# Slot Waveguide Enhanced Bloch Surface Waves
## 3 Results
### Waveguide Integration  
Simulations of the waveguide including the multilayer are performed using a commercial software based on the finite difference time domain method (OptiFDTD by OptiWave). The intensity distribution of the major field component (\(|E_{x}|^{2}\)) is shown in Figure 3 together with the field profile along \(x\) for three cases. Figure 3a corresponds to a slot waveguide gap of \(w_{\text{g}}\) = 70 nm, which is the ideal case. Figure 3b is the distribution for \(w_{\text{g}}\) = 400 nm, i.e., a far too large gap to enable the slot enhancement coming from the superimposition of the two BSW evanescent tails. Figure 3c is used as a comparison structure. It is identical in terms of geometry to the structure presented in Figure 3a, but the multilayer is replaced by a material of refractive index \(n\) = 1.91, equivalent to the average refractive index of the multilayer (\(n\simeq 1.91\)). One can see, in the case where \(w_{\text{g}}\) = 70 nm, that the electric field is confined in the slot region as expected, which is not the case when \(w_{\text{g}}\) = 400 nm. The field intensity distributions show the coupling zone between the feeding waveguides and the slot waveguide. It is clear that the evanescent tail of the BSW modes are not overlapping for large gaps, while a field confinement in the air slot is observed for thinner gaps smaller than the characteristic length L\({}_{\text{c}}\) = 155 nm, calculated considering the propagation constant of the BSW and the refractive index of the output medium (air) [20]. The field remains mainly inside the multilayer as shown in Figure 3b. The modal field profile shown in Figure 3a (\(w_{\text{g}}\) = 70 nm) shows the classical _cosh_ shape of the mode characteristic of a slot waveguide and coming from the sum of two evanescent waves with opposite signs. In Figure 3a, it is evident that the useful part of the field is inside the air region of the slot waveguide, while only the evanescent part of the field is accessible in case of a large gap. This second configuration is actually similar to the classical BSW platform illuminated using the Kretschmann configuration. The extinction ratio of 75% of the BSW yields to a back-reflection by the multilayer in the waveguide and therefore leakage inside the polymer device. However, since the whole structure  
Figure 3: Intensity distribution (left) and intensity mode profile (corresponding to the white dashed lines) of the major field component \(E_{x}\) (right) for (**a**) a thin gap \(w_{\text{g}}\) = 70 nm for the slot waveguide, (**b**) for a larger gap \(w_{\text{g}}\) = 400 nm, and (**c**) for a 70 nm gap structure where the multilayer is replaced by a homogeneous material of average refractive index \(n\) = 1.91. The far-right column displays zoom-in on the _slot_ regions, which are delimited by green dashed rectangles. is covered by the multilayer, one can see consecutive reflections inside the waveguide, always at the excitation angle of the BSW. The mechanism is similar to that observed in the case of an ARROW device (anti-reflective resonant waveguide). It follows that at each reflection the BSW is re-excited all along the slot waveguide. Such a mechanism leads to a dashed propagation inside the slot region. A trade-off must be found between a too high reflectivity allowing for a thin BSW, and a too low reflectivity leading to high losses. Finally, the output shape of the feeding waveguides, i.e., the two arms of the split input waveguide, has to be carefully designed in order to avoid injection of light inside the multilayer itself. For comparison, a third simulation has been performed on a polymer slot waveguide structure (\(w_{\rm g}=70\) nm) covered by a homogeneous material of refractive index \(n=1.91\). Results are presented in Figure 3c. One can clearly see the characteristic intensity distribution corresponding to a slot waveguide (right graph) but at a lower intensity than in Figure 3a.