## 2 Coupling MoS\({}_{2}\) Mono- and Bi-Layer Emission  
MoS\({}_{2}\) mono- and bi-layers are exfoliated on top of a DBR made by five pairs of TiO\({}_{2}\)/SiO\({}_{2}\) (101 nm/138 nm) alternating layers deposited on top of a glass substrate. An additional pair of TiO\({}_{2}\)/SiO\({}_{2}\) (14 nm/16 nm) is deposited on top of the photonic crystal in order to adapt the BSW energy dispersion to the excitonic transition of the MoS\({}_{2}\) mono- and bi-layer. The MoS\({}_{2}\) transition dipole moment (of the lowest energy excited state) lies in the plane of the device [37], therefore the MoS\({}_{2}\) emitted photons experience the best coupling when using a TE-polarized BSW, as in the case under our investigation. A prism coupler in Kretschmann configuration has been used for the reflectance and emission mapping of the signal lying beyond the critical angle (Figure 1a). The energy dispersion map is obtained by projecting the back focal plane of the detection lens on an imaging CCD camera placed after a spectrometer--which allows for energy resolution. In the case of the reflection map, the excitation line consists of a white light source focused on the sample (throughout the prism side) and the reflected signal is collected using a goniometric system (Figure 1a). The photoluminescence dispersion map uses the same detection line described above, but a 532 nm cw-laser source is focused on the mono-layer and bi-layer directly from the top deposition side. Figure 1c shows the BSW experimental dispersion in reflection configuration for the bare DBR (i.e., out of the mono- or bi-layer deposition) and Figure 1b shows the related transfer-matrix method (TMM) calculation. The bare BSW line width is below the setup energy resolution of 10 meV; we have estimated a 5 meV line width at 1.85 eV from the theoretical calculation. A second white light source is focused through the microscope objective on the sample (similarly to the laser source), while a second camera collects the reflected signal. This second detection line allows for the visualization of the top surface (i.e., deposition side) and helps for the accurate positioning of the laser excitation (FWHM \(\simeq\) 1 \(\upmu\)m) on the mono- or bi-layer structure. Figure 2a shows the real space map--reflectance from the top surface--of the MoS\({}_{2}\) mono- and bi-layers. Using this configuration, we can also detect the emission signal (when using the 532 nm laser instead of the white light source) coming from the deposition side (Figure 2b). As expected, the mono-layer emission is stronger than the bi-layer one [39]. Figure 2: **(a)** Reflection space map (from the top side of the DBR) revealing the mono (delimited by black dashed line) and bilayer (delimited by red dashed line) of MoS\({}_{2}\). **(b)** Emission signals of mono (black dots) and bilayer (red dots) detected from the top of the DBR. **(c)** Monolayer (upper pannel) and bilayer (lower panel) dispersion emission coupled to the BSW (i.e., detected from the prism side and across the total internal reflection regime). The green line defines the lightline dispersion, and the red line the excitonic absorption peak energy. Figure 1: **(a)** Schematic drawing of the experimental setup used for reflectivity and emission measurements in Kretschmann configuration. (Reproduced with permission from [38], OSA Publishing, 2014). **(b)** TMM calculation of the BSW reflectance dispersion using a DBR composed of five pairs of TiO\({}_{2}\)/SiO\({}_{2}\) (101 nm/138 nm) with and additional top-pair of TiO\({}_{2}\)/SiO\({}_{2}\) (14 nm/16 nm). The light line (green line) corresponds to an angle of about 42 degrees in glass; the Bloch surface mode is the dip visible in the total internal reflection regime (yellow line on the right side to the green line). **(c)** Experimental reflection signal. A very shallow BSW curve is visible, in a perfect agreement with the computation in **(b)**.