Transformation-optics description of nonlocal effects in plasmonic nanostructures

Impact of Surface Enhanced Raman Spectroscopy in Catalysis

Catalysis stands as an indispensable cornerstone of modern society, underpinning the production of over 80% of manufactured goods and driving over 90% of industrial chemical processes. As the demand for more efficient and sustainable processes grows, better catalysts are needed. Understanding the working principles of catalysts is key, and over the last 50 years, surface-enhanced Raman Spectroscopy (SERS) has become essential. Discovered in 1974, SERS has evolved into a mature and powerful analytical tool, transforming the way in which we detect molecules across disciplines. In catalysis, SERS has enabled insights into dynamic surface phenomena, facilitating the monitoring of the catalyst structure, adsorbate interactions, and reaction kinetics at very high spatial and temporal resolutions. This review explores the achievements as well as the future potential of SERS in the field of catalysis and energy conversion, thereby highlighting its role in advancing these critical areas of research.

Superanomalous skin-effect and enhanced absorption of light scattered on conductive media

Light scattering spectroscopy is a powerful tool for studying various media, but interpretation of its results requires a detailed knowledge of how media excitations are coupled to electromagnetic waves. In electrically conducting media, an accurate description of propagating electromagnetic waves is a non-trivial problem because of non-local light-matter interactions. Among other consequences, the non-locality gives rise to the anomalous (ASE) and superanomalous (SASE) skin effects. As is well known, ASE is related to an increase in the electromagnetic field absorption in the radio frequency domain. This work demonstrates that the Landau damping underlying SASE gives rise to another absorption peak at optical frequencies. In contrast to ASE, SASE suppresses only the longitudinal field component, and this difference results in the strong polarization dependence of the absorption. The mechanism behind the suppression is generic and is observed also in plasma. Neither SASE, nor the corresponding light absorption increase can be described using popular simplified models for the non-local dielectric response.

Spatially modulated light harvesting with plasmonic crescent metasurface

Harvesting light by metallic structures with sharp corners, or the so-called photonic singularities, has exhibit their potential in nanophotonics, sensing, and bio-medical applications. The high-quality light confinement of the light energy mainly relies on the precise preparation of nanoscale photonic singularities. However, the realization of massive photonic singularities still meets the challenges on integration and low-cost mask multiplexing. Here, we show an angle-dependent elevated nanosphere lithography to achieve massive photonic singularities for spatially modulated light harvesting at the near-infrared regime. The photonic geometrical singularity is constructed by the gold crescent array of plasmonic materials. The numerical simulation shows that the light can be localized at the spatially distributed singularities. This phenomenon is verified experimentally through the infrared spectral measurement. Our work provides the possibility to produce integrated light-harvesting devices for numerous optical applications in illumination, display, and enhanced nonlinear excitation.

Madelung Formalism for Electron Spill-Out in Nonlocal Nanoplasmonics

Current multiscale plasmonic systems pose a modeling challenge. Classical macroscopic theories fail to capture quantum effects in such systems, whereas quantum electrodynamics is impractical given the total size of the experimentally relevant systems, as the number of interactions is too large to be addressed one by one. To tackle the challenge, in this paper we propose to use the Madelung form of the hydrodynamic Drude model, in which the quantum effect electron spill-out is incorporated by describing the metal-dielectric interface using a super-Gaussian function. The results for a two-dimensional nanoplasmonic wedge are correlated to those from nonlocal full-wave numerical calculations based on a linearized hydrodynamic Drude model commonly employed in the literature, showing good qualitative agreement. Additionally, a conformal transformation perspective is provided to explain qualitatively the findings. The methodology described here may be applied to understand, both numerically and theoretically, the modular inclusions of additional quantum effects, such as electron spill-out and nonlocality, that cannot be incorporated seamlessly by using other approaches.

