## 5 Results and Discussion
### Ray Tracing Analysis of the Optical Wireless Channel  
RT reliability for on-chip propagation prediction is shown in Figure 7 against FDTD simulations of an optical wireless link between the plasmonic Vivaldi antenna shown in Figure 3a and presented in [9] and for different thickness of the silica layer. Path Gain (PG) plotted in Figure 7 is the ratio between the power seized by the receiving antenna and the power supplied to the transmitting one. In spite of the very different computation effort required by RT and FDTD, with computation time respectively equal to few seconds and several hours, the overall root mean square error is equal to 4.5 dB. Considering that RT accuracy for PG modeling in cellular systems for personal communications may commonly correspond to an average RMSE of several dBs, results are here quite in agreement. According to this outcome, surface wave propagation, which has been sometimes claimed as a major propagation mechanism [13; 16] does not seem so significant, at least in the considered situations. In fact, it would be accounted for by the FDTD simulation only and therefore would result in a much poorer comparison between the models. The sensitivity of the PG values to the SiO\({}_{2}\) layer thickness in Figure 7 provides further evidence of the strong multipath effect affecting the on-chip propagation, as variations comparable to the wavelength completely change the interference pattern of the rays, thus resulting in a shift of the maxima/minima of the power level. It is worth pointing out that in both cases PG is on the average greater compared to what it would be in free space (dotted line in Figure 7), thus meaning that on-chip wireless communications can benefit from better propagation conditions than free space. As outlined in [10], this is the result of a sort of guiding effect triggered by the multiple reflections within the antenna layer up to a distance \begin{table}
\begin{tabular}{c c} \hline \hline
**System Parameter** & **Value** \\ \hline P\({}_{\rm{in,av}}\) & 0 dBm \\ \(\rm{\eta_{PD}}\) & 0.7 A/W \\ \(\rm{R_{b}}\) & 10 Gbit/s \\ \(\rm{T_{eq}}\) & 600 K \\ \(\rm{R_{L}}\) & 1 k\(\Omega\) \\ K & \(1.38\times 10^{-23}\) J/k \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Reference system parameters. that depends on the antenna radiation properties, the material at the interfaces and the thickness of the layers [10]. Taking advantage of the computational agility of RT, the impact of materials, antennas and layers thickness on the optical wireless channel is further investigated in Figure 8. In addition to purely dielectric interfaces, which are representative on the on-chip layered environment, highly reflective interfaces has been also taken into account for the sake of comparison. In the RT tool, they have been implemented as metals based on the Drude theory [44]. As shown in Figure 8, interference is clearly stressed if total reflection occurs at the interface(s)--e.g., with metal filling the lower layer instead of silicon--as the ray's intensities keep similar compared to the case where a greater power leakage occurs at the interface. Increasing the antenna gain--e.g., considering an array of three/five plasmonic Vivaldi antennas instead of a single one--results in a greater PG on the average, although it can also impair the aforementioned guiding effect, to the extent that pursuing a directivity as large as possible may not represent a convenient target [10]. Finally, a reduction in the antenna layer thickness seems to alleviate multipath effects in Figure 8, although at the expense of the power decay trend at larger distance [10]. Therefore, the choice of the best thickness should also take into account the communication distance target. More in general, many aspects concur to the system performance in a somehow interlaced way, i.e., it is hardly possible  
Figure 8: On-chip wireless channel sensitivity to material-, antenna-, and layer-thickness.