that nonlocality can provide broader region in geometric parameter space for bistable near field as well as bistable transmittance of the nonlocal composite slab compared to local case. Furthermore, we investigate the bistable transmittance in wavelength spectrum, and find that besides the input intensity, the wavelength operation could as well make the transmittance jump from a high value to a low one. This kind of self-tunable nano-composite slab might have potential application in optical switching devices.

Mastering high resolution tip-enhanced Raman spectroscopy: towards a shift of perception

Recent years have seen tremendous improvement of our understanding of high resolution reachable in TERS experiments, forcing us to re-evaluate our understanding of the intrinsic limits of this field, but also exposing several inconsistencies.

Molecular fluorescence enhancement in plasmonic environments: exploring the role of nonlocal effects

Molecular spontaneous emission and fluorescence depend strongly on the emitter local environment. Plasmonic nanoparticles provide excellent templates for tailoring fluorophore emission, as they exhibit potential for both fluorescence enhancement and quenching, depending on emitter positioning in the nanoparticle vicinity. Here we explore the influence of hitherto disregarded nonclassical effects on the description of emitter-plasmon hybrids, focusing on the roles of the metal nonlocal response and especially size-dependent plasmon damping. Through extensive modelling of metallic nanospheres and nanoshells coupled to dipole emitters, we show that within a purely classical description a remarkable fluorescence enhancement can be achieved. However, once departing from the local-response approximation, and particularly by implementing the recent generalised nonlocal optical response theory, which provides a more complete physical description combining electron convection and diffusion, we show that not only are fluorescence rates dramatically reduced compared to the predictions of the local description and the common hydrodynamic Drude model, but the optimum emitter-nanoparticle distance is also strongly affected. In this respect, experimental measurements of fluorescence, the theoretical description of which requires a precise concurrent evaluation of far- and near-field properties of the system, constitute a novel, more sensitive probe for assessing the validity of state-of-the-art nonclassical theories.

Robustness of the far-field response of nonlocal plasmonic ensembles

Contrary to classical predictions, the optical response of few-nm plasmonic particles depends on particle size due to effects such as nonlocality and electron spill-out. Ensembles of such nanoparticles are therefore expected to exhibit a nonclassical inhomogeneous spectral broadening due to size distribution. For a normal distribution of free-electron nanoparticles, and within the simple nonlocal hydrodynamic Drude model, both the nonlocal blueshift and the plasmon linewidth are shown to be considerably affected by ensemble averaging. Size-variance effects tend however to conceal nonlocality to a lesser extent when the homogeneous size-dependent broadening of individual nanoparticles is taken into account, either through a local size-dependent damping model or through the Generalized Nonlocal Optical Response theory. The role of ensemble averaging is further explored in realistic distributions of isolated or weakly-interacting noble-metal nanoparticles, as encountered in experiments, while an analytical expression to evaluate the importance of inhomogeneous broadening through measurable quantities is developed. Our findings are independent of the specific nonclassical theory used, thus providing important insight into a large range of experiments on nanoscale and quantum plasmonics.

Quantum mechanical effects in plasmonic structures with subnanometre gaps

Metallic structures with nanogap features have proven highly effective as building blocks for plasmonic systems, as they can provide a wide tuning range of operating frequencies and large near-field enhancements. Recent work has shown that quantum mechanical effects such as electron tunnelling and nonlocal screening become important as the gap distances approach the subnanometre length-scale. Such quantum effects challenge the classical picture of nanogap plasmons and have stimulated a number of theoretical and experimental studies. This review outlines the findings of many groups into quantum mechanical effects in nanogap plasmons, and discusses outstanding challenges and future directions.

