FIG. 4: Structure of the magnetic field Real[ H$_{y}$ ] associated with a SPP mode leaking through a gold film of thickness 50 nm (medium 1) from the air side (medium 2) to the glass side (medium 0). The evolution is represented along the normal z to the interfaces. The optical wavelength considered is λ = 800 nm. The two horizontal lines show the interfaces separated by 50 nm. The inset shows the conventions for the axis x and z. The arrows indicate the direction of the real part of the wave vector normally and parallely to the interface. with SPP electromagnetic modes in this layered system is given by The coefficients α, β, γ are obtained by considering the boundary conditions and one finds As an illustration we show in Fig. 4 the evolution of the real part of the magnetic field across a 50 nm thick gold slab sandwiched between the glass substratum and the air superstratum for an optical wavelength λ = 800 nm . As visible the SPP field is located in the vicinity of the air/gold interface and is evanescent on the air side. This is clearly reminiscent of our former analysis of SPPs propagating at the single air/metal. In addition however the wave is leaking radiatively (i. e., propagatively) into the glass substrate. However from Eq. 18 H$_{0}$ = e ik$_{x}$$^{x}$eik 0 $^{z}$e − iωt H$_{1}$ = e ik$_{x}$$^{x}$[ α sin ( k$_{1}$z ) + β cos ( k$_{1}$z )] e − iωt H$_{2}$ = γe ik$_{x}$$^{x}$eik 2 ( z − D $^{)}$e − $^{iωt}$. (18) α = i k$_{0}$ϵ$_{1}$ k$_{1}$ϵ$_{0}$ , β = 1 γ = i k$_{0}$ϵ$_{1}$ k$_{1}$ϵ$_{0}$ sin ( k$_{1}$D ) + cos ( k$_{1}$D ) . (19) 10