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

Nonlocal Optical Response of Particle Plasmons in Single Gold Nanorods

The investigation of particle plasmons in metal nanoparticles has predominantly relied on local optical response approximations. However, as the nanoparticle size approaches the average distance of electrons to the metal surface, mesoscopic effects such as size-dependent plasmon line width broadening and resonance energy blue shifts are expected to become observable. In this work, we compared the experimental spectral characteristics with simulated values obtained by using a generalized nonlocal optical response theory-based local analogue model. Our results show that the nonlocal plasmon damping effects in single nanoparticles are less pronounced than those observed in plasmon-coupled systems. Furthermore, our research demonstrates that single-particle dark-field spectroscopy is an effective tool for investigating the nonlocal optical response of particle plasmons in single nanoparticles. These results have important implications for the rational design of novel nanophotonic devices.

Chemical and Physical Properties of Photonic Noble-Metal Nanomaterials

Colloidal noble metal nanoparticles (NPs) are composed of metal cores and organic or inorganic ligand shells. These NPs support size- and shape-dependent plasmonic resonances. They can be assembled from dispersions into artificial metamolecules which have collective plasmonic resonances originating from coupled bright and dark optical electric and magnetic modes that form depending on the size and shape of the constituent NPs and their number, arrangement, and interparticle distance. NPs can also be assembled into extended 2D and 3D metamaterials that are glassy thin films or ordered thin films or crystals, also known as superlattices and supercrystals. The metamaterials have tunable optical properties that depend on the size, shape, and composition of the NPs, and on the number of NP layers and their interparticle distance. Interestingly, strong light-matter interactions in superlattices form plasmon polaritons. Tunable interparticle distances allow designer materials with dielectric functions tailorable from that characteristic of an insulator to that of a metal, and serve as strong optical absorbers or scatterers, respectively. In combination with lithography techniques, these extended assemblies can be patterned to create subwavelength NP superstructures and form large-area 2D and 3D metamaterials that manipulate the amplitude, phase, and polarization of transmitted or reflected light.

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.

TeV/m catapult acceleration of electrons in graphene layers

Recent nanotechnology advances enable fabrication of layered structures with controllable inter-layer gap, giving the ultra-violet (UV) lasers access to solid-state plasmas which can be used as medium for electron acceleration. By using a linearly polarized 3 fs-long laser pulse of 100 nm wavelength and 10[Formula: see text] W/cm[Formula: see text] peak intensity, we show numerically that electron bunches can be accelerated along a stack of ionized graphene layers. Particle-In-Cell (PIC) simulations reveal a new self-injection mechanism based on edge plasma oscillations, whose amplitude depends on the distance between the graphene layers. Nanometre-size electron ribbons are electrostatically catapulted into buckets of longitudinal electric fields in less than 1 fs, as opposed to the slow electrostatic pull, common to laser wakefield acceleration (LWFA) schemes in gas-plasma. Acceleration then proceeds in the blowout regime at a gradient of 4.79 TeV/m yielding a 0.4 fs-long bunch with a total charge in excess of 2.5 pC and an average energy of 6.94 MeV, after travelling through a graphene target as short as 1.5 [Formula: see text]m. These parameters are unprecedented within the LWFA research area and, if confirmed experimentally, may have an impact on fundamental femtosecond research.

Visualizing screening in noble-metal clusters: static vs. dynamic

The localized surface-plasmon resonance of metal nanoparticles and clusters corresponds to a collective charge oscillation of the quasi-free metal electrons. The polarization of the more localized d electrons opposes the overall polarization of the electron cloud and thus screens the surface plasmon. By contrast, a static electric external field is well screened, as even very small noble-metal clusters are highly metallic: the field inside is practically zero except for the effect of the Friedel-oscillation-like modulations which lead to small values of the polarization of the d electrons. In the present article, we present and compare representations of the induced densities (i) connected to the surface-plasmon resonance and (ii) resulting from an external static electric field. The two cases allow for an intuitive understanding of the differences between the dynamic and the static screening.

