Surface-plasmon dispersion and size dependence of Mie resonance: Silver versus simple metals

Anisotropy Effects on the Plasmonic Response of Nanoparticle Dimers

We present an ab initio study of the anisotropy and atomic relaxation effects on the optical properties of nanoparticle dimers. Special emphasis is placed on the hybridization process of localized surface plasmons, plasmon-mediated photoinduced currents, and electric-field enhancement in the dimer junction. We show that there is a critical range of separations between the clusters (0.1-0.5 nm) in which the detailed atomic structure in the junction and the relative orientation of the nanoparticles have to be considered to obtain quantitative predictions for realistic nanoplasmonic devices. It is worth noting that this regime is characterized by the emergence of electron tunneling as a response to the driven electromagnetic field. The orientation of the particles not only modifies the attainable electric field enhancement but can lead to qualitative changes in the optical absorption spectrum of the system.

Nonlocal optical response in metallic nanostructures

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

Quantum effects in the optical response of extended plasmonic gaps: validation of the quantum corrected model in core-shell nanomatryushkas

Electron tunneling through narrow gaps between metal nanoparticles can strongly affect the plasmonic response of the hybrid nanostructure. Although quantum mechanical in nature, this effect can be properly taken into account within a classical framework of Maxwell equations using the so-called Quantum Corrected Model (QCM). We extend previous studies on spherical cluster and cylindrical nanowire dimers where the tunneling current occurs in the extremely localized gap regions, and perform quantum mechanical time dependent density functional theory (TDDFT) calculations of the plasmonic response of cylindrical core-shell nanoparticles (nanomatryushkas). In this axially symmetric situation, the tunneling region extends over the entire gap between the metal core and the metallic shell. For core-shell separations below 0.5 nm, the standard classical calculations fail to describe the plasmonic response of the cylindrical nanomatryushka, while the QCM can reproduce the quantum results. Using the QCM we also retrieve the quantum results for the absorption cross section of the spherical nanomatryushka calculated by V. Kulkarni et al. [Nano Lett. 13, 5873 (2013)]. The comparison between the model and the full quantum calculations establishes the applicability of the QCM for a wider range of geometries that hold tunneling gaps.

A classical treatment of optical tunneling in plasmonic gaps: extending the quantum corrected model to practical situations

The optical response of plasmonic nanogaps is challenging to address when the separation between the two nanoparticles forming the gap is reduced to a few nanometers or even subnanometer distances. We have compared results of the plasmon response within different levels of approximation, and identified a classical local regime, a nonlocal regime and a quantum regime of interaction. For separations of a few Ångstroms, in the quantum regime, optical tunneling can occur, strongly modifying the optics of the nanogap. We have considered a classical effective model, so called Quantum Corrected Model (QCM), that has been introduced to correctly describe the main features of optical transport in plasmonic nanogaps. The basics of this model are explained in detail, and its implementation is extended to include nonlocal effects and address practical situations involving different materials and temperatures of operation.

Nonlocal effects: relevance for the spontaneous emission rates of quantum emitters coupled to plasmonic structures

The spontaneous emission rate of dipole emitters close to plasmonic dimers are theoretically studied within a nonlocal hydrodynamic model. A nonlocal model has to be used since quantum emitters in the immediate environment of a metallic nanoparticle probe its electronic structure. Compared to local calculations, the emission rate is significantly reduced. The influence is mostly pronounced if the emitter is located close to sharp edges. We suggest to use quantum emitters to test nonlocal effects in experimentally feasible configurations.

Nanocrystalline materials: recent advances in crystallographic characterization techniques

Most properties of nanocrystalline materials are shape-dependent, providing their exquisite tunability in optical, mechanical, electronic and catalytic properties. An example of the former is localized surface plasmon resonance (LSPR), the coherent oscillation of conduction electrons in metals that can be excited by the electric field of light; this resonance frequency is highly dependent on both the size and shape of a nanocrystal. An example of the latter is the marked difference in catalytic activity observed for different Pd nanoparticles. Such examples highlight the importance of particle shape in nanocrystalline materials and their practical applications. However, one may ask 'how are nanoshapes created?', 'how does the shape relate to the atomic packing and crystallography of the material?', 'how can we control and characterize the external shape and crystal structure of such small nanocrystals?'. This feature article aims to give the reader an overview of important techniques, concepts and recent advances related to these questions. Nucleation, growth and how seed crystallography influences the final synthesis product are discussed, followed by shape prediction models based on seed crystallography and thermodynamic or kinetic parameters. The crystallographic implications of epitaxy and orientation in multilayered, core-shell nanoparticles are overviewed, and, finally, the development and implications of novel, spatially resolved analysis tools are discussed.

