## 5 Results and Discussion
### Link Level Assessment of Bit Error Probability  
BEP results are first presented for the scenario with one interfering link (Figure 6a), by considering the reference system parameters of Table 3, Vivaldi optical antennas and path gain values obtained from RT simulations. Since the BEP depends on the positions of both desired and interfering transmitters, the results are displayed in the form of a two-dimensional map where the BEP is reported for each pair of values (d,\(\Delta\)). The results in Figure 9a are derived for links using single plasmonic Vivaldi antennas placed in the middle of a SiO\({}_{2}\) layer with 6 \(\upmu\)m thickness. According to the system parameters values in Table 3, a received power at least equal to \(-25.7\) dBm is necessary to overcome the noise level to the extent corresponding to a target BEP = \(10^{-6}\). Link performance is significantly impaired by the multipath effects, which make the link reliability not uniform in the parameter space (d,\(\Delta\)) and fully unsatisfactory for d \(>70\)\(\upmu\)m due to the noise level, and for \(\Delta\)/d \(<1\)/3 due to the interference. The link is unreliable in a wide range of d values between 40 and 60 \(\upmu\)m due to a multipath induced path gain notch (Figure 8). The domains of the (d,\(\Delta\)) space with BEP lower than the target represent the coverage areas for the link (light to dark blue in Figure 9a). As the multipath conditions change by varying the SiO\({}_{2}\) layer thickness (Figures 7 and 8) also the coverage zones are likely to change accordingly. This is illustrated in Figure 9b where the thickness of the SiO\({}_{2}\) layer is decreased to 4 \(\upmu\)m. Comparison of the two figures shows that the width of path gain holes is reduced, but the maximum coverage shrinks to d \(<55\)\(\upmu\)m at the same time due to a worse range dependence of PG. In summary, on-chip wireless optical communications between plasmonic Vivaldi antenna buried in a few \(\upmu\)m silica layer are mainly noise limited, with a maximum coverage distance lower than 100 \(\upmu\)m. Interference represents a significant issue only in case the interfering links are quite close, with spacing not exceeding few tens of \(\upmu\)m.  
To extend the coverage region of a noise limited link, antennas should be designed to have a larger gain. As shown Figure 8, this may be accomplished with (Vivaldi) antenna arrays. The path gain increases by nearly 6 dB with 3 elements array and by nearly 8 dB with 5 elements array. An array of 5 plasmonic Vivaldi antenna in a SiO\({}_{2}\) layer with thickness of 6 \(\upmu\)m is considered in Figure 10a. As expected, the coverage zones are larger than those in Figure 9a, with a maximum communication distance equal to nearly 240 \(\upmu\)m. Since the antenna array has a narrower beamwidth than the single  
Figure 9: Bit error probability (BEP) map in the space (d,\(\Delta\)) for the scenario in Figure 6a with Vivaldi antennas and t = 6 \(\upmu\)m (**a**) and t = 4 \(\upmu\)m (**b**). element, the link is also more protected against interference, with interfering effects basically vanishing for \(\Delta\)/d \(>\) 1/12. Moreover, the coverage is more uniform in the (d, \(\Delta\)) domain, because the increase in the antenna gain reduces the occurrence of situation where the received signal intensity drops below the detection threshold. Figure 10b shows the BEP map obtained with a 5-element Vivaldi antenna array and SiO\({}_{2}\) thickness of 4 \(\upmu\)m. Similarly to the results shown in Figure 9b, the thinner dielectric layer mitigates the multipath effects by smoothing the path gain notches, and therefore the coverage area turns out to be more uniform on the whole. Nevertheless, it also becomes smaller compared to Figure 10a, with a maximum communication range equal to nearly 180 \(\upmu\)m. This value is smaller than the corresponding value in Figure 10a, as expected, because the path gain decays more rapidly at large distances if the layer thickness is reduced (see Figure 8).