Plasmonic Au-Cu nanostructures: Synthesis and applications

Plasmonic Au-Cu nanostructures composed of Au and Cu metals, have demonstrated advantages over their monolithic counterparts, which have recently attracted considerable attention. Au-Cu nanostructures are currently used in various research fields, including catalysis, light harvesting, optoelectronics, and biotechnologies. Herein, recent developments in Au-Cu nanostructures are summarized. The development of three types of Au-Cu nanostructures is reviewed, including alloys, core-shell structures, and Janus structures. Afterwards, we discuss the peculiar plasmonic properties of Au-Cu nanostructures as well as their potential applications. The excellent properties of Au-Cu nanostructures enable applications in catalysis, plasmon-enhanced spectroscopy, photothermal conversion and therapy. Lastly, we present our thoughts on the current status and future prospects of the Au-Cu nanostructures research field. This review is intended to contribute to the development of fabrication strategies and applications relating to Au-Cu nanostructures.

Quasinormal Mode Expansion Theory for Mesoscale Plasmonic Nanoresonators: An Analytical Treatment of Nonclassical Electromagnetic Boundary Condition

Nonclassical quantum effects will significantly affect the optical response of plasmonic nanoresonators with mesoscale feature sizes between about 2 and 20 nm, and can be fully described by the nonclassical electromagnetic boundary condition (NEBC) expressed with the surface-response Feibelman d parameters. In this Letter, a quasinormal mode (QNM) expansion theory under the NEBC is proposed. By adopting the easily solved classical QNMs under the classical electromagnetic boundary condition as a complete set of basis functions, rigorous expansions of the nonclassical source-free QNMs and source-excited electromagnetic field under the nonperturbative NEBC are provided. With the obtained nonclassical QNMs as basis functions, expansions of the nonclassical source-excited field and Green's function tensor are further obtained. These expansions have a fully analytical dependence on the NEBC and classical QNMs, thus transparently unveiling their impact on the nonclassical QNMs and source-excited electromagnetic field. For instance, a new expression of mode volume is proposed for analyzing the nonclassically corrected Purcell factor. The proposed theory is physically intuitive and computationally efficient which is enabled by the dominance of a small set of classical QNMs, thus providing an efficient tool for understanding and designing mesoscale plasmonic nanoresonators.

Do We Really Need Quantum Mechanics to Describe Plasmonic Properties of Metal Nanostructures?

Optical properties of metal nanostructures are the basis of several scientific and technological applications. When the nanostructure characteristic size is of the order of few nm or less, it is generally accepted that only a description that explicitly describes electrons by quantum mechanics can reproduce faithfully its optical response. For example, the plasmon resonance shift upon shrinking the nanostructure size (red-shift for simple metals, blue-shift for d-metals such as gold and silver) is universally accepted to originate from the quantum nature of the system. Here we show instead that an atomistic approach based on classical physics, ωFQFμ (frequency dependent fluctuating charges and fluctuating dipoles), is able to reproduce all the typical "quantum" size effects, such as the sign and the magnitude of the plasmon shift, the progressive loss of the plasmon resonance for gold, the atomistically detailed features in the induced electron density, and the non local effects in the nanoparticle response. To support our findings, we compare the ωFQFμ results for Ag and Au with literature time-dependent DFT simulations, showing the capability of fully classical physics to reproduce these TDDFT results. Only electron tunneling between nanostructures emerges as a genuine quantum mechanical effect, that we had to include in the model by an ad hoc term.

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.

Orbital-Free Methods for Plasmonics: Linear Response

Plasmonic systems, such as metal nanoparticles, are widely used in different application areas, going from biology to photovoltaics.The modeling of the optical response of such systems is of fundamental importance to analyze their behavior and to design new systems with required properties.When the characteristic sizes/distances reach a few nanometers, non-local and spill-out effects become relevant and conventional classical electrodynamics models are no more appropriate. Methods based on the Time-Dependent Density-Functional Theory (TD-DFT) represent the current reference for the description of quantum effects. However, TD-DFT is based on knowledge of all occupied orbitals whose calculation is computationally prohibitive to model large plasmonic systems of interest for applications.On the other hand, methods based on the Orbital-Free (OF) formulation of TD-DFT, can scale linearly with the system size.In this Review, OF methods ranging from semiclassical models to the quantum hydrodynamic theory, will be derived from the linear response TD-DFT, so that the key approximations and properties of each method can be clearly highlighted. The accuracy of the various approximations will be then validated for the linear optical properties of jellium nanoparticles, the most relevant model system in plasmonics. OF methods can describe the collective excitations in plasmonic systems with great accuracy andwithout system-tuned parameters. The accuracy on these methods depends only on the accuracy on the (universal) kinetic energy functional of the ground-state electronic density. Current approximations and future development directions will be indicated.

