Accounting for the local field when determining the dielectric loss spectra of metals in the region of the frequencies of volume, surface and localized plasmon oscillations

The optical constant of bulk metal is used to determine the dispersion of the local field under one-dimensional (1D), two-dimensional (2D) and three-dimensional (3D) confinement. 3D confinement, expressed as ε^mic₂ ω3D corresponds to the dielectric loss spectra of spherical particles with a diameter, d, much less than the wavelength of the beam used to measure the spectrum (d << λ). Excellent agreement with the results of Mie theory and experimental data for solid colloids within alkali halide crystals was observed. The function expressed as ε^mic₂ ω1D allows the measurement of spectral micro-characteristics in the frequency range of the longitudinal collective motion of the free electrons. This corresponds to the spectrum of dielectric losses of bulk plasma oscillations. The function ε^mic₂ ω3D describes the spectra of the dielectric losses of surface plasma oscillations in thin metal films. It is shown that the peak positions of ε^mic₂ ω3D, ε^mic₂ ω2D and ε^mic₂ ω1D spectra for simple metals, viz. alkali metals as well as Al, Be, Mg, Ga, In, Sn and Si, are in agreement with experimental results from electron-energy-loss spectroscopy and various optical techniques.