# Polarization Effect on the Performance of On-Chip Wireless Optical Point-to-Point Links
## 3 Wireless Propagation in On-Chip Multilayer Structure with TE and TM Polarizations
For the sake of comparison, the transmittance at the Rx port for a point-to-point link in a homogeneous medium (with refractive index equal to \(n_{\text{SO2}}=1.445\)) was also calculated by the well-known Friis transmission equation [49]:  
\[\text{T}=\frac{\text{P}_{\text{Rx}}}{\text{P}_{\text{Tx}}}=\text{G}_{\text{Tx}} \text{G}_{\text{Rx}}\bigg{(}\frac{\lambda_{\text{SiO}_{2}}}{4\pi\text{d}_{\text {link}}}\bigg{)}^{2} \tag{5}\]  
In Equation (5), \(\text{P}_{\text{Tx}}\) is the power in input to the transmitter waveguide, \(\text{P}_{\text{Rx}}\) is the power coupled to the receiver waveguide, \(\text{G}_{\text{Tx}}\) and \(\text{G}_{\text{Rx}}\) are the gains of the transmitting and of the receiving antenna (calculated, as before, when the antennas are immersed in a homogeneous SiO\({}_{2}\) medium), \(\lambda_{\text{SiO2}}\) is the wavelength in the propagation medium, and \(\text{d}_{\text{link}}\) is the link distance, i.e., the distance between the Rx and the Tx antennas. Friis-formula transmittance is also reported in Figure 9 for the TE and for the TM polarizations (black curves). Because the gain of the Vivaldi antenna is the same for the two polarizations, the curves calculated by the Friis transmission equation are equal for the TE and the TM propagations. As we can see from Figure 9a, for the lowest considered value of the PMMA layer thickness, i.e., d = 0.5 \(\upmu\)m, the transmittance T at the Rx waveguide (gray curve) is below the one pertaining to the Friis transmission equation (black curve). When the thickness d is increased, the effect of the propagation in the multilayer medium becomes advantageous because the received power is higher than that in the homogeneous medium. However, for d = 4 \(\upmu\)m (green curve) and d = 6 \(\upmu\)m (violet curve), oscillations are observed in the transmittance. These oscillations are typical of constructive and destructive interferences due to multipath propagation in multilayer media. When the TM polarization is considered, as shown in Figure 9b, the effect of the variation in the thickness d is more pronounced. For d = 0.5 \(\upmu\)m and d = 0.9 \(\upmu\)m, the received power is lower than that in the homogeneous medium (black curve). However, by increasing the thickness d (i.e., d = 1.5 \(\upmu\)m and d = 3 \(\upmu\)m in the reported examples), a significant increase in the received power is achieved with respect to the propagation in the homogeneous medium. Moreover, in the case of the TM polarization, oscillations occur in the transmittance curves for the thickness values d = 4 \(\upmu\)m (green curve) and d = 6 \(\upmu\)m (violet curve). Moreover, by comparing Figure 9a,b, we can see that a significant increase in the transmittance occurs for the larger values of the thickness d in the case of the TM polarization. As an example, for d\({}_{\text{link}}\) = 150 \(\upmu\)m and d = 3 \(\upmu\)m, the transmittances are T = \(-\)16.8 dB and T = \(-\)6.2 dB for the TE and the TM polarizations, respectively. Figure 9: Transmittance in dB, which is calculated at the receiver waveguide as a function of the link distance for different values of the PMMA top-layer thickness: (**a**) TE and (**b**) TM polarizations. The black curves denote the transmittance calculated by the Friis transmission equation for a point-to-point link in a homogeneous medium (with refractive index \(n_{\text{SiO2}}=1.445\)). The wavelength is \(\lambda=1.55\)\(\upmu\)m.  
In the on-chip multilayer structure, the optical wireless communication is influenced by the antenna radiation diagram, by the thicknesses and refractive indices of the layers, and by the wave polarization. The dominant electromagnetic field components of the waves radiated by the [PERSON] antenna are different for the two polarizations. In particular, \(\mathrm{E_{\Theta}}\) and \(\mathrm{H_{\Theta}}\) are the dominant components for the TE polarization, whereas \(\mathrm{E_{\Theta}}\) and \(\mathrm{H_{\Theta}}\) are the dominant ones for the TM polarization.