Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response

Ab Initio Atomistic Characterization of Confined Bulk and Bennett Plasmons in Metallic Nanoparticles as Probed by Penetrating Electrons

Despite the experimental observation of confined bulk plasmons (CBPs) in metallic nanostructures using electron energy-loss spectroscopy (EELS), there is still a limited theoretical understanding of their resonance structure when they are excited by penetrating electron beams. In this work, we use atomistic ab initio time-dependent density functional theory (TDDFT) to perform a first-principles study of the excitation of CBPs induced by swift electrons. Our quantum approach offers a parameter-free framework for the calculation of the EEL spectra of metallic nanoparticles with atomistic resolution, while jellium TDDFT and classical hydrodynamic calculations allow us to unravel the rich spectral pattern associated with CBPs. Additionally, the excitation of high-energy surface resonances characterized by an induced dipole moment across the nanoparticle surface, known as Bennett modes, is also explored. This study represents a significant step forward in the exploration of plasmonic signatures in the EELS of metallic nanoparticles.

A Computational Maxwell Solver for Nonlocal Feibelman Parameters in Plasmonics

Feibelman parameters provide a convenient means to account for quantum surface effects in classical Maxwell descriptions. Recent work has shown that for incoming fields with spatial variations in the nanometer range, for instance those produced by quantum emitters in the vicinity of metallic nanoparticles, nonlocality in the directions parallel to the interface must be considered. Here we develop the methodology for mesoscopic boundary conditions incorporating nonlocal Feibelman parameters, and show how to implement them in a computational Maxwell solver based on the boundary element method. We compare our results with Mie solutions for single and coupled spheres, and find very good agreement throughout.

Boosting Light-Matter Interactions in Plasmonic Nanogaps

Plasmonic nanogaps in strongly coupled metal nanostructures can confine light to nanoscale regions, leading to huge electric field enhancement. This unique capability makes plasmonic nanogaps powerful platforms for boosting light-matter interactions, thereby enabling the rapid development of novel phenomena and applications. This review traces the progress of nanogap systems characterized by well-defined morphologies, controllable optical responses, and a focus on achieving extreme performance. The properties of plasmonic gap modes in far-field resonance and near-field enhancement are explored and a detailed comparative analysis of nanogap fabrication techniques down to sub-nanometer scales is provided, including bottom-up, top-down, and their combined approaches. Additionally, recent advancements and applications across various frontier research areas are highlighted, including surface-enhanced spectroscopy, plasmon-exciton strong coupling, nonlinear optics, optoelectronic devices, and other applications beyond photonics. Finally, the challenges and promising emerging directions in the field are discussed, such as light-driven atomic effects, molecular optomechanics, and alternative new materials.

Nonlocal effects in plasmon-emitter interactions

Nonlocal and quantum mechanical phenomena in noble metal nanostructures become increasingly crucial when the relevant length scales in hybrid nanostructures reach the few-nanometer regime. In practice, such mesoscopic effects at metal-dielectric interfaces can be described using exemplary surface-response functions (SRFs) embodied by the Feibelman d-parameters. Here we show that SRFs dramatically influence quantum electrodynamic phenomena - such as the Purcell enhancement and Lamb shift - for quantum light emitters close to a diverse range of noble metal nanostructures interfacing different homogeneous media. Dielectric environments with higher permittivities are shown to increase the magnitude of SRFs calculated within the specular-reflection model. In parallel, the role of SRFs is enhanced in noble metal nanostructures characterized by large surface-to-volume ratios, such as thin planar metallic films or shells of core-shell nanoparticles, for which the spill-in of electron wave functions enhances plasmon hybridization. By investigating emitter quantum dynamics close to such plasmonic architectures, we show that decreasing the width of the metal region, or increasing the permittivity of the interfacing dielectric, leads to a significant change in the Purcell enhancement, Lamb shift, and visible far-field spontaneous emission spectrum, as an immediate consequence of SRFs. We anticipate that fitting the theoretically modelled spectra to experiments could allow for experimental determination of the d-parameters.

Footprints of atomic-scale features in plasmonic nanoparticles as revealed by electron energy loss spectroscopy

We present a first-principles theoretical study of the atomistic footprints in the valence electron energy loss spectroscopy (EELS) of nanometer-size metallic particles. Charge density maps of excited plasmons and EEL spectra for specific electron paths through a nanoparticle (Na380 atom cluster) are modeled using ab initio calculations within time-dependent density functional theory. Our findings unveil the atomic-scale sensitivity of EELS within this low-energy spectral range. Whereas localized surface plasmons (LSPs) are particularly sensitive to the atomistic structure of the surface probed by the electron beam, confined bulk plasmons (CBPs) reveal quantum size effects within the nanoparticle's volume. Moreover, we prove that classical local dielectric theories mimicking the atomistic structure of the nanoparticles reproduce the LSP trends observed in quantum calculations, but fall short in describing the CBP behavior observed under different electron trajectories.

Hot carrier creation in a nanoparticle dimer-molecule composite

Light-matter interactions have garnered considerable interest owing to their burgeoning applications in quantum optics and plasmonics. Utilizing first principles calculations, this work explores the hot carrier (HC) generation and distribution within a composite system made up of a plasmonic nanoparticle dimer and linear polycyclic aromatic hydrocarbon (PAH) molecules. We examine the spatial and energetic distributions of HCs by initiating photoexcitation and allowing localized surface plasmon dephasing. By positioning PAH molecules within the plasmonic nanodimer's gap region, our investigation uncovers HC tuning. Notably, depending on the size of the PAH molecules, there are significant alterations in the HC distribution. Hot electrons (HEs) are distributed across both the nanodimer and the PAH molecule, while hot holes (HHs) become entirely localized on the PAH as the PAH grows larger. These findings improve our understanding of plasmon-molecule coupled states and provide guidance on how to customize HC distributions through the creation of hybrid plasmonic materials.

