through F$_{2}$ and D$_{1}$ . Comparison with the corresponding cross-cut for a sample where no beam splitter BS is present (see Fig. 3) shows that the SPP intensity is reduced by a factor of two by the presence of the beam splitter. This justifies the assumption that no scattering takes place. The presented results are all consistent with the parameters of a 50/50 lossless beam splitter, i. e. | R | 2 ≃ | T | 2 ≃ 1 / 2. The SPP intensity decay in the branch D$_{1}$ located after F$_{2}$ can be well reproduced by an exponential function I$_{transmitted}$ ( r ) ∝ e − r/L SPP where r is the distance separating the observation point from F$_{2}$ , and L$_{SPP}$ ≃ 20 µ m is the SPP propagation length. The latter value agrees well with literature values for a 80 nm thick gold film [1]. It is important to note that with such an half-interferometer we do not have experimental access to the phase relation between the transmitted, reflected, and incident beams. In order to define this relation we must first recall some properties of a lossless BS . From the unitarity of the BS transfer matrix [9] and from energy conservation one can deduce that the relation 5 FIG. 3: (color online) (a) LRM image of a configuration without SPP beam splitter (see inset). (b) Longitudinal SPP intensity cross-cut from (a), corresponding to Fig. 2b. F1 F2 D1 (a) F2 0 1 Normalized Intensity Position (µm) 30 µm (b) 0 -15