Charge density formulation for plasmons in the retarded regime

In this paper we derive the retarded dispersion relation for plasmons at the interface between a semi-infinite metal and a semi-infinite dielectric starting from the charge density and the current density. We use the retarded electric and magnetic potentials to arrive at the surface plasmon dispersion relation. Additionally, we derive the electric and magnetic fields using the potentials and show that the derived field components obey the same relations with respect to each other as the plasmon fields. The approach we present in this paper is helpful for deriving transmission line models for plasmonic interconnect structures, which are proposed as replacements for the traditional copper interconnects in future VLSI systems. This in turn is important to study the properties of such structures as interconnects.