Plasmon induced hot carrier distribution in Ag20 -CO composite

The interaction between plasmons and the molecules leads to the transfer of plasmon-induced hot carriers, presenting innovative opportunities for controlling chemical reactions on sub-femtosecond timescales. Through real-time time-dependent density functional theory simulations, we have investigated the enhancement of the electric field due to plasmon excitation and the subsequent generation and transfer of plasmon-induced hot carriers in a linear atomic chain of Ag20 and an Ag20 -CO composite system. By applying a Gaussian laser pulse tuned to align with the plasmon frequency, we observe a plasmon-induced transfer of hot electrons from the occupied states of Ag to the unoccupied molecular orbitals of CO. Remarkably, there is a pronounced accumulation of hot electrons and hot holes on the C and O atoms. This phenomenon arises from the electron migration from the inter-nuclear regions of the C-O bond towards the individual C and O atoms. The insights garnered from our study hold the potential to drive advancements in the development of more efficient systems for catalytic processes empowered by plasmonic interactions.

Dispersive surface-response formalism to address nonlocality in extreme plasmonic field confinement

The surface-response formalism (SRF), where quantum surface-response corrections are incorporated into the classical electromagnetic theory via the Feibelman parameters, serves to address quantum effects in the optical response of metallic nanostructures. So far, the Feibelman parameters have been typically obtained from many-body calculations performed in the long-wavelength approximation, which neglects the nonlocality of the optical response in the direction parallel to the metal-dielectric interface, thus preventing to address the optical response of systems with extreme field confinement. To improve this approach, we introduce a dispersive SRF based on a general Feibelman parameter d ⊥(ω, k ‖), which is a function of both the excitation frequency, ω, and the wavenumber parallel to the planar metal surface, k ‖. An explicit comparison with time-dependent density functional theory (TDDFT) results shows that the dispersive SRF correctly describes the plasmonic response of planar and nonplanar systems featuring extreme field confinement. This work thus significantly extends the applicability range of the SRF, contributing to the development of computationally efficient semiclassical descriptions of light-matter interaction that capture quantum effects.

Nonlinear chaotic dynamics in nonlocal plasmonic core-shell nanoparticle dimer

Plasmonic nanoparticles can be employed as a promising integrated platform for lumped optical nanoelements with unprecedentedly high integration capacity and efficient nanoscale ultrafast nonlinear functionality. Further minimizing the size of plasmonic nanoelements will lead to a rich variety of nonlocal optical effects due to the nonlocal nature of electrons in plasmonic materials. In this work, we theoretically investigate the nonlinear chaotic dynamics of the plasmonic core-shell nanoparticle dimer consisting of a nonlocal plasmonic core and a Kerr-type nonlinear shell at nanometer scale. This kind of optical nanoantennae could provide novel switching functionality: tristable, astable multivibrators, and chaos generator. We give a qualitative analysis on the influence of nonlocality and aspect ratio of core-shell nanoparticles on the chaos regime as well as on the nonlinear dynamical processing. It is demonstrated that considering nonlocality is very important in the design of such nonlinear functional photonic nanoelements with ultra-small size. Compared to solid nanoparticles, core-shell nanoparticles provide an additional freedom to adjust their plasmonic property hence tuning the chaotic dynamic regime in the geometric parameter space. This kind of nanoscale nonlinear system could be the candidate for a nonlinear nanophotonic device with a tunable nonlinear dynamical response.

Multifunctional charge transfer plasmon resonance sensors

Charge transfer plasmon (CTP) modes arise when metallic nanoparticle dimers are connected by a conductive junction. This offers a unique opportunity to explore electron transport at optical frequencies as well as to attain narrow plasmon resonances that can be broadly modulated from visible to IR regimes, implying their potentials for applications in single-molecule electronics and sensing. This article showcases recent developments in theory and applications of charge transfer plasmon resonances (CTPRs) in various configurations of conductively linked plasmonic nanodimers. In particular, we give a due attention to exploiting ultratunable spectral features of charge transfer plasmon resonances for developing multifunctional plasmonic sensors for bulk, surface, gas and molecular sensing applications. We also discuss the implications of the charge and energy transfer between two plasmonic nanoparticles linked by sub-nanometer thick self-assembled monolayers for single-molecule conductance sensing and molecular electronics. In addition to the well-established plasmonic sensing schemes based on propagating and localized surface plasmon resonances, charge transfer plasmon resonance sensors may open up a new route in efforts to develop multifunctional sensing technologies.

Inelastic Light Scattering in the Vicinity of a Single-Atom Quantum Point Contact in a Plasmonic Picocavity

Electromagnetic fields can be confined in the presence of metal nanostructures. Recently, subnanometer scale confinement has been demonstrated to occur at atomic protrusions on plasmonic nanostructures. Such an extreme field may dominate atomic-scale light-matter interactions in "picocavities". However, it remains to be elucidated how atomic-level structures and electron transport affect plasmonic properties of a picocavity. Here, using low-temperature optical scanning tunneling microscopy (STM), we investigate inelastic light scattering (ILS) in the vicinity of a single-atom quantum point contact (QPC). A vibration mode localized at the single Ag adatom on the Ag(111) surface is resolved in the ILS spectrum, resulting from tip-enhanced Raman scattering (TERS) by the atomically confined plasmonic field in the STM junction. Furthermore, we trace how TERS from the single adatom evolves as a function of the gap distance. The exceptional stability of the low-temperature STM allows to examine distinctly different electron transport regimes of the picocavity, namely, in the tunneling and QPC regimes. This measurement shows that the vibration mode localized at the adatom and its TERS intensity exhibits a sharp change upon the QPC formation, indicating that the atomic-level structure has a crucial impact on the plasmonic properties. To gain microscopic insights into picocavity optomechanics, we scrutinize the structure and plasmonic field in the STM junction using time-dependent density functional theory. The simulations reveal that atomic-scale structural relaxation at the single-atom QPC results in a discrete change of the plasmonic field strength, volume, and distribution as well as the vibration mode localized at the single atom. These findings give a qualitative explanation for the experimental observations. Furthermore, we demonstrate that strong ILS is a characteristic feature of QPC by continuously forming, breaking, and reforming the atomic contact and how the plasmonic resonance evolves throughout the nontunneling, tunneling, and QPC regimes.

