Surface plasmons in Drude metals

We present here a detailed derivation of the dispersion relations for surface plasmons in classical Drude metals, taking into account the fact that the relative permittivity at high frequency may be different from 1, as in the case of dielectrics. We also retain the imaginary part of the dielectric response in the derivation of the dispersion relations for the surface plasmon, which exists up to a maximum frequency, ωs. This treatment has not previously been published. We compare the model with experiment, and show the importance of the relative permittivity in understanding the value of ωs in Ag. We show that the observed ratios of surface to volume plasmon peak energies in electron energy loss spectra can be understood in terms of the simple model, but that considerable care is needed in interpreting the physical circumstances of such experiments.