values of Eq. 8 occur for silver close to the interband region around λ ∼ 350 nm . Additionally a higher value of ϵ$_{0}$ will also change the sign in Eq. 8. Fig. 1 shows the behavior of the SPP magnetic field close to an interface gold/air and gold/glass at the optical wavelength λ = 800 nm. At such a wavelength the conditions given by Eqs. 5-8 impose the solutions The real parts of the k$_{z}$ components of the SPP wave vector are for both media oriented in the same direction corresponding to a wave propagating from the air side to the metal side (see inset in Fig. 1). Furthermore the waves are exponentially damped when going away from the interface in agreement with Eq. 7, 8 (see Fig. 1). Most important for us is that the Poynting vector [12] S = Real[ E × H ∗ ] / 2 is defined in the medium j by On the dielectric side the energy flow is as expected oriented in the direction of Real[ k ]. However it can be shown on the metal side and for wavelengths not too close from the spectral region associated with the interband transition of gold or silver that the energy flow in the x direction is oriented oppositely to the wave vector Real[ k$_{x}$ ] since Real[ k$_{x}$/ϵ$_{1}$ ] = ( k ′ $_{x}$ϵ ′ 1 + k ′′ $_{x}$ϵ ′′ $_{1}$) / | ϵ$_{1}$ | 2 is dominated by k ′ x · ϵ ′ 1 and since ϵ ′ 1 < 0. However the total energy flow in the x direction S$_{x}$ = ∫ + ∞ 0 S (air) x dz + ∫ 0 −∞ S (metal) x dz is oriented along k ′ $_{x}$. Additionally in the z direction Real[ k$_{1}$/ϵ$_{1}$ ] = ( k ′ $_{1}$ϵ ′ 1 + k ′′ $_{1}$ϵ ′′ $_{1}$) / | ϵ$_{1}$ | 2 is parallel to k ′ 1 since k ′′ $_{1}$ϵ ′′ 1 dominate. This implies in particular that the energy associated with the SPP wave is absorbed by the metal during its propagation through the interface from the air side to the glass side. It should be observed that already in the case of the ideal plasma model neglecting losses the wave vector k$_{x}$ = k ′ x is antiparallel to S$_{x}$ in the metal since there is no imaginary part and since ϵ$_{1}$ = 1 − ω 2 $_{p}$/ω 2 < 0 (see also [13, 14]). We show in Fig. 2 the curves associated with the dispersion relations of SPPs propagating along a gold/air and gold/glass interface respectively. Fig. 2A represents the dependencies ω versus k ′ x corresponding to Eq. 3. Fig. 2B shows the dependencies ω versus L$_{SPP}$ where L$_{SPP}$ = 1 / (2 k ′′ $_{x}$) is the propagation length of the SPP waves (for the metal optical constant we used the experimental values given in [15]). The typical back bending around λ = 520 nm corresponds to the resonance associated with the bound electrons and the interband transition (for a good discussion see [17]). Far away from the interband the real part of 5 S$_{j}$ = 1 2 c Real[ k$_{x}$ ˆ x + k$_{j}$ ˆ z ωϵ$_{j}$/c ] e − 2 k ′′ $_{x}$x − 2 k ′′ $^{$_{z}$z}$. (10) k$_{x}$ = ± ( ω/c ) √ ϵ$_{0}$ϵ$_{1}$ ϵ$_{0}$ + ϵ$_{1}$ , k$_{j}$ = − ( ω/c ) √ ϵ 2 j ϵ 0 + ϵ $_{1}$. (9)