Collective Electronic Motion in a Metallic Slab

Abstract

The virtual modes are obtained for a free-electron-gas model of a metallic slab. These modes, excitations of the crystal which couple to radiative fields outside the slab, correspond to a mixture of collective electron motion and photons. It is shown that a knowledge of the virtual modes leads to a complete understanding of those aspects of the optical properties related to the long-wavelength collective behavior of the electrons. In particular, the existence of radiative surface modes is established. These modes markedly affect the low-frequency optical properties. Manifestations of the virtual modes in experimental situations other than optical investigations are discussed. The dispersion of the ordinary nonradiative surface plasmons at long wavelengths is also calculated using the same general technique. The result is in accord with a previous calculation.