Nonlocal optical response in metallic nanostructures

Modulation of surface response in a single plasmonic nanoresonator

Scattering of light by plasmonic nanoparticles is classically described using bulk material properties with infinitesimally thin boundaries. However, because of the quantum nature of electrons, real interfaces have finite thickness, leading to nonclassical surface effects that influence light scattering in small particles. Electrical gating offers a promising route to control and study these effects, as static screening charges reside at the boundary. We investigate the modulation of the surface response upon direct electrical charging of single plasmonic nanoresonators. By analyzing measured changes in light scattering within the framework of surface response functions, we find the resonance shift well accounted for by modulation of the classical in-plane surface current. Unexpectedly, we also observed a change in the resonance width, indicating reduced losses for negatively charged resonators. This effect is attributed to a nonclassical out-of-plane surface response, extending beyond pure spill-out effects. Our experiments pave the way for electrically driven plasmonic modulators and metasurfaces, leveraging control over nonclassical surface effects.

Distribution of Single-Particle Resonances Determines the Plasmonic Response of Disordered Nanoparticle Ensembles

Understanding how colloidal soft materials interact with light is crucial to the rational design of optical metamaterials. Electromagnetic simulations are computationally expensive and have primarily been limited to model systems described by a small number of particles-dimers, small clusters, and small periodic unit cells of superlattices. In this work we study the optical properties of bulk, disordered materials comprising a large number of plasmonic colloidal nanoparticles using Brownian dynamics simulations and the mutual polarization method. We investigate the far-field and near-field optical properties of both colloidal fluids and gels, which require thousands of nanoparticles to describe statistically. We show that these disordered materials exhibit a distribution of particle-level plasmonic resonance frequencies that determines their ensemble optical response. Nanoparticles with similar resonant frequencies form anisotropic and oriented clusters embedded within the otherwise isotropic and disordered microstructures. These collectively resonating morphologies can be tuned with the frequency and polarization of incident light. Knowledge of particle resonant distributions may help to interpret and compare the optical responses of different colloidal structures, correlate and predict optical properties, and rationally design soft materials for applications harnessing light.

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.

Toward Optimum Coupling between Free Electrons and Confined Optical Modes

Free electrons are excellent tools to probe and manipulate nanoscale optical fields with emerging applications in ultrafast spectromicroscopy and quantum metrology. However, advances in this field are hindered by the small probability associated with the excitation of single optical modes by individual free electrons. Here, we theoretically investigate the scaling properties of the electron-driven excitation probability for a wide variety of optical modes including plasmons in metallic nanostructures and Mie resonances in dielectric cavities, spanning a broad spectral range that extends from the ultraviolet to the infrared region. The highest probabilities for the direct generation of three-dimensionally confined modes are observed at low electron and mode energies in small structures, with order-unity (∼100%) coupling demanding the use of <100 eV electrons interacting with eV polaritons confined down to tens of nanometers in space. Electronic transitions in artificial atoms also emerge as practical systems to realize strong coupling to few-eV free electrons. In contrast, conventional dielectric cavities reach a maximum probability in the few-percent range. In addition, we show that waveguide modes can be generated with higher-than-unity efficiency by phase-matched interaction with grazing electrons, suggesting a practical method to create multiple excitations of a localized optical mode by an individual electron through funneling the so-generated propagating photons into a confining cavity─an alternative approach to direct electron-cavity interaction. Our work provides a roadmap to optimize electron-photon coupling with potential applications in electron spectromicroscopy as well as nonlinear and quantum optics at the nanoscale.

Broadband unidirectional surface plasmon polaritons with low loss

Unidirectional surface plasmon polaritons (SPPs) have been proven to truly exist at an interface between a magnetized semiconductor and an opaque isotropic material, however, they suffer rather serious leakage loss (with propagation length shorter than two wavelengths) caused by nonlocality. In this work, we investigate an alternative category of unidirectional SPPs existing on a nonreciprocal plasmonic platform with a cladding composed of a dielectric heterostructure transversely terminated by metal. This unidirectional SPP mode exists for small wavenumbers within the entire upper bulk-mode bandgap of the magnetized semiconductor, hence it is robust against nonlocal effects over a broad band. In contrast to previous unidirectional SPPs, the leakage loss of the present unidirectional SPPs is significantly reduced by more than five times, since the portion of modal energy distributed in the cladding is substantially increased. A similar reduction in absorption losses associated with semiconductor dissipation is observed. Though the nonlocality induces a backward-propagating SPP with extremely large wavenumbers, it can be suppressed even at very small level of dissipation. Therefore, our proposed plasmonic waveguide actually exhibits exceptional unidirectional characteristics.