Quantum mechanical origin of the plasmon: from molecular systems to nanoparticles

The surface plasmon resonance (SPR) of noble metal nanoparticles is reviewed in terms of both classical and quantum mechanical approaches. The collective oscillation of the free electrons responsible for the plasmon is well described using classical electromagnetic theory for large systems (from about 10 to 100 nm). In cases where quantum effects are important, this theory fails and first principle approaches like time-dependent density functional theory (TDDFT) must be used. In this paper, we give an account of the current understanding of the quantum mechanical origin of plasmon resonances. We provide some insight into how the discrete absorption spectrum of small noble metal clusters evolves into a strong plasmon peak with increasing particle size. The collective character of the plasmon is described in terms of the constructive addition of single-particle excitations. As the system size increases, the number of single-particle excitations increases as well. A configuration interaction (CI) approach can be applied to describe the optical properties of particles of all shapes and sizes, providing a consistent definition of plasmon resonances. Finally, we expand our analysis to thiolate-protected nanoparticles and analyze the effects of ligands on the plasmon.

Surface scattering contribution to the plasmon width in embedded Ag nanospheres

Nanometer-sized metal particles exhibit broadening of the localized surface plasmon resonance (LSPR) in comparison to its value predicted by the classical Mie theory. Using our model for the LSPR dependence on non-local surface screening and size quantization, we quantitatively relate the observed plasmon width to the nanoparticle radius R and the permittivity of the surrounding medium ε(m). For Ag nanospheres larger than 8 nm only the non-local dynamical effects occurring at the surface are important and, up to a diameter of 25 nm, dominate over the bulk scattering mechanism. Qualitatively, the LSPR width is inversely proportional to the particle size and has a nonmonotonic dependence on the permittivity of the host medium, exhibiting for Ag a maximum at ε(m) ≈ 2.5. Our calculated LSPR width is compared with recent experimental data.

Surface plasmon dependence on the electron density profile at metal surfaces

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

Tunable plasmons in atomically thin gold nanodisks

The ability to modulate light at high speeds is of paramount importance for telecommunications, information processing and medical imaging technologies. This has stimulated intense efforts to master optoelectronic switching at visible and near-infrared frequencies, although coping with current computer speeds in integrated architectures still remains a major challenge. As a partial success, mid-infrared light modulation has been recently achieved through gating patterned graphene. Here we show that atomically thin noble metal nanoislands can extend optical modulation to the visible and near-infrared spectral range. We find plasmons in thin metal nanodisks to produce similar absorption cross-sections as spherical particles of the same diameter. Using realistic levels of electrical doping, plasmons are shifted by about half their width, thus leading to a factor-of-two change in light absorption. These results, which we substantiate on microscopic quantum theory of the optical response, hold great potential for the development of electrical visible and near-infrared light modulation in integrable, nanoscale devices.

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.

Effects of the atomic level shift in the Auger neutralization rates of noble metal surfaces

In this work we compare characteristics of Auger neutralization of [Formula: see text] ions at noble metal and free-electron metal surfaces. For noble metals, we find that the position of the energy level of He with respect to the Fermi level has a non-negligible influence on the values of the calculated Auger rates through the evaluation of the surface dielectric susceptibility. We conclude that even though our calculated rates are accurate, further theoretical effort is needed to obtain realistic values of the energy level of He in front of these surfaces.

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

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

Quantum effects and nonlocality in strongly coupled plasmonic nanowire dimers

Using a fully quantum mechanical approach we study the optical response of a strongly coupled metallic nanowire dimer for variable separation widths of the junction between the nanowires. The translational invariance of the system allows to apply the time-dependent density functional theory (TDDFT) for nanowires of diameters up to 10 nm which is the largest size considered so far in quantum modeling of plasmonic dimers. By performing a detailed analysis of the optical extinction, induced charge densities, and near fields, we reveal the major nonlocal quantum effects determining the plasmonic modes and field enhancement in the system. These effects consist mainly of electron tunneling between the nanowires at small junction widths and dynamical screening. The TDDFT results are compared with results from classical electromagnetic calculations based on the local Drude and non-local hydrodynamic descriptions of the nanowire permittivity, as well as with results from a recently developed quantum corrected model. The latter provides a way to include quantum mechanical effects such as electron tunneling in standard classical electromagnetic simulations. We show that the TDDFT results can be thus retrieved semi-quantitatively within a classical framework. We also discuss the shortcomings of classical non-local hydrodynamic approaches. Finally, the implications of the actual position of the screening charge density at the gap interfaces are discussed in connection with plasmon ruler applications at subnanometric distances.

