Surface plasmon polaritons in multilayer jellium systems: Dispersion and spatial description

Surface-plasmon polaritons (SPPs) are electromagnetic waves that propagate along metal-dielectric interfaces, with important applications in sensing, energy, and nanotechnology. While the behavior of SPPs in single metal slabs is well understood, the coupling between plasmon modes in multilayer systems has received less attention. In this paper, we explore the response functions of SPPs in single-slab, double-slab, and two-different-slab systems using the jellium model. Thanks to a comparison with classical models, in this paper, we reveal how quantum effects influence the resonance frequencies of these modes. We also detail the spatial description of the different SPP modes and unveil how their coupling occurs in two-different-slab systems. These findings provide insights into the behavior of SPPs, especially in complex nanostructures.