Tunable SERS Enhancement via Sub-nanometer Gap Metasurfaces

Raman sensing is a powerful technique for detecting chemical signatures, especially when combined with optical enhancement techniques such as using substrates containing plasmonic nanostructures. In this work, we successfully demonstrated surface-enhanced Raman spectroscopy (SERS) of two analytes adsorbed onto gold nanosphere metasurfaces with tunable subnanometer gap widths. These metasurfaces, which push the bounds of previously studied SERS nanostructure feature sizes, were fabricated with precise control of the intersphere gap width to within 1 nm for gaps close to and below 1 nm. Analyte Raman spectra were measured for samples for a range of gap widths, and the surface-affected signal enhancement was found to increase with decreasing gap width, as expected and corroborated via electromagnetic field modeling. Interestingly, an enhancement quenching effect was observed below gaps of around 1 nm. We believe this to be one of the few studies of gap-width-dependent SERS for the subnanometer range, and the results suggest the potential of such methods as a probe of subnanometer scale effects at the interface between plasmonic nanostructures. With further study, we believe that tunable sub-nanometer gap metasurfaces could be a useful tool for the study of nonlocal and quantum enhancement-quenching effects. This could aid the development of optimized Raman-based sensors for a variety of applications.

Towards realistic modeling of plasmonic nanostructures: a comparative study to determine the impact of optical effects on solar cell improvement

Plasmonic structures may improve cell performance in a variety of ways. More accurate determining of the optical influence, unlike ideal simulations, requires modeling closer to experimental cases. In this modeling and simulation, irregular nanostructures were chosen and divided into three groups and some modes. For each mode, different sizes of nanoparticles were randomly selected, which could result in pre-determined average particle size and standard deviation. By 3D finite-difference time-domain (3D-FDTD), the optical plasmonic properties of that mode in a solar cell structure were investigated when the nanostructure was added to the buffer/active layer of the organic solar cell. The far- and near-field results were used to compare the plasmonic behavior, relying on the material and geometry. By detailed simulations, Al and Ag nanostructure at the interface of the ZnO/active layer can improve organic solar cell performance optically, especially by the near-field effect. Unlike Au and relative Ag, the Al nanostructured sample showed less parasitic absorption loss.

SUPPLEMENTARY INFORMATION

The online version contains supplementary material available at 10.1007/s10825-021-01829-x.

Polaritonic quantization in nonlocal polar materials

In the Reststrahlen region, between the transverse and longitudinal phonon frequencies, polar dielectric materials respond metallically to light, and the resulting strong light-matter interactions can lead to the formation of hybrid quasiparticles termed surface phonon polaritons. Recent works have demonstrated that when an optical system contains nanoscale polar elements, these excitations can acquire a longitudinal field component as a result of the material dispersion of the lattice, leading to the formation of secondary quasiparticles termed longitudinal-transverse polaritons. In this work, we build on previous macroscopic electromagnetic theories, developing a full second-quantized theory of longitudinal-transverse polaritons. Beginning from the Hamiltonian of the light-matter system, we treat distortion to the lattice, introducing an elastic free energy. We then diagonalize the Hamiltonian, demonstrating that the equations of motion for the polariton are equivalent to those of macroscopic electromagnetism and quantize the nonlocal operators. Finally, we demonstrate how to reconstruct the electromagnetic fields in terms of the polariton states and explore polariton induced enhancements of the Purcell factor. These results demonstrate how nonlocality can narrow, enhance, and spectrally tune near-field emission with applications in mid-infrared sensing.

Impact of Nonlocality on Group Delay and Reflective Behavior Near Surface Plasmon Resonances in Otto Structure

In this work, we study the effects of nonlocality on the optical response near surface plasmon resonance of the Otto structure, and such nonlocality is considered in the hydrodynamic model. Through analyzing the dispersion relations and optical response predicted by the Drude’s and hydrodynamic model in the system, we find that the nonlocal effect is sensitive to the large propagation wavevector, and there exists a critical incident angle and thickness. The critical point moves to the smaller value when the nonlocal effect is taken into account. Before this point, the absorption of the reflected light pulse enhances; however, the situation reverses after this point. In the region between the two different critical points in the frequency scan calculated from local and nonlocal theories, the group delay of the reflected light pulse shows opposite behaviors. These results are explained in terms of the pole and zero phenomenological model in complex frequency plane. Our work may contribute to the fundamental understanding of light–matter interactions at the nanoscale and in the design of optical devices.