Nonlocal optical effects on the Goos-Hänchen shift at an interface of a composite material of metallic nanoparticles

We present a theoretical study on the nonlocal optical effects on the Goos-Hänchen (GH) shift of reflected light from a composite material of metallic nanoparticles (MNPs). Using different nonlocal effective medium models, it is observed that such effects can be significant for small MNP of sizes down to a few nanometers. For small metallic volume fractions, the composite behaves like dielectric and the nonlocal effects lead to significant different Brewster angles, at which large negative GH shifts take place. For larger volume fractions or shorter wavelengths, the composite behaves more like metals and the nonlocal effects also lead to different Brewster angles but at values close to grazing incidence. These results will have significant implications in the application of different effective medium models for the characterization of these nanometallic composites when the MNPs are down to a few nanometers in size.

Robust subnanometric plasmon ruler by rescaling of the nonlocal optical response

We present the optical response of two interacting metallic nanowires calculated for separation distances down to angstrom range. State-of-the-art local and nonlocal approaches are compared with full quantum time-dependent density functional theory calculations that give an exact account of nonlocal and tunneling effects. We find that the quantum results are equivalent to those from classical approaches when the nanoparticle separation is defined as the separation between centroids of the screening charges. This establishes a universal plasmon ruler for subnanometric distances. Such a ruler not only impacts the basis of many applications of plasmonics, but also provides a robust rule for subnanometric metrology.

Evidence for rod-shaped DNA-stabilized silver nanocluster emitters

Fluorescent DNA-stabilized silver nanoclusters contain both cationic and neutral silver atoms. The absorbance spectra of compositionally pure solutions follow the trend expected for rod-shaped silver clusters, consistent with the polarized emission measured from individual nanoclusters. The data suggest a rod-like assembly of silver atoms, with silver cations mediating attachment to the bases.

Tunable molecular plasmons in polycyclic aromatic hydrocarbons

We show that chemically synthesized polycyclic aromatic hydrocarbons (PAHs) exhibit molecular plasmon resonances that are remarkably sensitive to the net charge state of the molecule and the atomic structure of the edges. These molecules can be regarded as nanometer-sized forms of graphene, from which they inherit their high electrical tunability. Specifically, the addition or removal of a single electron switches on/off these molecular plasmons. Our first-principles time-dependent density-functional theory (TDDFT) calculations are in good agreement with a simpler tight-binding approach that can be easily extended to much larger systems. These fundamental insights enable the development of novel plasmonic devices based upon chemically available molecules, which, unlike colloidal or lithographic nanostructures, are free from structural imperfections. We further show a strong interaction between plasmons in neighboring molecules, quantified in significant energy shifts and field enhancement, and enabling molecular-based plasmonic designs. Our findings suggest new paradigms for electro-optical modulation and switching, single-electron detection, and sensing using individual molecules.

Perfect imaging, epsilon-near zero phenomena and waveguiding in the scope of nonlocal effects

Plasmons in metals can oscillate on a sub-wavelength length scale and this large-k response constitutes an inherent prerequisite for fascinating effects such as perfect imaging and intriguing wave phenomena associated with the epsilon-near-zero (ENZ) regime. While there is no upper cut-off within the local-response approximation (LRA) of the plasma polarization, nonlocal dynamics suppress response beyond ω/v(F), where v(F) is the Fermi velocity of the electron gas. Nonlocal response has previously been found to pose limitations to field-enhancement phenomena. Accounting for nonlocal hydrodynamic response, we show that perfect imaging is surprisingly only marginally affected by nonlocal properties of a metal slab, even for a deep subwavelength case and an extremely thin film. Similarly, for the ENZ response we find no indications of nonlocal response jeopardizing the basic behaviors anticipated from the LRA. Finally, our study of waveguiding of gap plasmons even shows a positive nonlocal influence on the propagation length.

