Optical Excitation of Plasmons in Metals: Microscopic Theory

The electromagnetic fields in a semi-infinite free-electron-model metal (plasma) excited by an incident $p$-polarized electromagnetic (EM) wave are calculated by the Reuter and Sondheimer method. It is shown that both a transverse and a longitudinal wave are excited and that they have the usual plane-wave exponential forms at distances greater than a fraction of the electron mean free path from the surface. The dispersion relations for these waves are calculated, and they are found to be independent of whether the electron surface scattering is diffuse or specular. The dispersion relation of the transverse wave is found to be identical to that of an EM wave in an unbounded plasma, while within the approximations made, the dispersion relation of the longitudinal wave is found to be that of the plasma density wave (plasmon).