Electron Spill-Out Effect in Singular Metasurfaces

The electron spill-out effect is considered in a singular metasurface. Using the hydrodynamic model, we found that electron spill-out effectively smears the sharp singularity. The introduction of the electron spill-out effect also significantly changes the reflection spectrum, charge distribution, field profile for a singular metasurface. Therefore, this spill-out contribution is crucial and cannot be ignored for a realistic description of optical response in a singular system.

Sum frequency generation from touching wires: a transformation optics approach

We employ transformation optics to study analytically nonlinear wave mixing from a singular geometry of touching plasmonic wires. We obtain the analytic solution of the near field and complement it with a solution of far-field properties. We find, somewhat surprisingly, that optimal efficiency (in both regimes) is obtained for the degenerate case of second-harmonic generation. We exploit the analytic solution obtained to trace this behavior to the spatial overlap of input fields near the geometric singularity.

Nonreciprocal and Topological Plasmonics

Metals, semiconductors, metamaterials, and various two-dimensional materials with plasmonic dispersion exhibit numerous exotic physical effects in the presence of an external bias, for example an external static magnetic field or electric current. These physical phenomena range from Faraday rotation of light propagating in the bulk to strong confinement and directionality of guided modes on the surface and are a consequence of the breaking of Lorentz reciprocity in these systems. The recent introduction of relevant concepts of topological physics, translated from condensed-matter systems to photonics, has not only given a new perspective on some of these topics by relating certain bulk properties of plasmonic media to the surface phenomena, but has also led to the discovery of new regimes of truly unidirectional, backscattering-immune, surface-wave propagation. In this article, we briefly review the concepts of nonreciprocity and topology and describe their manifestation in plasmonic materials. Furthermore, we use these concepts to classify and discuss the different classes of guided surface modes existing on the interfaces of various plasmonic systems.

Functional Charge Transfer Plasmon Metadevices

Reducing the capacitive opening between subwavelength metallic objects down to atomic scales or bridging the gap by a conductive path reveals new plasmonic spectral features, known as charge transfer plasmon (CTP). We review the origin, properties, and trending applications of this modes and show how they can be well-understood by classical electrodynamics and quantum mechanics principles. Particularly important is the excitation mechanisms and practical approaches of such a unique resonance in tailoring high-response and efficient extreme-subwavelength hybrid nanophotonic devices. While the quantum tunneling-induced CTP mode possesses the ability to turn on and off the charge transition by varying the intensity of an external light source, the excited CTP in conductively bridged plasmonic systems suffers from the lack of tunability. To address this, the integration of bulk plasmonic nanostructures with optothermally and optoelectronically controllable components has been introduced as promising techniques for developing multifunctional and high-performance CTP-resonant tools. Ultimate tunable plasmonic devices such as metamodulators and metafilters are thus in prospect.

A general theoretical and experimental framework for nanoscale electromagnetism

The macroscopic electromagnetic boundary conditions, which have been established for over a century¹, are essential for the understanding of photonics at macroscopic length scales. Even state-of-the-art nanoplasmonic studies^2-4, exemplars of extremely interface-localized fields, rely on their validity. This classical description, however, neglects the intrinsic electronic length scales (of the order of ångström) associated with interfaces, leading to considerable discrepancies between classical predictions and experimental observations in systems with deeply nanoscale feature sizes, which are typically evident below about 10 to 20 nanometres^5-10. The onset of these discrepancies has a mesoscopic character: it lies between the granular microscopic (electronic-scale) and continuous macroscopic (wavelength-scale) domains. Existing top-down phenomenological approaches deal only with individual aspects of these omissions, such as nonlocality^11-13 and local-response spill-out^14,15. Alternatively, bottom-up first-principles approaches-for example, time-dependent density functional theory^16,17-are severely constrained by computational demands and thus become impractical for multiscale problems. Consequently, a general and unified framework for nanoscale electromagnetism remains absent. Here we introduce and experimentally demonstrate such a framework-amenable to both analytics and numerics, and applicable to multiscale problems-that reintroduces the electronic length scale via surface-response functions known as Feibelman d parameters^18,19. We establish an experimental procedure to measure these complex dispersive surface-response functions, using quasi-normal-mode perturbation theory and observations of pronounced nonclassical effects. We observe nonclassical spectral shifts in excess of 30 per cent and the breakdown of Kreibig-like broadening in a quintessential multiscale architecture: film-coupled nanoresonators, with feature sizes comparable to both the wavelength and the electronic length scale. Our results provide a general framework for modelling and understanding nanoscale (that is, all relevant length scales above about 1 nanometre) electromagnetic phenomena.

