## 2 Materials and Methods
To couple incident light with the surface waves, we use the Kretschmann configuration [38]. The schematic of the experimental setup is shown in Figure 1, where a glass prism is required to fulfill the phase-matching condition to excite the BSWs. We illuminate the sample with a focused Gaussian beam to couple light with the BSW. At an incident angle '9', which is higher than the critical angle, the incident light is coupled with the BSW at a specific wavelength. We keep the BSW coupling zone approximately 30 \(\upmu\)m away from the graphene layer. The phenomenon of BSW coupling can be seen as a reflection dip of the angular reflectance plot in the far-field (FF). We use CCD IR camera to collect the reflected light in the far-field on the other side of prism, see Figure 1. More details can be found in reference [8]. For BML, the BSWs can be coupled at an incident angle \(\theta\) = 50.15\({}^{\circ}\), at the corresponding wavelength \(\lambda\) = 1558 nm. The m-line pattern can be observed in the prism coupling configuration. These lines are defined as the order of the modes that can be excited in thin films at a specific angle [39]. The light of these propagating modes leaks out of the multilayer due to the presence of the prism. The interference of these leaky modes and total internally reflected incident light produces a specific  
Figure 2: **(a,b)** SEM characterization of continuous and clean graphene grown on a Cu foil. The arrows in (**b**) indicate the presence of the Cu grain boundaries; (**c**) Raman spectroscopy performed on graphene on Cu foil, showing the two typical peaks of graphene; G and 2D at 1580 and 2680 cm\({}^{-1}\), respectively. The absence of the defect-related D peak at 1350 cm\({}^{-1}\) confirms the growth of high-quality graphene. Scale bar: 5 \(\upmu\)m.  
-fringe pattern, which can be observed in the far-field, see Figure 3a. The fringe pattern can also be understood as an interaction of total internally reflected incident beam and leaky propagating surface wave [40]. The reflected beam is a divergent Gaussian beam, while the leaky surface wave is more flat. The intersection of two wave-fronts having different curvatures produces the interference pattern. The absence of either of the two will cause the fringes to cease to exist. For example, fringes will not appear either in the case of non-diverging (flat waveforms) reflected light, or when there is no leaky propagating surface wave. In the present study, the latter is imposed by the absorption in the presence of the graphene layer. In the case of BML+ graphene layers, the optimum condition of BSW coupling is found at the same angle of incidence as BML at the wavelength \(\lambda=1558\) nm. The thicknesses of the graphene layers (<1 nm) might be the reason behind the same coupling angle [33]. However, in the presence of graphene layers, only a broad dark band can be observed, as shown in Figure 3b. The dark band represents the significant absorption of propagating BSWs in the presence of graphene. The absorption reduces the propagation, and hence the leakage, of propagated BSWs. In consequence, we do not observe an interference fringe pattern in the far-field (see Figure 3b). To perform the near-field measurements, we work with a multi-heterodyne scanning near-field optical microscope (MH-SNOM) in collection mode, which collects the evanescent electric field with a subwavelength aperture fiber probe. Because BSWs propagate at the interface of multilayers, near-field microscopy is an optimum tool for performing the spatial field distribution mapping locally. Further details about MH-SNOM can be found elsewhere [10].