Surface plasmon dispersion relation at an interface between thin metal film and dielectric using a quantum hydrodynamic model

The plasmon excited at the surface of a thin metal film covering on a semi-infinite dielectric substrate is investigated in detailed. The surface plasmon dispersion relation is derived and presented by using the quantum hydrodynamic theory with taking into the quantum statistical and quantum diffraction effects. The effects of the thin metal film character rs and the dielectric constant ε1 on the dispersion relations are shown and discussed, i.e., without and with quantum effects. The results show that increasing rs weakens the quantum effects while increasing ε1 can enhance the quantum effects. In addition, the plasmon dispersion relation with quantum effects is also compared to a classical model. This simple structure proposed in the paper with quantum hydrodynamic theory can be used for yielding meaningful results for studying more complex systems related to surface plasmons.