# 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
A further performance indicator for the proposed Vivaldi antenna is the power reflection coefficient \(\mid\)S\({}_{11}\)\(\mid^{2}\) at the input strip waveguide. The Vivaldi antenna is a single port device with negligible dielectric losses. Therefore, if the back reflection at the input port is low, most of the input power is coupled from the strip waveguide to the Vivaldi antenna, and then, it is radiated in the surrounding space. Figure 6 shows the power reflection coefficient \(\mid\)S\({}_{11}\)\(\mid^{2}\) calculated at the input port for the TE (solid curve) and TM (dashed curves) modes as a function of the initial slot gap value g. The blue, red, and yellow curves correspond to the configurations A (w = 600 nm), B (w = 900 nm), and C (w = 1100 nm), respectively. The curves in Figure 6 take into account both the power coupling between the strip and the slot waveguide and the radiation in the surrounding medium. Because the \(\mid\)S\({}_{11}\)\(\mid^{2}\) coefficient is less than \(-\)21 dB for all the considered cases, the power is efficiently coupled  
Figure 5: Maximum gain for (**a**) the TE (solid curves) and (**b**) the TM (dashed curves) in the case of the three configurations A (w = 600 nm), B (w = 900 nm), and C (w = 1100 nm). In all the considered cases, the gain maximum occurs at \(\Phi=0\) and \(\theta=\pi/2\). The antenna length is L\({}_{\rm a}\) = 25 \(\upmu\)m, and the wavelength is \(\lambda\) = 1.55 \(\upmu\)m.  
Figure 6: Power reflection coefficient \(\mid\)S\({}_{11}\)\(\mid^{2}\) calculated at the input port for the TE (solid curve) and TM modes (dashed curves) as a function of the initial slot gap value g. The blue, red, and yellow curves correspond to configurations A (w = 600 nm), B (w = 900 nm), and C (w = 1100 nm), respectively. For each value of the slot gap g, the slot rail width s can be calculated from the formula s = (w -g)/2. The wavelength is \(\lambda\) = 1.55 \(\upmu\)m.  
from the strip waveguide to the Vivaldi antenna coherently with the mode overlap integral in Figure 2.  
By considering the gain curves in Figure 5, we can say that, given a certain strip width w, the gap g can be optimized to maximize the gain. Once the antenna cross section has been optimized, another geometrical parameter that influences the achievable antenna gain is the length L\({}_{\text{a}}\) of the Vivaldi radiator. As an example, Figure 7 shows the maximum gain as a function of the antenna length L\({}_{\text{a}}\) for the TE (solid curve) and the TM (dashed curve) modes, in the case of configuration B (w = 900 nm) with slot gap g = 300 nm and slot rail width s = 300 nm. The results of the other configurations are not reported to avoid redundancies. As can be seen from Figure 7, the gain increases with the length of the antenna for both the TE and the TM polarizations. Moreover, the gain values for the two polarizations are very close (less than 0.4 dB difference), thus showing that the polarization-insensitive behavior of the gain is preserved also for the different lengths of the Vivaldi radiator. Similar behavior is obtained also for the A and C configurations. The results discussed above, which refer to 3D-FDTD simulations of the dielectric Vivaldi antenna surrounded by a homogeneous SiO\({}_{2}\) medium, are useful for defining the design criteria of the antenna and for identifying those configurations that show similar radiation characteristics, which are expressed in terms of gain, for both the TE and the TM polarizations. This makes it possible to study the TE and TM propagation in on-chip point-to-point wireless links with the same antenna gain. According to the well-known Friis transmission equation, when the wireless communication takes place in homogeneous medium, the received power is related to the antenna gain of the transmitter and of the receiver. Therefore, the same received power is estimated, in homogeneous medium, for both the TE and TM polarizations in point-to-point links between two integrated Vivaldi antennas.