Optical Properties of a Particle above a Dielectric Interface: Cross Sections, Benchmark Calculations, and Analysis of the Intrinsic Substrate Effects

We show that the optical properties of a particle above a plane dielectric interface differ dramatically from those of the same particle embedded in a homogeneous matrix. Calculations for gold and silver spheres have been carried out in using the exact multipole expansion method, providing thus benchmark results for testing the accuracy of the available numerical methods. For silver spheres, the dependence of the extinction cross-section has been studied in detail as a function of the parameters characterizing the particle/interface system, namely, the radius of the sphere, the particle-surface distance, and the dielectric index of the substrate, as well as those characterizing the light excitation, that is, the angle of incidence and the polarization. Throughout this study we have separated the effects arising from the inhomogeneity of the applied field (interference between the incoming and reflected plane waves) from the intrinsic substrate effects resulting from the interaction with the induced surface charges on the surface. These last effects are, in the present formalism, encoded in the reflected scattered field impinging on the particle. For particles close to the interface, a rich multipolar plasmonic structure is observed, which can be described in the frame of a hybridization scheme similar to that developed for dealing with layered particles or dimers. Comparison with approximate models is also provided

Surface Plasmon Resonance Damping in Spheroidal Metal Particles: Quantum Confinement, Shape, and Polarization Dependences

A key parameter for optimizing nanosized optical devices involving small metal particles is the spectral width of their localized surface plasmon resonances (LSPR). In the small size range the homogeneous LSPR line width is to a large extent ruled by the spatial confinement-induced broadening contribution which, within a classical description, underlies the popular phenomenological limited mean free path model. This unavoidable contribution to the LSPR line width is basically a quantum finite-size effect rooted in the finite extent of the electronic wave functions. This broadening reflects the surface-induced decay of the coherent collective plasmon excitations into particle–hole (<i>p</i>–<i>h</i>) excitations (Landau damping), the signature of which is a size-dependent fragmented LSPR band pattern which is clearly evidenced in absorption spectra computed within the time-dependent local density approximation (TDLDA). In this work we analyze the spatial confinement-induced LSPR damping contribution in the framework on an exact Hamiltonian formalism, assuming for convenience a jellium-type ionic density. In resorting to the harmonic potential theorem (HPT), a theorem stating that in the case of a harmonic external interaction the electronic center-of-mass coordinates separate strictly from the intrinsic motions of the individual electrons, we derive a simple approximate formula allowing to (i) quantify the size dependence of the LSPR damping in spherical nanoparticles (1/<i>R</i> law, where <i>R</i> is the sphere radius) and (ii) bring to the fore the main factors ruling the confinement-induced LSPR broadening. Then the modeling is straightforwardly generalized to the case of spheroidal (prolate or oblate) metal particles. Our investigations show that the LSPR damping is expected to depend strongly on both the aspect ratio of the spheroidal particles and the polarization of the irradiating electric field, that is, on the naturetransverse or longitudinalof the collective excitation. It is found that the magnitude of the damping is tightly related to that of the LSPR frequency which rules the number of <i>p</i>–<i>h</i> excitations degenerate with the plasmon energy. Qualitative analysis suggests that the results are quite general and probably hold for other nonspherical particle shapes. In particular, in the case of elongated particles, as rods, the enlargement of the longitudinal LSPR band by the confinement effects is predicted to be much smaller than that of the transverse LSPR band

Photo-Oxidation of Individual Silver Nanoparticles: A Real-Time Tracking of Optical and Morphological Changes