Curvature dependent onset of quantum tunneling in subnanometer gaps

The quantum tunneling in subnanometer gap sizes in gold dimers is studied in order to account for the dependency of the onset of quantum tunneling on the dimer's radius and accordingly the gap wall's curvature, realized in experiments. Several nanodimers both nanowires and nanospheres with various radii and gap sizes are modelled and simulated based on the quantum corrected model, determining the onset of the quantum tunneling. Results show that the onset of quantum tunneling is both dependent on the gap size as well as on the dimer's radius. As larger dimers result in larger effective conductivity volumes, the influence of the quantum tunneling begins in larger gap sizes in larger dimers.

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.

Electrically driven nanogap antennas and quantum tunneling regime

The optical and electrical characteristics of electrically-driven nanogap antennas are extremely sensitive to the nanogap region where the fields are tightly confined and electrons and photons can interplay. Upon injecting electrons in the nanogap, a conductance channel opens between the metal surfaces modifying the plasmon charge distribution and therefore inducing an electrical tuning of the gap plasmon resonance. Electron tunneling across the nanogap can be harnessed to induce broadband photon emission with boosted quantum efficiency. Under certain conditions, the energy of the emitted photons exceeds the energy of electrons, and this overbias light emission is due to spontaneous emission of the hot electron distribution in the electrode. We conclude with the potential of electrically controlled nanogap antennas for faster on-chip communication.

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.

An Optimized Schwarz Method for the Optical Response Model Discretized by HDG Method

An optimized Schwarz domain decomposition method (DDM) for solving the local optical response model (LORM) is proposed in this paper. We introduce a hybridizable discontinuous Galerkin (HDG) scheme for the discretization of such a model problem based on a triangular mesh of the computational domain. The discretized linear system of the HDG method on each subdomain is solved by a sparse direct solver. The solution of the interface linear system in the domain decomposition framework is accelerated by a Krylov subspace method. We study the spectral radius of the iteration matrix of the Schwarz method for the LORM problems, and thus propose an optimized parameter for the transmission condition, which is different from that for the classical electromagnetic problems. The numerical results show that the proposed method is effective.

Spatial nonlocality effect on the surface plasmon propagation in plasmonic nanospheres waveguide

Spatial nonlocality affects the plasmonic characteristics of nanostructures. We used the quasi-static hydrodynamic Drude model to obtain the surface plasmon excitation energies in various metallic nanosphere structures. The surface scattering and radiation damping rates were phenomenologically incorporated into this model. We demonstrate that spatial nonlocality increases the surface plasmon frequencies and total plasmon damping rates in a single nanosphere. This effect was amplified for small nanospheres and higher multipole excitation. In addition, we find that spatial nonlocality reduces the interaction energy between two nanospheres. We extended this model to a linear periodic chain of nanospheres. Then we obtain the dispersion relation of surface plasmon excitation energies using Bloch's theorem. We also show that spatial nonlocality decreases the group velocities and energy decay lengths of the propagating surface plasmon excitations. Finally, we demonstrated that the effect of spatial nonlocality is significant for very small nanospheres separated by short distances.

Theory of radial oscillations in metal nanoparticles driven by optically induced electron density gradients

We provide a microscopic approach to describe the onset of radial oscillation of a silver nanoparticle. Using the Heisenberg equation of motion framework, we find that the coupled ultrafast dynamics of coherently excited electron occupation and the coherent phonon amplitude initiate periodic size oscillations of the nanoparticle. Compared to the established interpretation of experiments, our results show a more direct coupling mechanism between the field intensity and coherent phonons. This interaction triggers a size oscillation via an optically induced electron density gradient occurring directly with the optical excitation. This source is more efficient than the incoherent heating process currently discussed in the literature and well-describes the early onset of the oscillations in recent experiments.