Probing the in-Plane Near-Field Enhancement Limit in a Plasmonic Particle-on-Film Nanocavity with Surface-Enhanced Raman Spectroscopy of Graphene

When the geometric features of plasmonic nanostructures approach the subnanometric regime, nonlocal screening and charge spill-out of metallic electrons will strongly modify the optical responses of the structures. While quantum tunneling resulting from charge spill-out has been widely discussed in the literature, the near-field enhancement saturation caused by the nonlocal screening effect still lacks a direct experimental verification. In this work, we use surface-enhanced Raman spectroscopy (SERS) of graphene to probe the in-plane near-field enhancement limit in gold nanosphere-on-film nanocavities where different layers of graphene are sandwiched between a gold nanosphere and a gold film. Together with advanced transmission electron microscopy cross-sectional imaging and nonlocal hydrodynamic theoretical calculations, the cavity gap width correlated SERS and dark-field scattering measurements reveal that the intrinsic nonlocal dielectric response of gold limits the near-field enhancement factors and mitigates the plasmon resonance red-shift with decreasing the gap width to less than one nanometer. Our results not only verify previous theoretical predictions in both the near-field and far-field regime but also demonstrate the feasibility of controlling the near- and far-field optical response in such versatile plasmonic particle-graphene-on-film nanocavities, which can find great potential in applications of graphene-based photonic devices in the visible and near-infrared region.

Electronic-dimensionality reduction of bulk MoS2 by hydrogen treatment

A reduction in the electronic-dimensionality of materials is one method for achieving improvements in material properties. Here, a reduction in electronic-dimensionality is demonstrated using a simple hydrogen treatment technique. Quantum well states from hydrogen-treated bulk 2H-MoS2 are observed using angle resolved photoemission spectroscopy (ARPES). The electronic states are confined within a few MoS2 layers after the hydrogen treatment. A significant reduction in the band-gap can also be achieved after the hydrogen treatment, and both phenomena can be explained by the formation of sulfur vacancies generated by the chemical reaction between sulfur and hydrogen.

An eigenvalue approach to quantum plasmonics based on a self-consistent hydrodynamics method

Plasmonics has attracted much attention not only because it has useful properties such as strong field enhancement, but also because it reveals the quantum nature of matter. To handle quantum plasmonics effects, ab initio packages or empirical Feibelman d-parameters have been used to explore the quantum correction of plasmonic resonances. However, most of these methods are formulated within the quasi-static framework. The self-consistent hydrodynamics model offers a reliable approach to study quantum plasmonics because it can incorporate the quantum effect of the electron gas into classical electrodynamics in a consistent manner. Instead of the standard scattering method, we formulate the self-consistent hydrodynamics method as an eigenvalue problem to study quantum plasmonics with electrons and photons treated on the same footing. We find that the eigenvalue approach must involve a global operator, which originates from the energy functional of the electron gas. This manifests the intrinsic nonlocality of the response of quantum plasmonic resonances. Our model gives the analytical forms of quantum corrections to plasmonic modes, incorporating quantum electron spill-out effects and electrodynamical retardation. We apply our method to study the quantum surface plasmon polariton for a single flat interface.

