for a SPP wave propagating along the x direction. The choice of the sign convention con- necting the z and x components of the wave vector is a priori arbitrary and must be done only on a physical ground. Indeed, due to ohmic losses in the metal we expect an expo- nentially decaying SPP wave propagating along the interface. This condition implies the relation k ′ x · k ′′ x ≥ 0 [11]. This inequality is actually always fulfilled since from Eq. 3 one deduces which is indeed positive because ϵ ′′ 1 > 0. By writing k$_{zj}$ = k ′ j + ik ′′ j one additionally obtains the relation This relation fixes the sign conventions since the wave must also decay exponentially when going away from the interface in both media. More precisely one gets The product k ′ 1 · k ′′ 1 is positive if ϵ ′ 1 ≥ −| ϵ$_{1}$ | $^{2}$/ (2 ϵ$_{0}$ ), a fact which is indeed true for silver and gold interfaces with air or glass in most of the visible optical domain. However small negative 4 k ′ 0 · k ′′ 0 ≤ 0 , (7) k ′ 1 · k ′′ 1 = ≥ 0 . (8) − k ′ 0 · k ′′ 0 = ( ω/c ) $^{2}$ϵ ′′ $_{1}$/ 2 − k ′ 1 · k ′′ 1 = k ′ x · k ′′ x ≥ 0 . (6) k ′ x · k ′′ x = 1 2 ( ω/c ) 2 ϵ 2 $_{0}$ϵ ′′ 1 ( ϵ$_{0}$ + ϵ ′ $_{1}$) 2 + ( ϵ ′′ $_{1}$) 2 > 0 (5) FIG. 1: Structure of the SPP magnetic field Real[ H$_{y}$ ] across an interface air/gold (thick line) and glass/gold (dashed line). The optical wavelength considered is λ = 800 nm. The permittivity of glass is taken to be ϵ$_{glass}$ = 2 . 25. The inset shows the conventions for the axes x and z. The arrows indicate the direction of the real part of the wave vector normally and parallely to the interface.