# Polarization Effect on the Performance of On-Chip Wireless Optical Point-to-Point Links
## 2 Design of the Dielectric Vivaldi Antenna
### Vivaldi Antenna Radiation Analysis
Figure 3: (a,b) Gain as a function of (**a**) the angle \(\theta\) (with \(\Phi\) = 0) and (**b**) the angle \(\Phi\) (with \(\theta\) = \(\pi/2\)), for the TE (solid curves) and TM (dashed curves) modes in the case of the Vivaldi antenna with strip width w = 900 nm, slot gap g = 300 nm, slot rail width s = 300 nm, and antenna length L\({}_{\text{a}}\) = 25 \(\upmu\)m. (**c,d**) Electric field pattern calculated via 3D-FDTD in the xy plane for z = 0 \(\upmu\)m (i.e., in the middle of the antennas) for the TE (**c**) and TM (**d**) polarizations. The color bar represents the normalized amplitude of the electric field in logarithmic scale. The wavelength is \(\lambda\) = 1.55 \(\upmu\)m.  
Considering the reference axes in Figure 1, the maximum values of the Vivaldi antenna gain occur for \(\Phi=0\) and \(\theta=\pi/2\), and they are equal to 23.8 dB and 23.52 dB for the TE and the TM modes, respectively. Therefore, the analyzed Vivaldi antenna can be considered polarization-insensitive, in the sense that it has the same radiation characteristics, expressed in terms of antenna gain, in both polarizations. Moreover, the gain of the proposed Vivaldi antenna is much higher than that of plasmonic antennas [32; 33; 34; 35], but it is also higher than that of the dielectric antenna proposed in [29]. As a drawback the proposed Vivaldi antenna is longer. Compared to a simple truncated waveguide (with width w = 900 nm and height t = 300 nm), the Vivaldi antenna enhances both the gain and the polarization insensitivity. In fact, the calculated maximum gain values for a simple truncated waveguide are G = 18.32 dB and G = 15.14 dB for the TM and the TE polarizations, respectively (corresponding to a more than 3 dB difference between the two polarizations). It is worth pointing out that the dominant electromagnetic field components of the radiated waves are different for the two polarizations. In particular, E\({}_{\Phi}\) and H\({}_{\Phi}\) are the dominant components for the TE polarization, whereas E\({}_{\Phi}\) and H\({}_{\Phi}\) are the dominant ones for the TM polarization. As will be shown in the following, although the gain is the same, the difference in the dominant components will lead to a different behavior of the wireless propagation in the multilayer on-chip structure. As said before, the radiation performances of the Vivaldi antenna depend on different parameters such as the width of the strip waveguide w, the slot gap g, and the length of the Vivaldi directors L\({}_{\text{a}}\). Figure 5a,b show the maximum gain for the TE (solid curves) and the TM (dashed curves) modes, respectively, in the case of the three configurations A (w = 600 nm--blue curve), B (w = 900 nm--red curve), and C (w = 1100 nm--yellow curve). The results reported in Figure 5 were calculated by arbitrarily choosing the antenna length value L\({}_{\text{a}}\) = 25 \(\upmu\)m. In each case, the radiation diagrams are similar to those shown in Figure 3a,b. Figure 4: (**a,b**) Gain as a function of (**a**) the angle \(\theta\) (with \(\Phi=0\)) and (**b**) the angle \(\Phi\) (with \(\theta=\pi/2\)), for the TE (solid curves) and TM (dashed curves) modes in the case of the truncated waveguide. (**c,d**) Electric field pattern calculated via 3D-FDTD in the xy plane for z = 0 \(\upmu\)m (i.e., in the middle of the antennas) for the TE (**c**) and TM (**d**) polarizations. The color bar represents the normalized amplitude of the electric field in logarithmic scale. The wavelength is \(\lambda\) = 1.55 \(\upmu\)m.  
From Figure 5a,b, we can infer that the gap value g can be suitably chosen to achieve the maximum gain for both the TE and TM polarizations. With reference to the three configurations A, B, and C, the maximum gain values for both the polarizations correspond to g = 100 nm, g = 300 nm, and g = 500 nm, respectively. For these three gap values, the maximum gain difference between the two polarizations is minimized, and it is less than 0.4 dB.