Interrogating Quantum Nonlocal Effects in Nanoplasmonics through Electron-Beam Spectroscopy

A rigorous account of quantum nonlocal effects is paramount for understanding the optical response of metal nanostructures and for designing plasmonic devices at the nanoscale. Here, we present a scheme for retrieving the quantum surface response of metals, encapsulated in the Feibelman d-parameters, from electron energy-loss spectroscopy (EELS) and cathodoluminescence (CL) measurements. We theoretically demonstrate that quantum nonlocal effects have a dramatic impact on EELS and CL spectra, in the guise of spectral shifts and nonlocal damping, when either the system size or the inverse wave vector in extended structures approaches the nanometer scale. Our concept capitalizes on the unparalleled ability of free electrons to supply deeply subwavelength near-fields and, thus, probe the optical response of metals at length scales in which quantum-mechanical effects are apparent. These results pave the way for a widespread use of the d-parameter formalism, thereby facilitating a rigorous yet practical inclusion of nonclassical effects in nanoplasmonics.

Hot Electron-Driven Photocatalysis Using Sub-5 nm Gap Plasmonic Nanofinger Arrays

Semiconductor photocatalysis has received increasing attention because of its potential to address problems related to the energy crisis and environmental issues. However, conventional semiconductor photocatalysts, such as TiO₂ and ZnO, can only be activated by ultraviolet light due to their wide band gap. To extend the light absorption into the visible range, the localized surface plasmon resonance (LSPR) effect of noble metal nanoparticles (NPs) has been widely used. Noble metal NPs can couple incident visible light energy to strong LSPR, and the nonradiative decay of LSPR generates nonthermal hot carriers that can be injected into adjacent semiconductor material to enhance its photocatalytic activity. Here we demonstrate that nanoimprint-defined gap plasmonic nanofinger arrays can function as visible light-driven plasmonic photocatalysts. The sub-5 nm gaps between pairs of collapsed nanofingers can support ultra-strong plasmon resonance and thus boost the population of hot carriers. The semiconductor material is exactly placed at the hot spots, providing an efficient pathway for hot carrier injection from plasmonic metal to catalytic materials. This nanostructure thus exhibits high plasmon-enhanced photocatalytic activity under visible light. The hot carrier injection mechanism of this platform was systematically investigated. The plasmonic enhancement factor was calculated using the finite-difference time-domain (FDTD) method and was consistent with the measured improvement of the photocatalytic activity. This platform, benefiting from the precise controllable geometry, provides a deeper understanding of the mechanism of plasmonic photocatalysis.

Quantum surface effects in the electromagnetic coupling between a quantum emitter and a plasmonic nanoantenna: time-dependent density functional theory vs. semiclassical Feibelman approach

We use time-dependent density functional theory (TDDFT) within the jellium model to study the impact of quantum-mechanical effects on the self-interaction Green's function that governs the electromagnetic interaction between quantum emitters and plasmonic metallic nanoantennas. A semiclassical model based on the Feibelman parameters, which incorporates quantum surface-response corrections into an otherwise classical description, confirms surface-enabled Landau damping and the spill out of the induced charges as the dominant quantum mechanisms strongly affecting the nanoantenna-emitter interaction. These quantum effects produce a redshift and broadening of plasmonic resonances not present in classical theories that consider a local dielectric response of the metals. We show that the Feibelman approach correctly reproduces the nonlocal surface response obtained by full quantum TDDFT calculations for most nanoantenna-emitter configurations. However, when the emitter is located in very close proximity to the nanoantenna surface, we show that the standard Feibelman approach fails, requiring an implementation that explicitly accounts for the nonlocality of the surface response in the direction parallel to the surface. Our study thus provides a fundamental description of the electromagnetic coupling between plasmonic nanoantennas and quantum emitters at the nanoscale.

Extremely confined gap plasmon modes: when nonlocality matters

Historically, the field of plasmonics has been relying on the framework of classical electrodynamics, with the local-response approximation of material response being applied even when dealing with nanoscale metallic structures. However, when the confinement of electromagnetic radiation approaches atomic scales, mesoscopic effects are anticipated to become observable, e.g., those associated with the nonlocal electrodynamic surface response of the electron gas. Here, we investigate nonlocal effects in propagating gap surface plasmon modes in ultrathin metal-dielectric-metal planar waveguides, exploiting monocrystalline gold flakes separated by atomic-layer-deposited aluminum oxide. We use scanning near-field optical microscopy to directly access the near-field of such confined gap plasmon modes and measure their dispersion relation via their complex-valued propagation constants. We compare our experimental findings with the predictions of the generalized nonlocal optical response theory to unveil signatures of nonlocal damping, which becomes appreciable for few-nanometer-sized dielectric gaps.