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.

Direct Electro Plasmonic and Optic Modulation via a Nanoscopic Electron Reservoir

Direct electrical tuning of localized plasmons at optical frequencies boasts the fascinating prospects of being ultrafast and energy efficient and having an ultrasmall footprint. However, the prospects are obscured by the grand challenge of effectively modulating the very large number of conduction electrons in three-dimensional metallic structures. Here we propose the concept of nanoscopic electron reservoir (NER) for direct electro plasmonic and electro-optic modulation. A NER is a few-to-ten-nanometer size metal feature on a metal host and supports a localized plasmon mode. We provide a general guideline to construct highly electrically susceptible NERs and theoretically demonstrate pronounced direct electrical tuning of the plasmon mode by exploiting the nonclassical effects of conduction electrons. Moreover, we show the electro-plasmonic tuning can be efficiently translated into modulation of optical scattering by utilizing the antenna effect of the metal host for the NER. Our work extends the landscape of electro plasmonic modulation and opens appealing new opportunities for quantum plasmonics.

Nonlocal response of plasmonic core-shell nanotopologies excited by dipole emitters

In light of the emergence of nonclassical effects, a paradigm shift in the conventional macroscopic treatment is required to accurately describe the interaction between light and plasmonic structures with deep-nanometer features. Towards this end, several nonlocal response models, supplemented by additional boundary conditions, have been introduced, investigating the collective motion of the free electron gas in metals. The study of the dipole-excited core-shell nanoparticle has been performed, by employing the following models: the hard-wall hydrodynamic model; the quantum hydrodynamic model; and the generalized nonlocal optical response. The analysis is conducted by investigating the near and far field characteristics of the emitter-nanoparticle system, while considering the emitter outside and inside the studied topology. It is shown that the above models predict striking spectral features, strongly deviating from the results obtained via the classical approach, for both simple and noble constitutive metals.

Numerical scheme for a nonlinear optical response of a metallic nanostructure: quantum hydrodynamic theory solved by adopting an effective Schrödinger equation

Quantum hydrodynamic theory (QHT) can describe some of the characteristic features of quantum electron dynamics that appear in metallic nanostructures, such as spatial nonlocality, electron spill-out, and quantum tunneling. Furthermore, numerical simulations based on QHT are more efficient than fully quantum mechanical approaches, as exemplified by time-dependent density functional theory using a jellium model. However, QHT involves kinetic energy functionals, the practical implementation of which typically induces significant numerical instabilities, particularly in nonlinear optical phenomena. To mitigate this problem, we develop a numerical solution to QHT that is quite stable, even in a nonlinear regime. The key to our approach is to rewrite the dynamical equation of QHT using the effective Schrödinger equation. We apply the new method to the linear and nonlinear responses of a metallic nanoparticle and compare the results with fully quantum mechanical calculations. The results demonstrate the numerical stability of our method, as well as the reliability and limitations of QHT.

Kinetic Energy Density Functionals Based on a Generalized Screened Coulomb Potential: Linear Response and Future Perspectives

We consider kinetic energy functionals that depend, beside the usual semilocal quantities (density, gradient, Laplacian of the density), on a generalized Yukawa potential, that is the screened Coulomb potential of the density raised to some power. These functionals, named Yukawa generalized gradient approximations (yGGA), are potentially efficient real-space semilocal methods that include significant non-local effects and can describe different important exact properties of the kinetic energy. In this work, we focus in particular on the linear response behavior for the homogeneous electron gas (HEG). We show that such functionals are able to reproduce the exact Lindhard function behavior with a very good accuracy, outperforming all other semilocal kinetic functionals. These theoretical advances allow us to perform a detailed analysis of a special class of yGGAs, namely the linear yGGA functionals. Thus, we show how the present approach can generalize the yGGA functionals improving the HEG linear behavior and leading to an extended formula for the kinetic functional. Moreover, testing on several jellium cluster model systems allows highlighting advantages and limitations of the linear yGGA functionals and future perspectives for the development of yGGA kinetic functionals.