Absolute extinction measurements on individual silver nanoparticles under illumination show a steady evolution of their localized surface plasmon resonance. Their progressive transformation during light exposure and the influence of various parameters such as the nature of stabilizers, the local environment (oxygen rate), the spectral range of the incident light, and the shape of the nanoparticle (spheres or nanocubes) have been carefully investigated in correlation with transmission electron microscopy imaging. A combination of optics and electron microscopy gives evidence that photoaging mainly consists of the progressive formation of an oxide shell around a metallic silver core during light illumination. Moreover, in the case of nanocubes, the metallic core not only decreases in volume but also changes morphologically since edges and corners are rounded off during the photo-oxidation process. The generalized Mie theory and finite element method, used to calculate the optical extinction cross-section of core/shell Ag@Ag_<i>x</i>O nanoparticles, well account for the observed time evolutions of the absolute extinction spectra of the silver nanospheres and nanocubes. Furthermore, the calculated electromagnetic field at the nanocube surface, enhanced on edges and corners, can explain the higher efficiency of the photo-oxidation on edges and corners and the rounding increase under illumination

Plasmon Spectroscopy and Chemical Structure of Small Bimetallic Cu_{(1–<i>x</i>)}Ag_<i>x</i> Clusters

The optical properties of small Cu–Ag bimetallic clusters have been experimentally and theoretically investigated in relation to their chemical structure analyzed by high resolution transmission electron microscopy (HRTEM). Cu _{(1–<i>x</i>)}Ag_<i>x</i> clusters of about 5 nm in diameter are produced in a laser vaporization source with a well-defined stoichiometry (<i>x</i> = 0, 25, 50, 75, and 100%) and dispersed in an alumina matrix. Absorption spectra are dominated by a broad and strong surface plasmon resonance whose shape and location are dependent on both cluster composition and sample aging. Detailed modeling and systematic calculations of the optical response of pure and oxidized mixed clusters of various chemical structures have been carried out in the framework of classical and semiquantal formalisms. Optical and HRTEM measurements combined with theoretical predictions lead to the conclusion that these bimetallic clusters are not alloyed at the atomic scale but rather present a segregation of chemical phases. Most likely, they adopt a Cu@Ag core–shell configuration. Moreover, the nanoparticle oxidation process is consistent with the formation of a copper oxide layer by dragging out inner copper atoms to the cluster surface

Vibrational Properties of Metal Nanoparticles: Atomistic Simulation and Comparison with Time-Resolved Investigation

Knowledge of the vibrational spectrum of metal clusters and nanoparticles is of fundamental interest since it is a signature of their morphology, and it can be used to determine their mechanical, thermodynamical, and other physical properties. It is expected that such a vibrational spectrum depends on the material, size, and shape of clusters and nanoparticles. In this work, we report the vibrational spectra and density of states of Au, Pt, and Ag nanoparticles in the size range of 0.5–4 nm (13–2057 atoms), with icosahedral, Marks decahedral, and FCC morphologies. The vibrational spectra were calculated through atomistic simulations (molecular dynamics and a normal-mode analysis) using the many-body Gupta potential. A discussion on the dependence of the vibrational spectrum on the material, size, and shape of the nanoparticle is presented. Linear relations with the nanoparticle diameter were obtained for the periods of two characteristic oscillations: the quasi-breathing and the lowest frequency (acoustic gap) modes. These linear behaviors are consistent with the calculation of the periods corresponding to the breathing and acoustic gap modes of an isotropic, homogeneous metallic nanosphere, performed with continuous elastic theory using bulk properties. Additionally, experimental results on the period corresponding to isotropic volume oscillations of Au nanoparticles measured by time-resolved pump–probe spectroscopy are presented, indicating a linear variation with the mean diameter in the size range of 2–4 nm. These, and similar results previously obtained for Pt nanoparticles with size between 1.3 and 3 nm, are in good agreement with the calculated quasi-breathing mode periods of the metal nanoparticles, independently of their morphologies. On the other hand, the calculated period of the mode with the highest (cutoff) frequency displays weak size and shape dependencies up to ∼4 nm, for all nanoparticles under study. In contrast with the behavior of other physicochemical properties, the clear consistency between experiments with atomistic and continuous media approaches resulting from this work indicates the existence of simple relations with size and weak dependence with the material and shape, for vibrational properties of metal nanoparticles