Kramers Kronig analysis of the optical properties of small silver particles

In order to complete a preceding paper the dielectric constant? of the particle material of small silver particles with diameters between 210 and 25 Å is computed in the wavelength region 365≦λ≦455 nm from the measured spectra of thesmall particle plasma reasonance absorption. For this purpose a properKramers Kronig relation is derived, and is checked by applying to particles with Drude free electron gas. The results, concerning the silver particles, are that the real part of? changes slightly, whereas the imaginary part is markedly enhanced (up to the ten-fold of the bulk values) if the particle size decreases. This size dependence of? can quantitatively be described with thefree path effect within the accuracy of the measured values. Conversely, thebulk dielectric constant of silver is obtained by applying the free path effect to the measured dielectric constant of the small particles.