Bulk and surface dielectric response of a superlattice with an arbitrary varying dielectric function: A general analytical solution in the local theory in the long-wave limit

We present an analytical solution for the dielectric response of infinite and semi-infinite superlattices with the constituent dielectric function ε(ω,z) being an arbitrary periodic function of one coordinate z. The long-wave limit in the local theory is used. All results are expressed in terms of the two bulk quantities, namely, the average over one period of the functions ε(ω,z) and 1/ε(ω,z). The damping of the bulk and the surface plasmon modes specific for superlattices with a continuously varying constituent dielectric function is obtained and discussed. Our theory provides deeper insight into the role of the local-field effects in the dielectric response of a superlattice.