Real-space grids and the Octopus code as tools for the development of new simulation approaches for electronic systems

Real-space grids are a powerful alternative for the simulation of electronic systems. One of the main advantages of the approach is the flexibility and simplicity of working directly in real space where the different fields are discretized on a grid, combined with competitive numerical performance and great potential for parallelization. These properties constitute a great advantage at the time of implementing and testing new physical models. Based on our experience with the Octopus code, in this article we discuss how the real-space approach has allowed for the recent development of new ideas for the simulation of electronic systems. Among these applications are approaches to calculate response properties, modeling of photoemission, optimal control of quantum systems, simulation of plasmonic systems, and the exact solution of the Schrödinger equation for low-dimensionality systems.

Nanoantenna for Electrical Generation of Surface Plasmon Polaritons

Light emission by inelastic tunneling has been known for many years. Recently, this technique has been used to generate surface plasmons using a scanning tunneling microscope tip. The emission process suffers from a very low efficiency lower than a photon in 10^{4} electrons. We introduce a resonant plasmonic nanoantenna that allows both enhancing the power conversion to surface plasmon polaritons by more than 2 orders of magnitude and narrowing the emission spectrum. The physics of the emission process is analyzed in terms of local density of states and the efficiency of the nanoantenna to radiate surface plasmon polaritons.

Polarization State of Light Scattered from Quantum Plasmonic Dimer Antennas

Plasmonic antennas are able to concentrate and re-emit light in a controllable manner through strong coupling between metallic nanostructures. Only recently has it found that quantum mechanical effects can drastically change the coupling strength as the feature size approaches atomic scales. Here, we present a comprehensive experimental and theoretical study of the evolution of the resonance peak and its polarization state as the dimer-antenna gap narrows to subnanometer scale. We clearly can identify the classical plasmonic regime, a crossover regime where nonlocal screening plays an important role, and the quantum regime where a charge transfer plasmon appears due to interparticle electron tunneling. Moreover, as the gap decreases from tens of to a few nanometers, the bonding dipole mode tends to emit photons with increasing polarizability. When the gap narrows to quantum regime, a significant depolarization of the mode emission is observed due to the reduction of the charge density of coupled quantum plasmons. These results would be beneficial for the understanding of quantum effects on emitting-polarization of nanoantennas and the development of quantum-based photonic nanodevices.

From tunable core-shell nanoparticles to plasmonic drawbridges: Active control of nanoparticle optical properties

The optical properties of metallic nanoparticles are highly sensitive to interparticle distance, giving rise to dramatic but frequently irreversible color changes. By electrochemical modification of individual nanoparticles and nanoparticle pairs, we induced equally dramatic, yet reversible, changes in their optical properties. We achieved plasmon tuning by oxidation-reduction chemistry of Ag-AgCl shells on the surfaces of both individual and strongly coupled Au nanoparticle pairs, resulting in extreme but reversible changes in scattering line shape. We demonstrated reversible formation of the charge transfer plasmon mode by switching between capacitive and conductive electronic coupling mechanisms. Dynamic single-particle spectroelectrochemistry also gave an insight into the reaction kinetics and evolution of the charge transfer plasmon mode in an electrochemically tunable structure. Our study represents a highly useful approach to the precise tuning of the morphology of narrow interparticle gaps and will be of value for controlling and activating a range of properties such as extreme plasmon modulation, nanoscopic plasmon switching, and subnanometer tunable gap applications.

Projected Dipole Model for Quantum Plasmonics

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-the only introduced parameter-is mapped from the free-electron distribution near the metal surface as obtained with 1D quantum calculations, such as time-dependent density-functional theory (TDDFT), and is determined once and for all. The model can be applied in two and three dimensions to any system size that is tractable within classical electrodynamics, while capturing quantum plasmonic aspects of nonlocal response and a finite work function with TDDFT-level accuracy. Applying the theory to dimers, we find quantum corrections to the hybridization even in mesoscopic dimers, as long as the gap itself is subnanometric.