Nonlocal effects investigation via the coupling between localized and acoustic plasmons

A scheme to investigate nonlocal effects in metal using the coupling between localized graphene plasmons (GPs) and acoustic plasmons (APs) is proposed. Because of the extremely strong field confinement property, the APs on a configuration consisting of monolayer graphene and a metal film have different dispersions when the nonlocal response is considered or not. A graphene nanoribbon array can efficiently couple incident light to the localized GPs on the ribbons and subsequently the APs. The strong coupling between the two kinds of plasmon, equivalent to electric field dipole interaction, is highly related to the acoustic plasmonic dispersion and induces different absorption spectra, depending on the dispersion. Using a very simple model, nonlocal effects can be extracted from the spectra. The investigation provides a promising platform to manipulate nanophotonics and study nonlocal effects.

NV-plasmonics: modifying optical emission of an NV- center via plasmonic metal nanoparticles

The nitrogen-vacancy (NV) center in diamond is very sensitive to magnetic and electric fields, strain, and temperature. In addition, it is possible to optically interrogate individual defects, making it an ideal quantum-limited sensor with nanoscale resolution. A key limitation for the application of NV sensing is the optical brightness and collection efficiency of these defects. Plasmonic resonances of metal nanoparticles have been used in a variety of applications to increase the brightness and efficiency of quantum emitters, and therefore are a promising tool to improve NV sensing. However, the interaction between NV centers and plasmonic structures is largely unexplored. In particular, the back-action between NV and plasmonic nanoparticles is nonlinear and depends on optical wavelength, nanoparticle position, and metal type. Here we present the general theory of NV-plasmonic nanoparticle interactions. We detail how the interplay between NV response, including optical and vibrational signatures, and the plasmonic response of the metal nanoparticle results in modifications to the emission spectra. Our model is able to explain quantitatively the existing experimental measurements of NV centers near metal nanoparticles. In addition, it provides a pathway to developing new plasmonic structures to improve readout efficiencies in a range of applications for the NV center. This will enable higher precision sensors, with greater bandwidth as well as new readout modalities for quantum computing and communication.

Ill-Defined Topological Phases in Local Dispersive Photonic Crystals

In recent years there has been a great interest in topological materials and in their fascinating properties. Topological band theory was initially developed for condensed matter systems, but it can be readily applied to arbitrary wave platforms with few modifications. Thus, the topological classification of optical systems is usually regarded as being mathematically equivalent to that of condensed matter systems. Surprisingly, here we find that both the particle-hole symmetry and the dispersive nature of nonreciprocal photonic materials may lead to situations where the usual topological methods break down and the Chern topology becomes ill defined. It is shown that due to the divergence of the density of photonic states in plasmonic systems the gap Chern numbers can be noninteger notwithstanding that the relevant parametric space is compact. In order that the topology of a dispersive photonic crystal is well defined, it is essential to take into account the nonlocal effects in the bulk materials. We propose two different regularization methods to fix the encountered problems. Our results highlight that the regularized topologies may depend critically on the response of the bulk materials for large k.

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.

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.

In silico design of graphene plasmonic hot-spots

We propose a route for the rational design of engineered graphene-based nanostructures, which feature enormously enhanced electric fields in their proximity. Geometrical arrangements are inspired by nanopatterns allowing single molecule detection on noble metal substrates, and are conceived to take into account experimental feasibility and ease in fabrication processes. The attention is especially focused on enhancement effects occurring close to edge defects and grain boundaries, which are usually present in graphene samples. There, very localized hot-spots are created, with enhancement factors comparable to noble metal substrates, thus potentially paving the way for single molecule detection from graphene-based substrates.

Spatial Dispersion in Hypercrystal Distributed Feedback Lasing

This work is a first approach to investigate the role of spatial dispersion in photonic hypercrystals (PHCs). The scope of the presented analysis is focused on exploiting nonlocality, which can be controlled by appropriate design of the structure, to obtain new light generation effects in a distributed feedback (DFB) laser based on PHC, which are not observable under weak spatial dispersion. Here, we use effective medium approximation and our original model of threshold laser generation based on anisotropic transfer matrix method. To unequivocally identify nonlocal generation phenomena, the scope of our analysis includes comparison between local and nonlocal threshold generation spectra, which may be obtained for different geometries of PHC structure. In particular, we have presented that, in the presence of strong spatial dispersion, it is possible to obtain spectrally shifted Bragg wavelengths of TE- and TM-polarization spectra, lowered generation threshold levels for both light polarizations, generation of light of selected light polarization (TE or TM), or simultaneous generation of TE- and TM-polarized waves at different frequencies with controllable spectral separation, instead of single mode operation anticipated with local approach.

