Plasmon‐Enhanced Second‐ and Third‐Order Harmonic Generation in Spherical Free‐Electron Nanoclusters with Diffuse Surface

The nonlinear scattering of a laser pulse off spherical nanoclusters with free electrons and with a diffuse surface is examined in the collisionless hydrodynamics approximation in the framework of perturbation theory with respect to the laser pulse intensity, as well as of the steady‐state approximation. In a previous publication [S.V. Fomichev and W. Becker, Phys. Rev. A 81 , 063201 (2010)] we reported the full nonlinear hydrodynamic model of forced collective electron motion confined to a cluster with diffuse surface and introduced two different perturbation theories corresponding to different laser intensity regimes. In the current paper, in the framework of this hydrodynamic model we focus on the properties of plasmon resonance‐enhanced third‐harmonic generation in a spherical cluster and its dependence on the shape of its diffuse surface whose role increases for nonlinear processes. At the same time, the quadrupole second‐harmonic generation in a spherical cluster is also inspected as a necessary intermediate step. Both cold metal clusters in vacuum or in a dielectric surrounding and hot laser‐heated and laser‐ionized clusters are considered within the same approach for a wide range of the fundamental laser frequency. Nonlinear laser excitation of the dipole plasmon Mie resonance in spherical clusters, as well as of other respective multipole plasmon resonances is investigated analytically and numerically in detail (position, width, and strength) versus the cluster‐surface diffuseness, the outer ionization degree in charged clusters, the electron‐density diffuseness, and their interplay. Under certain conditions, depending on the various cluster parameters, different secondary nonlinear resonances are found. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of metallic surface microroughness on the probability and spectrum of plasmon excitation by a fast charged particle moving parallel to the surface

The Green’s function of the electric field of plasmons is determined in a semi-infinite medium with an abrupt plasma boundary where nonequilibrium conduction electrons either undergo elastic reflection from the boundary or “stick” to it and give rise to a stationary surface charge. The angular reflection of elastically scattered electrons can be either specular or diffuse. The Green’s function is used to find the singleevent spectrum of energy loss by a fast electron moving parallel to the boundary. The effect of electronboundary scattering parameters on the structure of bulk and surface plasmon resonances is analyzed. The probability of transition radiation of bulk plasmon by an electron moving in vacuum is examined. A new type of surface resonance is found under conditions of perfectly elastic scattering of conduction electrons from the plasma boundary, similar in structure to a tangential surface plasmon.     

Resonant Scattering of Picosecond Laser Pulses by Atoms in Alkali Metal Vapors

Resonant scattering of ultrashort laser pulses (ULPs) in the vicinity of spectral doublets in monatomic lithium and sodium vapors is studied theoretically. The scattering probability over the entire time of pulse action is calculated as a function of various parameters of the problem (carrier frequency and ULP duration, as well as vapor pressure and temperature). It is shown that the dependence of the total scattering probability on the pulse duration is generally nonlinear by nature.     

Excitation of hydrogen atom by ultrashort laser pulses in optically dense plasma

The features of excitation of a hydrogen atom by ultrashort laser pulses (USP ) with a Gaussian envelope in optically dense plasma at a Lyman‐beta transition are studied theoretically. The problem is of interest for diagnostics of optically dense media. USP have two doubtless advantages over conventional laser excitation: (a) the USP carrier frequency is shifted to the region of short wavelengths allowing exciting atoms from the ground state and (b) the wide spectrum of USP allows them to penetrate into optically dense media to much longer distances as compared with monochromatic radiation. As actual realistic cases, two examples are considered: hot rarefied plasma (the coronal limit) and dense cold plasma (the Boltzmann equilibrium). Universal expressions for the total probability of excitation of the transition under consideration are obtained in view of absorption of radiation in a medium. As initial data for the spectral form of a line, the results of calculations by methods of molecular dynamics are used. The probability of excitation of an atom is analysed for different values of problem parameters: the pulse duration, the optical thickness of a medium, and the detuning of the pulse carrier frequency from the eigenfrequency of an electron transition.     

