## 4 Results
### Influence of the Slab Height  
In EO modulators the slab is responsible for contacting the waveguide to the device, in order to apply an electric field to the slot and thereby changing the EO properties of the organic material. A greater slab height \(h\) leads to higher values for \(n_{\text{eff}}\), while \(\Delta n_{\text{eff}}\) decreases and is more affected by \(s\), presented in Figure 10a. During the simulation study we observed the propagation of higher modes starting from \(h=60\,\mathrm{nm}\) and shown as an extreme example for \(h=100\,\mathrm{nm}\) in Figure 11. This effect was already visible in Figure 10b at \(h=60\,\mathrm{nm}\), where \(\Delta\Gamma_{\text{slot}}\) starts to drop. However, the manufacturing resolution and the electrical properties of the slab have to be taken into account for such small slab heights, which is why larger \(h\) become necessary. In Appendix A we provide the raw data of our results; i.e., the effective refractive index and field confinement factor are plotted for each concentration. From these figures, optimized geometrical parameters for each concentration can be deduced, which are are summarized in Table 2. Please note that the general dependency on each parameter is the same for \(C=0\,\mathrm{wt}\%\) and \(C=10\,\mathrm{wt}\%\) and therefore the optimized values regarding field confinement factor are valid for both concentrations. It is also noticeable that field confinement factor is continuously increasing by decreasing the slab height. As a consequence, the slab height of \(10\,\mathrm{nm}\) is only the optimized value in our simulation but in general it holds that the smaller the slab height the higher the field confinement factor. In summary, a thorough investigation on modal and confinement of silicon slot-waveguides covered by a nonlinear optical polymer has been performed. We calculated the effective refractive index \(n_{\text{eff}}\) and the field confinement factor \(\Gamma_{\text{slot}}\) for numerous geometry parameters of the slot-waveguide using a FEM-based 2D-model. As the cladding and slot material, the EO organic co-polymer PMMA+DR1 has been employed, which was taken from experimental data. Additionally, the resulting differences in the effective refractive index and field confinement factor between the two mass concentrations \(C=0\,\mathrm{wt}\%\) and \(C=10\,\mathrm{wt}\%\) of the DR1 chromophore in the PMMA matrix have been studied. In the first step we investigated the influence of non-vertical waveguide sidewalls, due to possible manufacturing tolerances during silicon etching. At \(\theta=0^{\circ}\) and \(s=60\,\mathrm{nm}\) the highest confinement \(\Gamma_{\text{slot}}=0.18\) has been found. A linear percentual shift \(\eta(\theta)\) of \(n_{\text{eff}}\) from 1.6% to 7.9% has \begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Parameter** & **Optimized Value** \\ \hline \(\theta\) & tilt angle & \(0^{\circ}\) \\ \(w\) & waveguide width & \(200\,\mathrm{nm}\) \\ \(h\) & slab height & \(10\,\mathrm{nm}\) \\ \(s\) & slot width & \(60\,\mathrm{nm}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Optimized slot-waveguide parameters in terms of field confinement factor. Figure 9: Effect of the waveguide width \(w\) on the modal properties. A higher confinement can be found for larger \(w\). been observed with increasing tilt angle in a range of \(\theta=3^{\circ}\)-\(9^{\circ}\). The influence was less pronounced for larger slot widths \(s\). The difference \(\Delta n_{\text{eff}}\) between the two concentrations \(C=0\,\text{wt}\%\) and \(C=10\,\text{wt}\%\) ranged from 0.0157 up to 0.0187, while for \(\Delta\Gamma_{\text{slot}}\) the difference was negligible. Afterwards we varied the waveguide width \(w\) from \(125\,\text{nm}\) to \(250\,\text{nm}\). A distinct maximum \(\Gamma_{\text{slot}}=0.19\) became visible at \(w=200\,\text{nm}\) and \(s=60\,\text{nm}\). The difference \(\Delta n_{\text{eff}}\) stayed almost constant over the entire range of \(s\) for \(w=200\,\text{nm}\). No higher modes were observed.