Modified field enhancement and extinction by plasmonic nanowire dimers due to nonlocal response

We study the effect of nonlocal optical response on the optical properties of metallic nanowires, by numerically implementing the hydrodynamical Drude model for arbitrary nanowire geometries. We first demonstrate the accuracy of our frequency-domain finite-element implementation by benchmarking it in a wide frequency range against analytical results for the extinction cross section of a cylindrical plasmonic nanowire. Our main results concern more complex geometries, namely cylindrical and bow-tie nanowire dimers that can strongly enhance optical fields. For both types of dimers we find that nonlocal response can strongly affect both the field enhancement in between the dimers and their respective extinction cross sections. In particular, we give examples of blueshifted maximal field enhancements near hybridized plasmonic dimer resonances that are still large but nearly two times smaller than in the usual local-response description. For the same geometry at a fixed frequency, the field enhancement and cross section can also be significantly more enhanced in the nonlocal-response model.

Plasmonic eigenmodes in individual and bow-tie graphene nanotriangles

In classical electrodynamics, nanostructured graphene is commonly modeled by the computationally demanding problem of a three-dimensional conducting film of atomic-scale thickness. Here, we propose an efficient alternative two-dimensional electrostatic approach where all calculation procedures are restricted to the graphene sheet. Furthermore, to explore possible quantum effects, we perform tight-binding calculations, adopting a random-phase approximation. We investigate multiple plasmon modes in 20 nm equilateral triangles of graphene, treating the optical response classically as well as quantum mechanically. Compared to the classical plasmonic spectrum which is "blind" to the edge termination, we find that the quantum plasmon frequencies exhibit blueshifts in the case of armchair edge termination of the underlying atomic lattice, while redshifts are found for zigzag edges. Furthermore, we find spectral features in the zigzag case which are associated with electronic edge states not present for armchair termination. Merging pairs of triangles into dimers, plasmon hybridization leads to energy splitting that appears strongest in classical calculations while splitting is lower for armchair edges and even more reduced for zigzag edges. Our various results illustrate a surprising phenomenon: Even 20 nm large graphene structures clearly exhibit quantum plasmonic features due to atomic-scale details in the edge termination.

Nonlocal optical response in metallic nanostructures

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

Multipole plasmons and their disappearance in few-nanometre silver nanoparticles

Electron energy-loss spectroscopy can be used for detailed spatial and spectral characterization of optical excitations in metal nanoparticles. In previous electron energy-loss experiments on silver nanoparticles with radii smaller than 20 nm, only the dipolar surface plasmon resonance was assumed to play a role. Here, applying electron energy-loss spectroscopy to individual silver nanoparticles encapsulated in silicon nitride, we observe besides the usual dipole resonance an additional surface plasmon resonance corresponding to higher angular momenta for nanoparticle radii as small as 4 nm. We study the radius and electron beam impact position dependence of both resonances separately. For particles smaller than 4 nm in radius the higher-order surface plasmon mode disappears, in agreement with generalized non-local optical response theory, while the dipole resonance blueshift exceeds our theoretical predictions. Unlike in optical spectra, multipole surface plasmons are important in electron energy-loss spectra even of ultrasmall metallic nanoparticles.

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

Inspired by recent measurements on individual metallic nanospheres that cannot be explained with traditional classical electrodynamics, we theoretically investigate the effects of nonlocal response by metallic nanospheres in three distinct settings: atomic spontaneous emission, electron energy loss spectroscopy, and light scattering. These constitute two near-field and one far-field measurements, with zero-, one-, and two-dimensional excitation sources, respectively. We search for the clearest signatures of hydrodynamic pressure waves in nanospheres. We employ a linearized hydrodynamic model, and Mie-Lorenz theory is applied for each case. Nonlocal response shows its mark in all three configurations, but for the two near-field measurements, we predict especially pronounced nonlocal effects that are not exhibited in far-field measurements. Associated with every multipole order is not only a single blueshifted surface plasmon but also an infinite series of bulk plasmons that have no counterpart in a local-response approximation. We show that these increasingly blueshifted multipole plasmons become spectrally more prominent at shorter probe-to-surface separations and for decreasing nanosphere radii. For selected metals, we predict hydrodynamic multipolar plasmons to be measurable on single nanospheres.

Nanophotonic control of the Förster resonance energy transfer efficiency

We have studied the influence of the local density of optical states (LDOS) on the rate and efficiency of Förster resonance energy transfer (FRET) from a donor to an acceptor. The donors and acceptors are dye molecules that are separated by a short strand of double-stranded DNA. The LDOS is controlled by carefully positioning the FRET pairs near a mirror. We find that the energy transfer efficiency changes with LDOS, and that, in agreement with theory, the energy transfer rate is independent of the LDOS, which allows one to quantitatively control FRET systems in a new way. Our results imply a change in the characteristic Förster distance, in contrast to common lore that this distance is fixed for a given FRET pair.