General Framework of Canonical Quasinormal Mode Analysis for Extreme Nano-optics

Optical phenomena associated with an extremely localized field should be understood with considerations of nonlocal and quantum effects, which pose a hurdle to conceptualize the physics with a picture of eigenmodes. Here we first propose a generalized Lorentz model to describe general nonlocal media under linear mean-field approximation and formulate source-free Maxwell's equations as a linear eigenvalue problem to define the quasinormal modes. Then we introduce an orthonormalization scheme for the modes and establish a canonical quasinormal mode framework for general nonlocal media. Explicit formalisms for metals described by a quantum hydrodynamic model and polar dielectrics with nonlocal response are exemplified. The framework enables for the first time a direct modal analysis of mode transition in the quantum tunneling regime and provides physical insights beyond usual far-field spectroscopic analysis. Applied to nonlocal polar dielectrics, the framework also unveils the important roles of longitudinal phonon polaritons in optical response.

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.

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.

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.

Bright Optical Eigenmode of 1 nm^{3} Mode Volume

We report on the discovery and rationale to devise bright single optical eigenmodes that feature quantum-optical mode volumes of about 1  nm^{3}. Our findings rely on the development and application of a quasinormal mode theory that self-consistently treats fields and electron nonlocality, spill-out, and Landau damping around atomistic protrusions on a metallic nanoantenna. By outpacing Landau damping with radiation via properly designed antenna modes, the extremely localized modes become bright with radiation efficiencies reaching 30% and could provide up to 4×10^{7} times intensity enhancement.

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.

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.

Surface chemistry of quantum-sized metal nanoparticles under light illumination

Size reduction of metal nanoparticles increases the exposure of metal surfaces significantly, favoring heterogeneous chemistry at the surface of the nanoparticles. The optical properties of metal nanoparticles, such as light absorption, also exhibit a strong dependence on their size. It is expected that there will be strong coupling of light absorption and surface chemistry when the metal nanoparticles are small enough. For instance, metal nanoparticles with sizes in the range of 2–10 nm exhibit both surface plasmon resonances, which can efficiently produce high-energy hot electrons near the surface of the nanoparticles under light illumination, and the Coulomb blockade effect, which favors electron transfer from the metal nanoparticles to the surface adsorbates. The synergy of efficient hot electron generation and electron transfer on the surface of small metal nanoparticles leads to double-faced effects: (i) surface (adsorption) chemistry influences optical absorption in the metal nanoparticles, and (ii) optical absorption in the metal nanoparticles promotes (or inhibits) surface adsorption and heterogeneous chemistry. This review article focuses on the discussion of typical quantum phenomena in metal nanoparticles of 2–10 nm in size, which are referred to as “quantum-sized metal nanoparticles”. Both theoretical and experimental examples and results are summarized to highlight the strong correlations between the optical absorption and surface chemistry for quantum-sized metal nanoparticles of various compositions. A comprehensive understanding of these correlations may shed light on achieving high-efficiency photocatalysis and photonics.

Size reduction of metal nanoparticles increases the exposure of metal surfaces significantly, favoring heterogeneous photochemistry at the surface of the nanoparticles.

Extremely large third-order nonlinear optical effects caused by electron transport in quantum plasmonic metasurfaces with subnanometer gaps

In this study, a third-order nonlinear optical responses in quantum plasmonic metasurfaces composed of metallic nano-objects with subnanometer gaps were investigated using time-dependent density functional theory, a fully quantum mechanical approach. At gap distances of ≥ 0.6 nm, the third-order nonlinearities monotonically increased as the gap distance decreased, owing to enhancement of the induced charge densities at the gaps between nano-objects. Particularly, when the third harmonic generation overlapped with the plasmon resonance, a large third-order nonlinearity was achieved. At smaller gap distances down to 0.1 nm, we observed the appearance of extremely large third-order nonlinearity without the assistance of the plasmon resonance. At a gap distance of 0.1 nm, the observed third-order nonlinearity was approximately three orders of magnitude larger than that seen at longer gap distances. The extremely large third-order nonlinearities were found to originate from electron transport by quantum tunneling and/or overbarrier currents through the subnanometer gaps.

Plasmonic evolution of atomically size-selected Au clusters by electron energy loss spectrum

The plasmonic response of gold clusters with atom number (N) = 100–70 000 was investigated using scanning transmission electron microscopy-electron energy loss spectroscopy. For decreasing N, the bulk plasmon remains unchanged above N = 887 but then disappears, while the surface plasmon firstly redshifts from 2.4 to 2.3 eV above N = 887 before blueshifting towards 2.6 eV down to N = 300, and finally splitting into three fine features. The surface plasmon's excitation ratio is found to follow N^0.669, which is essentially R². An atomically precise evolution picture of plasmon physics is thus demonstrated according to three regimes: classical plasmon (N = 887–70 000), quantum confinement corrected plasmon (N = 300–887) and molecule related plasmon (N < 300).

