Showing papers on "Plasmon published in 1971"

Optical Absorption and Dispersion in Solids

Abstract: 1. Macroscopic Theory.- 1.1 Electromagnetic field in a solid.- 1.2 Dielectric constant and optical conductivity.- 1.3 Crystal symmetry.- 1.4 Propagation of waves.- 1.5 Kramers-Kronig relations.- 1.6 The sum rule.- 1.7 Dispersion theory of classical oscillators.- 2. Crystal Lattice Absorption.- 2.1 Vibrational modes of a crystal lattice.- 2.2 Photon-phonon interaction.- 2.3 Microscopic theory of infra-red dispersion.- 2.4 Two-phonon absorption.- 3. Interband Transitions.- 3.1 Electron energy bands.- 3.2 Direct transitions.- 3.3 Critical points.- 3.4 Absorption band edges.- 3.5 Indirect transitions.- 3.6 Infra-red absorption in superconductors.- 4. Free Carrier Absorption.- 4.1 Classical theory.- 4.2 Intraband transitions.- 4.3 Electron transport.- 4.4 Surface admittance.- 4.5 Infra-red absorption in metals.- 4.6 Free carrier absorption in semiconductors.- 5. Plasma Effects.- 5.1 Free electron model.- 5.2 Volume plasmons.- 5.3 Surface plasmons.- 6. Exciton Effects.- 6.1 Electron-hole interaction.- 6.2 Optical absorption.- 6.3 Inert-atom solids and alkali halides.- 6.4 Semiconductors.- 6.5 Spatial dispersion.- 7. Non-Linear Optics.- 7.1 Classification of non-linear effects.- 7.2 Non-linear susceptibilities.- 7.3 Second harmonic generation.- 7.4 Parametric amplification and oscillation.- 7.5 Third order effects.- References.

Surface Plasmon in a Semi-Infinite Free-Electron Gas

Abstract: When electron-lifetime effects, electron-hole pair excitations, or both are included in the description of an electron gas, the frequency associated with the surface plasmon is a complex quantity, the imaginary part providing a measure of the damping of the plasmon. The surface-plasmon dispersion relation then involves the specification of this complex frequency as a function of the wave vector parallel to the surface. A general theory is developed for such a surface-plasmon dispersion relation in a semi-infinite free-electron gas bounded by a surface that scatters the electrons specularly. The properties of the electron gas enter through the nonlocal transverse and longitudinal dielectric functions ${\ensuremath{\epsilon}}_{t}(q,\ensuremath{\omega})$ and ${\ensuremath{\epsilon}}_{l}(q,\ensuremath{\omega})$, both of which include a finite electron lifetime here. The results obtained using local and hydrodynamic approximations for the dielectric functions are presented briefly, and the self-consistent-field approximation is discussed in detail. The calculations are done both with and without retardation.

Fast-Electron Spectroscopy of Surface Excitations

Abstract: New theoretical results are presented for the probability of exciting surface oscillations (optical phonons or plasmons) by fast electrons reflected from the surface of a thin crystal film. Both specular and Bragg reflections are considered and the effect of the finite slab thickness is included. The theory explains successfully the energy-loss spectra measured by Powell on metallic surfaces and recent measurements by Ibach on ZnO surfaces.

Optically Excited Longitudinal Plasmons in Potassium

Abstract: Oscillatory structure in the absorption of thin potassium films has been observed for energies just above the plasmon energy in a wavelength-modulated photoemission experiment. This structure is shown to be due to resonant excitation of longitudinal plasmons. Observation of up to ten resonances allows the evaluation of the dispersion relation, which shows a quadratic behavior in agreement with a theoretical formula based on the Boltzmann equation.

Experimental Verification of Optically Excited Longitudinal Plasmons

Abstract: Anomalous optical absorption is observed in thin Ag films just above the bulk plasma frequency. The result is interpreted as excitation of longitudinal plasmons, an effect which is normally neglected when discussing optical properties. The dispersion relation of the plasma wave is obtained from the data.

Insensitivity of the Infinite-Wavelength Surface Plasmon Frequency to the Electron Density Profile

Abstract: Assuming that the ground-state electron density at a jellium-vacuum interface is the self-consistent Hartree density, and using the random-phase approximation to describe the electronic excitation spectrum, we show that the infinite-wavelength surface plasmon frequency is $\frac{1}{\sqrt{2}}$ times the bulk plasma frequency. This result is independent of the shape of the jellium background, and thus applies to a wide range of self-consistent electron density profiles.

Some Implications of an Expression for the Response of the Electron Liquid

Abstract: The pair correlation function, the screening of a fixed impurity charge, the correlation energy, the cohesive energy of alkali metals, and the plasmon dispersion relation in the small-$k$ limit are calculated using an expression for the dielectric function derived in a previous paper. Results are compared with those obtained from other theories.