Quantum tunneling effect on the surface enhanced Raman process in molecular systems

In this paper, we theoretically study the effect of quantum tunneling on the surface enhanced Raman scattering (SERS) of a generic molecule confined in sub-nanometer nanocavities formed by metallic dimers. The tunneling effect was described by the quantum corrected model in combination with finite element simulations. The SERS spectra were calculated by a density matrix method. Simulation results demonstrate that both the field enhancement and the molecular SERS spectra are very sensitive to the size of the cavity. By decreasing the gap size, the local field enhancement first increases then starts to be significantly suppressed as a result of the tunneling effect which neutralizes the positive and negative induced charges in the nanocavity. Consequently, the SERS intensity also experienced dramatic decrease in the short gap distance region. We also show that both the plasmonic enhancement to the local field and the enhanced molecular decay rates have to be taken into account to understand the SERS properties of the molecule in such sub-nanometer nanocavities. These results could be helpful for the understanding of the surface enhanced spectral properties of molecular systems at sub-nanometer nanocavities.

Quantum Plasmonics: Energy Transport Through Plasmonic Gap

At the interfaces of metal and dielectric materials, strong light-matter interactions excite surface plasmons; this allows electromagnetic field confinement and enhancement on the sub-wavelength scale. Such phenomena have attracted considerable interest in the field of exotic material-based nanophotonic research, with potential applications including nonlinear spectroscopies, information processing, single-molecule sensing, organic-molecule devices, and plasmon chemistry. These innovative plasmonics-based technologies can meet the ever-increasing demands for speed and capacity in nanoscale devices, offering ultrasensitive detection capabilities and low-power operations. Size scaling from the nanometer to sub-nanometer ranges is consistently researched; as a result, the quantum behavior of localized surface plasmons, as well as those of matter, nonlocality, and quantum electron tunneling is investigated using an innovative nanofabrication and chemical functionalization approach, thereby opening a new era of quantum plasmonics. This new field enables the ultimate miniaturization of photonic components and provides extreme limits on light-matter interactions, permitting energy transport across the extremely small plasmonic gap. In this review, a comprehensive overview of the recent developments of quantum plasmonic resonators with particular focus on novel materials is presented. By exploring the novel gap materials in quantum regime, the potential quantum technology applications are also searched for and mapped out.

Electronic Exciton-Plasmon Coupling in a Nanocavity Beyond the Electromagnetic Interaction Picture

The optical response of a system formed by a quantum emitter and a plasmonic gap nanoantenna is theoretically addressed within the frameworks of classical electrodynamics and the time-dependent density functional theory (TDDFT). A fully quantum many-body description of the electron dynamics within TDDFT allows for analyzing the effect of electronic coupling between the emitter and the nanoantenna, usually ignored in classical descriptions of the optical response. We show that the hybridization between the electronic states of the quantum emitter and those of the metallic nanoparticles strongly modifies the energy, the width, and the very existence of the optical resonances of the coupled system. We thus conclude that the application of a quantum many-body treatment that correctly addresses charge-transfer processes between the emitter and the nanoantenna is crucial to address complex electronic processes involving plasmon-exciton interactions directly impacting optoelectronic applications.

Plasmon Couplings from Subsystem Time-Dependent Density Functional Theory

Many applications in plasmonics are related to the coupling between metallic nanoparticles (MNPs) or between an emitter and a MNP. The theoretical analysis of such a coupling is thus of fundamental importance to analyze the plasmonic behavior and to design new systems. While classical methods neglect quantum and spill-out effects, time-dependent density functional theory (TD-DFT) considers all of them and with Kohn-Sham orbitals delocalized over the whole system. Thus, within TD-DFT, no definite separation of the subsystems (the single MNP or the emitter) and their couplings is directly available. This important feature is obtained here using the subsystem formulation of TD-DFT, which has been originally developed in the context of weakly interacting organic molecules. In subsystem TD-DFT, interacting MNPs are treated independently, thus allowing us to compute the plasmon couplings directly from the subsystem TD-DFT transition densities. We show that subsystem TD-DFT, as well as a simplified version of it in which kinetic contributions are neglected, can reproduce the reference TD-DFT calculations for gap distances greater than about 6 Å or even smaller in the case of hybrid plasmonic systems (i.e., molecules interacting with MNPs). We also show that the subsystem TD-DFT can be also used as a tool to analyze the impact of charge-transfer effects.

Plasmonic metal nanostructures with extremely small features: new effects, fabrication and applications

Surface plasmons in metals promise many fascinating properties and applications in optics, sensing, photonics and nonlinear fields. Plasmonic nanostructures with extremely small features especially demonstrate amazing new effects as the feature sizes scale down to the sub-nanometer scale, such as quantum size effects, quantum tunneling, spill-out of electrons and nonlocal states etc. The unusual physical, optical and photo-electronic properties observed in metallic structures with extreme feature sizes enable their unique applications in electromagnetic field focusing, spectra enhancing, imaging, quantum photonics, etc. In this review, we focus on the new effects, fabrication and applications of plasmonic metal nanostructures with extremely small features. For simplicity and consistency, we will focus our topic on the plasmonic metal nanostructures with feature sizes of sub-nanometers. Subsequently, we discussed four main and typical plasmonic metal nanostructures with extremely small features, including: (1) ultra-sharp plasmonic metal nanotips; (2) ultra-thin plasmonic metal films; (3) ultra-small plasmonic metal particles and (4) ultra-small plasmonic metal nanogaps. Additionally, the corresponding fascinating new effects (quantum nonlinear, non-locality, quantum size effect and quantum tunneling), applications (spectral enhancement, high-order harmonic wave generation, sensing and terahertz wave detection) and reliable fabrication methods will also be discussed. We end the discussion with a brief summary and outlook of the main challenges and possible breakthroughs in the field. We hope our discussion can inspire the broader design, fabrication and application of plasmonic metal nanostructures with extremely small feature sizes in the future.