Superanomalous Skin Effect for Surface Plasmon Polaritons

It is commonly assumed that surface plasmon-polariton (SPP) excitations on a metal-dielectric interface decay exponentially inside the metallic sample. Here, we show that in a wide spectral interval the SPP field decays much slower, being inversely proportional to the distance to the interface modified by an additional logarithmic factor. This dependence differs from the standard anomalous skin effect and is provisionally referred to as superanomalous. Its origin is the nonlocality and the logarithmic singularity of the dielectric permittivity in metals. This type of decay is pronounced for SPP modes of higher frequencies, but it is suppressed for light waves.

Perfectly matched layers for nonlocal media with hydrodynamic-Drude description: a transformation optics approach

We develop a transformation optics theory for the nonlocal media in the hydrodynamic Drude model by generalizing the free-electron current density equation to a transformation invariant form. Applying the transformation optics theory, perfectly matched layers (PMLs) for the nonlocal media are theoretically formulated and implemented in frequency domain with finite element method. The nonlocal PMLs are shown to absorb outgoing surface and volume plasmons without inducing unphysical reflections. The effectiveness of the nonlocal PMLs is quantitatively demonstrated by the behaviors that the numerical errors continuously approach zero with increasing linear mesh density.

Ultrathin metasurface-based carpet cloak for terahertz wave

Ultrathin metasurfaces with local phase compensation deliver new schemes to cloaking devices. Here, a large-scale carpet cloak consisting of an ultrathin metasurface is demonstrated numerically and experimentally in the terahertz regime. The proposed carpet cloak is designed based on discontinuous-phase metallic resonators fabricated on a polyimide substrate, offering a wide range of reflection phase variations and an excellent wavefront manipulation along the edges of the bump. The invisibility is verified when the cloak is placed on a reflecting triangular surface (bump). The multi-step discrete phase design method would greatly simplify the design process and is probable to achieve large-dimension cloaks, for applications in radar and antenna systems as a thin, lightweight, and easy-to-fabricate solution for radio and terahertz frequencies.

Optical Observation of Plasmonic Nonlocal Effects in a 2D Superlattice of Ultrasmall Gold Nanoparticles

The advances in recent nanofabrication techniques have facilitated explorations of metal structures into nanometer scales, where the traditional local-response Drude model with hard-wall boundary conditions fails to accurately describe their optical responses. The emerging nonlocal effects in single ultrasmall silver nanoparticles have been experimentally observed in single-particle spectroscopy enabled by the unprecedented high spatial resolution of electron energy loss spectroscopy (EELS). However, the unambiguous optical observation of such new effects in gold nanoparticles has yet not been reported, due to the extremely weak scattering and the obscuring fingerprint of strong interband transitions. Here we present a nanosystem, a superlattice monolayer formed by sub-10 nm gold nanoparticles. Plasmon resonances are spectrally well-separated from interband transitions, while exhibiting clearly distinguishable blueshifts compared to predictions by the classical local-response model. Our far-field spectroscopy was performed by a standard optical transmission and reflection setup, and the results agreed excellently with the hydrodynamic nonlocal model, opening a simple and widely accessible way for addressing quantum effects in nanoplasmonic systems.

Rapidly fabricating large-scale plasmonic silver nanosphere arrays with sub-20 nm gap on Si-pyramids by inverted annealing for highly sensitive SERS detection

An inverted annealing method is developed to fabricate rapidly plasmonic silver nanosphere arrays with sub-20 nm gaps for highly sensitive SERS detection.

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.

Ultratransparent Media and Transformation Optics with Shifted Spatial Dispersions

By using pure dielectric photonic crystals, we demonstrate the realization of ultratransparent media, which allow near 100% transmission of light for all incident angles and create aberration-free virtual images. The ultratransparency effect is well explained by spatially dispersive effective medium theory for photonic crystals, and verified by both simulations and proof-of-principle microwave experiments. Designed with shifted elliptical equal frequency contours, such ultratransparent media not only provide a low-loss and feasible platform for transformation optics devices at optical frequencies, but also enable new freedom for phase manipulation beyond the local medium framework.

