and the condition k ′ 0 · k ′′ 0 ≤ 0 it is clear that the leaking wave is exponentially growing in the -z direction when going away from the gold slab. This is already the result we obtained when we considered the limit of the thick slab. An exponentially growing wave looks non physical and is in particular associated with infinite radiated energy in the far field. There is now the question of how to connect a growing wave with the basic reasoning giving rise to Eq. 11 and the idea of phase matching between the (real part) of the SPP wave vector with a propagative plane wave vector in the glass substrate. However such paradoxes disappear for two reasons: First, an infinite energy occurs only because we considered an infinite interface or equivalently because we did not consider how the SPP is locally launched on the metal film. When such conditions are taken into account this paradox must disappear [11]. Second, the SPP wave defined by Eq. 18 is actually a wave packet when looked at through the Fourier basis of propagative TM plane waves. Since in the far field (i. e., in the glass substrate) one actually detect such plane waves one must do a Fourier transform in order to generalize Eq. 11 [1, 11]. Instead of Eq. 11 one obtains consequently a statistical distribution of (real) wavevectors K$_{x}$ given by where 2 k ′′ x defines the full width at half maximum (FWHM) of this Lorentz distribution of radiated plane waves. By noting as usual θ the angle between the wave vectors K of the plane waves refracted into the glass substrate and the normal z to the interfaces one has by definition K$_{x}$ = 2 π √ ϵ$_{0}$/λ sin θ and the angular distribution of radiated power is in the far field given by: Historically the first observations of leakage radiation by SPP propagating on a thin metal film were reported by analyzing scattering by rough metal surfaces of light into SPPs [1, 20]. The possibility of using rough surface to excite SPPs was extensively studied in the past [1] and is based on the fact that the scattering by small defects on a flat film can represent a source of evanescent momentum sufficient for the light waves to match the SPP dispersion relation. Equivalently the amount of momentum needed can be carried by grating coupling I ( K$_{x}$ ) = const. ( K$_{x}$ − k ′ $_{x}$) 2 + ( k ′′ $_{x}$) $_{2}$, (20) I ( θ ) = const. (2 π √ ϵ$_{0}$/λ sin θ − k ′ $_{x}$) 2 + ( k ′′ $_{x}$) $_{2}$. (21) III. LEAKAGE RADIATION MICROSCOPY 11