Quantum surface-response of metals revealed by acoustic graphene plasmons

A quantitative understanding of the electromagnetic response of materials is essential for the precise engineering of maximal, versatile, and controllable light-matter interactions. Material surfaces, in particular, are prominent platforms for enhancing electromagnetic interactions and for tailoring chemical processes. However, at the deep nanoscale, the electromagnetic response of electron systems is significantly impacted by quantum surface-response at material interfaces, which is challenging to probe using standard optical techniques. Here, we show how ultraconfined acoustic graphene plasmons in graphene-dielectric-metal structures can be used to probe the quantum surface-response functions of nearby metals, here encoded through the so-called Feibelman d-parameters. Based on our theoretical formalism, we introduce a concrete proposal for experimentally inferring the low-frequency quantum response of metals from quantum shifts of the acoustic graphene plasmons dispersion, and demonstrate that the high field confinement of acoustic graphene plasmons can resolve intrinsically quantum mechanical electronic length-scales with subnanometer resolution. Our findings reveal a promising scheme to probe the quantum response of metals, and further suggest the utilization of acoustic graphene plasmons as plasmon rulers with ångström-scale accuracy.

Electron dynamics in plasmons

The Particle-in-Cell (PIC) method for plasmons provides a mechanical, single-particle picture of plasmon resonances by tracking in time the movement of all the individual conduction electrons. By applying it to gold nanorods, we demonstrate the usefulness of PIC for extracting time-domain information of plasmons such as plasmon decay times, the relative contribution of each plasmon damping channel, detailed electron movement, as well as radiation and hot electron-emission during damping. An analysis of the time-resolved velocity distribution of the conduction electrons shows that only a small offset in this distribution in each cycle constitutes the plasmon oscillation. We show how PIC can be used to separately analyse Landau damping and Drude damping, and how their decay times can be calculated. Electron-electron scattering and surface scattering are both shown to gradually increase the overall kinetic energy of the electrons and decrease their coherence.

Role of diffusive surface scattering in nonlocal plasmonics

The recent generalised nonlocal optical response (GNOR) theory for plasmonics is analysed, and its main input parameter, namely the complex hydrodynamic convection-diffusion constant, is quantified in terms of enhanced Landau damping due to diffusive surface scattering of electrons at the surface of the metal. GNOR has been successful in describing plasmon damping effects, in addition to the frequency shifts originating from induced-charge screening, through a phenomenological electron diffusion term implemented into the traditional hydrodynamic Drude model of nonlocal plasmonics. Nevertheless, its microscopic derivation and justification is still missing. Here we discuss how the inclusion of a diffusion-like term in standard hydrodynamics can serve as an efficient vehicle to describe Landau damping without resorting to computationally demanding quantum-mechanical calculations, and establish a direct link between this term and the Feibelmandparameter for the centroid of charge. Our approach provides a recipe to connect the phenomenological fundamental GNOR parameter to a frequency-dependent microscopic surface-response function. We therefore tackle one of the principal limitations of the model, and further elucidate its range of validity and limitations, thus facilitating its proper application in the framework of nonclassical plasmonics.

Strong Coupling of Carbon Quantum Dots in Plasmonic Nanocavities

Confining light in extremely small cavities is crucial in nanophotonics, central to many applications. Employing a unique nanoparticle-on-mirror plasmonic structure and using a graphene film as a spacer, we create nanoscale cavities with volumes of only a few tens of cubic nanometers. The ultracompact cavity produces extremely strong optical near-fields, which facilitate the formation of single carbon quantum dots in the cavity and simultaneously empower the strong coupling between the excitons of the formed carbon quantum dot and the localized surface plasmons. This is manifested in the optical scattering spectra, showing a magnificent Rabi splitting of up to 200 meV under ambient conditions. In addition, we demonstrate that the strong coupling is tuneable with light irradiation. This opens new paradigms for investigating the fundamental light emission properties of carbon quantum dots in the quantum regime and paves the way for many significant applications.

Terahertz and infrared nonlocality and field saturation in extreme-scale nanoslits

With advances in nanofabrication techniques, extreme-scale nanophotonic devices with critical gap dimensions of just 1-2 nm have been realized. The plasmonic response in these extreme-scale gaps is significantly affected by nonlocal electrodynamics, quenching field enhancement and blue-shifting the resonance with respect to a purely local behavior. The extreme mismatch in lengthscales, ranging from millimeter-long wavelengths to atomic-scale charge distributions, poses a daunting computational challenge. In this paper, we perform computations of a single nanoslit using the hybridizable discontinuous Galerkin method to solve Maxwell's equations augmented with the hydrodynamic model for the conduction-band electrons in noble metals. This method enables the efficient simulation of the slit while accounting for the nonlocal interactions between electrons and the incident light. We study the impact of gap width, film thickness and electron motion model on the plasmon resonances of the slit for two different frequency regimes: (1) terahertz frequencies, which lead to 1000-fold field amplitude enhancements that saturate as the gap shrinks; and (2) the near- and mid-infrared regime, where we show that narrow gaps and thick films cluster Fabry-Pérot (FP) resonances towards lower frequencies, derive a dispersion relation for the first FP resonance, in addition to observing that nonlocality boosts transmittance and reduces enhancement.

Unveiling the radiative local density of optical states of a plasmonic nanocavity by STM

Atomically-sharp tips in close proximity of metal surfaces create plasmonic nanocavities supporting both radiative (bright) and non-radiative (dark) localized surface plasmon modes. Disentangling their respective contributions to the total density of optical states remains a challenge. Electroluminescence due to tunnelling through the tip-substrate gap could allow the identification of the radiative component, but this information is inherently convoluted with that of the electronic structure of the system. In this work, we present a fully experimental procedure to eliminate the electronic-structure factors from the scanning tunnelling microscope luminescence spectra by confronting them with spectroscopic information extracted from elastic current measurements. Comparison against electromagnetic calculations demonstrates that this procedure allows the characterization of the meV shifts experienced by the nanocavity plasmonic modes under atomic-scale gap size changes. Therefore, the method gives access to the frequency-dependent radiative Purcell enhancement that a microscopic light emitter would undergo when placed at such nanocavity.