Projected Dipole Model for Quantum Plasmonics

Quantum effects of plasmonic phenomena have been explored through ab initio studies, but only for exceedingly small metallic nanostructures, leaving most experimentally relevant structures too large to handle. We propose instead an effective description with the computationally appealing features of classical electrodynamics, while quantum properties are described accurately through an infinitely thin layer of dipoles oriented normally to the metal surface. The nonlocal polarizability of the dipole layer-the only introduced parameter-is mapped from the free-electron distribution near the metal surface as obtained with 1D quantum calculations, such as time-dependent density-functional theory (TDDFT), and is determined once and for all. The model can be applied in two and three dimensions to any system size that is tractable within classical electrodynamics, while capturing quantum plasmonic aspects of nonlocal response and a finite work function with TDDFT-level accuracy. Applying the theory to dimers, we find quantum corrections to the hybridization even in mesoscopic dimers, as long as the gap itself is subnanometric.

Controlled generation of luminescent centers in hexagonal boron nitride by irradiation engineering

Luminescent centers in the two-dimensional material hexagonal boron nitride have the potential to enable quantum applications at room temperature. To be used for applications, it is crucial to generate these centers in a controlled manner and to identify their microscopic nature. Here, we present a method inspired by irradiation engineering with oxygen atoms. We systematically explore the influence of the kinetic energy and the irradiation fluence on the generation of luminescent centers. We find modifications of their density for both parameters, while a fivefold enhancement is observed with increasing fluence. Molecular dynamics simulations clarify the generation mechanism of these centers and their microscopic nature. We infer that V_NC_B and [Formula: see text] are the most likely centers formed. Ab initio calculations of their optical properties show excellent agreement with our experiments. Our methodology generates quantum emitters in a controlled manner and provides insights into their microscopic nature.

Surface plasmon modes of a single silver nanorod: an electron energy loss study

We present an electron energy loss study using energy filtered TEM of spatially resolved surface plasmon excitations on a silver nanorod of aspect ratio 14.2 resting on a 30 nm thick silicon nitride membrane. Our results show that the excitation is quantized as resonant modes whose intensity maxima vary along the nanorod's length and whose wavelength becomes compressed towards the ends of the nanorod. Theoretical calculations modelling the surface plasmon response of the silver nanorod-silicon nitride system show the importance of including retardation and substrate effects in order to describe accurately the energy dispersion of the resonant modes.

Coupling nitrogen-vacancy centers in diamond to superconducting flux qubits

We propose a method to achieve coherent coupling between nitrogen-vacancy (NV) centers in diamond and superconducting (SC) flux qubits. The resulting coupling can be used to create a coherent interaction between the spin states of distant NV centers mediated by the flux qubit. Furthermore, the magnetic coupling can be used to achieve a coherent transfer of quantum information between the flux qubit and an ensemble of NV centers. This enables a long-term memory for a SC quantum processor and possibly an interface between SC qubits and light.

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

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

Gauging a quantum heat bath with dissipative Landau-Zener transitions

We calculate the exact Landau-Zener transition probabilities for a qubit with an arbitrary linear coupling to a bath at zero temperature. The final quantum state exhibits a peculiar entanglement between the qubit and the bath. In the special case of diagonal coupling, the bath does not influence the transition probability, whatever the speed of the Landau-Zener sweep. It is proposed to use Landau-Zener transitions to determine both the reorganization energy and the integrated spectral density of the bath. Possible applications include circuit QED and molecular nanomagnets.

Nonlocal study of ultimate plasmon hybridization

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

Surface-enhanced Raman spectroscopy: nonlocal limitations

Giant field enhancement and field singularities are a natural consequence of the commonly employed local-response framework. We show that a more general nonlocal treatment of the plasmonic response leads to new and possibly fundamental limitations on field enhancement with important consequences for our understanding of surface-enhanced Raman spectroscopy (SERS). The intrinsic length scale of the electron gas serves to smear out assumed field singularities, leaving the SERS enhancement factor finite, even for geometries with infinitely sharp features. For silver nanogroove structures, mimicked by periodic arrays of half-cylinders (up to 120 nm in radius), we find no enhancement factors exceeding 10 orders of magnitude (10(10)).