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.

Gaptronics: multilevel photonics applications spanning zero-nanometer limits

With recent advances in nanofabrication technology, various metallic gap structures with gap widths reaching a few to sub-nanometer, and even 'zero-nanometer', have been realized. At such regime, metallic gaps not only exhibit strong electromagnetic field confinement and enhancement, but also incorporate various quantum phenomena in a macroscopic scale, finding applications in ultrasensitive detection using nanosystems, enhancement of light-matter interactions in low-dimensional materials, and ultralow-power manipulation of electromagnetic waves, etc. Therefore, moving beyond nanometer to 'zero-nanometer' can greatly diversify applications of metallic gaps and may open the field of dynamic 'gaptronics.' In this paper, an overview is given on wafer-scale metallic gap structures down to zero-nanometer gap width limit. Theoretical description of metallic gaps from sub-10 to zero-nanometer limit, various wafer-scale fabrication methods and their applications are presented. With such versatility and broadband applicability spanning visible to terahertz and even microwaves, the field of 'gaptronics' can be a central building block for photochemistry, quantum optical devices, and 5/6G communications.

Strong and weak polarization-dependent interactions in connected and disconnected plasmonic nanostructures

We explore numerically and experimentally the formation of hybridized modes between a bright mode displayed by a gold nanodisc and either dark or bright modes of a nanorod - both elements being either separated by a nanometer-size gap (disconnected system) or relied on a metal junction (connected system). In terms of modeling, we compare the scattering or absorption spectra and field distributions obtained under oblique-incidence plane wave illumination with quasi-normal mode computation and an analytical model based on a coupled oscillator model. Both connected and disconnected systems have very different plasmon properties in longitudinal polarization. The disconnected system can be consistently understood in terms of the nature of hybridized modes and coupling strength using either QNMs or coupled oscillator model; however the connected configuration presents intriguing peculiarities based on the strong redistribution of charges implied by the presence of the metal connection. In practice, the fabrication of disconnected or connected configurations depends on the mitigation of lithographic proximity effects inherent to top-down lithography methods, which can lead to the formation of small metal junctions, while careful lithographic dosing allows one to fabricate disconnected systems with a gap as low as 20 nm. We obtained a very good agreement between experimentally measured scattering spectra and numerical predictions. The methods and analyses presented in this work can be applied to a wide range of systems, for potential applications in light-matter interactions, biosensing or strain monitoring.

Influence of Spatial Dispersion on the Electromagnetic Properties of Magnetoplasmonic Nanostructures

Magnetoplasmonics based on composite nanostructures is widely used in many biomedical applications. Nanostructures, consisting of a magnetic core and a gold shell, exhibit plasmonic properties, that allow the concentration of electromagnetic energy in ultra-small volumes when used, for example, in imaging and therapy. Magnetoplasmonic nanostructures have become an indispensable tool in nanomedicine. The gold shell protects the core from oxidation and corrosion, providing a biocompatible platform for tumor imaging and cancer treatment. By adjusting the size of the core and the shell thickness, the maximum energy concentration can be shifted from the ultraviolet to the near infrared, where the depth of light penetration is maximum due to low scattering and absorption by tissues. A decrease in the thickness of the gold shell to several nanometers leads to the appearance of the quantum effect of spatial dispersion in the metal. The presence of the quantum effect can cause both a significant decrease in the level of energy concentration by plasmon particles and a shift of the maxima to the short-wavelength region, thereby reducing the expected therapeutic effect. In this study, to describe the influence of the quantum effect of spatial dispersion, we used the discrete sources method, which incorporates the generalized non-local optical response theory. This approach made it possible to account for the influence of the nonlocal effect on the optical properties of composite nanoparticles, including the impact of the asymmetry of the core-shell structure on the energy characteristics. It was found that taking spatial dispersion into account leads to a decrease in the maximum value of the concentration of electromagnetic energy up to 25%, while the blue shift can reach 15 nm.