Disentangling the radiative and non-radiative plasmon mode contributions to the total photonic density of states is a challenge. Here, the authors report a procedure to eliminate the electronic-structure factors from scanning tunnelling microscope luminescence spectra to isolate the radiative component.

Flickering nanometre-scale disorder in a crystal lattice tracked by plasmonic flare light emission

The dynamic restructuring of metal nanoparticle surfaces is known to greatly influence their catalytic, electronic transport, and chemical binding functionalities. Here we show for the first time that non-equilibrium atomic-scale lattice defects can be detected in nanoparticles by purely optical means. These fluctuating states determine interface electronic transport for molecular electronics but because such rearrangements are low energy, measuring their rapid dynamics on single nanostructures by X-rays, electron beams, or tunnelling microscopies, is invasive and damaging. We utilise nano-optics at the sub-5nm scale to reveal rapid (on the millisecond timescale) evolution of defect morphologies on facets of gold nanoparticles on a mirror. Besides dynamic structural information, this highlights fundamental questions about defining bulk plasma frequencies for metals probed at the nanoscale.

Dynamic restructuring of metal nanoparticle surfaces greatly influences their catalytic, electronic transport, and chemical binding functionalities. Here, the authors show that non-equilibrium atomic-scale lattice defects can be detected in nanoparticles by using nano-optics at the sub-5nm scale.

Present and Future of Surface-Enhanced Raman Scattering

The discovery of the enhancement of Raman scattering by molecules adsorbed on nanostructured metal surfaces is a landmark in the history of spectroscopic and analytical techniques. Significant experimental and theoretical effort has been directed toward understanding the surface-enhanced Raman scattering (SERS) effect and demonstrating its potential in various types of ultrasensitive sensing applications in a wide variety of fields. In the 45 years since its discovery, SERS has blossomed into a rich area of research and technology, but additional efforts are still needed before it can be routinely used analytically and in commercial products. In this Review, prominent authors from around the world joined together to summarize the state of the art in understanding and using SERS and to predict what can be expected in the near future in terms of research, applications, and technological development. This Review is dedicated to SERS pioneer and our coauthor, the late Prof. Richard Van Duyne, whom we lost during the preparation of this article.

Plasmon-emitter interactions at the nanoscale

Plasmon-emitter interactions are of central importance in modern nanoplasmonics and are generally maximal at short emitter-surface separations. However, when the separation falls below 10-20 nm, the classical theory deteriorates progressively due to its neglect of quantum effects such as nonlocality, electronic spill-out, and Landau damping. Here we show how this neglect can be remedied in a unified theoretical treatment of mesoscopic electrodynamics incorporating Feibelman [Formula: see text]-parameters. Our approach incorporates nonclassical resonance shifts and surface-enabled Landau damping-a nonlocal damping effect-which have a dramatic impact on the amplitude and spectral distribution of plasmon-emitter interactions. We consider a broad array of plasmon-emitter interactions ranging from dipolar and multipolar spontaneous emission enhancement, to plasmon-assisted energy transfer and enhancement of two-photon transitions. The formalism gives a complete account of both plasmons and plasmon-emitter interactions at the nanoscale, constituting a simple yet rigorous platform to include nonclassical effects in plasmon-enabled nanophotonic phenomena.

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.

Extreme nanophotonics from ultrathin metallic gaps

Ultrathin dielectric gaps between metals can trap plasmonic optical modes with surprisingly low loss and with volumes below 1 nm³. We review the origin and subtle properties of these modes, and show how they can be well accounted for by simple models. Particularly important is the mixing between radiating antennas and confined nanogap modes, which is extremely sensitive to precise nanogeometry, right down to the single-atom level. Coupling nanogap plasmons to electronic and vibronic transitions yields a host of phenomena including single-molecule strong coupling and molecular optomechanics, opening access to atomic-scale chemistry and materials science, as well as quantum metamaterials. Ultimate low-energy devices such as robust bottom-up assembled single-atom switches are thus in prospect.

Nanostructured metals for light-based technologies

The basic theoretical understanding of light interacting with nanostructured metals that has existed since the early 1900s has become more relevant in the last two decades, largely because of new approaches to structure metals down to the nanometer scale or smaller. Here, a broad overview of the concepts and applications of nanostructuring metals for light-based technologies is given. The theory of the response of metals to an applied oscillating field is given, including a discussion of nonlocal, nonlinear and quantum effects. Using this metal response, the guiding of electromagnetic (light) waves using metals is given, with a particular emphasis on the impact of nanostructured metals for tighter confinement and slower propagation. Similarly, the influence of metal nanostructures on light scattering by isolated metal structures, like nanoparticles and nanoantennas, is described, with basic results presented including plasmonic/circuit resonances, the single channel limit, directivity enhancement, the maximum power transfer theorem, limits on the magnetic response from kinetic inductance and the scaling of gap plasmons to the nanometer scale and smaller. A brief overview of nanofabrication approaches to creating metal nanostructures is given. Finally, existing and emerging light-based applications are presented, including those for sensing, spectroscopy (including local refractive index, Raman, IR absorption), detection (including Schottky detectors), switching (including terahertz photoconductive antennas), modulation, energy harvesting and photocatalysis, light emission (including lasers and tunneling based light emission), optical tweezing, nonlinear optics, subwavelength imaging and lithography and high density data storage.

