Surface plasmon-polaritons on ultrathin metal films

We discuss the surface plasmon-polaritons used for ultrathin metal films with the aid of linear response theory and make comparisons with the known result given by Economou E N. In this paper we consider transverse electromagnetic fields and assume that the electromagnetic field in the linear response formula is the induced field due to the current of the electrons. It satisfies the Maxwell equation and thus we replace the current (charge) term in the Maxwell equation with the linear response expectation value. Finally,taking the external field to be zero,we obtain the dispersion relation of the surface plasmons from the eigenvalue equation. In addition,the charge-density and current-density in the z direction on the surface of ultrathin metal films are also calculated. The results may be helpful to the fundamental understanding of the complex phenomenon of surface plasmon-polaritons.