Artificial neural networks used to retrieve effective properties of metamaterials

We propose using deep neural networks for the fast retrieval of effective properties of metamaterials based on their angular-dependent reflection and transmission spectra from thin slabs. While we noticed that non-uniqueness is an issue for a successful application, we propose as a solution an automatic algorithm to subdivide the entire parameter space. Then, in each sub-space, the mapping between the optical response (complex reflection and transmission coefficients) and the corresponding material parameters (dielectric permittivity and permeability) is unique. We show that we can easily train one neural network per sub-space. For the final parameter retrieval, predictions from the different sub-networks are compared, and the one with the smallest error expresses the desired effective properties. Our approach allows a significant reduction in run-time, compared to more traditional least-squares fitting. Using deep neural networks to retrieve effective properties of metamaterials is a significant showcase for the application of AI technology to nanophotonic problems. Once trained, the nets can be applied to retrieve properties of a larger number of different metamaterials.

Strongly direction-dependent magnetoplasmons in mixed Faraday-Voigt configurations

The electrostatic theory of surface magnetoplasmons on a semi-infinite magnetized electron gas is generalized to mixed Faraday-Voigt configurations. We analyze a mixed Faraday-Voigt type of electrostatic surface waves that is strongly direction-dependent, and may be realized on narrow-gap semiconductors in the THz regime. A general expression for the dispersion relation is presented, with its dependence on the magnitude and orientation of the applied magnetic field. Remarkably, the group velocity is always perpendicular to the phase velocity. Both velocity and energy relations of the found magnetoplasmons are discussed in detail. In the appropriate limits the known surface magnetoplasmons in the higher-symmetry Faraday and Voigt configurations are recovered.

Spectral and photophysical modifications of porphyrins attached to core-shell nanoparticles. Theory and experiment

Plasmonic nanostructures, of which gold nanoparticles are the most elementary example, owe their unique properties to localized surface plasmons (LSP), the modes of free electron oscillation. LSP alter significantly electromagnetic field in the nanostructure neighborhood (i.e., near-field), which can modify the electric dipole transition rates in organic emitters. This study aims at investigating the influence of Au@SiO₂core-shell nanoparticles on the photophysics of porphyrins covalently attached to the nanoparticles surface. Guided by theoretical predictions, three sets of gold nanoparticles of different sizes were coated with a silica layer of similar thickness. The outer silica surface was functionalized with either free-basemeso-tetraphenylporphyrin or its zinc complex. Absorption and emission bands of porphyrin overlap in energy with a gold nanoparticle LSP resonance that provides the field enhancement. Silica separates the emitters from the gold surface, while the gold core size tunes the energy of the LSP resonance. The signatures of weak-coupling regime have been observed. Apart from modified emission profiles and shortened S₁lifetimes, Q band part intensity of the excitation spectra significantly increased with respect to the Soret band. The results were explained using classical transfer matrix simulations and electronic states kinetics, taking into account the photophysical properties of each chromophore. The calculations could reasonably well predict and explain the experimental outcomes. The discrepancies between the two were discussed.

Comparative Simulations of Conductive Nitrides as Alternative Plasmonic Nanostructures for Solar Cells

Particle layers employing conductive transition metal nitrides have been proposed as possible alternative plasmonic materials for photovoltaic applications due to their reduced losses compared to metal nanostructures. We critically compare the potential photocurrent gain from an additional layer made of nanopillars of nitrides with other material classes obtained in an optimized c-Si baseline solar cell, considering an experimental doping profile. A relative photocurrent gain enhancement of on average 5% to 10% is observed, achieving for a few scenarios around 30% gain. The local field enhancement is moderate around the resonances for nitrides which spread over the whole ultraviolet and visible range. We can characterize two types of nitrides: nitrides for which the shading effect remains a problem similar to for metals, and others which behave like dielectric scatterers with high photocurrent gain.

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.

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.

Combining density functional theory with macroscopic QED for quantum light-matter interactions in 2D materials

A quantitative and predictive theory of quantum light-matter interactions in ultra thin materials involves several fundamental challenges. Any realistic model must simultaneously account for the ultra-confined plasmonic modes and their quantization in the presence of losses, while describing the electronic states from first principles. Herein we develop such a framework by combining density functional theory (DFT) with macroscopic quantum electrodynamics, which we use to show Purcell enhancements reaching 10⁷ for intersubband transitions in few-layer transition metal dichalcogenides sandwiched between graphene and a perfect conductor. The general validity of our methodology allows us to put several common approximation paradigms to quantitative test, namely the dipole-approximation, the use of 1D quantum well model wave functions, and the Fermi's Golden rule. The analysis shows that the choice of wave functions is of particular importance. Our work lays the foundation for practical ab initio-based quantum treatments of light-matter interactions in realistic nanostructured materials.