Non-linear optical response by functionalized gold nanospheres: identifying design principles to maximize the molecular photo-release

In a recent study by Voliani et al. [Small, 2011, 7, 3271], the electromagnetic field enhancement in the vicinity of the gold nanoparticle surface has been exploited to achieve photocontrolled release of a molecular cargo conjugated to the nanoparticles via 1,2,3-triazole, a photocleavable moiety. The aim of the present study is to investigate the mechanism of the photorelease by characterizing the nanoparticle aggregation status within the cells and simulating the electric field enhancement in a range of experimentally realistic geometries, such as single Au nanoparticles, dimers, trimers and random aggregates. Two plasmon-enhanced processes are examined for triazole photocleavage, i.e. three-photon excitation and third-harmonic-generation (one-photon) excitation. Taking into account the absorption cross sections of the triazole, we conclude that the latter mechanism is more efficient, and provides a photocleavage rate that explains the experimental findings. Moreover, we determine which aggregate geometries are required to maximize the field enhancement, and the dependence of such enhancement on the excitation wavelength. Our results provide design principles for maximizing the multiphoton molecular photorelease by such functionalized gold nanoparticles.

Numerical tool to take nonlocal effects into account in metallo-dielectric multilayers

We provide a numerical tool to quantitatively study the impact of nonlocality arising from free electrons in metals on the optical properties of metallo-dielectric multilayers. We found that scattering matrices are particularly well suited to take into account the electron response through the application of the hydrodynamic model. Though effects due to nonlocality are, in general, quite small, they, nevertheless, can be important for very thin (typically below 10 nm) metallic layers, as in those used in structures characterized by exotic dispersion curves. Such structures include those with a negative refractive index, hyperbolic metamaterials, and near-zero index materials. Higher wave vectors mean larger nonlocal effects, so that it is not surprising that subwavelength imaging capabilities of hyperbolic metamaterials are found to be sensitive to nonlocal effects. We find in all cases that the inclusion of nonlocal effects leads to at least a 5% higher transmission through the considered structure.

Anisotropy Effects on the Plasmonic Response of Nanoparticle Dimers

We present an ab initio study of the anisotropy and atomic relaxation effects on the optical properties of nanoparticle dimers. Special emphasis is placed on the hybridization process of localized surface plasmons, plasmon-mediated photoinduced currents, and electric-field enhancement in the dimer junction. We show that there is a critical range of separations between the clusters (0.1-0.5 nm) in which the detailed atomic structure in the junction and the relative orientation of the nanoparticles have to be considered to obtain quantitative predictions for realistic nanoplasmonic devices. It is worth noting that this regime is characterized by the emergence of electron tunneling as a response to the driven electromagnetic field. The orientation of the particles not only modifies the attainable electric field enhancement but can lead to qualitative changes in the optical absorption spectrum of the system.

Nonlocal optical response in metallic nanostructures

This review provides a broad overview of the studies and effects of nonlocal response in metallic nanostructures. In particular, we thoroughly present the nonlocal hydrodynamic model and the recently introduced generalized nonlocal optical response (GNOR) model. The influence of nonlocal response on plasmonic excitations is studied in key metallic geometries, such as spheres and dimers, and we derive new consequences due to the GNOR model. Finally, we propose several trajectories for future work on nonlocal response, including experimental setups that may unveil further effects of nonlocal response.

Atomistic near-field nanoplasmonics: reaching atomic-scale resolution in nanooptics

Electromagnetic field localization in nanoantennas is one of the leitmotivs that drives the development of plasmonics. The near-fields in these plasmonic nanoantennas are commonly addressed theoretically within classical frameworks that neglect atomic-scale features. This approach is often appropriate since the irregularities produced at the atomic scale are typically hidden in far-field optical spectroscopies. However, a variety of physical and chemical processes rely on the fine distribution of the local fields at this ultraconfined scale. We use time-dependent density functional theory and perform atomistic quantum mechanical calculations of the optical response of plasmonic nanoparticles, and their dimers, characterized by the presence of crystallographic planes, facets, vertices, and steps. Using sodium clusters as an example, we show that the atomistic details of the nanoparticles morphologies determine the presence of subnanometric near-field hot spots that are further enhanced by the action of the underlying nanometric plasmonic fields. This situation is analogue to a self-similar nanoantenna cascade effect, scaled down to atomic dimensions, and it provides new insights into the limits of field enhancement and confinement, with important implications in the optical resolution of field-enhanced spectroscopies and microscopies.

