# Monolitic Hybrid Transmitter-Receiver Lens for Rotary On-Axis Communications
## 4 Discussion
### Full-Channel Performance  
\(P_{\text{PD PP}}\) is in a sufficient range for data transfer, but how does it correspond to the data rate? For a bit error rate of \(10^{-12}\) [PERSON] calculates a sensitivity of \(-26.5\,\text{dBm}\) for a \(2.5\,\text{Gbit/s link}\) and \(-20.5\,\text{dBm}\) for a \(10\,\text{Gbit/s link}\)[26]. [PERSON] et al. [54] demonstrated a sensitivity of \(-21.5\,\text{dBm}\) for a \(10\,\text{Gbit/s link}\). It can be concluded from Table 3 that \(P_{\text{PD PP}}\) is sufficient for data transmission in the Gbit/s data rate range and even provides a margin for ageing effects and other nonidealities. The optical crosstalk introduces a power penalty of up to 0.9 dB. The magnitude of \(P_{\text{PD cross}}\) depends directly on \(P_{\text{TX}}\). A lower \(P_{\text{TX}}\) leads to reduced \(P_{\text{PD cross}}\). The downside is that the SNR cannot be improved by increasing \(P_{\text{TX}}\) if the crosstalk is the dominant noise factor. The constant crosstalk part \(P_{\text{PD cross 1}}\) is alignment-independent. Therefore, it has to be the internal optical crosstalk. In contrast, the back-reflected signal \(P_{\text{PD cross 2}}\) from the opposite transceiver depends on the transceiver alignment. The crosstalk and thus the power penalty is reduced if \(z\) is increased. In the far field, \(P_{\text{PD}}\) is decreasing with approximately \(P_{\text{PD}}\propto z^{-2}\) and the crosstalk scales with \(P_{\text{PD cross 2}}\propto z^{-4}\), since the back-reflected rays have to travel twice the distance. Although this relation is not fully correct for the near field, the trend is still valid. The crosstalk \(P_{\text{PD cross 2}}\) can be lowered by reducing the Fresnel-reflections \(\zeta_{\text{RX,F}}\). The planar top surface is well suited for an AR coating. The problem is that the nonplanar top surface of the TX lens part is also affected by the coating. If one is able to solve the TX coating problem, a single coating is twice as effective, because the ray passes the coating two times: first at TX and second at RX. The link-budget is improved by approx. 6 % per coating instead of only approx. 3 %. Moreover, \begin{table}
\begin{tabular}{l c c c c c c c c} \hline \hline
**Misalignment/mm** & \(\mathbf{-0}\) & \(\mathbf{-0.5}\) & \(\mathbf{-1}\) & \(\mathbf{-1.5}\) & \(\mathbf{-2}\) & \(\mathbf{-2.5}\) & \(\mathbf{-3}\) & \(\mathbf{-3.5}\) \\ \hline H TX-RX: \(P_{\text{PD}}/\text{dBm}\) & \(-10.1\) & \(-8.5\) & \(-9.5\) & \(-12.0\) & \(-14.1\) & \(-15.3\) & \(-16.0\) & \(-26.4\) \\ H TX-RX: \(P_{\text{PD cross}}/\text{dBm}\) & \(-19.2\) & \(-22.7\) & \(-23.9\) & \(-22.9\) & \(-25.2\) & \(-27.4\) & \(-28.8\) & \(-30.4\) \\ H TX-RX: \(P_{\text{PD PP}}/\text{dBm}\) & \(-10.7\) & \(-8.7\) & \(-9.7\) & \(-12.4\) & \(-14.5\) & \(-15.6\) & \(-16.2\) & \(-28.6\) \\ S TX-RX: \(P_{\text{PD}}/\text{dBm}\) & \(-13.7\) & \(-15.2\) & \(-20.6\) & \(\leftarrow\)\(-40\) & \(\leftarrow\)\(-40\) & \(\leftarrow\)\(-40\) & \(\leftarrow\)\(-40\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Minimum \(P_{\text{PD}}\) depending on the misalignment in negative x-direction (\(y=0\)). Values are determined by choosing the minimum value \(P_{\text{PD}}\) on a circle around the center with a radius of the misalignment. Values lower than 40 dBm are very noisy due to the finite number of simulated rays. the crosstalk \(P_{\text{PD cross 2}}\) is reduced. Alternatively, the top surface of the RX lens part could be designed nonplanar in a way that back-reflected rays miss the transmitting device. Although TX exhibits a quite homogeneous performance, \(P_{\text{PD FP}}\) varies about 6.9 dB along radial direction for misalignment \(\leq 3\) mm according to Figure 8a and Table 3. Thus, there is clearly some room for improvement for the RX lens part. The main issue results from the mismatch between near and far field in terms of ray optics. This can be seen in Figure 6a: the incident ray bundle (green) exhibits a large divergence. The situation is different at \(z=50\) mm, for instance.