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.

Nonreciprocal and Topological Plasmonics

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

Nanoelectromechanical modulation of a strongly-coupled plasmonic dimer

The ability of two nearly-touching plasmonic nanoparticles to squeeze light into a nanometer gap has provided a myriad of fundamental insights into light-matter interaction. In this work, we construct a nanoelectromechanical system (NEMS) that capitalizes on the unique, singular behavior that arises at sub-nanometer particle-spacings to create an electro-optical modulator. Using in situ electron energy loss spectroscopy in a transmission electron microscope, we map the spectral and spatial changes in the plasmonic modes as they hybridize and evolve from a weak to a strong coupling regime. In the strongly-coupled regime, we observe a very large mechanical tunability (~250 meV/nm) of the bonding-dipole plasmon resonance of the dimer at ~1 nm gap spacing, right before detrimental quantum effects set in. We leverage our findings to realize a prototype NEMS light-intensity modulator operating at ~10 MHz and with a power consumption of only 4 fJ/bit.

Broadband/multiband absorption through surface plasmon engineering in graphene-wrapped nanospheres

In this paper, a thin film constructed by a periodic assembly of graphene-wrapped particles with spherical geometry has been proposed as a polarization-insensitive reconfigurable perfect absorber. The performance of the proposed structure is based on the cooperative excitation of the quadrupole localized surface plasmons on graphene shells. By sweeping the quality of graphene shells, it is recognized that the low-quality graphene material is the best choice for the absorber design. Moreover, the effect of graphene chemical potential and periodicity of the particles on the absorptivity of the structure is investigated. The physical mechanism of performance is clarified by investigating the excited localized surface plasmon resonances. In addition, the angle-independent behavior up to around 60 degrees for both transverse electric (TE) and transverse magnetic (TM) waves is proved. Interestingly, by engineering the substrate height, our proposed absorber exhibits dynamic broadband performance due to the impedance matching and multiband absorption by enhancing the Fabry-Perot resonances of a micrometer-sized substrate. The possibility of attaining a similar static broadband response by stacking multiple layers is also proved. Our proposed sub-wavelength absorber can be suitable for novel optoelectronic devices due to its simple geometry.

Approaching the upper limits of the local density of states via optimized metallic cavities

By computational optimization of air-void cavities in metallic substrates, we show that the local density of states (LDOS) can reach within a factor of ≈10 of recent theoretical upper limits and within a factor ≈4 for the single-polarization LDOS, demonstrating that the theoretical limits are nearly attainable. Optimizing the total LDOS results in a spontaneous symmetry breaking where it is preferable to couple to a specific polarization. Moreover, simple shapes such as optimized cylinders attain nearly the performance of complicated many-parameter optima, suggesting that only one or two key parameters matter in order to approach the theoretical LDOS bounds for metallic resonators.

Numerical method for analyzing the near-field enhancement of nonspherical dielectric-core metallic-shell particles accounting for the nonlocal dispersion

Over the last few decades, dielectric core and metallic plasmonic shell (Die@Me) nanoparticles have found a wide variety of applications. The trend to reduce the thickness of the metallic coating requires to account for the influence of the nonlocal dispersion on the spectral response of such nanoparticles. In this paper, we use the discrete sources method and the generalized nonlocal optical response model to describe the nonlocality within the plasmonic metal shell. We found that the variation of the plasmonic shell thickness and the elongation of the nonspherical core-shell particle can enlarge the near-field enhancement and the absorption cross section by an order of magnitude. Besides, we show that the nonlocal dispersion can decrease the field enhancement in the wavelength domain up to 2.5 times with a small blue-shift of about 5 nm.

