Spectra of Electromagnetic Plasmon Bands in an Infinite Superlattice Made of Lossless and Lossy Media

The dispersion relation of electromagnetic surface plasmon bands is calculated in closed form for an infinite metallic superlattice of two alternating arbitrary metallic layers. The well known electrostatic dispersion relation of plasmon bands is recovered. Inclusion of retardation effects and conductivity contributions give rise to the effect that the bands do not start at the plasma frequencies for low wave numbers. Furthermore, conductivity gives rise to damping, i.e. the spectra acquire imaginary parts, and for very large conductivities the waves are proved to be overdamped. The special case of an Al-Mg superlattice is discussed and the spectra and group velocities are calculated for various conductivities and layer thicknesses.