Compton Scattering of Attosecond X-Ray Pulses on a Hydrogen Atom

The Compton scattering of attosecond X-ray pulses on a hydrogen atom has been studied theoretically in terms of the spectral angular scattering probability during the action of a pulse. The dependence of scattering on the carrier frequency, pulse duration, and scattering angle has been analyzed. It has been shown that the probability of the process at certain parameters of the problem is a nonlinear function of the pulse duration.     

Influence of the cross section and the permittivity on the plasmon-resonance spectrum of silver nanowires

We investigate the plasmon resonances for silver nanowires with a non-regular cross section. To study the relationship between the cross section and the spectrum of the plasmon resonances, we consider cross sections evolving from a rectangular shape to a triangular one. In particular, we study the influence of the sharpness of a corner on the near-field enhancement at the vicinity of a particle and discuss its implications for surface-enhanced Raman scattering. We also investigate the influence of the absorption on the plasmon-resonance spectrum and on the near-field enhancement. Received: 15 August 2001 / Published online: 10 October 2001     

The nanoparticle shape's effect on the light scattering cross-section

In the framework of kinetic approach we develop a theory for light scattering by ellipsoidal metallic nanoparticles whose dimensions are less than those of a free electron path. In this case, the surface of the particle starts to play a dominant role in electron scattering. When the size of the particle decreases below the free electron path at least in one direction, the optical conductivity becomes a tensor quantity, and the diagonal components of this tensor define the half-widths of the plasmon resonances peaks. Thus, the effect of the particles' shape both on the frequencies of plasmon resonances and on their half-widths is considered. Additionally, the expression for a cross-section of the light scattering by a collection of chaotically oriented spheroidal nanoparticles is obtained and averaged over different directions of particles in the collection. Our results highlight the plasmonic properties of metallic nanospheroids, notably, the spectrum of the light scattering has two peaks at the frequencies of plasmon resonances even if there is no preferential direction in the collection of particles.     

Plasmonic extraordinary transmittance in array of metal nanorods

The optical response of an array of metal nanorods is studied in the case when the cylinders almost touch by their generatrices. As the cylinders approach each other, a series of surface plasmon resonances are excited. The first longitudinal mode is different from the higher-order lateral modes. The lateral resonances occur near the frequency where the real part of the metal permittivity changes sign. The plasmon resonances result in maxima and minima in the reflectance and transmittance. The resonances also result in a huge enhancement of the local electric field in the gap between cylinders.     

Resonant Raman scattering by plasmons in n-type Ge

We have measured the Raman efficiency for plasmon scattering in n-type Ge as a function of laser excitation frequency in the range of the E₁ and E₁+Δ₁ optical gaps (2.1–2.5 eV). Our results can be explained by a mechanism involving the macroscopic electric field that accompanies the plasma oscillation in a manner similar to that responsible for Fröhlich-interaction-induced forbidden LO-phonon resonances in polar semiconductors plus some contribution of the standard cdf mechanism for scattering by plasmons.     

Resonant mechanisms of inelastic light scattering by low-dimensional electron gases

The contribution of elementary excitations in low-dimensional electron gases to resonant inelastic light scattering is found to be determined by interband transitions involving states at specific wave vectors. In modulation-doped GaAs/GaAlAs quantum wells, we detect only the single-particle excitations (SPE) at resonances with electron-hole transitions at the Fermi wave vector, and only plasmons at resonances with zone-center excitons. The plasmon cross section is comparable to the SPE when double electronic resonance is achieved by tuning the plasmon energy to a valence subband separation.     

Control of molecular energy redistribution pathways via surface plasmon gating

Strong coupling of molecular electronic states with tunable surface plasmon resonances is used to control electronic energy redistribution pathways in molecules adsorbed on a silver film. Ultrafast excitation of porphyrinic molecular J aggregates into the S2 state is followed by a second pulse of varying incident wave vector to produce a tunable plasmon in the film. When the plasmon overlaps the S1 state, energy flows from S2 to S1 at high efficiency. If the plasmon hybridizes with the S2 state, the excitation remains in the S2 vibrational manifold during quenching to the ground state. These results could have significant impact on the design of active molecular devices.     

