## 2 Materials and Methods  
The dielectric multilayer platform presented in this study consists of six periods of alternating high and low index layers. The low index and high index material layers are silicon dioxide (SiO\({}_{2}\)) and silicon nitride (SiN\({}_{x}\)) with refractive indexes of 1.45 and 1.79, respectively, around the wavelength \(\lambda=1550\) nm. The thicknesses of the SiN\({}_{x}\) and SiO\({}_{2}\) layers are 283 nm and 472 nm, respectively. To terminate the precocity of the multilayers, a 50-nm-thick layer of SiN\({}_{x}\) is deposited on the top. This top layer is addressed as a defect layer. The complete stack (periodic multilayers + defect layer) is called the bare multilayer (BML) platform. The BML structure is deposited on a glass wafer, as shown in Figure 1. In the present study, multilayers are designed to support transverse electric (TE) polarization of incident light at telecommunication wavelengths. The multilayer platform is fabricated using the Plasma-Enhanced Chemical Vapor Deposition (PECVD, PlasmaLab 80+ by Oxford Instruments, Abingdon-on-Thames, UK) technique. For graphene growth, we used a Cu foil of 25 \(\upmu\)m thickness (Sigma Aldrich, Saint Louis, MO, USA) as a catalytic substrate on which monolayer graphene is deposited by Chemical Vapor Deposition (CVD, Black Magic 4-inch, AIXTRON, Herzogenrath, Germany) under the following conditions: CH\({}_{4}\):H\({}_{2}\) (1:4), 25 mbar and 10 min. Prior to the graphene growth, the cleaning and thermal treatment of the Cu foil is crucial for obtaining high quality graphene. The foil was cleaned by rinsing it in organic solvents and DI water (acetone:isopropyl alcohol:H\({}_{2}\)O, 2 min each), and finally in 0.1 M aqueous acetic acid (CH\({}_{3}\)COOH) for 2 min to remove the oxides formed on the Cu surface. After that, the Cu foil was immediately placed inside the CVD chamber to prevent oxidation, and it was heated at 50 \({}^{\circ}\)C min\({}^{-1}\)--from room temperature to 900 \({}^{\circ}\)C under an Ar/H\({}_{2}\) flow for 15 min--performing an annealing step to improve the foil quality (grain size and crystallinity). Finally, the temperature was increased to 1000 \({}^{\circ}\)C, and the gases were fed into the chamber for graphene deposition. After cooling down the system, the graphene on the Cu foil is characterized by SEM, as shown in Figure 2a,b. In both images, a very clean and homogeneous graphene can be observed, whereby the presence of large Cu grain boundaries is highlighted in Figure 2b. Raman spectroscopy in Figure 2c has also been performed on the graphene on Cu foil, which detected the two typical peaks of graphene; G and 2D peaks, at 1580 cm\({}^{-1}\) and 2680 cm\({}^{-1}\), respectively. The absence of the D peak at 1350 cm\({}^{-1}\)--which is related to structural defects--confirms the growth of a high-quality graphene monolayer. After growth, the graphene is transferred from the Cu foil to the BML platform. The procedure used is a wet-transfer method where poly (methyl methacrylate), (PMMA) is spin-coated on graphene/Cu at 4000 rpm. After drying it in air for 30 min, the whole structure is placed floating on a Cu etchant solution (0.05 g/mL, ammonium persulfate) for 4 h. The PMMA avoids the graphene collapse during the Cu etching. To avoid etchant residues, PMMA/graphene is rinsed three times in deionized (DI) water and placed on the BML platform. After drying the structure and storing it overnight in vacuum to remove H\({}_{2}\)O residues between graphene and the substrate, PMMA is removed  
Figure 1: Illustration of the Kretschmann configuration setup for BSW coupling with dielectric multilayers deposited on a glass wafer. The SNOM probe collects the evanescent field on top of the 2D structures. On the other side of the prism, there is a CCD camera to collect the light reflected in the far-field. by dipping the samples in acetone and isopropyl alcohol (15 min at each solvent). In order to build bilayer graphene structures on top of the BML platform, the PMMA transfer was repeated twice [37].