# 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 completeness, Figures 12 and 13 show, for the TE and for the TM polarizations, respectively, the electric field calculated via the 3D-FDTD simulation in the xy-horizontal plane for z = 0 \(\upmu\)m (i.e., in the middle of the antennas), for a fixed link distance dlink = 100 \(\upmu\)m. Different values of 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. The solid lines denote the geometry of the antennas, and the color bar represents the normalized amplitude of the electric field in logarithmic scale. In the case of TE polarization (Figure 12), the electromagnetic field spreads in the xy-horizontal plane around the transmitting antenna, and it couples at the receiving one, as expected for a point-to-point wireless link. Owing to the presence of the multilayer structure, oscillations appear in the xy-plane field distributions, especially in the case of d = 4 \(\upmu\)m (Figure 12d), where an interference pattern is apparent. In the case of the TM polarization, when the cladding thickness is d = 0.5 \(\upmu\)m (Figure 13a), the electromagnetic field rapidly decays due to the dominant radiation towards the bulk layer (see Figure 11a for comparison). For larger thicknesses, i.e., Figure 13b-d, the electromagnetic field spreads around the transmitting antenna and reaches the receiving one. Some oscillations in the field pattern are present due to the multipath interference, but the contribution of the destructive interference is less pronounced than in the TE case. Figure 11: Normalized electric field (in logarithmic scale) calculated in the xz-vertical plane for y = 0 \(\upmu\)m (i.e., in the middle of the antennas), for the TM polarization  
As mentioned before, the dominant electromagnetic field components of the radiated waves are different for the two polarizations. In particular, \(\mathrm{E_{\Phi}}\) and \(\mathrm{H_{\Phi}}\) are the dominant components for the TE polarization, whereas \(\mathrm{E_{\theta}}\) and \(\mathrm{H_{\Phi}}\) are the dominant ones for the TM polarization. The electromagnetic propagation in the multilayer structure can be regarded as the superposition of multiple reflected and transmitted rays at the different interfaces (e.g., silicon-silica, silica-polymer, polymer-air interfaces), each characterized by different Fresnel coefficients. The effect of the multipath propagation is, therefore, different for the two polarizations, given that the Fresnel coefficients are different. In particular, when the cladding thickness is small, the recombination of the multiple rays is, in general, destructive in the cladding layer, and the field tends to be radiated toward the Si bulk layer. Therefore, the transmittance at the receiving antenna is lower than that in free space. When the cladding thickness is increased, the point-to-point link in the multilayer shows an increased transmittance with respect to that in free space, especially in the case of  
Figure 12: Normalized electric field (in logarithmic scale) calculated in the xy-vertical plane for \(\mathrm{z=0\;\upmu m}\) (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 are denoted by the black lines. The wavelength is \(\lambda=1.55\;\upmu\)m.  
Figure 13: Normalized electric field (in logarithmic scale) calculated in the xy-vertical plane for \(\mathrm{z=0\;\upmu m}\) (i.e., in the middle of the antennas) for the TM 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 are denoted by the black lines.