The Coupling between Gold or Silver Nanocubes in Their Homo-Dimers: A New Coupling Mechanism at Short Separation Distances

Using the DDA method, we investigated the near-field coupling between two excited Au or Ag 42 nm nanocubes in a face-to-face dimer configuration at small separation distances where the exponential coupling behavior distinctly changes. This could be due to the failure of the dipole approximation at short distances or a change in the electromagnetic field distribution between the adjacent monomers. A detailed calculation of the plasmonic field distribution strongly suggests that the latter mechanism is responsible for the failure of the expected exponential coupling behavior at small separation distances. The results suggest that the observed optical properties of the pair of Au or Ag nanocubes separated by distances larger than 6 nm, result from the electromagnetic coupling between the oscillating dipoles at the corners of the adjacent facets of the nanocubes. At separations smaller than 6 nm, the distribution of the plasmonic dipoles along both the facets and the corners of the adjacent monomers control the plasmonic spectra and the distance dependent optical properties of the dimer.

Antiboding and bonding lasing modes with low gain threshold in nonlocal metallic nanoshell

Based on a full-wave nonlocal Mie theory, we establish the spaser generation condition for compact plasmonic nanolasers in the long-wavelength limit for dielectric-metal core-shell nanoparticles. We found that there exist two lasing states arising from the hybridized antibonding and bonding modes for this coated nanolaser. By varying the surrounding medium and the gain materials, we can achieve low gain threshold for each mode with flexible radii ratios on the purpose of realistic easy fabrication. Numerical results show that nonlocal effects have different influences on the required gain threshold and gain refractive index of these two lasing modes, which may be of great importance in the design of such kind of ultrasmall nanoparticle lasers.

Theory of light emission from quantum noise in plasmonic contacts: above-threshold emission from higher-order electron-plasmon scattering

We develop a theoretical framework for the description of light emission from plasmonic contacts based on the nonequilibrium Green function formalism. Our theory establishes a fundamental link between the finite-frequency quantum noise and ac conductance of the contact and the light emission. Calculating the quantum noise to higher orders in the electron-plasmon interaction, we identify a plasmon-induced electron-electron interaction as the source of experimentally observed above-threshold light emission from biased STM contacts. Our findings provide important insight into the effect of interactions on the light emission from atomic-scale contacts.

Quantum effects in the optical response of extended plasmonic gaps: validation of the quantum corrected model in core-shell nanomatryushkas

Electron tunneling through narrow gaps between metal nanoparticles can strongly affect the plasmonic response of the hybrid nanostructure. Although quantum mechanical in nature, this effect can be properly taken into account within a classical framework of Maxwell equations using the so-called Quantum Corrected Model (QCM). We extend previous studies on spherical cluster and cylindrical nanowire dimers where the tunneling current occurs in the extremely localized gap regions, and perform quantum mechanical time dependent density functional theory (TDDFT) calculations of the plasmonic response of cylindrical core-shell nanoparticles (nanomatryushkas). In this axially symmetric situation, the tunneling region extends over the entire gap between the metal core and the metallic shell. For core-shell separations below 0.5 nm, the standard classical calculations fail to describe the plasmonic response of the cylindrical nanomatryushka, while the QCM can reproduce the quantum results. Using the QCM we also retrieve the quantum results for the absorption cross section of the spherical nanomatryushka calculated by V. Kulkarni et al. [Nano Lett. 13, 5873 (2013)]. The comparison between the model and the full quantum calculations establishes the applicability of the QCM for a wider range of geometries that hold tunneling gaps.