Graphene-based nano-patch antenna for terahertz radiation

The scattering of terahertz radiation on a graphene-based nano-patch antenna is numerically analyzed. The extinction cross section of the nano-antenna supported by silicon and silicon dioxide substrates of different thickness are calculated. Scattering resonances in the terahertz band are identified as Fabry–Perot resonances of surface plasmon polaritons supported by the graphene film. A strong tunability of the antenna resonances via electrostatic bias is numerically demonstrated, opening perspectives to design tunable graphene-based nano-antennas. These antennas are envisaged to enable wireless communications at the nanoscale.     

Size characteristics of surface plasmons and their manifestation in scattering properties of metal particles

The change of the scattering properties of sodium, gold and silver spherical particles with size is discussed in the context of surface multipolar plasmon resonances. The presented surface plasmon size characteristics are abstracted from the quantity which is observed and deliver multipolar plasmon resonance frequencies and plasmon damping rates in the form of a continuous function of particle radius. The performed analysis of the plasmon dispersion relation is analogous to the problem of surface plasmon localized at a semi-infinite, flat metal/dielectric interface.Correlation between the multipolar plasmon resonance parameters, and the spectroscopic optical properties of conductive nanoparticles appearing as peaks in the measurable light intensities is analyzed. We discuss the fact, that such peaks arise from interference of all the electromagnetic fields contributing to the measured intensity, and not solely to the fields due to surface plasmon multipolar modes.We describe the results of light scattering experiment in orthogonal polarization geometries with use of spontaneously growing sodium droplets. The polarization geometry of the experiment allows for distinct separation of resonant contribution of dipole and quadrupole plasmon TM mode contributions to the measured intensities as a function of size.Predictions concerning size characteristics for dipole and quadrupole plasmons are compared with the results of light scattering experiments using spherical sodium droplets (our results) and gold and silver particles in suspension [other authors: Sönnichsen C, Franzl T, Wilk T, von Plessen G, Feldmann J. Plasmon resonances in large noble-metal clusters. New J Phys 2002; 4:93.1–8; Haiss W, Thanh NTK, Aveyard J, Fernig DG. Determination of size and concentration of gold nanoparticles from UV–vis spectra. Anal Chem 2007; 79:4215–21; Njoki PN, Lim I-IS, Mott D, Park H-Y, Khan B, Mishra S, et al. Size correlation of optical and spectroscopic properties for gold nanoparticles. J Phys Chem C 2007; 111:14664–9; Mock JJ, Barbic M, Smith DR, Schultz DA, Schultz S. Shape effects in plasmon resonance of individual colloidal silver nanoparticles. J Chem Phys 2002; 116:6755–9].     

Collective plasmon resonances in monolayers of metal nanoparticles and nanoshells

The collective plasmon resonances in a monolayer formed by metal or metal-dielectric nanoparticles with dipole or quadrupole single-particle resonances are theoretically and experimentally studied. The extinction, scattering, and absorption spectra are calculated using an exact many-particle solution for the system of interacting particles. With increasing surface density of particles in the monolayer, the dipole resonance is suppressed, and the spectrum of the collective system is determined by the quadrupole plasmon only. It is shown that the selective suppression of the long-wavelength extinction band is caused by the collective suppression of the dipole scattering mode, whereas the short-wavelength absorption spectrum of the monolayer differs little from the single-particle spectrum. Using dark-field light and atomic force microscopy, the kinetics of self-assembling of nanoshells is studied. It is shown that the universal linear relation between the relative shift of the wavelength of the collective quadrupole resonance and the relative increment of the refractive index of the surrounding medium is implemented.     

Determination of Plasma Frequency and the Pulse Relaxation Time in Doped Semiconductors by FIR Surface Waves

The Surface Electromagnetic waves method was applied for determination of plasma frequency and pulse relaxation time in doped A³B⁵ semiconductors. The influence of plasmon phonon interaction, nonparabolity of the conduction band, electron scattering peculiarities, presence of disturbed layers are under consideration.     