Effect of nonlocality in spatially uniform anisotropic metamaterials

In this study, we investigate an effect of spatial dispersion in anisotropic metamaterials of regular periodic geometry. We indicate conditions under which a local and nonlocal approach are convergent, as well as the areas of particularly strong nonlocality. Our analysis also reveals that new resonance transitions altering the topology of an iso-frequency surface arise in the presence of spatial dispersion. For the first time, we demonstrate that nonlocality can serve as a new mechanism for tailoring effective dispersion of an anisotropic metamaterial, which opens new venues for novel applications requiring strong direction discrimination of the incident radiation.

Importance of substrates for the visibility of "dark" plasmonic modes

Dark plasmonic modes have interesting properties, including longer lifetimes and narrower linewidths than their radiative counterpart, and little to no radiative losses. However, they have not been extensively studied yet due to their optical inaccessibility. In this work, we systematically investigated the dark radial breathing modes (RBMs) in monocrystalline gold nanodisks, specifically their outcoupling behavior into the far-field by cathodoluminescence spectroscopy. Increasing the substrate thickness resulted in an up to 4-fold enhanced visibility. This is attributed to breaking the mirror symmetry by the high-index substrate, creating an effective dipole moment. Furthermore, the resonance energy of the dark RMBs can be easily tuned by varying the nanodisk diameter, making them promising candidates for nanophotonic applications.

Physical Violations of the Bulk-Edge Correspondence in Topological Electromagnetics

In this Letter, we discuss two general classes of apparent violations of the bulk-edge correspondence principle for continuous topological photonic materials, associated with the asymptotic behavior of the surface modes for diverging wave numbers. Considering a nonreciprocal plasma as a model system, we show that the inclusion of spatial dispersion (e.g., hydrodynamic nonlocality) formally restores the bulk-edge correspondence by avoiding an unphysical response at large wave numbers. Most importantly, however, our findings show that, for the considered cases, the correspondence principle is physically violated for all practical purposes, as a result of the unavoidable attenuation of highly confined modes even if all materials are assumed perfect, with zero intrinsic bulk losses, due to confinement-induced Landau damping or nonlocality-induced radiation leakage. Our work helps clarifying the subtle and rich topological wave physics of continuous media.

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.

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.

Ultraviolet Interband Plasmonics With Si Nanostructures

Although Si acts as an electrical semiconductor, it has properties of an optical dielectric. Here, we revisit the behavior of Si as a plasmonic metal. This behavior was previously shown to arise from strong interband transitions that lead to negative permittivity of Si across the ultraviolet spectral range. However, few have studied the plasmonic characteristics of Si, particularly in its nanostructures. In this paper, we report localized plasmon resonances of Si nanostructures and the observation of plasmon hybridization in the UV (∼250 nm wavelength). In addition, simulation results show that Si nanodisk dimers can achieve a local intensity enhancement greater than ∼500-fold in a 1 nm gap. Lastly, we investigate hybrid Si-Al nanostructures to achieve sharp resonances in the UV, due to the coupling between plasmon resonances supported by Si and Al nanostructures. These results will have potential applications in the UV range, such as nanostructured devices for spectral filtering, plasmon-enhanced Si photodetectors, interrogation of molecular chirality, and catalysis. It could have significant impact on UV photolithography on patterned Si structures.

Towards rational design and optimization of near-field enhancement and spectral tunability of hybrid core-shell plasmonic nanoprobes

In biology, sensing is a major driver of discovery. A principal challenge is to create a palette of probes that offer near single-molecule sensitivity and simultaneously enable multiplexed sensing and imaging in the “tissue-transparent” near-infrared region. Surface-enhanced Raman scattering and metal-enhanced fluorescence have shown substantial promise in addressing this need. Here, we theorize a rational design and optimization strategy to generate nanostructured probes that combine distinct plasmonic materials sandwiching a dielectric layer in a multilayer core shell configuration. The lower energy resonance peak in this multi-resonant construct is found to be highly tunable from visible to the near-IR region. Such a configuration also allows substantially higher near-field enhancement, compared to a classical core-shell nanoparticle that possesses a single metallic shell, by exploiting the differential coupling between the two core-shell interfaces. Combining such structures in a dimer configuration, which remains largely unexplored at this time, offers significant opportunities not only for near-field enhancement but also for multiplexed sensing via the (otherwise unavailable) higher order resonance modes. Together, these theoretical calculations open the door for employing such hybrid multi-layered structures, which combine facile spectral tunability with ultrahigh sensitivity, for biomolecular sensing.