Optics of multilayered conducting systems: Normal modes of periodic superlattices

We develop a 4×{}4 transfer-matrix formalism in order to study, within the hydrodynamic model of electron dynamics, the optics of multilayered conducting heterostructures, taking into account retardation and the coupling between transverse and longitudinal waves at the conductor boundaries. The dispersion relation of the electromagnetic normal modes of an infinite periodic superlattice is calculated in the retarded and the nonretarded regimes, yielding a very rich structure, as a consequence of several propagation mechanisms which are discussed in detail. The dependence of the results on the set of additional boundary conditions imposed at the surfaces is also examined.