Monitoring morphological changes in 2D monolayer semiconductors using atom-thick plasmonic nanocavities

Nanometer-sized gaps between plasmonically coupled adjacent metal nanoparticles enclose extremely localized optical fields, which are strongly enhanced. This enables the dynamic investigation of nanoscopic amounts of material in the gap using optical interrogation. Here we use impinging light to directly tune the optical resonances inside the plasmonic nanocavity formed between single gold nanoparticles and a gold surface, filled with only yoctograms of semiconductor. The gold faces are separated by either monolayers of molybdenum disulfide (MoS2) or two-unit-cell thick cadmium selenide (CdSe) nanoplatelets. This extreme confinement produces modes with 100-fold compressed wavelength, which are exquisitely sensitive to morphology. Infrared scattering spectroscopy reveals how such nanoparticle-on-mirror modes directly trace atomic-scale changes in real time. Instabilities observed in the facets are crucial for applications such as heat-assisted magnetic recording that demand long-lifetime nanoscale plasmonic structures, but the spectral sensitivity also allows directly tracking photochemical reactions in these 2-dimensional solids.

A classical treatment of optical tunneling in plasmonic gaps: extending the quantum corrected model to practical situations

The optical response of plasmonic nanogaps is challenging to address when the separation between the two nanoparticles forming the gap is reduced to a few nanometers or even subnanometer distances. We have compared results of the plasmon response within different levels of approximation, and identified a classical local regime, a nonlocal regime and a quantum regime of interaction. For separations of a few Ångstroms, in the quantum regime, optical tunneling can occur, strongly modifying the optics of the nanogap. We have considered a classical effective model, so called Quantum Corrected Model (QCM), that has been introduced to correctly describe the main features of optical transport in plasmonic nanogaps. The basics of this model are explained in detail, and its implementation is extended to include nonlocal effects and address practical situations involving different materials and temperatures of operation.

van der Waals interactions at the nanoscale: the effects of nonlocality

Calculated using classical electromagnetism, the van der Waals force increases without limit as two surfaces approach. In reality, the force saturates because the electrons cannot respond to fields of very short wavelength: polarization charges are always smeared out to some degree and in consequence the response is nonlocal. Nonlocality also plays an important role in the optical spectrum and distribution of the modes but introduces complexity into calculations, hindering an analytical solution for interactions at the nanometer scale. Here, taking as an example the case of two touching nanospheres, we show for the first time, to our knowledge, that nonlocality in 3D plasmonic systems can be accurately analyzed using the transformation optics approach. The effects of nonlocality are found to dramatically weaken the field enhancement between the spheres and hence the van der Waals interaction and to modify the spectral shifts of plasmon modes.

Probing the quantum tunneling limit of plasmonic enhancement by third harmonic generation

Metal nanostructures provide extreme focusing of optical energy that is limited fundamentally by quantum tunneling. We directly probe the onset of the quantum tunneling regime observed by a sharp reduction in the local field intensity in subnanometer self-assembled monolayer gaps using third harmonic generation. Unlike past works that have inferred local limits from far-field spectra, this nonlinear measurement is sensitive to the near-field intensity as the third power. We calculate the local field intensity using a quantum corrected model and find good quantitative agreement with the measured third harmonic. The onset of the quantum regime occurs for double the gap size of past studies because of the reduced barrier height of the self-assembled monolayer, which will be critical for many applications of plasmonics, including nonlinear optics and surface enhanced Raman spectroscopy.

Nonlocal effects: relevance for the spontaneous emission rates of quantum emitters coupled to plasmonic structures

The spontaneous emission rate of dipole emitters close to plasmonic dimers are theoretically studied within a nonlocal hydrodynamic model. A nonlocal model has to be used since quantum emitters in the immediate environment of a metallic nanoparticle probe its electronic structure. Compared to local calculations, the emission rate is significantly reduced. The influence is mostly pronounced if the emitter is located close to sharp edges. We suggest to use quantum emitters to test nonlocal effects in experimentally feasible configurations.