Surface Plasmons and the Reflectivity of n-Type InSb

Abstract: The reflectivity of $n$-type InSb has been measured in the far infrared. The doping of the samples was such that the free-carrier plasma frequency was near the LO mode frequency. The results suggest that samples with a sufficiently thick damage layer show effects due to surface plasmons. Use of a simple model indicates that the surface-plasma excitations are coupled to the phonons.

Theory of Plasmon Damping in Metals. II. Effects of Electron-Ion Interaction

Abstract: Effects of electron-ion interaction on the plasmon damping in metals are investigated by using a general formulation developed in a previous paper. Damping of a plasmon with small wavenumber q is mainly determined by the processes in which the plasmon dacays into (i) one electron-hole pair by interband transition and (ii) one electron-hole pair with simultaneous absorption or emission of a phonon. These processes give negative q 2 -coefficient of damping in the small wavenumber region. On the other hand, the process in which the plasmon decays into another plasmon with simultaneous absorption or emission of a phonon gives the damping nearly proportional to q . As a whole, with including the contribution of the electron-electron interaction discussed in I, plasmon half-width in Al slightly decreases as q increases in the small q region, while the damping in Na slightly increases with q .

A note on surface plasmons

Abstract: We consider the dispersion of the surface plasmons in an approximate RPA. It is shown that the usual linear dependence of the frequency on the wave vector is valid in the high density limit.

Surface-Plasmon Dispersion: A Comparison of Microscopic and Hydrodynamic Theories

Abstract: The hydrodynamic theory of the electron gas, first applied to surface plasmons in metals by Ritchie, is critically examined using the equation of motion for the Wigner distribution function in the random-phase approximation (RPA). It is found that the theory does not agree with the RPA in the case of surface plasmons, though it does for bulk plasmons.

Elastic and Inelastic Diffraction of Low-Energy Electrons from Al (100): Double-Diffraction Model

Abstract: The isotropic-scatterer, inelastic-collision model is used to analyze experimental elastic intensity profiles characteristic of electrons in the energy range 10≤E≤120 eV scattered from Al(100). Using the double-diffraction approximation a satisfactory description of these profiles is achieved for a variety of incident beam angles, θ≤25°. The temperature dependence of these profiles due to both thermal expansion and lattice vibrations is examined. Using the inelastic-collision-model description of the elastic scattering, the RPA plasmon dispersion relations and lifetimes, and the sharp-junction, “uniform” electron fluid electron-plasmon interaction vertices, the inelastic energy and angular profiles for the two-step excitation of bulk and surface plasmons are predicted using a double-diffraction analysis of this process. Observation of these profiles and their correlation with such an analysis constitutes a critical test of existing models of inelastic diffraction.

Influence of plasmons on Compton scattering

Abstract: An attempt has been made to analyse the effect of the plasmons on Compton scattering. Equations for the conservation of momentum and energy have been formulated and solved taking into consideration plasmon excitation in the scattering process. A comparison of the theoretical results with the experimental observations for beryllium is discussed. It has been pointed out that this formalism can be used to study the electron plasma in solids.

Simplified Intensity Calculation Method for Low-Energy Electron Diffraction

Abstract: A simplified intensity calculation method for low-energy electron diffraction is proposed. The effects of inelastic process are included by the use of the optical potential. A set of coupled differential equations obtained through the two-dimensional Fourier transform of the potential is reduced to a set of coupled linear algebraic equations, which is solved numerically. Applications are made to the (001) surfaces of LiF, NaF, PbSe, Al, Ni, Cu, Pd, Ag, Au, and the (0001) surface of graphite. The contributions to the optical potential from plasmons and longitudinal optical phonons are estimated for a continuum model.

Light Scattering by Collective Excitations in Dielectrics and Semiconductors

Abstract: The early experimental and theoretical investigations of spontaneous Raman scattering in solids were concerned with first and second order Raman scattering by lattice vibrations which provided information about the frequencies and symmetries of the long wavelength (q ≈ 0) modes as well as information about modes at two phonon density of states “critical points” in the Brillouin zone. Largely, as a result of the availability of cw lasers, covering a range of frequencies extending from the infrared to the ultraviolet, and improved photo-detectors and associated electronics, these investigations have now been extended to essentially all of the other “low energy” excitations in solids, namely to plasmons and their linearly coupled modes with LO phonons, polaritons (coupled TO phonon-photon modes), excitons, magnons and their linearly coupled modes with acoustic phonons, single particle electron-hole pair excitations, and vibrational and electronic excitation of impurities.1 Furthermore, they have been extended to opaque solids, i.e., metals and narrow gap semiconductors.

Light emission from non radiative plasmons excited by electrons on smooth surfaces

Abstract: Theoretical results are reported on the possibility to observe light emitted from the non radiative surface plasmons which are excited by fast electrons traversing a smooth vacuum-metal boundary. By covering the backside of the metal film with a medium of refractive indexn>1, light can be decoupled from the non radiative plasmons. In the angular intensity distribution this light has a strong characteristic peak exceeding the ordinary transition radiation by a factor of the order of 102.