Coherent light scattering from semicontinuous silver nanoshells near the percolation threshold

We report on measurements of visible extinction spectra of semicontinuous silver nanoshells grown on colloidal silica spheres. We find that thin, fractal shells below the percolation threshold exhibit geometrically tunable plasmon resonances. A modified scaling theory approach is used to model the dielectric response of such shells, which is then utilized to obtain the extinction cross section in a retarded Mie scattering formalism. We show that such spherical resonators support unique plasmon dynamics: in the visible there is a new regime of coherently driven cluster-localized plasmons, while crossover to homogeneous response in the infrared predicts a delocalized shell plasmon.     

Surface plasmon characteristics of tunable photoluminescence in single gold nanorods

Light emission resulting from two-photon excited gold nanoparticles has been proposed to originate from the radiative decay of surface plasmon resonances. In this vein, we investigated luminescence from individual gold nanorods and found that their emission characteristics closely resemble surface plasmon behavior. In particular, we observed spectral similarities between the scattering spectra of individual nanorods and their photoluminescence emission. We also measured a blueshift of the photoluminescence peak wavelength with decreasing aspect ratio of the nanorods as well as an optically tunable shape-dependent spectrum of the photoluminescence. The emission yield of single nanorods strongly depends on the orientation of the incident polarization consistent with the properties of surface plasmons.     

Control of light scattering by nanoparticles with optically-induced magnetic responses

Conventional approaches to control and shape the scattering pattems of light generated by different nanostructures are mostly based on engineering of their electric response due to the fact that most metallic nanostructures support only electric resonances in the optical frequency range. Recently, fuelled by the fast development in the fields of metamaterials and plasmonics, artificial optically-induced magnetic responses have been demonstrated for various nanostructures. This kind of response can be employed to provide an extra degree of freedom for the efficient control and shaping of the scattering patterns of nanoparticles and nanoantennas. Here we review the recent progress in this research direction of nanoparticle scattering shaping and control through the interference of both electric and optically-induced magnetic responses. We discuss the magnetic resonances supported by various structures in different spectral regimes, and then summarize the original results on the scattering shaping involving both electric and magnetic responses, based on the interference of both spectrally separated （with different resonant wavelengths） and overlapped dipoles （with the same resonant wavelength）, and also other higher-order modes. Finally, we discuss the scattering control utilizing Fano resonances associated with the magnetic responses.     

Probability and shape of the spectral line of a single bulk characteristic energy loss of a fast electron in a medium with electron absorption and strong spatial dispersion

The probability of single characteristic energy loss of a fast electron in a reflection experiment has been calculated. Unlike many works concerning this subject, the bremsstrahlung of bulk plasmons in the non- Cherenkov ranges of frequencies and wavevectors of a plasmon has been taken into account. The contributions to the probability of single loss and to the shape of the spectral line from a quantum correction that is due to the interference of elastic and inelastic electron scattering events have been determined. The probability has been calculated in the kinetic approximation for the relative permittivity, where the short-wavelength range of the plasmon spectrum is correctly taken into account. In view of these circumstances, the expression for the mean free path of the electron with respect to the emission of a bulk plasmon that was obtained by Pines [D. Pines, Elementary Excitations in Solids (Benjamin, New York, 1963)] has been refined. The coherence length of the fast electron in the medium-energy range under consideration has been estimated. The shape of the spectral line of energy losses in the non-Cherenkov frequency range has been determined. It has been shown that the probability of the single emission of the bulk plasmon incompletely corresponds to the Poisson statistics.     

Charge carrier interaction with a purely electronic collective mode: plasmarons and the infrared response of elemental bismuth

We present a detailed optical study of single-crystal bismuth using infrared reflectivity and ellipsometry. Large changes in the plasmon frequency are observed as a function of temperature due to charge transfer between hole and electron Fermi pockets. In the optical conductivity, an anomalous temperature dependent midinfrared absorption feature is observed. An extended Drude model analysis reveals that it can be connected to a sharp upturn in the scattering rate, the frequency of which exactly tracks the temperature dependent plasmon frequency. We interpret this absorption and increased scattering as direct optical evidence for a charge carrier interaction with a collective mode of purely electronic origin, here electron-plasmon scattering. The observation of a plasmaron as such is made possible only by the unique coincidence of various energy scales and exceptional properties of semimetal bismuth.