# Polarization Effect on the Performance of On-Chip Wireless Optical Point-to-Point Links
## 1 Introduction
It is worth mentioning that, at the optical frequencies, the attenuation due to wireless propagation in free space (i.e., homogeneous medium) can be very high, and it can reach tens of dBs for 1 cm length of propagation, as it can be roughly estimated by the well-known Friis formula [31]. This attenuation limits the maximum distance between the transmitter and the receiver, but high-gain antennas can compensate for the loss associated with the wireless signal spread. Different configurations of dielectric and plasmonic antennas have been proposed in the literature for on-chip wireless communications [29; 30; 32; 33; 34; 35]. The plasmonic antennas have very small dimensions (a few microns), but they suffer non-negligible losses due to plasmonic mode propagation in the lossy metal. These losses limit the maximum achievable antenna gain. For example, Yagi-Uda plasmonic nanoantennas can achieve directivities of about 10 dB [32; 33]. Integrated plasmonic Vivaldi antennas have also been proposed as single radiators or in array configurations [34; 35], reaching gains up to about 14 dB with antenna size in the order of 2 \(\upmu\)m.  
All-dielectric antennas have low losses butthey are less compact. For example, in [29] a high-gain (approximately 21 dB) dielectric antenna was demonstrated. The configuration consisted of a tapered waveguide and a series of rectangular directors for a total antenna length of about 15 \(\upmu\)m.  
The antenna gain is not the only significant parameter for the evaluation of the on-chip wireless link performances. In fact, on-chip wireless propagation does not occur in a homogeneous medium, but in a multilayer one. The typical structures of photonic integrated chips are composed of different materials tiled up in different layers. Indeed, the complexity of the on-chip wireless propagation medium influences the overall communication link performance, causing multiple reflections and multipath interference (thus making the Friis formula too simplified and inaccurate). In particular, as demonstrated by the authors in [36; 37; 38], the propagation in the multilayer medium can be beneficial in terms of propagation losses with respect to the propagation in a homogeneous medium, thanks to constructive interference. In this paper, we aim to numerically investigate the effect of wave polarization (either transverse electric TE or transverse magnetic TM) in on-chip wireless communication. For this purpose, we first introduce the design of a polarization-insensitive, dielectric Vivaldi antenna, which has the same radiation characteristics, expressed in terms of antenna gain, in both polarizations. Then, the performances of different point-to-point links between two dielectric Vivaldi antennas are analyzed in connection with the variation in the multi-layer medium characteristics (i.e., layer thicknesses and material refractive indices). We assume that the polarization is selected in input to the waveguide of the transmitting antenna, i.e., the input waveguide is excited either with a TE or with a TM mode through suitable grating couplers or polarization selectors [39; 40; 41; 42; 43; 44]. The polarized wave is then radiated into the surrounding space and received at the output antenna, always keeping the same polarization. Silicon nitride Si\({}_{3}\)N\({}_{4}\) technology has been chosen in this paper as a case of study, but the Vivaldi antenna design criteria and the multilayer propagation analysis can be virtually extended to any technology. Silicon nitride (SiN) is one of the platforms, together with silicon-on-insulator (SOI), that enable the on-chip integration of the optical networks thanks to the compatibility with Complementary Metal-Oxide Semiconductor (CMOS) technology. The proposed dielectric antenna can be regarded as a building block for optical wireless NoCs (OWiNoCs). Moreover, thanks to its compatibility with standard optical integrated technology, this antenna building block can be combined with standard waveguide components, thus widening the possibility of network design exploration.