Transformation Optics: A Time- and Frequency-Domain Analysis of Electron-Energy Loss Spectroscopy

Electron energy loss spectroscopy (EELS) and cathodoluminescence (CL) play a pivotal role in many of the cutting edge experiments in plasmonics. EELS and CL experiments are usually supported by numerical simulations, which-though accurate-may not provide as much physical insight as analytical calculations do. Fully analytical solutions to EELS and CL systems in plasmonics are rare and difficult to obtain. This paper aims to narrow this gap by introducing a new method based on transformation optics that allows to calculate the quasistatic frequency- and time-domain response of plasmonic particles under electron beam excitation. We study a nonconcentric annulus (and ellipse in the Supporting Information ) as an example.

Surface plasmon resonances of arbitrarily shaped nanometallic structures in the small-screening-length limit

According to the hydrodynamic Drude model, surface plasmon resonances of metallic nanostructures blueshift owing to the non-local response of the metal's electron gas. The screening length characterizing the non-local effect is often small relative to the overall dimensions of the metallic structure, which enables us to derive a coarse-grained non-local description using matched asymptotic expansions; a perturbation theory for the blueshifts of arbitrary-shaped nanometallic structures is then developed. The effect of non-locality is not always a perturbation and we present a detailed analysis of the 'bonding' modes of a dimer of nearly touching nanowires where the leading-order eigenfrequencies and eigenmode distributions are shown to be a renormalization of those predicted assuming a local metal permittivity.

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.

Classification of scalar and dyadic nonlocal optical response models

Nonlocal optical response is one of the emerging effects on the nanoscale for particles made of metals or doped semiconductors. Here we classify and compare both scalar and tensorial nonlocal response models. In the latter case the nonlocality can stem from either the longitudinal response, the transverse response, or both. In phenomenological scalar models the nonlocal response is described as a smearing out of the commonly assumed infinitely localized response, as characterized by a distribution with a finite width. Here we calculate explicitly whether and how tensorial models, such as the hydrodynamic Drude model and generalized nonlocal optical response theory, follow this phenomenological description. We find considerable differences, for example that nonlocal response functions, in contrast to simple distributions, assume negative and complex values. Moreover, nonlocal response regularizes some but not all diverging optical near fields. We identify the scalar model that comes closest to the hydrodynamic model. Interestingly, for the hydrodynamic Drude model we find that actually only one third (1/3) of the free-electron response is smeared out nonlocally. In that sense, nonlocal response is stronger for transverse and scalar nonlocal response models, where the smeared-out fractions are 2/3 and 3/3, respectively. The latter two models seem to predict novel plasmonic resonances also below the plasma frequency, in contrast to the hydrodynamic model that predicts standing pressure waves only above the plasma frequency.

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.

Resonance shifts and spill-out effects in self-consistent hydrodynamic nanoplasmonics

The standard hydrodynamic Drude model with hard-wall boundary conditions can give accurate quantitative predictions for the optical response of noble-metal nanoparticles. However, it is less accurate for other metallic nanosystems, where surface effects due to electron density spill-out in free space cannot be neglected. Here we address the fundamental question whether the description of surface effects in plasmonics necessarily requires a fully quantum-mechanical ab initio approach. We present a self-consistent hydrodynamic model (SC-HDM), where both the ground state and the excited state properties of an inhomogeneous electron gas can be determined. With this method we are able to explain the size-dependent surface resonance shifts of Na and Ag nanowires and nanospheres. The results we obtain are in good agreement with experiments and more advanced quantum methods. The SC-HDM gives accurate results with modest computational effort, and can be applied to arbitrary nanoplasmonic systems of much larger sizes than accessible with ab initio methods.

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.

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.

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.

Nonlocal study of ultimate plasmon hybridization

Within our recently proposed generalized nonlocal optical response (GNOR) model, where nonlocal response is included by taking into account both convective and diffusive currents of the conduction electrons, we revisit the fundamental problem of an optically excited plasmonic dimer. We consider the transition from separated dimers via touching dimers to finally overlapping dimers. In particular, we focus on the touching case, showing a fundamental limit on the hybridization of the bonding plasmon modes due to nonlocality. Using transformation optics, we determine a simple analytical equation for the resonance energies.