Surface scattering contribution to the plasmon width in embedded Ag nanospheres

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 LSPR width is inversely proportional to the particle size and has a nonmonotonic dependence on the permittivity of the host medium, exhibiting for Ag a maximum at ε(m) ≈ 2.5. Our calculated LSPR width is compared with recent experimental data.

Quantum mechanical limit to plasmonic enhancement as observed by surface-enhanced Raman scattering

Plasmonic nanostructures enable light to be concentrated into nanoscale 'hotspots', wherein the intensity of light can be enhanced by orders of magnitude. This plasmonic enhancement significantly boosts the efficiency of nanoscale light-matter interactions, enabling unique linear and nonlinear optical applications. Large enhancements are often observed within narrow gaps or at sharp tips, as predicted by the classical electromagnetic theory. Only recently has it become appreciated that quantum mechanical effects could emerge as the feature size approaches atomic length-scale. Here we experimentally demonstrate, through observations of surface-enhanced Raman scattering, that the emergence of electron tunnelling at optical frequencies limits the maximum achievable plasmonic enhancement. Such quantum mechanical effects are revealed for metallic nanostructures with gap-widths in the single-digit angstrom range by correlating each structure with its optical properties. This work furthers our understanding of quantum mechanical effects in plasmonic systems and could enable future applications of quantum plasmonics.

Dynamical coupling of plasmons and molecular excitations by hybrid quantum/classical calculations: time-domain approach

The presence of plasmonic material influences the optical properties of nearby molecules in untrivial ways due to the dynamical plasmon-molecule coupling. We combine quantum and classical calculation schemes to study this phenomenon in a hybrid system that consists of a Na(2) molecule located in the gap between two Au/Ag nanoparticles. The molecule is treated quantum-mechanically with time-dependent density-functional theory, and the nanoparticles with quasistatic classical electrodynamics. The nanoparticle dimer has a plasmon resonance in the visible part of the electromagnetic spectrum, and the Na(2) molecule has an electron-hole excitation in the same energy range. Due to the dynamical interaction of the two subsystems the plasmon and the molecular excitations couple, creating a hybridized molecular-plasmon excited state. This state has unique properties that yield e.g. enhanced photoabsorption compared to the freestanding Na(2) molecule. The computational approach used enables decoupling of the mutual plasmon-molecule interaction, and our analysis verifies that it is not legitimate to neglect the back coupling effect when describing the dynamical interaction between plasmonic material and nearby molecules. Time-resolved analysis shows nearly instantaneous formation of the coupled state, and provides an intuitive picture of the underlying physics.

Effect of surface roughness on self-assembled monolayer plasmonic ruler in nonlocal regime

Recently, self-assembled monolayers (SAMs) have been used for plasmonic rulers to measure the nonlocal influence on the Au nanoparticle - metal film resonance wavelength shift and probe the ultimate field enhancement. Here we examine the influence of surface roughness on this plasmonic ruler in the nonlocal regime by comparing plasmonic resonance shifts for as-deposited and for ultra-flat Au films. It is shown that the resonance shift is larger for ultra-flat films, suggesting that there is not the saturation from nonlocal effects previously reported for the spacer range from 0.7 nm to 1.6 nm. We attribute the previously reported saturation to the planarization of the as-deposited films by thinner SAMs, as measured here by atomic-force microscopy. This work is of interest both in probing the ultimate limits of plasmonic enhancement with SAMs for applications in Raman and nonlinear optics, but also in the study of SAMs planarization as a function surface roughness.

