# 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
Therefore, when the fundamental TE mode is given in input to the transmitting antenna, the radiated electromagnetic field can be considered to be s-polarized with respect to the multilayer interfaces, being the electric field \(\mathrm{E_{\Theta}}\) parallel to the interfaces. Similarly, the TM mode gives a p-polarized electromagnetic field. The different behavior of the TE- and the TM-polarized waves is, therefore, associated to the different boundary conditions at the interfaces and to the different Fresnel coefficients. To better understand the results reported in Figure 9, Figure 10 shows the normalized electric field amplitude (in logarithmic scale) calculated in the xz-vertical plane for \(\mathrm{y=0\;\upmu m}\) (i.e., in the middle of the antennas), for the TE polarization. The link distance is \(\mathrm{d_{link}=100\;\upmu m}\), and different values of the thickness \(\mathrm{d}\) are considered, namely: (a) \(\mathrm{d=0.5\;\upmu m}\), (b) \(\mathrm{d=0.9\;\upmu m}\), (c) \(\mathrm{d=3\;\upmu m}\), and (d) \(\mathrm{d=4\;\upmu m}\). The antennas and the multilayer interfaces are denoted by the black lines. Considering Figure 10, in the TE case of \(\mathrm{d=0.5\;\upmu m}\), the field tends to concentrate in the substrate (\(\mathrm{SiO_{2}}\)) layer, and it experiences a decay while propagating from the Tx to the Rx antenna because it is partly transmitted in the Si bulk substrate and in the air overlayer. Therefore, the Rx antenna can collect only a small part of the overall electromagnetic field. When \(\mathrm{d=0.9\;\upmu m}\) (Figure 10b), the field tends to concentrate more in the cladding layer (PMMA), and it is received more efficiently by the Rx antenna. This guiding effect in the PMMA layer becomes more apparent in the case of \(\mathrm{d=3\;\upmu m}\) (Figure 10c). In the case of \(\mathrm{d=4\;\upmu m}\) (Figure 10d), we can still consider the field to be mainly confined in the PMMA cladding, but an interference pattern is clearly visible, which explains the oscillations of the transmittance (green curve in Figure 9a) as a function of the link distance. Similarly, Figure 11 shows the electric field pattern calculated via 3D-FDTD simulations in the xz plane for \(\mathrm{y=0\;\upmu m}\) (i.e., in the middle of the antennas) for the TM polarization and for a fixed link distance \(\mathrm{d_{link}=100\;\upmu m}\). Furthermore, in this case, different values of  
Figure 10: Normalized electric field (in logarithmic scale) calculated in the xz-vertical plane for \(\mathrm{y=0\;\upmu m}\) (i.e., in the middle of the antennas) for the TE polarization. The link distance is \(\mathrm{d_{link}=100\;\upmu m}\) and different values of the thickness \(\mathrm{d}\) are considered, namely: (a) \(\mathrm{d=0.5\;\upmu m}\), (b) \(\mathrm{d=0.9\;\upmu m}\), (c) \(\mathrm{d=3\;\upmu m}\), and (d) \(\mathrm{d=4\;\upmu m}\). The antennas and the multilayer interfaces are denoted by the black lines. The wavelength is \(\lambda=1.55\;\upmu m\). the thickness d are considered, namely: (a) d = 0.5 \(\upmu\)m, (b) d = 0.9 \(\upmu\)m, (c) d = 3 \(\upmu\)m, and (d) d = 4 \(\upmu\)m.  
In Figure 11a,b, it is apparent that the field is strongly attenuated due to the prevalent radiation toward the Si bulk layer, for both d = 0.5 \(\upmu\)m and d = 0.9 \(\upmu\)m. When the thickness d is increased, the electromagnetic field tends to concentrate in the PMMA layer, giving rise to a guiding effect. In fact, when d = 3 \(\upmu\)m (Figure 11c), the field appears to be well confined in the PMMA layer. Moreover, the oscillations due to the multiple reflections and transmissions at the interfaces are less pronounced with respect to the TE case (see Figure 10c). Additionally, for the TM polarization, in the case of d = 4 \(\upmu\)m (Figure 11d), the field is confined mainly in the PMMA cladding, but an interference pattern is clearly visible in agreement with the oscillations of the transmittance as a function of the link distance (green curve in Figure 9b).