Growth kinetics and size-dependent wetting of Ag/α-Al₂O₃(0001) nanoparticles studied via the plasmonic response

The growth of vapour-deposited silver nanoparticles on α-Al₂O₃ was studied in situ from 190 to 675 K by surface differential reflectivity spectroscopy in the UV-visible range. Changes in size, shape and density were derived from the plasmonic response modelled in the framework of interface susceptibilities by assuming that supported clusters were in the form of truncated spheres. The sticking coefficient of silver on alumina is close to one up to T ≃ 575 K before entering a regime of incomplete condensation. The Arrhenius dependence of the saturation density indicates a nucleation on defects at low temperature (T ≤ 300 K) and detrapping above. The particle size D evolution follows temporal power laws, independent of temperature and flux, which characterize the growth (D ∼ t(0.31)) and coalescence (D ∼ t(0.55)) of the film. These are indicative of the growth of isolated particles at constant density and dynamic coalescence, respectively. The wetting angle of the silver clusters is shown to increase during the growth regime, which is assigned to a combination of surface stress and mismatch-induced strain, and to decrease upon coalescence, which is attributed to plastic relaxation. For particles larger than 10 nm in size, the values of contact angle and adhesion energy level off with asymptotic limits (θ(c) = 127.5° ± 1° and 0.48 ± 0.02 J m⁻²) that nicely agree with tabulated data. This work highlights the ability of nanoplasmics to monitor in situ the growth kinetics of thin supported films.

Quantitative analysis of nanoparticle growth through plasmonics

Plasmon excitation appears to be a powerful and flexible tool for probing in situ and in real time the growth of supported conducting metal nanoparticles. However, although models exist for analysing optical profiles, limitations arise in the realistic modelling of particle shape from the lack of knowledge of temperature effects and of broadening sources. This paper reports on the growth of silver on alumina at 190-675 K monitored by surface differential reflectivity spectroscopy in the UV-visible range. In the framework of plasmonic response analysis, particles are modelled by truncated spheres. Their polarizabilities are computed within the quasi-static approximation and used as an input to the interface susceptibilities model in order to determine the Fresnel reflection coefficient. The pivotal importance of the thermal variation of the metal dielectric constant is demonstrated. Finite-size effects are accounted for. As size distribution fluctuations contribute marginally to the lineshape compared to the aspect ratio (diameter/height) distribution, a convolution method for representing the experimental broadening is introduced. Effects of disorder on the lineshape are discussed. It is highlighted that beside the quality of the fit (not a proof by itself!), physical meaning of the parameters related to the sticking probability, growth and wetting is crucially required for validating models. The proposed modelling opens interesting perspectives for the quantitative study of growth via plasmonics, in particular in the case of noble metals.

Growth and optical properties of Ag clusters deposited on poly(ethylene terephthalate)

The growth and concomitant evolution of the optical properties of Ag nano-clusters deposited on biaxially extruded poly(ethylene terephthalate) films is studied by reflectance difference spectroscopy. It is demonstrated by low energy ion scattering and simulated optical spectra that the clusters form a two-dimensional layer buried beneath the surface of the substrate. The experimental spectra are described by simulations in which different configurations of the host such as anisotropy, amorphization, and dilution are considered in an effective medium approach. The contribution of the anisotropic substrate is used to explain the resulting line shapes. We also discuss the role of the rate of change of the filling fraction with Ag coverage in the evolution of the spectra and the detection of the onset of coalescence by optical means.

Strain effects on the SERS enhancements for spherical silver nanoparticles

We demonstrate in the present work through the utilization of classical Mie scattering theory in conjunction with a radiation damping and dynamic depolarization-corrected electrostatic approximation the significant effect that mechanical strain has on the optical properties of spherical silver nanoparticles. Through appropriate modifications of the bulk dielectric functions, we find that the application of tensile strain generates significant enhancements in the local electric field for the silver nanoparticles, leading to large SERS enhancements of more than 300% compared to bulk, unstrained nanoparticles when a 5% tensile strain is applied. While the strain-induced SERS enhancements are found to be strongest for nanoparticle diameters where radiation damping effects are minimized, we find that the surface plasmon resonance wavelengths are relatively unchanged by mechanical strain, and that the various measures of the far field optical efficiencies (absorption, scattering, extinction) can be enhanced by up to 150% through the application of tensile strain. The present findings indicate the opportunity to actively engineer and enhance the optical properties of silver nanoparticles through the application of mechanical deformation.