Size-Dependent Plasmonic Resonances from Large-Scale Quantum Simulations

For metallic nanoparticles less than 10 nm in diameter, localized surface plasmon resonances (LSPRs) become sensitive to the quantum nature of conduction electrons. In this regime, experimental probes of size-dependent LSPRs are particularly challenging, and contradictory results are often reported. Unfortunately, quantum mechanical simulations based on time-dependent Kohn-Sham density functional theory (TD-KSDFT) are computationally too expensive to tackle metal particles larger than 2 nm. Herein, we present a time-dependent orbital-free density functional theory (TD-OFDFT) that accurately captures the dynamic response of electrons in the presence of realistic ionic potentials. The TD-OFDFT method offers a comparable accuracy as TD-KSDFT but with a much lower computational cost. Using TD-OFDFT, we study size-dependent LSPRs on Na nanoparticles with diameters from 0.7 to 12.3 nm. The optical absorption spectra exhibit a nonmonotonic behavior from blue shift to red shift and back to blue shift as the particle size decreases. Three principal plasmon modes are identified, and their physical origins are elucidated. Competing physical mechanisms responsible for the nonmonotonic size dependence are discussed. The TD-OFDFT provides a unified theoretical framework that bridges the gap between classical electromagnetic theory and quantum mechanical theory for plasmonics and nanophotonics.

Nonlocal response of metallic nanospheres probed by light, electrons, and atoms

Inspired by recent measurements on individual metallic nanospheres that cannot 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, and Mie-Lorenz theory is applied for each case. Nonlocal response shows its mark in all three configurations, but for the two near-field measurements, we predict especially pronounced nonlocal effects that are not exhibited in far-field measurements. Associated with every multipole order is not only a single blueshifted surface plasmon but also an infinite series of bulk plasmons that have no counterpart in a local-response approximation. We show that these increasingly blueshifted multipole plasmons become spectrally more prominent at shorter probe-to-surface separations and for decreasing nanosphere radii. For selected metals, we predict hydrodynamic multipolar plasmons to be measurable on single nanospheres.

Plexciton quenching by resonant electron transfer from quantum emitter to metallic nanoantenna

Coupling molecular excitons and localized surface plasmons in hybrid nanostructures leads to appealing, tunable optical properties. In this respect, the knowledge about the excitation dynamics of a quantum emitter close to a plasmonic nanoantenna is of importance from fundamental and practical points of view. We address here the effect of the excited electron tunneling from the emitter into a metallic nanoparticle(s) in the optical response. When close to a plasmonic nanoparticle, the excited state localized on a quantum emitter becomes short-lived because of the electronic coupling with metal conduction band states. We show that as a consequence, the characteristic features associated with the quantum emitter disappear from the optical absorption spectrum. Thus, for the hybrid nanostructure studied here and comprising quantum emitter in the narrow gap of a plasmonic dimer nanoantenna, the quantum tunneling might quench the plexcitonic states. Under certain conditions the optical response of the system approaches that of the individual plasmonic dimer. Excitation decay via resonant electron transfer can play an important role in many situations of interest such as in surface-enhanced spectroscopies, photovoltaics, catalysis, or quantum information, among others.

Quantum plasmonics: optical properties of a nanomatryushka

Quantum mechanical effects can significantly reduce the plasmon-induced field enhancements around nanoparticles. Here we present a quantum mechanical investigation of the plasmon resonances in a nanomatryushka, which is a concentric core-shell nanoparticle consisting of a solid metallic core encapsulated in a thin metallic shell. We compute the optical response using the time-dependent density functional theory and compare the results with predictions based on the classical electromagnetic theory. We find strong quantum mechanical effects for core-shell spacings below 5 Å, a regime where both the absorption cross section and the local field enhancements differ significantly from the classical predictions. We also show that the workfunction of the metal is a crucial parameter determining the onset and magnitude of quantum effects. For metals with lower workfunctions such as aluminum, the quantum effects are found to be significantly more pronounced than for a noble metal such as gold.