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.

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.

Surface plasmon dependence on the electron density profile at metal surfaces

We use an extension of the hydrodynamic model to study nonlocal effects in the collective plasmon excitations at metal surfaces and narrow gaps between metals, including the surface spill-out of conduction band electrons. In particular, we simulate metal surfaces consisting of a smooth conduction-electron density profile and an abrupt jellium edge. We focus on aluminum and gold as prototypical examples of simple and noble metals, respectively. Our calculations agree with the dispersion relations measured from planar surfaces for these materials. Systems involving small gaps display a regime of tunnelling electrons, which is partially captured by the overlap of electron densities. This extension of the hydrodynamic model to cope with inhomogeneous density profiles provides a relatively fast and accurate way of describing the optical response of metal surfaces at subnanometer distances.

Full-wave electromagentic analysis of a plasmonic nanoparticle separated from a plasmonic film by a thin spacer layer

This paper presents a theoretical analysis of the electromagnetic response of a plasmonic nanoparticle-spacer-plasmonic film system. The physical system consists of a spherical nanoparticle of a plasmonic material such as gold or silver over a plasmonic metal film and separated from the same by a dielectric spacer material. This paper presents a complete analytical solution of the Maxwell's equations, to determine the optical fields near the gold nanoparticle. It was found that the electromagnetic fields in between the plasmonic nanoparticle and the plasmonic film are extremely sensitive to the spacing between the nanoparticle and the film. This could enable the use of such a system for various sensing applications. The non-local nature of the plasmonic medium was also included in our analysis and it's effect on the resonances of the system was studied. The analytical solution was compared with an independent numerical method, the Finite Difference Time Domain (FDTD) method, to demonstrate the accuracy of the solution.

Effects of surface roughness of Ag thin films on surface-enhanced Raman spectroscopy of graphene: spatial nonlocality and physisorption strain

Metallic nanostructures are widely used for surface-enhanced Raman spectroscopy (SERS). Nanoscale surface corrugation significantly affects the localized plasmon response and the subsequent Raman intensity of the molecules in close proximity to the nanostructures. Experimentally, the surface roughness of metal films can be controlled by adjusting the deposition conditions, and the resulting localized near-field properties can be probed by measuring the Raman spectrum of the conformally coated monolayer graphene. The well-known Raman characteristics of graphene and its atomic-level 2D nature make it an ideal test-bed for SERS measurements on corrugated metal films. In this work, we experimentally and theoretically study the effects of surface roughness of Ag thin films on the SERS of graphene. We find that the nonlocality effect of the metal dielectric response has to be taken into account for more accurate prediction of the SERS enhancement at large surface roughness. Our results also reveal that the effect of physisorption strain should be included to understand the Raman peak shift and spectral broadening. These observations are fundamentally important for understanding the SERS from metallic nanostructures with sub-nanoscale corrugation.

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.

Blueshift of the surface plasmon resonance in silver nanoparticles: substrate effects

We study the blueshift of the surface plasmon (SP) resonance energy of isolated Ag nanoparticles with decreasing particle diameter, which we recently measured using electron energy loss spectroscopy (EELS) [1]. As the particle diameter decreases from 26 down to 3.5 nm, a large blueshift of 0.5 eV of the SP resonance energy is observed. In this paper, we base our theoretical interpretation of our experimental findings on the nonlocal hydrodynamic model, and compare the effect of the substrate on the SP resonance energy to the approach of an effective homogeneous background permittivity. We derive the nonlocal polarizability of a small metal sphere embedded in a homogeneous dielectric environment, leading to the nonlocal generalization of the classical Clausius-Mossotti factor. We also present an exact formalism based on multipole expansions and scattering matrices to determine the optical response of a metal sphere on a dielectric substrate of finite thickness, taking into account retardation and nonlocal effects. We find that the substrate-based calculations show a similar-sized blueshift as calculations based on a sphere in a homogeneous environment, and that they both agree qualitatively with the EELS measurements.

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.