Numerical Analysis of Nonlocal Optical Response of Metallic Nanoshells

Nonlocal and quantum effects play an important role in accurately modeling the optical response of nanometer-sized metallic nanoparticles. These effects cannot be described by conventional classical theories, as they neglect essential microscopic details. Quantum hydrodynamic theory (QHT) has emerged as an excellent tool to correctly predict the nonlocal and quantum effects by taking into account the spatial dependence of the charge density. In this article, we used a QHT to investigate the impact of nonlocality and electron spill-out on the plasmonic behavior of spherical Na and Au nanoshells. We adopted a self-consistent way to compute the equilibrium charge density. The results predicted by QHT were compared with those obtained with the local response approximation (LRA) and the Thomas–Fermi hydrodynamic theory (TFHT). We found that nonlocal effects have a strong impact on both the near- and far-field optical properties of nanoshells, in particular, for the antibonding resonant mode. We also investigated the optical response of these systems for different thicknesses of the shell, both for Na and Au metals.

Anomalously Large Spectral Shifts near the Quantum Tunnelling Limit in Plasmonic Rulers with Subatomic Resolution

The resonance wavelength of a coupled plasmonic system is extremely sensitive to the distance between its metallic surfaces, resulting in "plasmon rulers". We explore this behavior in the subnanometer regime using self-assembled monolayers of bis-phthalocyanine molecules in a nanoparticle-on-mirror (NPoM) construct. These allow unprecedented subangstrom control over spacer thickness via choice of metal center, in a gap-size regime at the quantum-mechanical limit of plasmonic enhancement. A dramatic shift in the coupled plasmon resonance is observed as the gap size is varied from 0.39 to 0.41 nm. Existing theoretical models are unable to account for the observed spectral tuning, which requires inclusion of the quantum-classical interface, emphasizing the need for new treatments of light at the subnanoscale.

Molecular Tunnel Junction-Controlled High-Order Charge Transfer Plasmon and Fano Resonances

Quantum tunneling plays an important role in coupled plasmonic nanocavities with ultrasmall gap distances. It can lead to intriguing applications such as plasmon mode excitation, hot carrier generation, and construction of ultracompact electro-optic devices. Molecular junctions bridging plasmonic nanocavities can provide a tunneling channel at moderate gap distances and therefore allow for the facile fabrication of quantum plasmonic devices. Herein we report on the large-scale bottom-up fabrication of molecular junction-bridged plasmonic nanocavities formed from Au nanoplate-Au nanosphere heterodimers. When the molecular junction turns from insulating to conductive, a distinct spectral change is observed, together with the emergence of a high-order charge transfer plasmon mode. The evolution of the electron tunneling-induced plasmon mode also greatly affects the Fano resonance feature in the scattering spectrum of the individual heterodimers. The molecular conductance at optical frequencies is estimated. The molecular junction-assisted electron tunneling is further verified by the reduced surface-enhanced Raman intensities of the molecules in the plasmonic nanocavity. We believe that our results provide an interesting system that can boost the investigation on the use of molecular junctions to modulate quantum plasmon resonances and construct molecular plasmonic devices.

Plasmonic refractive index sensing using strongly coupled metal nanoantennas: nonlocal limitations

Localized surface plasmon resonance based on coupled metallic nanoparticles has been extensively studied in the refractive index sensing and the detection of molecules. The amount of resonance peak-shift depends on the refractive index of surrounding medium and the geometry/symmetry of plasmonic oligomers. It has recently been found that as the feature size or the gap distance of plasmonic nanostructures approaches several nanometers, quantum effects can change the plasmon coupling in nanoparticles. However, most of the research on plasmonic sensing has been done based on classical local calculations even for the interparticle gap below ~3 nm, in which the nonlocal screening plays an important role. Here, we theoretically investigate the nonlocal effect on the evolution of various plasmon resonance modes in strongly coupled nanoparticle dimer and trimer antennas with the gap down to 1 nm. Then, the refractive index sensing in these nonlocal systems is evaluated and compared with the results in classical calculations. We find that in the nonlocal regime, both refractive index sensibility factor and figure of merit are actually smaller than their classical counterparts mainly due to the saturation of plasmon shifts. These results would be beneficial for the understanding of interaction between light and nonlocal plasmonic nanostructures and the development of plasmonic devices such as nanosensors and nanoantennas.

Optical properties of plasmonic core-shell nanomatryoshkas: a quantum hydrodynamic analysis

Plasmonic response of the metallic structure characterized by sub-nanometer dielectric gaps can be strongly affected by nonlocal or quantum effects. In this paper, we investigate these effects in spherical Na and Au nanomatryoshka structures with sub-nanometer core-shell separation. We use the state-of-the-art quantum hydrodynamic theory (QHT) to study both near-field and far-field optical properties of these systems: results are compared with the classical local response approximation (LRA), Thomas-Fermi hydrodynamic theory (TF-HT), and the reference time-dependent density functional theory (TD-DFT). We find that the results obtained using the QHT method are in a very good agreement with TD-DFT calculations, whereas other LRA and TF-HT significantly overestimate the field-enhancements. Thus, the QHT approach efficiently and accurately describes microscopic details of multiscale plasmonic systems whose sizes are computationally out-of-reach for a TD-DFT approach; here, we report results for Na and Au nanomatryoshka with a diameter of 60 nm.

Probing the ultimate plasmon confinement limits with a van der Waals heterostructure

The ability to confine light into tiny spatial dimensions is important for applications such as microscopy, sensing, and nanoscale lasers. Although plasmons offer an appealing avenue to confine light, Landau damping in metals imposes a trade-off between optical field confinement and losses. We show that a graphene-insulator-metal heterostructure can overcome that trade-off, and demonstrate plasmon confinement down to the ultimate limit of the length scale of one atom. This is achieved through far-field excitation of plasmon modes squeezed into an atomically thin hexagonal boron nitride dielectric spacer between graphene and metal rods. A theoretical model that takes into account the nonlocal optical response of both graphene and metal is used to describe the results. These ultraconfined plasmonic modes, addressed with far-field light excitation, enable a route to new regimes of ultrastrong light-matter interactions.