Second-harmonic generation from subwavelength metal heterodimers

We experimentally study the optical second-harmonic generation (SHG) from deep subwavelength gold-silver heterodimers, and silver-silver and gold-gold homodimers. Our results indicate a heterodimer SHG that is an order of magnitude more intense than that of the homodimers. In contrast, full-wave calculations that consider the surface and bulk contribution of individual particles, which is the conventional view on such processes, suggest that it is the silver-silver homodimer that should prevail. Based on the deep subwavelength dimension of our structure, we propose that the heterodimer nonlinearity results from a Coulomb interaction between lumped oscillating charges and not from the surface nonlinearity of each particle, as convention would have it. Our proposed model can explain the larger SHG emission observed in gold-silver heterodimers and reproduces its unique spectral lineshape.

Plasmon-Enhanced Resonant Photoemission Using Atomically Thick Dielectric Coatings

By proposing an atomically thick dielectric coating on a metal nanoemitter, we theoretically show that the optical field tunneling of ultrafast-laser-induced photoemission can occur at an ultralow incident field strength of 0.03 V/nm. This coating strongly confines plasmonic fields and provides secondary field enhancement beyond the geometrical plasmon field enhancement effect, which can substantially reduce the barrier and enable more efficient photoemission. We numerically demonstrate that a 1 nm thick layer of SiO₂ around a Au-nanopyramid will enhance the resonant photoemission current density by 2 orders of magnitude, where the transition from multiphoton absorption to optical field tunneling is accessed at an incident laser intensity at least 10 times lower than that of the bare nanoemitter. The effects of the coating properties such as refractive index, thickness, and geometrical settings are studied, and tunable photoemission is numerically demonstrated by using different ultrafast lasers. Our approach can also directly be extended to nonmetal emitters, to-for example-2D material coatings, and to plasmon-induced hot carrier generation.

Optical bistability in gap-plasmon metasurfaces in consideration of classical nonlocal effects

Optical bistability of linear reflectance and third-harmonic generation is investigated in a metasurface consisting of metallic grating coupled with metallic film spaced with nonlinear dielectric material. Linear optical reflectance and electric field enhancement are achieved for gaps <20 nm in the presence of classical nonlocality in metallic nanostructures. Enlarged thresholds from the higher to lower reflectance states are observed from 140 kW/cm² for the local model to 300 kW/cm² for the nonlocal model for 0.5-nm gaps. Though the linear reflectance almost overlaps for local and nonlocal models for 20-nm gaps, the optical bistability hysteresis loops retain large differences because local field differences are amplified owing to the relation of nonlinear refraction with square of local field and historical evolution of the optical bistability.

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.

Improved surface-enhanced Raman scattering (SERS) sensitivity to molybdenum oxide nanosheets via the lightning rod effect with application in detecting methylene blue

MoO₂ nanomaterials show a superior surface-enhanced Raman scattering (SERS) property due to their high concentration of free electrons and low resistivity. However, the physical process of semiconductor-based SERS is still elusive because there are many factors that affect the local electromagnetic field intensity and the subsequent Raman intensity of the molecules in close proximity to the semiconductor nanomaterials. Herein, we investigate the important contribution of surface morphology to molybdenum oxide SERS. The MoO₃/MoO₂ nanosheets (NSs) are synthesized by oxidizing MoO₂ NS, and the surface roughness of MoO₃ can be controlled through adjusting the oxidization time. Compared with the MoO₂ NS before oxidization, the MoO₃/MoO₂ NSs exhibit a much stronger SERS signal, which favors their application as a SERS substrate to detect trace amounts of methylene blue molecules. The minimum detectable concentration is up to 10^-9 M and the maximum enhancement factor is about 1.4 × 10⁵. Meanwhile, excellent signal reproducibility is also observed using the MoO₃/MoO₂ NSs as the SERS substrate. A simulated electric field distribution shows that a stronger electric field enhancement is formed due to the lightning rod effect in the gap of corrugated MoO₃ NSs. These results demonstrate that the surface topography of molybdenum oxide may play a more important role than their oxidation state in SERS signal enhancement.

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.

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.