Sub-10 ohm resistance gold films prepared by removal of ligands from thiol-stabilized 6 nm gold nanoparticles

The optical and electrical properties of dodecanethiol-stabilized nanoparticles (6 nm diameter gold core) have been investigated over a range of film thicknesses and temperatures. The surface plasmon resonance absorbance is found to be dependent on temperature. Heating of the nanoparticle film causes desorption of the thiol from the surface of the gold nanoparticle, resulting in irreversible changes to the absorption spectra of the nanoparticle film. Atomic force microscopy images of the samples before and after heating for different film thicknesses reveal structural changes and increased domain connectivity for thicker films leading to sub-10 ohm resistances measured for the 15-layer film.

Size effects in thermal and photochemistry of (NO)2 on Ag nanoparticles

NO dimers adsorbed on alumina supported silver nanoparticles (Ag NPs, radii R approximately 1-6 nm) show decreasing desorption temperatures and complex behavior of photoinduced desorption with decreasing NP size. In particular, for resonant excitation of the (1,0) Mie plasmon at 3.5 eV the photoinduced desorption cross section increases with 1/R, showing a pronounced enhancement (40 times) at R approximately 2.5 nm compared to Ag(111). At 4.7 eV the translational temperature of photodesorbed NO increases strongly with 1/R. We discuss these trends and peculiarities in terms of the size-dependent properties of the Ag NPs.

Hyperthermal chaotic photodesorption of xenon from alumina-supported silver nanoparticles: plasmonic coupling and plasmon-induced desorption

Excitation of Xe monolayers on alumina-supported silver nanoparticles (AgNPs) by laser light in the (1,0) Mie plasmon resonance can lead to desorption of Xe atoms with hyperthermal energy and chaotic time structure. The chaotic behavior is most likely due to plasmonic coupling between AgNPs. We argue that the desorption is induced by direct energy transfer to the adsorbate from the Pauli repulsion of the collectively oscillating electrons of the plasmon at the surface. A simple model calculation shows that this is possible. A connection between both effects appears likely.

Adsorption orientations and interactions of methyl orange on negatively and positively charged colloidal silver particles

Both positively and negatively charged colloidal silver particles were prepared from chemical deoxidized methods. Then UV-visible absorption, fluorescence, and surface-enhanced Raman scattering of methyl orange adsorbed onto surfaces of these two kinds of particles were observed and compared with each other. The results indicate that dye molecules may adsorb onto these two kinds of silver surface in differing adsorption orientations with different interactions, which caused the different phenomena.

Optical Effects of Metallic Nanoparticles

Metallic nanoparticles show a rich optical behaviour because of their strong light absorption and scattering, wide spectral tunability, and interesting optical near-field effects. Research into optical effects of metallic nanoparticles, a field with a long tradition, has been developing rapidly in recent years as a result of progress in nanoparticle fabrication, spectroscopic techniques, and computational methods. This article provides a survey of optical effects of metallic nanoparticles, covering both fundamental phenomena and emerging applications.

Finite-size effects in surface-enhanced Raman scattering in noble-metal nanoparticles: a semiclassical approach

We study finite-size effects in surface-enhanced Raman scattering (SERS) from molecules adsorbed on small metal particles. Within an electromagnetic description of SERS, the enhancement of the Raman signal originates from the local field of the surface plasmon resonance in a nanoparticle. With decreasing particle sizes, this enhancement is reduced due to the size-dependent Landau damping of the surface plasmon. We show that, in small noble-metal particles, the reduction of interband screening in the surface layer leads to an additional increase in the local field acting on a molecule close to the metal surface. The overall size dependence of Raman signal enhancement is determined by the interplay between Landau damping and underscreening effects. Our calculations, based on a two-region model, show that the role of the surface layer increases for smaller nanoparticle sizes due to a larger volume fraction of the underscreened region.

Photoemission electron microscopy as a tool for the investigation of optical near fields

Photoemission electron microscopy was used to image the electrons photoemitted from specially tailored Ag nanoparticles deposited on a Si substrate (with its native oxide SiO(x)). Photoemission was induced by illumination with a Hg UV lamp (photon energy cutoff homega(UV) = 5.0 eV, wavelength lambda(UV) = 250 nm) and with a Ti:sapphire femtosecond laser (homega(l) = 3.1 eV, lambda(l) = 400 nm, pulse width below 200 fs), respectively. While homogeneous photoelectron emission from the metal is observed upon illumination at energies above the silver plasmon frequency, at lower photon energies the emission is localized at tips of the structure. This is interpreted as a signature of the local electrical field therefore providing a tool to map the optical near field with the resolution of emission electron microscopy.