Microscopic Electron Dynamics in Metal Nanoparticles for Photovoltaic Systems

Nanoparticles—regularly patterned or randomly dispersed—are a key ingredient for emerging technologies in photonics. Of particular interest are scattering and field enhancement effects of metal nanoparticles for energy harvesting and converting systems. An often neglected aspect in the modeling of nanoparticles are light interaction effects at the ultimate nanoscale beyond classical electrodynamics. Those arise from microscopic electron dynamics in confined systems, the accelerated motion in the plasmon oscillation and the quantum nature of the free electron gas in metals, such as Coulomb repulsion and electron diffusion. We give a detailed account on free electron phenomena in metal nanoparticles and discuss analytic expressions stemming from microscopic (Random Phase Approximation—RPA) and semi-classical (hydrodynamic) theories. These can be incorporated into standard computational schemes to produce more reliable results on the optical properties of metal nanoparticles. We combine these solutions into a single framework and study systematically their joint impact on isolated Au, Ag, and Al nanoparticles as well as dimer structures. The spectral position of the plasmon resonance and its broadening as well as local field enhancement show an intriguing dependence on the particle size due to the relevance of additional damping channels.

Broadened region for robust optical bistability in a nonlocal core and Kerr shell nanoparticle

With the self-consistent mean field approximation in the framework of full-wave nonlocal scattering theory, we carry out a theoretical study on the optical bistability in a nonlocal nanoparticle coated with a Kerr-type nonlinear shell. A nonlocality-enhanced Fano profile is found in its scattering spectrum. We demonstrate the nonlocality-broadened bistable region in the geometrical parameter space. We perform the investigation of the nonlinear dependences of the near-field intensity and far-field scattering on the incident wavelength and find the input-wavelength-controllable as well as the input-field-intensity-controllable scattering. We check the stability of the nonlinear steady states and perform its temporal dynamical evolutions.

Quantum plasmonic epsilon near zero: field enhancement and cloaking

We investigate the effect of the electron wave function producing permittivity (epsilon) near zero in sub-nanometer gaps and at surfaces. The field enhancement is calculated for gaps and nanoparticles, as well as the absorption from nanoparticles. Our modified quantum corrected model shows reduced absorption for nanoparticles due to "cloaking" of the epsilon near zero region, which has lower loss than the bulk region. We demonstrate that a modified quantum corrected model finite-difference time-domain simulation of metal slits with sub-nanometer gaps are in good agreement with the analytic expression for the quantum corrected plasmonic resonance wavelength as a function of gap size coming from Re{ε} = 0.

Coupling of Molecular Emitters and Plasmonic Cavities beyond the Point-Dipole Approximation

As the size of a molecular emitter becomes comparable to the dimensions of a nearby optical resonator, the standard approach that considers the emitter to be a point-like dipole breaks down. By adoption of a quantum description of the electronic transitions of organic molecular emitters, coupled to a plasmonic electromagnetic field, we are able to accurately calculate the position-dependent coupling strength between a plasmon and an emitter. The spatial distribution of excitonic and photonic quantum states is found to be a key aspect in determining the dynamics of molecular emission in ultrasmall cavities both in the weak and strong coupling regimes. Moreover, we show that the extreme localization of plasmonic fields leads to the selection rule breaking of molecular excitations.

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.

Atomic-Scale Lightning Rod Effect in Plasmonic Picocavities: A Classical View to a Quantum Effect

Plasmonic gaps are known to produce nanoscale localization and enhancement of optical fields, providing small effective mode volumes of about a few hundred nm³. Atomistic quantum calculations based on time-dependent density functional theory reveal the effect of subnanometric localization of electromagnetic fields due to the presence of atomic-scale features at the interfaces of plasmonic gaps. Using a classical model, we explain this as a nonresonant lightning rod effect at the atomic scale that produces an extra enhancement over that of the plasmonic background. The near-field distribution of atomic-scale hot spots around atomic features is robust against dynamical screening and spill-out effects and follows the potential landscape determined by the electron density around the atomic sites. A detailed comparison of the field distribution around atomic hot spots from full quantum atomistic calculations and from the local classical approach considering the geometrical profile of the atoms' electronic density validates the use of a classical framework to determine the effective mode volume in these extreme subnanometric optical cavities. This finding is of practical importance for the community of surface-enhanced molecular spectroscopy and quantum nanophotonics, as it provides an adequate description of the local electromagnetic fields around atomic-scale features with use of simplified classical methods.

Controlled Patterning of Plasmonic Dimers by Using an Ultrathin Nanoporous Alumina Membrane as a Shadow Mask

We report on design and fabrication of patterned plasmonic dimer arrays by using an ultrathin anodic aluminum oxide (AAO) membrane as a shadow mask. This strategy allows for controllable fabrication of plasmonic dimers where the location, size, and orientation of each particle in the dimer pairs can be independently tuned. Particularly, plasmonic dimers with ultrasmall nanogaps down to the sub-10 nm scale as well as a large dimer density up to 1.0 × 10¹⁰ cm^-2 are fabricated over a centimeter-sized area. The plasmonic dimers exhibit significant surface-enhanced Raman scattering (SERS) enhancement with a polarization-dependent behavior, which is well interpreted by finite-difference time-domain (FDTD) simulations. Our results reveal a facile approach for controllable fabrication of large-area dimer arrays, which is of fundamental interest for plasmon-based applications in surface-enhanced spectroscopy, biochemical sensing, and optoelectronics.