Quantum effects and nonlocality in strongly coupled plasmonic nanowire dimers

Using a fully quantum mechanical approach we study the optical response of a strongly coupled metallic nanowire dimer for variable separation widths of the junction between the nanowires. The translational invariance of the system allows to apply the time-dependent density functional theory (TDDFT) for nanowires of diameters up to 10 nm which is the largest size considered so far in quantum modeling of plasmonic dimers. By performing a detailed analysis of the optical extinction, induced charge densities, and near fields, we reveal the major nonlocal quantum effects determining the plasmonic modes and field enhancement in the system. These effects consist mainly of electron tunneling between the nanowires at small junction widths and dynamical screening. The TDDFT results are compared with results from classical electromagnetic calculations based on the local Drude and non-local hydrodynamic descriptions of the nanowire permittivity, as well as with results from a recently developed quantum corrected model. The latter provides a way to include quantum mechanical effects such as electron tunneling in standard classical electromagnetic simulations. We show that the TDDFT results can be thus retrieved semi-quantitatively within a classical framework. We also discuss the shortcomings of classical non-local hydrodynamic approaches. Finally, the implications of the actual position of the screening charge density at the gap interfaces are discussed in connection with plasmon ruler applications at subnanometric distances.

Nonlocal propagation and tunnelling of surface plasmons in metallic hourglass waveguides

The nanofocusing performance of hourglass plasmonic waveguides is studied analytically and numerically. Nonlocal effects in the linearly tapered metal-air-metal stack that makes up the device are taken into account within a hydrodynamical approach. Using this hourglass waveguide as a model structure, we show that spatial dispersion drastically modifies the propagation of surface plasmons in metal voids, such as those generated between touching particles. Specifically, we investigate how nonlocal corrections limit the enormous field enhancements predicted by local electromagnetic treatments of geometric singularities. Finally, our results also indicate the emergence of nonlocality assisted tunnelling of plasmonic modes across hourglass contacts as thick as 0.5 nm.

Probing of optical near-fields by electron Rescattering on the 1 nm scale

We present a new method of measuring optical near-fields within ~1 nm of a metal surface based on rescattering of photoemitted electrons. With this method, we precisely measure the field enhancement factor for tungsten and gold nanotips as a function of tip radius. The agreement with Maxwell simulations is very good. Further simulations yield a field enhancement map for all materials, which shows that optical near-fields at nanotips are governed by a geometric effect under most conditions, while plasmon resonances play only a minor role. Last, we consider the implications of our results on quantum mechanical effects near the surface of nanostructures and discuss features of quantum plasmonics.

Surface plasmons and nonlocality: a simple model

Surface plasmons on metals can concentrate light into subnanometric volumes and on these near atomic length scales the electronic response at the metal interface is smeared out over a Thomas-Fermi screening length. This nonlocality is a barrier to a good understanding of atomic scale response to light and complicates the practical matter of computing the fields. In this Letter, we present a local analogue model and show that spatial nonlocality can be represented by replacing the nonlocal metal with a composite material, comprising a thin dielectric layer on top of a local metal. This method not only makes possible the quantitative analysis of nonlocal effects in complex plasmonic phenomena with unprecedented simplicity and physical insight, but also offers great practical advantages in their numerical treatment.

Electron-energy loss study of nonlocal effects in connected plasmonic nanoprisms

We investigate the emergence of nonlocal effects in plasmonic nanostructures through electron-energy loss spectroscopy. To theoretically describe the spatial dispersion in the metal permittivity, we develop a full three-dimensional nonlocal hydrodynamic solution of Maxwell's equations in frequency domain that implements the electron beam as a line current source. We use our numerical approach to perform an exhaustive analysis of the impact of nonlocality in the plasmonic response of single triangular prisms and connected bowtie dimers. Our results demonstrate the complexity of the interplay between nonlocal and geometric effects taking place in these structures. We show the different sensitivities to both effects of the various plasmonic modes supported by these systems. Finally, we present an experimental electron-energy loss study on gold nanoprisms connected by bridges as narrow as 1.6 nm. The comparison with our theoretical predictions enables us to reveal in a phenomenological fashion the enhancement of absorption damping that occurs in these atomistic junctions due to quantum confinement and grain boundary electron scattering.