## 3 Results and Discussion  
The light is coupled evanescently to the graphene layer using a Kretschmann configuration. Further, with the aid of MH-SNOM, propagation lengths of BSWs (L\({}_{\text{BSW}}\)) for BML, monolayer graphene and bilayer graphene are measured in the near-field, as shown in Figure 4. For the comparison of absorption of the propagating field, we show here the propagation of BSW without any graphene layer/bare multilayer (Figure 4a), with monolayer graphene (Figure 4b) and with bilayer graphene (Figure 4c).  
The propagation lengths are defined as the distance at which the amplitude of the propagating field drops to 1/e of its maximum value. The L\({}_{\text{BSWS}}\) are deduced by exponentially fitting the decay of the measured field amplitude of the surface wave along the propagation direction [10]. Figure 5 shows the logarithmic scale of the cross-section of the exponentially decaying field amplitude profiles of the BML, monolayer and bilayer graphene, respectively. The measured L\({}_{\text{BSW}}\) for BML when using  
Figure 3: M-line pattern observed in the far-field image of the reflected light captured with a CCD camera in Kretschmann coupling configuration for (**a**) Bare multilayer; (**b**) Monolayer graphene.  
monolayer and bilayer graphene are approximately 1300 \(\upmu\)m [8], 75 \(\upmu\)m and 55 \(\upmu\)m, respectively. From the measurement results, we observe that the propagation lengths in graphene layers are reduced drastically in comparison to BML; roughly 17 times shorter for the monolayer and 23 times shorter for the bilayer of graphene. This is due to strong absorption resulting from the presence of graphene layers along the direction of propagation. The reason behind the smaller influence of the graphene bilayer on absorption than the monolayer is the difference in the level of doping between both cases. The intrinsic absorption properties of graphene depend on the level of doping. In the case of monolayer, the graphene is sitting on the substrate and has air on the other side. The first layer of the bilayer graphene has graphene on the other side, unlike the monolayer. While the second layer of the bilayer graphene has graphene on one side and air on other side. These boundary conditions can justify a different doping [41].  
Figure 4: Near-field amplitude distribution acquired by MH-SNOM demonstrating BSW propagation for (**a**) Bare multilayer; (**b**) Monolayer graphene; and (**c**) Bilayer graphene.  
Figure 5: The normalized field amplitude cross section (in logarithmic scale) along the direction of propagation of BML, monolayer and bilayer of graphene.  
The propagation length of leaky modes in a prism coupling system can also be deduced from the angular width of reflection anomaly in far-field [8]. The propagation lengths vary in a fashion inversely proportional to the width of the reflection spectrum. More details of the method can be found in ref. [8].  
Thanks to the atomic layer thicknesses of graphene layers (3 angstroms and 6 angstrom for the monolayer and bilayer, respectively), graphene does not require an additional propagation constant other than the bare multilayer, and hence the coupling condition. Therefore, surface waves are directly absorbed by graphene layers without the necessity of external coupling devices, unlike silicon photonics. In a study of integrated GaInAsSb photodiode on silicon waveguide, the diffraction gratings are employed as an external coupling device to interface the silicon waveguide with the photodiode [42]. The poor coupling efficiency of the grating coupler is stated as the main reason behind the degraded performance of the detector [42].  
In addition, the CVD graphene growth and its transfer to the multilayer platform by the wet-transfer method using PMMA provides an easier fabrication (integration) process in comparison to conventional silicon photonics integration processes.