Plasmons in ultra-thin gold slabs with quantum spill-out: Fourier modal method, perturbative approach, and analytical model

We numerically study the effect of the quantum spill-out (QSO) on the plasmon mode indices of an ultra-thin metallic slab, using the Fourier modal method (FMM). To improve the convergence of the FMM results, a novel nonlinear coordinate transformation is suggested and employed. Furthermore, we present a perturbative approach for incorporating the effects of QSO on the plasmon mode indices, which agrees very well with the full numerical results. The perturbative approach also provides additional physical insight, and is used to derive analytical expressions for the mode indices using a simple model for the dielectric function. The analytical expressions reproduce the results obtained from the numerically-challenging spill-out problem with much less effort and may be used for understanding the effects of QSO on other plasmonic structures.

The Role of the Reduced Laplacian Renormalization in the Kinetic Energy Functional Development

The Laplacian of the electronic density diverges at the nuclear cusp, which complicates the development of Laplacian-level meta-GGA (LLMGGA) kinetic energy functionals for all-electron calculations. Here, we investigate some Laplacian renormalization methods, which avoid this divergence. We developed two different LLMGGA functionals, which improve the kinetic energy or the kinetic potential. We test these KE functionals in the context of Frozen-Density-Embedding (FDE), for a large palette of non-covalently interacting molecular systems. These functionals improve over the present state-of-the-art LLMGGA functionals for the FDE calculations.

Modeling and observation of mid-infrared nonlocality in effective epsilon-near-zero ultranarrow coaxial apertures

With advances in nanofabrication techniques, extreme-scale nanophotonic devices with critical gap dimensions of just 1-2 nm have been realized. Plasmons in such ultranarrow gaps can exhibit nonlocal response, which was previously shown to limit the field enhancement and cause optical properties to deviate from the local description. Using atomic layer lithography, we create mid-infrared-resonant coaxial apertures with gap sizes as small as 1 nm and observe strong evidence of nonlocality, including spectral shifts and boosted transmittance of the cutoff epsilon-near-zero mode. Experiments are supported by full-wave 3-D nonlocal simulations performed with the hybridizable discontinuous Galerkin method. This numerical method captures atomic-scale variations of the electromagnetic fields while efficiently handling extreme-scale size mismatch. Combining atomic-layer-based fabrication techniques with fast and accurate numerical simulations provides practical routes to design and fabricate highly-efficient large-area mid-infrared sensors, antennas, and metasurfaces.

Mode Splitting Induced by Mesoscopic Electron Dynamics in Strongly Coupled Metal Nanoparticles on Dielectric Substrates

We study strong optical coupling of metal nanoparticle arrays with dielectric substrates. Based on the Fermi Golden Rule, the particle–substrate coupling is derived in terms of the photon absorption probability assuming a local dipole field. An increase in photocurrent gain is achieved through the optical coupling. In addition, we describe light-induced, mesoscopic electron dynamics via the nonlocal hydrodynamic theory of charges. At small nanoparticle size (<20 nm), the impact of this type of spatial dispersion becomes sizable. Both absorption and scattering cross sections of the nanoparticle are significantly increased through the contribution of additional nonlocal modes. We observe a splitting of local optical modes spanning several tenths of nanometers. This is a signature of semi-classical, strong optical coupling via the dynamic Stark effect, known as Autler–Townes splitting. The photocurrent generated in this description is increased by up to 2%, which agrees better with recent experiments than compared to identical classical setups with up to 6%. Both, the expressions derived for the particle–substrate coupling and the additional hydrodynamic equation for electrons are integrated into COMSOL for our simulations.

Nonlocal and Size-Dependent Dielectric Function for Plasmonic Nanoparticles

We develop a theoretical approach to investigate the impact that nonlocal and finite-size effects have on the dielectric response of plasmonic nanostructures. Through simulations, comprehensive comparisons of the electron energy loss spectroscopy (EELS) and the optical performance are discussed for a gold spherical dimer system in terms of different dielectric models. Our study offers a paradigm of high efficiency compatible dielectric theoretical framework for accounting the metallic nanoparticles behavior combining local, nonlocal and size-dependent effects in broader energy and size ranges. The results of accurate analysis and simulation for these effects unveil the weight and the evolution of both surface and bulk plasmons vibrational mechanisms, which are important for further understanding the electrodynamics properties of structures at the nanoscale. Particularly, our method can be extended to other plasmonic nanostructures where quantum-size or strongly interacting effects are likely to play an important role.

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.