Robustness of the far-field response of nonlocal plasmonic ensembles

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

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

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

Surface plasmon wave adapter designed with transformation optics

On the basis of transformation optics, we propose the design of a surface plasmon wave adapter which confines surface plasmon waves on non-uniform metal surfaces and enables adiabatic mode transformation of surface plasmon polaritons with very short tapers. This adapter can be simply achieved with homogeneous anisotropic naturally occurring materials or subwavelength grating-structured dielectric materials. Full wave simulations based on a finite-element method have been performed to validate our proposal.

Combining experiments on luminescent centres in hexagonal boron nitride with the polaron model and ab initio methods towards the identification of their microscopic origin

The two-dimensional material hexagonal boron nitride (hBN) hosts luminescent centres with emission energies of ∼2 eV which exhibit pronounced phonon sidebands. We investigate the microscopic origin of these luminescent centres by combining ab initio calculations with non-perturbative open quantum system theory to study the emission and absorption properties of 26 defect transitions. Comparing the calculated line shapes with experiments we narrow down the microscopic origin to three carbon-based defects: C2CB, C2CN, and VNCB. The theoretical method developed enables us to calculate so-called photoluminescence excitation (PLE) maps, which show excellent agreement with our experiments. The latter resolves higher-order phonon transitions, thereby confirming both the vibronic structure of the optical transition and the phonon-assisted excitation mechanism with a phonon energy ∼170 meV. We believe that the presented experiments and polaron-based method accurately describe luminescent centres in hBN and will help to identify their microscopic origin.

Local optical density of states in finite crystals of plane scatterers

Spontaneous emission rates in a dielectric structure are position dependent and proportional to the local optical density of states. The latter can be calculated when the Green function is known. In our scalar formalism, we model dielectric slabs as infinitely thin planes and use the T-matrix formalism of multiple-scattering theory to find an exact analytical expression for the Green function of a dielectric mirror of arbitrary number of unit cells N. All the propagating and guided modes of the structure are found. There are at most N guided modes and their dispersion relations are studied. The guided modes appear around frequencies corresponding to the first stop band in normal direction. Local densities of propagating and guided modes are presented, also for frequencies where the layered structure acts as an omnidirectional mirror.

Quantum optical effective-medium theory for loss-compensated metamaterials

A central aim in metamaterial research is to engineer subwavelength unit cells that give rise to desired effective-medium properties and parameters, such as a negative refractive index. Ideally one can disregard the details of the unit cell and employ the effective description instead. A popular strategy to compensate for the inevitable losses in metallic components of metamaterials is to add optical gain material. Here we study the quantum optics of such loss-compensated metamaterials at frequencies for which effective parameters can be unambiguously determined. We demonstrate that the usual effective parameters are insufficient to describe the propagation of quantum states of light. Furthermore, we propose a quantum optical effective-medium theory instead and show that it correctly predicts the properties of the light emerging from loss-compensated metamaterials.

Spontaneous-emission rates in finite photonic crystals of plane scatterers

The concept of a plane scatterer that was developed earlier for scalar waves is generalized so that polarization of light is included. Starting from a Lippmann-Schwinger formalism for vector waves, we show that the Green function has to be regularized before T matrices can be defined in a consistent way. After the regularization, optical modes and Green functions are determined exactly for finite structures built up of an arbitrary number of parallel planes, at arbitrary positions, and where each plane can have different optical properties. The model is applied to the special case of finite crystals consisting of regularly spaced identical planes, where analytical methods can be taken further and only light numerical tasks remain. The formalism is used to calculate position- and orientation-dependent spontaneous-emission rates inside and near the finite photonic crystals. The results show that emission rates and reflection properties can differ strongly for scalar and for vector waves. The finite size of the crystal influences the emission rates. For parallel dipoles close to a plane, emission into guided modes gives rise to a peak in the frequency-dependent emission rate.

Hyperbolic metamaterial lens with hydrodynamic nonlocal response

We investigate the effects of hydrodynamic nonlocal response in hyperbolic metamaterials (HMMs), focusing on the experimentally realizable parameter regime where unit cells are much smaller than an optical wavelength but much larger than the wavelengths of the longitudinal pressure waves of the free-electron plasma in the metal constituents. We derive the nonlocal corrections to the effective material parameters analytically, and illustrate the noticeable nonlocal effects on the dispersion curves numerically. As an application, we find that the focusing characteristics of a HMM lens in the local-response approximation and in the hydrodynamic Drude model can differ considerably. In particular, the optimal frequency for imaging in the nonlocal theory is blueshifted with respect to that in the local theory. Thus, to detect whether nonlocal response is at work in a hyperbolic metamaterial, we propose to measure the near-field distribution of a hyperbolic metamaterial lens.

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.